page no 200----compressor and different types
page no --47. separator
Contents
--------~~~~~~~~~--------------------------------------------t_-------.r".cfiaf<cc"C,c,c,c,c,c,c,c,c,c,c,c,c,cc
.. , ..
To ProjC!J30r Donold L. Katz , University oj Michigan , jor his innumerable
contributions to natural gas engineering; and my family Jor their
constant encouragement and support.
, .... , .............................
VII
1. Natural Gas- Origin and Development ....................... 1
J!llJ"Cyl!!9tian. What Is Natural Gas? Origin of Natural Gas. Other Sources of
Caseous Fuel. ~ral Cas Production and Processing System. Questions and
Problems. References.
Gas Properties
Contributions in Petroleum Ceology and Engineering
2. Phase Behavior Fundamentals . ..... . ..... . ................. 18
, . / ' Introduction. Qualitative Hydrocarbon Phase Behavior. Quantitative Phase
Behavior and Vapor. Liquid Equilibrium. Applications. Prediction of the
Phase Envelope. QuestiOns and Problems. References.
Volume 4
Gas~~lu!:ti" on-Engineering
~
9
f~
* '"::\01
01 .,10'
3 . .Properties of Natural Gases ..............................•. 39
."./'
~
~~~g
Copyri
@.t. , ' .
Company,
Houston, 1l
1i1~. Printed in the
United States of America. This book, or parts thereof,
may not be reproduced in any form without
permission of the publisher.
Introduction. Equations of State. Critical Pressure and Temperature Deter·
mination. The Cas Compressibility Factor. Some Z·Factor Related Proper.
ties. Compressibility of Cases. Viscosity of Gases. Specific Heat for Hydrocar.
bon Gases. Questions and Problems. References.
Gas Processing
4. Gas and Liquid Separation ............. . ... . ...... . ..... .. . 18
Library of Congress Cataloging-in-Publication Data
Kumar, S. (Sanjay), 1960Cas production engineering.
(Contributions in petroleum geology & engineering; v. 4)
Includes index.
1. Cas drilling (Petroleum engineering) 2. Gas
engineering. I. Title. II. Series.
TN880.2.KS6 1987 622'.3385 87-7452
ISBN 0·.87201-577_7
v
Introduction. Separation Equipment. Types of Separators. Separation Princi·
pies. Factors Affecting Separation. Separator Design. Stage Separation. Low.
Temperature Separation. Cas Cleaning. Flash Calculations. Questions and
Problems. References.
~ Gas-Water Systems and Dehydration Processing
ISBN 0-87201-066-X (serie!;)
Iv
.•..•......... 169
Introduction. Water Content of Natural Gjlses. Gas fudrates. Hydrate Inhi·
bition b~ Additive In~on. Absorption Dehydration. Adsorption Oenyara.
tion. De ydration by Expansfon Refrigeration. QuestiOns and Problems. Ref·
erences.
v
•
6. Desulfurization Processes ........... , , , ' , ..... . ............ 255
Introduction. Removal Processes. Solid Bed Sweetening Processes. Physical
Absorption Processes. Chemical Absorption- The Alkanol·Amine Processes.
Chemical Absorption-The Carbonate Processes. Questions and Problems.
References .
Gas Production and Flow
7. Steady-State Flow or Gas Through Pipes .................... 275
Introduction. Gas Flow Fundamentals. Vertical and Inclined Single-Phase
Flow of Gas. Gas Flow Over Hilly Terrain. Gas Flow Through Restrictions.
Temperature Profile in Flowing Gas Systems. Questions and Problems. References.
8. ~tiltiphase Gas--Liquid Flow .............................. 365
.....- Introduction. Approximate Method for Two-Phase Systems. Multiphase Flow.
~ Loading in Gas \Vells. Questions and Problems. References.
9. Gas Compression ..................... , ... , .............. 394
Introduction. Types of Compressors. Compressor Selection. Compression
Processes. Compressor Design Fundamentals. Designing Reciprocating COIllpressors. Designing Centrifugal Compressors. Designing Rotary Compressors.
Questions and Problems. References.
10. Gas Flow Measurement ................•.............. . ... 451
J
--/ Introduction. Measurement Fundamentals. Methods of Measurement. Orlfice Meters. Other Types of Measurement. Questions and Problems. Refer-
ences.
11. Gas Gathering and Transport ................ . ............. 529
Introduction. Gathering Systems. Steady-State Flow in Simple Pipeline Systems. Steady-State Flow in Pipeline Networks. Unsteady-State flow in Pipelines. Some Approximate Solutions for Transient Flow. Pipeline Economics.
Questions and Problems. References.
Appendix A. General Data and Unit Conversion Factors .. , , ....... 585
Appendix B. Computer Programs (FORTRAN Subroutines) ... , ... , 623
Index ....................... , ... , ... . .. , . . , ... , .. .. ........ 651
Preface
With this book I have sought to provide a rigorous and comprehensive
text that reHects a broad spectrum or natural gas engineering experience.
My motivation came primarily from some gas engineering courses I taught
in the United States and overseas that made me realize the limitations of the
existing material and the frustration or having to use several different publications, some of which would contradict others. Notwithstanding the enormity or the task, I decided to write a book to eliminate this conrusion and
provide a wider and more detailed coverage of this topic. Much of the material presented here was drawn from these lectures .
This book is designed to be a moderately advanced textbook ror students
and a handy reference for practicing engineers. It was written with the assumption that some readers with little or no background in gas engineering
will use it as their first book. To keep things interesting for the expert. I have
sought to include the most current developments reported in the latest published works to the extent possible without dragging this book into an interminably long series of books on these topics. Pertinent references are included at the end of each chapter for those wanting more details. Almost
every chapter includes worked examples to enhance understanding and
some practice questions and problems that will aid in testing this understanding. (Answers to the questions and problems are available in a separate
instructor's guide.)
Chapter 1, an introduction to the scope of natural gas engineering, can be
skipped by most seasoned readers. Chapters 2 and 3 describe the properties
of natural gas that are crucial in designing and operating natural gas systems. Chapters 4, 5, and 6 deal with gas processing-Chapter 4 discusses
the separation or gas from oil and water from a typical reservoir; Chapter 5
provides insight into gas-water systems and dehydration processing techniques for natural gas; and Chapter 6 examines some or the important and
widely used desulrurization processes for natural gas,
Chapters 7-11 present important topics in gas production and HowChapter 7 describes relationships for the steady state flow or gas through
horizontal, inclined, and vertical pipes; Chapter 8 outlines the methods of
handling multiphase flow encountered in gas production; Chapter 9 provides information on gas compression; Chapter 10 discusses gas flow measurement; and finally, Chapter 11 describes gas gathering and transmission
systems, and deal.s with the design and modeling of the complete production
"
•
and transport system. Appendix A will be helpful in handling the several
frequent1y confusing systems of units that, unfortunately, are our legacy in
engineering. Appendix B presents some general FORTRAN subroutines that
will help readers write computers programs to implement many of the techniques presented in this book.
It has been my good fortune to have had close associations with many
v 10 ment of this work. I am thankful to Drs.
Kern H Guppy and George v. Chilingar for their enthusiastic interest,
comments, and suggestions for this book. The figures and drawing.. provided by several companies and institutions are gratefully acknowledged.
Many sections of the book could only be included because of the interest and
curiosity of my students. They never failed to ask pertinent questions and
draw the discussion to related relevant issues. Finally, the moral support
from my family has been of great value in the moments of frustration during
this work, I thank my father. Dr. Kundan L. Coyal, for his many discussions
and suggestions for this book and his insistence that I keep at it.
I submit this work to the engineering community with the hope that it
shall inspire many minds, both the young and the elCperienced, to greater
understanding and creativity in this endless search for knowledge.
San;ay Kumar, Ph.D.
Los Angeles, California
1
and
Introduction
The earliest records of natural gas go back to A.D. 221-263 when it was
first used as a fuel in China during the Shu Han dynasty. The gas, obtained
from shallow wells, was distributed through an interesting piping system:
hollow bamboos. Later evidence is not found until the early 17th century.
when natural gas was used on a small scale for heating and lighting in
northern Italy. In the United States, natural gas was first discovered in Fredonia, New York, in 1821. It is this latter discovery that has led, for the most
part, to the developments we see today. In the years following this discovery,
natural gas was used merely as a fuel locally: it was difficult to store and
transport and had Iitt1e or no commercial value. Even in the 19205 and '30s,
natural gas was only produced as an unwanted byproduct of crude oil production. Only a small amount of gas was pipelined to industrial areas for
commercial use, most of it being vented to the air or flared. From these
humble beginning.., the natural gas industry has burgeoned. especially in
the years following World War II. Natural gas now accounts for almost onefifth of the world's primary energy consumption, surpassing coal and second
only to oil (see Tables 1-1 and 1-2).
Several factors are responsible for these developments: New processes permit the manufacture of myriad petrochemicals and fertilizers from natural
gas; gas is a clean, efficient, easily combustible, low-sulfur fuel and has consequently replaced coal as a domestic, industrial, and power generation fuel
in many parts of the world; difficulties in storing and transporting gas have
been overcome by the development of long-distance, large-diameter steel
pipelines and powerful compression equipment; liquefied natural gas
(LNG), produced by liquefying natural gas by a refrigeration cycle to less
(text continued on poge 4)
1
•
---
Table 1·1
World Energy Consumption and Fuel Shares-History, 1960, 1973 and 1979"
(Quadrillion Btu)
1160
1973
Fuel Shares
(Pen:enl)
Region or Country
1979
Fuel Shares
(Percent)
Fuel Shllr.s
Tolli
Tot.'
Totl'
(Percent)
Energy
Energy
Energy
Consumed Coal eNt Gas Other Conaumed Coal 011 Gas Other Consumed Coal 011 Gas Oth.r
;Uc"c"Cod~s,C.C,a~••CCCC-O---C44C.~2--C23OC-C4:5-~28;-CCC4--C~7:5C.IC--CI~8-C4:7-~30;--C5CCanada
Japan
Western Europe'
Finland/Norway/Sweden
Unit....:! Kingdom/Ireland
IknclUlIDcnmark!T
West GermallY
france
Australia/Switzerland
Spain/Portugal
Italy
GreecefThrkcy
Australia/New Zealand
ThtalOEeD'
Thta.l Non·OECD'
OPEC
Other
Thtal Free \\urld'
J,g
3.9
26.9
1.8
8.0
2.7
6.2
14
48
49
36
10
I
27
15
8.1
15.3
H
14
46
79
20
2
26
5
3.7
55
13
70
53
73
51
35
49
29
47
25
35
2
0
0
0
0
3
8
38
I
0
2
11
54.0
3.9
10.4
7.3
11.5
8.2
HI
5
35
II
30
15
63
5H
51
67
58
70
10
0
11
22
10
7
8
37
3
0
2
8
0.9
l.0
2.2
0.4
1.4
BO.4
10.5
1.7
8.8
90.9
24
41
14
41
54
35
31
3
37
35
34
41
54
55
4J
42
57
75
53
43
6
36
0
18
II
21
0"
0
3
16
7
6
6
21
4
6
15
7
2.0
3.0
6.2
1.4
2.9
155.4
25.0
5.0
20.0
180.3
8
]4
15
21
35
18
21
I
25
18
58
70
78
76
50
56
60
66
59
56
7
2
10
0
6
19
II
30
7
18
27
\4
7
3
9
7
8
3
9
8
, From 0.0.£:. 1981 Annu.1 Report 10 Congrrso, Volu1M' 3.
" Indud.. ~o Rico, Virgin Islands, .nd purclll_ fm- tbe Stra,egic Pdroleum
I Numben mly not .dd to l"'lb dlW to f'OOlIIding
°t Oetw:IIU eountoa.ne Belgium, the Ndtw-rl.nd>.. and Ltuembourll.
R~rlnloo with (Wrm~n In:om IIPI. 19fI..I
79.3
10.0
16.1
571
4.9
10.3
6.8
12.4
8.8
17
..,
3.8
2.0
3.8
166.2
35.7
7.0
287
201.9
19
48 26
7
8
41
21
30
II
74
6
9
19 56 14
1I
449245
33
44 18
5
12 57 28
3
25
53 17
5
16 61
10
13
6 41
12
41
16 68
3
13
66917
8
35
00
0
S
39
42
11
8
18 52 20
10
1962910
74 22
3
2J 59
6
12
18 54 18
10
\tee..-,.
Table 1· 2
World Energy Consumption and Fuel Shares: Base Scenario Midprlce Projections· 1985, 1990, and 1995*
(Quadrillion Btu)
..
,,
1990
1995
Fuel Shares
(Percent)
Region or Country
Fuel Shares
Fuel Share.
Total
(Percent)
Totsl
(Percent)
Energy
Energy
Energy
Consumed Cosl 011 Gas Other Consumed Coal 011 Gas Other Consumed Coal Oil Gas Other
~~~~~~~~~~~CCCC~~
United Ststes"
Canada
Japan
Western Europe'
Finland/Norway/Sweden
United Kingdomllrelsnd
Benelux/Denmark"
west Germany
France
Australia/Switzerland
Spain/Portugal
Italy
Creeee/1tJrkey
AustraliafNew Zealand
ThIIIOECD'
Thtal Non-OEeD'
OPEC
Other
Thlal Free World'
82.3
10.1
19.4
54.6
4.8
9.1
6.5
11.7
8.7
2.2
3.5
6.4
1.8
3.9
170.3
45.6
10.3
35.3
2 15.9
23
8
18
22
4
36
20
32
13
9
14
20
28
33
22
20
0
25
21
42
36
55
46
44
38
46
41
52
41
54
50
55
44
45
59
72
55
47
24
20
15
15
2
18
29
19
9
14
3
20
0
15
19
II
27
6
18
II
36
12
17
50
8
5
8
26
36
29
10
17
8
14
iO
14
14
86.5
\I 2
22.6
58.8
5.2
9.5
7.0
12.6
9.5
2.3
3.8
7.0
1.9
4.3
183.3
55.0
14.0
41.0
238.3
27
5
22
2J
4
37
28
34
1I
9
10
2J
21
33
24
19
0
2S
23
38
32
50
42
40
37
43
37
48
3'.1
53
44
53
39
40
57
74
52
44
·~~CCCC~CCCC~~==
22
22
IS
IS
2
18
23
17
10
17
5
21
0
19
19
II
25
6
17
13
41
13
20
54
8
6
12
31
35
32
12
26
\)
17
13
17
16
93.9
12.4
26.0
63.3
5.7
9.8
7.6
13.4
10.4
2.4
4.1
7.8
2.1
4.6
200.2
66.0
19.0
47.0
266.2
31
3
24
24
5
39
32
36
9
8
10
24
19
32
27
19
0
26
25
35
29
46
39
37
37
41
32
44
37
49
41
52
37
37
58
76
51
42
21
23
14
15
2
16
22
19
13
17
5
22
0
22
18
11
23
7
16
13
45
16
22
56
8
5
13
34
38
36
13
29
9
18
12
1
16
17
, From 0.0.[:. 1981 Annual RqIOrt to Congrea. Volume 3.
I'rojrctlon rangela", baJed on UlUmed prioce patm for imported oil.tated In 1979 constant dollars. The low prl« Ke".rlo .... u"',,;. tkh~e ...ed world 011 price of $32
per btlrnel, the mld·rlnp {used abo~)",1 ~r boor..,l, Ind the high rlnge $49(Wr bar..,l
.. IncludN Puerto Rico. Virgin Islands .•nd pun;ha.... for tbe Strategic I'I:troleum Reset"C
1 Numben may not.dd to tOilb due to rooDding.
11 1IeneIu.. evuntriet are Iklglum, the Nd~lands, and LunmOOurg.
R~nnt..J w,th ptrmioslon from API. 191\04
..
•
Natural eas-Origin and DeVf!lopmeJlt
eo" Production Engineering
.
(text continued from page 1)
than J!600 of its original volume, can now be transported acrQS5 the oceans
by insulated tankers.
Cas is now a highly desirable hydrocarbon resource. It is no longer cheap;
the price has gone up from a mere $O.07!Mscf (1.000 standard cubic feet) in
1950 to $2.79IMscf currenUy (1987). The price of gas peaked in 1984, when
gas was being sold at $4.80iMsci. and as much as $9.00'\iscf in some areas.
Production costs for natur..J g~ have also been rlSing over the years. Average
costs in the USA have gone up from $O.86/M.scf in 1976 to about $3.90IMscf
in 1982. But natural gas is still competitive with other fuels. as shown in
Table 1-3.
:
~
~~
O~M
O " ' ....... cg
<>iOcgoo <>IO!:,=!~,=!
~~
-- --
r-
~~
~~~ ~~~~~
~~. ";cici
~!2
01"'_'"
~il~
8~~~!:i e;
"'''''''
5
g~
Table 1-3
Cost Comparison of Vlrious Commercial Fuels
~<OO'!o~
Fuel
Price
Ca.wl.il'k'
Ileating oil
$1.20, gallon
$I iOlgallon
Low-sulfur fuel oil
S30.0ibbl
7.5 cenu:kWh
I3S,Oiton
51.9 centsITh'
Electricity
C~I
"atural gllS
• ", indicates the unit "Thenn"' used
aft~n
",,:r-:~-:o-
~aH~ U~~~
Price, s/MM Btu
9.00
1.95
4.'"
22.00
'OO
•
5.79
far gas. 1 Th _ 10' Rtu
Table 1-4 shows the production for the twenty leading natural gas producers in the world. The foremost gas producers today are the USA and
USSR, with a gas production of 52 Bscf/d (billion standard cubic feet per
day) and 45 Bscfld, respectively.
What Is Natura1 Cas?
NaturaJ gas is simply a naturally occurring mixture of combustible hydrocarbon (HC) gases and impurities. Typical natural gas components are
shown in Table 1-5. The non-hydrocarbon components of natural gas contain two types of materials: dilllerlts, such as N 2 , CO 2 , and water vapor, and
COntaminants, such as H.aS and other sulfur compounds. Diluents are noncombustible gases that reduce the heating value of the gas. They are not
"very harmful, and may actually be used sometimes as "fillers" to reduce the
heat content. of the supply gas. The disadvantages include greater horsepower ~nd plpelining requirements for the same energy content of the gas,
greater Internal corrosion, and freezing. Contaminants are very detrimental
to production and transport equipment (some are hazardous pollutants),
I/) ...
<0 '" '" cg CIO CIO .... 0
CIO 0- 0- 0- ..,
~~.;;;~~ ~~~~~ ~~~~~
•
Natural Go,t- Orlgln and Development
GtU Product/on Engineering
7
Table 1·5
Typical Constituents of Natural G•• (Modified after McCain, 1974)
Category
Paraffinic lie's
Cyclic He's
Aromatic HC's
Non.h)·drocarbon
Component
Methane (CIi,)
Ethane (C1He)
Propane (CJ{.)
Butane (C, H ,o)
Pentane (4ti,u
Hexa ne (CJ{,,)
Heptane &- higher (G, .. )
Cyclopropane (C,I~)
Crclohexane (CJi u )
Benzene (Celie). others
Nitrogen (Nt)
Carbon dioxide (COl)
H}'drogen sulfide ( H ~)
<>I "'t-<O<')
~~~i'i:;
Helium (lie)
Other sulfur and nitrogen compounds
Wilter (H,O)
Amount, 'MI
70·98'\
1 - 1OC%.
trace . 5~
trace· 2'"
trace -1%
trace·0.5'70
11011(' • trace
".~
traces
".~
trace· 15%
trace· 1%
trace occasionalhtrace _ 5'1'"
trace occasionallr
trace·5"',
and the primary reason for gas conditioning and processing is to remove
them as soon as possible from the gas stream. Hundreds of processes and
processing plants have been developed to deal with this problem. Some of
the major contaminants in natural gas are (Curry, 1981):
00000
~~~~~
-- -.....
"":;~C'>
1. Acid gases, chiefly HzS, and to some extent, CO 2 ,
2. Water vapor in excess of about 5- 7 Ibm /M.Mscf.
3. All entrained free water, or water in condensed form.
4. Any liquids in the gas, such as well inhibitors, lube oil, scrubber oil,
methanol, and heavier-end hydrocarbons.
5. AJI solid matter, sometimes called "pipeline trash," that may be present. This includes silica (sand), pipe scale, and dirt .
Like all gases, natural gas is a homogeneous fluid of low density and viscosity. It is odorless; odor-generating additives are added to it during processing to enable detection of gas leaks. Natural gas is one of the more stable
flammable gases (Curry, 1981). It is flammable within the limits of a 515% mixture with air, and its ignition temperature ranges from 1,100 to
1,300"F (compare this with HzS, which is flammable within 4-46% in air
at a much lower ignition temperature). Typically, natural gas has an energy
content of 1,000 Btu/seC, which is an important parameter because gas these
days is very often priced in terms of its energy content, rather than mass or
volume.
1 btu = 778.1693 lbf-ft
•
8
CQ"
Natural Ga.r-Origin and
Production Enginemng
Dev~lopment
9
Origin of Natural Cas
Many theories have been proposed for the origin of petroleum flu.ids.
None is perfect, and it is almost impossible to fully explain the origins of any
gi'.:en reservoir. The two most widely accepted theories are inorganic and
organic. According to the inorganic theory, hydrogen and carbon reacted
together under the immense pressure and temperature rar below the earth's
surface and formed oil and gas. These hydrocarbons then migrated through
porous rocks to collect in various subsurface traps. The more widely accepted organic thoory states that the hydrocarbons were generated from organic matter (land and sea plants and animals) under the influence of pressure and temperature over geologic time. Layers of mud and silt settled on
these dead organisms by various prooesses-rivers emptying huge amounts
of mud and silt into the oceans, wind-blown dust and sediment, etc. These
layers accumulated, continually compacted by the weight of succeeding layers to fonn sedimentary rock. Hydrocarbon deposits are entrapped in these
sedimentary rocks (sandstones, shale, limestones), and may migrate from
their place of formation (source-rock) through suitable porous and permeable strata to suitable geologic traps where they accumulate.
The type of organic matter and the temperature have an important bearing on the formation of oil or gas. Some scientists believe that terrestrial
(land) plants and animals predominantly produced natural gas and some
waxy crudes, whereas the aquatic (sea) organisms produced normal crude
oil. Because rivers playa major role in transporting terrestrial matter to the
sea, river deltas are favorable places for gas to exist. Typically, the deepest
sediments, deposited in the continental rift and rich in terrestrial organic
matter, are overlain by marine sediments rich in aquatic matter. Thus, a vertical sequence has been envisaged, with the gas-generating material at the
bottom and the oil-generating material at the top.
It is believed that hydrocarbons generally move upward from their place
of formation to their accumwation sites, displacing the sea water that originally filled the pore spaces of the sedimentary rock. This upward movement
is inhibited when the oil and gas reach an impervious rock that traps or seals
the reservoir.
There are man)' types, shapes, and sizes of geologic structure'> that form
the reservoirs for the accumwation of oil and gas, such as anticlines and
domes, fault traps, unconformities, dome and plug traps, len.se traps. and
combination traps. Some of these are shown in Figures 1-1 through 1·4. It
has been found that methane can remain stable at depths of 40,000 ft and
beyond (Barker and Kemp, 1980). The amount of methane surviving is a
function of the reservoir lithology-cooler, clean sandstones are more favorable than carbonates. Thus, it can be safely assumed that considerable re-
Figure ,.1. Common types of geologic features and structural traps. (From
Wheeler and Whited, 1985.)
•
•
Figure 1·2. Structural traps: (a) anticline, formed by upfolding; (b) normal fault.
(From McElroy, 1987.)
serves of natural gas may be found at depths of 15,000-30,000 ft that have
currently not been explored.
Occurrence of Natural Cas in Conventional Reservoirs
Cas is found in sedimentary subsurface strata composed of sandstone,
limestone, or dolomite. An oil reservoir always has some amount of natural
gas associated with it (either free gas, or gas in solution in the oil), and some
reservoirs may be completely gas reservoirs. Each well in the reservoir may
produce gas with a different composition, and the composition of the gasstream from each individual well may change as the reservoir is depleted.
Thus, production equipment may need to be changed from time to time to
compensate for the altered composition of the gas.
I
"
10
Nawral Gas-Origin (lnd Development
Gal Production Engineering
II
2. Dissolved or associated. Cas in solution with crude oil is tenned dissolved gas, whereas the gas found in contact with the crude oil as gas
cap gas is termed associated gas. Typically, associated gas is poorer in
elL. but richer in heavier components.
3. Gas condensates. Gas condensates have high amounts of hydrocarbon
liquids and may occur as gas in the re5en·oir.
The most desirable gas is the non-associated type. because it can be produced at high pressure. Associated or dissolved gas is separated from the
crude oil at lower o;eparator pressure; and. therefore. entails more compression expenses. Such gas is often flared or vented. Gas condensates represent
a greater amount of gas associated with the liquid than the associated or
dissolved gas types. but ~mil&r..e.paration facilities and compression
Figure '-3. Common types of stratigraphic traps. (From Brown and Miller, 1985.)
=.
..-- - -----. "The naturallY'QCCU~ing resour~pf gas ,,\e ot en classified into two categories:
'301~
r
FrlJi~:l
1. Proved res . . I Is figure
1(lthe lantities found by the drill.
The estimates e~p'
ft
updated by ~r\'oir characteristics (productio
transient analysis, ~rvoir modeling, other data) and, therefore, can be determined quite accurately
(see Table 1·6).
2. Potrntiai reserves: These are the additional resources of gas believed to
exist in the earth, as inferred from the prevailing geologic evidence,
but not actually found by the drill yet. This figure, therefore. cannot
be known verr precisely. It is, at best, a "guesstimate" that may vary
widely from one investigator to another.
c
For the estimation of mineral reserves and resources, McKelvey (1972)
provides an e:tcellent guide, shown in Figure 1-5. In this figure, the probable
"'00«1
.
I P,oIHbIt r Po."bIt
~
~
indlc.Md
me....ed
""t<ttd
Figure 1·4. Stratigraphic traps in various geologiC features: (a) "permeability
pinchout"; (b) sand pinchout; (e) angular nonconformity. (From McElroy, 1987),
In addition to its composition and Btu content, natural gas is frequently
characterized in terms of its nature of occurrence underground, as follows:
' ......'''n..
1. Non-associated. Found in reservoirs with no or minimal amounts of
crude oil, non-associated gas is typically richer in CH~. poorer in
heavier components.
Sut.m.grn..
~...,
R""",c"
l-
•
--"
F.... ,b,hly 01
•
•
•
I
I
I
0... of un."'ly
-
Figure 1-5. Classification
of mineral reserves and resources. (Aller McKelvey.
1972, courtesy of American Scientist.)
'"
12
Natural CQ.f- Origin and Development
Go, Produ('tlon Engineering
Table 1-6
estimated Proved World Reserves of Natural Glill o
(Billions of cubic feet)
.-
13
reserves indicate the amount of gas expected to be found in close proximity
to, or associated with, known producing fields in known areas with similar
geological conditions. Possible reserves are similar to probable reserves, but
in more distant regions where the uncertainty is greater. Undiscovered, spec·
ulative, or potentioi reserves are those that are expected to be found in areas
that have not been, or amy partially, explored and tested.
According to Crow (1980). the 1978 estimated US reserves (conventional
reservoirs/conventional methods) are approximately 1,019 Tscf (trillion
standard cubic feet). Thtal world reserves are 7,500 Tscf undiscovered,
2,200 Tscf proved. Current world production is 70 Tscfiyear. Key areas
where substantial potential exists for increasing production in the next decade are the OPEC group countries and the USSR.
'N,rq
,.-'"
un
OUlcr Sources of Caseous Fuel
u
-.
,~
y• . 101
.,.,
~,103
,--
..... :an
ISH
'7.otT
.~
Besides conventional sancbtone and limestone reservoirs, sources of natural gas include: tight sands, tight shales, geopressured aquifers, and coal.
~
~~
~.
,.)u. ~
.~
~
,m
1,515
.~
,-
1.300,000
'"
~
.~
,~
7 .. ,
1.32_ :101
3.101
21M •• '
'07000
,-,..,-- -.-..,--
212 ....
110.000
Tight Sands
•. 01'
,,- ,••
,~
1.ITO
',115
,,~
~­
~
.,~
~
n
~­
.,=
~
,~
~
137._
.n.• ,
'"IV,OOO
370.000
.~
M._
~.­
:t:Z.70!;
u_
,,".
.-
UfI.OOO
1301.
on
1.10'
H~.=
Large amounts of gas are locked within very tight formations, with porosities in the range of 5-15 % , irreducible water saturation of 50-70%, and
ultralow permeabilities in the range of 0.001 to 1 md (millidarcy). Many
geologic formations, especially in the Rocky Mountain area of the USA, contain such gas, which is not possible to produce using conventional fracturing
and completion methods .
There is a need to develop special artificial fracturing techniques to
produce gas economically from tight sands. Three major techniques have
been proposed: nuclear explosives, chemical explosives, and massive hydrauHc fracturing (MHF). Nuclear blasts are dangerous and probablY not
feasible at this time. Chemical explosives are also quite dangerous, and effective only in areas where natural fractures: exist (which is not the case for
most tight sands). MHF has been quite successful, and is presently the subject of much research. An MHF treatment typically requires the injection of
a fracturing fluid (water) at high pressures for many hours to induce a fracture, followed by a fluid containing the propping agents (glass beads or
sand). When pumping stops, the fluids £low back into the well bore, leaving
the proppant behind to hold the fracture open.
Tight Shales
"----
Shales are generally rich in organic matter, finely laminated, with a permeability of the order of 1 md. Shales. predominantly composed of quartz,
..
14
Nall/ral Gas-Origin and Development
Gal Production Engineering
with some kaolinite. pyrite. feldspar. and other minerals, constitute about
5% of all sedimentary rocks in the USA. The De\-onian ..hales in eastern
Kentuch and western West Virginia are well known gas producers. In these
shales. p~oduction is controlled by natural fractures. The production profile
exhibits a long. slow decline. The gas has a high Btu "alue, as high as 1.250
Btu sci \1HF techniques are useful for tight shales also. These tight shales
are an attracth"c source of gas and may contribute very significantly to gas
production in the coming years.
tONSUIO(RS
t0f01lOII1I'IG
"_
..... ,
"'.... ".,1
ToViME_ I lRlitlt
, ... _1
a~"
!
~IOII[fAcr(l"
SU\.I'\IR.
ILliG 1
fEIIliU$UI
M~"
...
!
fLtaO
_
~-,
1
Methane gas occluded in coal in minable coal beds with depths less than
3,000 ft has been estimated to be 260 Tscf in the US. This significant resource base, however, may only produce less than 40 Tscf due to practical
constraints.
Another source of gas generation is coal gasification. The gas derived
from coal usually has a lower heating value than natural gas. The commercial viability of coal gasification is not favorable yet.
..
TO
ptT~OOW:"'"
"'''"'c"
~;"CIt.~
_'"'
UQUlOS
TO
tOlOOlllONftG
If..........'"91
PfIOtUS IfOCUSTItY
RECQYEfll
,
~
a.L-WAlEfI-OU
S(P,",f1/t.llllOl
_......
~
c;
ST~_£I)GAS
...
'''-
"....... , ,
Co.1
_UIOIE TII""SPOIIT
u,
Ccopressured Aquifers
High-pressure brine in geopressured aquifers, which can form due to
rapid subsidence, may contain up to 40 sef of natural gas per barrel of \...·ater.
In the USA, sueh geopressured aquifers are located predominantly in a band
that extends onshore and offshore from Texas to Florida along the Culf of
Mexico. An estimated 2,700 Tscf of gas reserves (unproven at this time) are
associated with this region, Howe\-'er, no commercial means of recovering
this gas ha\'e been de\'cloped to date,
15
,IU.T14[RI'«lSUT[III
wAut ...... l
C.. OMES
U
SUR raCE
VEIl TICAL IIHCUI<[O
rUM TI'IROUGI1 PlPU
\'.'5 REU:""
\
Figure 1-6. A typical gas production and processing system.
Natural Cas Pnxluction and Processing System
Figure 1-6 outlines a typical gas production and processing system. From
a design viewpoint, the total system consists of the following calculation
modules:
1. The ~r\'oir module that deals with the flow of gas (and oil) through
subsurface strata.
2. Flow module for the flow of fluids from the ~rvoir to the wellhead
at the surface.
3. Gas gathering system module. This module calculates the flow of gas
through the pipeline network at the surface that is used to collect gas
from several wells for separation and processing.
4. Separation module for calculating the amounts of gas, oil and water
generated by the wellstream. and their compositions.
5. Metering devices for measuring the amount of gas and oil from the
separators.
6. Gas conditioning module for the removal of contaminants from the
g"',
7. Natural gas liquids recovery module.
8. Gas compression/liquefaction for economic transport by tankers, railroad, and road transport.
9. Flow module for the pipeline transport of gas to consumption sites.
,
16
Natural Cas-Origin and Development
GO! Prcxlul'tjqn Engilleerlng
This book has been desib'lled to provide information on the design. operation, and engineering calculations for all of these modules. except the reser.
voir module. Chapters 2 and 3 pro"ide the basic gas properties that are an
essential input in all computations. Chapters 4 through 6 describe separation and processing for natural gas. Flow calculations are covered in Chapters i and 8. Chapters 9 and 10 provide information on related topics.
namely, gas compression and gas metering, respectively. FinsHv. Chapter 11
describes i!:as gathering and transmission systems and the ~mputational
techniques for handling the complete production system.
'M
Questions and Problems
1. (a) List some factors that may enhance the appeal of natural gas as a
domestic and industrial fuel. (b) What are some of the factors that
may reduce the appeal of natural gas as a domestic and industrial
fuel?
2. Why is natural gas termed a ··stable" flammable gas?
3. What impurities can one expect to find in natural gas produced from a
gas field?
4. Why are gas flares a common sight in many petroleum producing ar.
eas? Can such flares be hazardous to the environment? If yes, then
when and why?
5. As a petroleum engineer you are taken to tour a gas-producing field.
Can you tell what type of gas (associated, dissolved, etc.) is being produced? What is the minimum information required to draw such a
conclusion?
6. How are gas reserves estimated?
7 Besides conventional reservoirs, what types of gas reserves hold promise for the Cuture? Why?
References
American Petroleum Institute, 1984. Basic Petroleum Data Book: Petroleum
Industry Statistics. Vol. IV, No.2 (May). API, Washington, D.C.
Barker. C. and Kemp, M. K., 1980. "Generation of Natural Cas and its Sur·
vival in the Deep Subsurface," presented at the Conf. on Natural Gas Res.
(}e\'. in Mid·Cont. Basins: Prodn. & Expl. Techniques, Univ. of Tulsa,
Tulsa. Oklahoma, March 11-12.
17
Brown, T. E. and Miller. S., 1985. Layman's Guide to Oil & Gas Investments & Royalty Income, 2nd Edition. Culf Publishing Company, Houston. Texas.
Curr\', R. N., 1981. Fundamentals oj Natural Cas Conditioning. PennWeli
Pub!. Co., Tulsa, Oklahoma. 118 pp.
Crow. C. C .. 1980. "Future Potential Cas Supply in the United StatesCurrent Estimates and Methods of the Potential Cas Committee," presented at the Am. lnst. of Chern. Engrs. Meeting, Philadelphia, PA. June
9.
~lcCain, W. D., jr., 1974. The Properties oj Petroleum Fluids. PennWell
Publ. Co .. Tulsa. Oklahoma, pp. 3-42.
McElroy. O. P., 1987. Fundamentals oj Petroleum Maps. Culf Publishing
Company, Houston , Texas.
McKelvey, V. E., 1972. "M ineral Resource Estimates and Public Policy,"
American Scientist. 60, Jan.-Feb., 32-40.
Wheeler, R. R. and Whited, M., 1985. Oil-From Prospect to Pipeline, 5th
Edition. Gulf Publishing Company, Houston , Texas.
•
PhQM! Behavior Fundamentals
19
where N ,. number of degrees of freedom of the system
C _ number of distinct chemical components (or compounds) in the
system
P _ number of phases in the system
2
Phase Behavior Fundamentals
Introduction
The properties exhibited by any substance depend upon its phase,
namely, whether it is in the solid, liquid, or gaseous phase. Substances can
be cla~ified into two types-pure or single component, and mwticomponent. Phase behavior relationships can be determined from laboratory pVT
(pressure, volume. temperature) studies, or using theoretical/empirical
methods such as the equations of state. These relationships are frequently
shown graphically as "phase diagrams" to enhance qualitative understanding. For design purposes, howc\:er, precise quantitative phase behavior data
are crucial. In this chapter, some fundamental concepts in phase equilibrium are introduced.
Qualitative Hydrocarbon Phase Behavior
A phase diagram for a single component system has three axes: p. Y, and
T. Usually, p. T diagrams only are used for a single component system. For
multicomponent systems, the mixture composition becomes an additional
variable. Generally, three types of phase diagrams are used for mixtures: (a)
pressure versus temperature (p,T) diagrams, holding the composition fixed;
(b) composition-composition diagrams, keeping pressure and temperature
fixed; and (c) pressure-composition diagrams. keeping temperature fixed.
The number of degrees of freedom of a system is the number of variables
that must be defined to fix the physical state of the system. Usually, pressure,
temperature. and composition serve as the variables.
The phase rule can easily be verified. Consider a mixture consisting of C
components distributed in P phases. Then. at equilibrium, the chemical p0tentials (see pages xx-xx for thermodynamic criteria for equilibrium) for
each component are equal in each phase:
Pn - J.li2" .,. - J.I"p, for i = 1,2, .... C
Thus, we have (P - 1) equations for every component, or a total of
C(P - 1) equation.~. The unknowns are the mole fractions of each component in each phase, which represent (C - I)P unknowns, since knowing the
mole fractions of (C - 1) components in any phase P fixes the mole fraction
of the last component (the sum of the mole fractions equals unity). Also, the
pressure p and temperature T are unknown. Thus, the total number of unknowns are (C - l)P + 2. So, the number of degrees of freedom are:
N "" number of unknowns - number of equations
- (C - l)P + 2 - C(p - 1)
or, N - CP - P + 2 - CP + C ,. C - P + 2
Single-Component Systems
Figure 2-1 shows a typical p,T phase diagram for a single-component system. The equilibrium lines, AB, BC. and BO indicate the combinations of
pressure and temperature at which the adjacent phases shown on the dia-
o
ta
I .. ·· __ ·-U
:I
Camru~
liqu d ,
Solid b£ ____
C
I
I
Critical pall'll
,
: Suptrll,alld
i _' ___h!vapar
Liquid
The Phase Rule
Vapar
B
Cibbs' phase rule for the degrees of freedom of a system is written as:
Tripi, pOll'll
Figure 2-1. Pressure--temperature
diagram lor a single component
Tlmp,ralure -
system.
A
N-C-P+2
18
•
20
Ph4&e &haclQr Fundamentals
GO! Production Engineering
gram exist in equilibrium. Line AD represents the equilibrium between solid
and vapor. A solid above this line will sublime direct1y to the vapor phase,
without ever going through the liquid phase, on n..oduction of pressure to below line AB. An example of this is "dry ice:' Line DO indicates the solid
liquid equilibrium. Line BC is the equilibrium between liquid and vapor
phases. At the triple point. B, all three phases exist in equilibrium. Applying
the phase rule. it can be seen that for a single-component system with three
phases, the degrees of freedom, N - I - 3 + 2 - O. Hence, the triple point
is a unique point that defines the whole sy,rtem. The equilibrium lines, howe\'er, reprt:M:nt only two phases in equilibrium and the degrees of freedom
N - 1. Therefore, specifyin)i!; either the pressure or the temperature fixes the
other variables for the system. In the single phase regions, N - 2, and both
pressure and temperature must be known to determine the location (or state)
of the system in the phase diagram.
The liquid-\'apor equilibrium line (BC) begins at the triple point. B, and
ends at the critical point, C. At the critical point, liquid and gaseous phases
become indistinguishable and their intensive properties (that is, properties
independent of the amount of fluid: for example: density, viscosity) become
identical. The pressure and temperature corresponding to the critical point
are termed critical pressure, Pc. and critical temperature, T e , respectively,
and are a uniquely defined numerical \'alue for every pure substance. More
formal definitions are as follows:
1. Critical temperature: The temperature above which a substance cannot be liquefied by the application of pressure alone.
2. Critical pressure: The pressure at which gas exists in equilibrium with
liquid phase at the critical temperature. Also defined as the saturation
pressure corresponding to the critical temperature.
Consider a constant pressure (isobaric) process represented by the line
alx:deh of Figure 2-1. From a to b the system is completely solid, and the
energy requirements for achieving the increase in temperature are simply
proportional to the specific heat of the solid phase. From b to c, pressure and
temperature remain constant, but an energy equal to the latent heat of fusion is required to convert the solid phase to liquid. The energy supplied is
converted into internal energy. The temperature Increase from c to d requires energy proportional to the specific heat of the liquid phase. At d the
liquid is a saturated liquid-any further addition of energy will cause vaporization at constant pressure and temperature. Energy equal to the latent
heat of vaporization is required to accomplish the change of phase from d to
e. At e, the vapor is termed saturated. At higher temperatures, for example
at h, it is called superheated. The energy spent for going from saturated vapor state at e to a superheated state at h requires an amount of energy proportional to the specific heat of the vapor.
21
To better understand vapor-liquid phase behavior, consider the region
near the critical point in greater detail. IT one proceeds from d by a compression process at constant temperature to f, liquid will at some point begin to
disappear into a seemingly gaseous phase. Above the critical point at f, the
system is in a "fourth" phase that exhibits properties different from gas. The
properties of this fluid are in between those of gas and liquid. though not
corre1atable to either. For example, it is denser than regular gas, and is more
compressible than a regular liquid. By going further from f to a point g beyond the critical temperature at constant pressure, from g to h at constant
temperature, and finally, back to e, a phase transition from the liquid state
at d to a vapor state at e can be achieved without any abrupt change of
phase.
This shows that liquid and vapor phases are in reality quite similar: They
represent separate forms of the same condition of matter, and it is possible to
pass from one state to the other without an abrupt change of phase. Thus,
the terms liquid and vapor have a definite meaning only in the two phase
region. For conditions far removed from the two-phase region, particularly
at pressure and temperature conditions above the critical point, it is impossible to define the state of the system, and is best referred to as being in the
fluid state.
Multicomponent Systems
•
p, T Diagrams JOT a Fixed Compollition
Figures 2-2a and 2-2b show typical p,T phase diagrams for a reservoir
fluid. The system has three regions: (a) single phase oil, in the region above
S!o;I.......
'"
o
,
,
to
40
60 110
Figure 2-2 • . Pressure.temperature diagram lor a multicomponent reservoir
fluid.
Figure 2-2b, Phase diagram showing two retrograde regions.
22
Ph4se Behavior Frmdamentou
Ga.r Production £nginunng
the bubble point (SP) curve; (b) single phase gas, in the region towards the
right of the dew point (OP) curve, and (c) the two phase region, which is the
portion bounded by the SP and OP curves. The BP and OP cur\-'es intersect
and terminate at the critical point, C.
Point A represents the maximum pressure at which liquid and vapor may
exist in equilibrium. This pressure is known as the cricondenbar. Similarly,
the cricondentherm is defined as the maximum temperature at which liquid
and vapor can exist in equilibrium. This is indicated as point B in Figure
2-Za. Along \\<;th the critical point. these serve as valuable tools for reconThe
region
retrograde region . exhibits quite an
interesting behavior. Usually, on lowering the pressure, a liquid phase vaporizes to gas. But in this region, on lowering the pressure, the gas at a hegins to generate liquid at b (see Figure 2-2a). On further reduction in pressure, more and more liquid is condensed (refer to the quality lines). until
point c is reached. Outside the retrograde region fTOm c to d,liquid begins to
vaporize until the 100% gas quality line (or the dew-point curve) is reached
at d. It is evident that the retrograde region results from the shape of the
phase envelope and the quality lines. The inflection points of the quality
lines govern the retrograde area, which is bounded by the critical point, C.
the cricondenbar at A. and the cricondentherm at B.
For naturally occurring hydrocarbon mixtures, the critical point has always been found to occur to the left of the cricondenbar (Campbell, 1984).
If the critical point is to the right of the cricondenbar, two retrograde regions will occur as shown in Figure 2-2b.
p, T Dtagmnu for \'tlrialJle Composition
The case discussed earlier concerned studring the phase diagram at a
given fluid composition. When fluid is produced from a reservoir, pressure
decreases over time. If we started off with an oil reservoir for example, a
two-phase region will eventually be encountered at pressures below the bub-ble-point curve. The heavier components in the reservoir f1wd will begin to
vaporize, leading to altered reservoir fluid compositions. Whenever the reservoir fluid is in the two-phase region, compositions also change due to the
selective removal of components in the mobile phase. Therefore, the phase
equilibrium relationships change with time for a typical ~rvoir system,
and the shifts in the phase envelopes as a function of composition must be
studied carefully.
Figure 2-3 shows a p,T diagram for a binary mixture of ethane (C 2 l4)
and normal-heptane (n-C,H 16)_ It can be seen that with a shift in the mixture cOmposition from 100% ethane to 100 % n-heptane, the phase envelope
shifts towards the right. This shows that the shape and location of the phase
23
-,~
.0000
ou
-".~
••
'.
Figure 2-3. Pressuretemperature diagram
for the ethaneln-heptane system. (Alter
Stalkup. 1978, 1983;
•
courtesy of SPE of
AIME.)
•
envelope are composition dependent. The dashed line drawn tangent to all
the phase envelopes at their critical points is called the critical locus. The
critical point for a mixture is thus a function of its composition. Mixtures
with more than two components have more than one critical locus, and the
problem becom~ quite complex. Simple mixing rules have been devised (to
be discussed later) to represent this shift in terms of -'pseudocritical" properties for correlation purposes. The only reliable method at this point is laboratory measurement, since none of the correlations are very exact.
Compoation-Composition Diagrams (Fiud p. T)
According to the Gibbs phase rule, N - C - P + 2 degrees of freedom
must be specified for completely defining the phase behavior of a mixture
with C components distributed in P phases. Such a rigorous description,
however, is neither practically feasible nor usually necessary. Ternary diagrams are used as an approximate method for representing the phase behavior of multicomponent mixtures. These diagrams represent the phase behavior of a ternary (three-component) mixture exactly; mixtures with more
components are approximated by three pseudocomponents. For hydrocar-
-
Ga6 Production Engineering
Phose Behavior Fundammtou
Figure 2-5. Pressurs-<:omposition
diagram lor a reservoir fluid.
Figure 2·4. A typical ternary
phase diagram for a reservoIr
fluid.
Plllil poinl
25
,,
:
•
0:
C,
JOO%
bon systems, the three pseudocomponents generally used are methane (C,),
ethane through hexane (C 2- 4), and C;., which represents all hydrocarbon
fractions with molecular weight greater than hexane.
Figure 2-4 shows a typical ternary phase diagram for a reservoir fluid.
Each corner of the triangle represents 100% of the component indicated,
whereas the side opposite to this corner represents 0 % of that component.
The distance in between a corner and the opposite side is divided into equal
parts to rep~nt fractions between 100% and 0% of the component. Thus,
the point A in Figure 2-4 represents a mixture containing 67% Cit 18.5%
Ct-Cts. and 15% C7 +. lying in the two-phase region. Such a mixture, under
equilibrium conditions, would result in a gas phase of composition y in equilibrium with a liquid phase of composition x. The dashed line connecting
these equilibrium gas and liquid compositions, occurring on the dew-point
and bubble-point curves, respectively, is called a tie-line. Clearly, there can
be an infinite number of such tie-lines. The tie-lines disappear at the critical
point, also called the plait point, where the liquid and gas phases become
identical. Outside the phase envelope, single-phase gas occurs above the
dew-point curve, whereas single-phase liquid occurs below the bubble-point
curve. The size of the two-phase region depends upon the pressure and temperature. With increasing pressure, the two-phase region collapses to
smaller sizes, whereas with increasing temperature it expands in size.
Lever's rule can be applied to determine the relative amounts of gas and
l~qu~d in ~uilibrium. For example, the mixture at A would split into a gasl~qUld ratio equal to the ratio of the distance of A, along the applicable tiehne, from the bubble-point and dew-point curves, that is, Ax/Ay.
Pml8Urt-Compoeition Diagrarm (Fixed T)
. Pressure-com~ition diagrams also serve as a useful method for displaymg phase behaVior data. These diagrams are obtained for reservoir oi1.s by
o
100
ConCenlrOl1Ol\ of CI' " J f . -
adding the desired injection fluid to the oil in a high-pressure visual cell.
The appropriate (bubble-point or dew-point) saturation pressures are measured as a function of the injection fluid mole fraction in the total mixture
that ~ults from the mixing of the injection fluid with the reservoir oil. Such
diagrams are easier to obtain than the ternary diagrams, which require obtaining equilibrium samples and compositions, but their applicability is limited since they do not offer information of a general nature. Figure 2-5
sbows a pressure-composition diagram for a reservoir oil as a function of the
mole % methane in the mixture.
•
Quantitative Phase Behavior and Vapor-Liquid Equilibrium
In most petroleum production operations, it is important to know the
phases present in order to design the system. In processing and other postproduction operations, it is desirable to control these phases by controlling
the operating conditions, or condensing or vaporizing selected components.
The single-phase regions are relatively easier to define. The two-phase region is more difficult, since we need to know additional parameters such as
the vapor-liquid ratio, and the compositions of both the phases, as a function of pressure and temperature.
Thermodynamic Criteria for Equilibrium
Phase equilibrium is reached when there is no net transfer of material
from one phase to another. Such transfers involve a decrease in the total free
energy of the s)'Stem. Thus, when equilibrium is attained, the total free energy, G, also called Gibbs free energy, will be at its minimum value. This
can be mathematically expressed, at a given p and T as:
Phase Behavior Fundamentah
26
de -0
(2-1)
Note that "no net transFer" does not imply that the system is static. There is
still a continuous exchange or transfer of material between the phases. But
the rate of transfer of each component from one phase to another is just balanced by the same transfer /XCurring in the opposite direction from the latter to the former phase. Thus. there is no IIet transfer of any molecular species from one phase to another, and no net change in composition occurs in
any of the phases.
An equivalent idea is expressed using the condition that dE "" O. where E
is the total energy content of the system. Note that the derh'ative in Equation 2-1 is "'ith respect to all possible variations. except those of p and T
Gibbs defined chemical potential, p., to express these ideas. The chemical
potential of any component i in a phase is the rate at which the total free
eneTgy of that phase changes as one changes the amount of the component i,
keeping p, T, and amounts of all other components of the phase constant:
(2-2)
where n j represents the moles of any component i. V is the system volume.
and S is the system entropy. Chemical potentials are intensh'e properties and
depend upon the composition of the mixture. but not on the total mass. For
a s'ingie--com{X)nent ideal gas, the chemical potential is given by:
It - Po·
+ RT In (pIp·)
(2-3)
where R is the gas constant. and the superscript· refers to any arbitrary
standard state. For a perfect gas mixture, the chemical potential for any
component i, is given by:
Po, - 1'1" + RT In (p,/pt)
(2-4)
where Yj is the mole fraction of component i in the mixture. It is not possible
to ascribe absolute numeric values to quantities such as free energy and
chemical potential. The ratio between two isothermal states as previously
defined suffices for application purposes.
Equation 2-2 can be manipulated to yield the result that the necessary
condition for equilibrium is that the chemical potentials of a given component are equal in all the phases. Thus, the chemical potential can be considered as a kind of driving force for mass transfer between phases.
27
The change in free energy, dC, for any substance is given by dC - v dp.
For an ideal gas (pv - RT: see Chapter 3 for further detail), this becomes:
(2-5)
de - RT d In p
To preserve this simple mathematical form of this equation for other cases
where the system is not an ideal gas, Lewis defined a special function called
fugacity, f, as follows:
(2-6)
de" RT d In f
Integrating Equation 2-6. we can obtain:
C -
co -
RT In(fW) -
r,.
vdp
(2-7)
Fugacity can, therefore, be defined as a quantity whose numeric value is
equal to the pressure when the substance is in the state of an ideal gas. It can
be easily seen on comparing Equations 2-5 and 2-6 that fugacity has the
units of pressure, and is proportional to pressure for an ideal gas. From a
purely theoretical standpoint. any substance in any phase-solid. liquid. or
gas-can be brought into an ideal gas state by sufficient pressure reduction
at constant temperature. It can be seen also in the equations of state, which
reduce to the ideal gas form, pv ,. RT, at the limit when p = 0 or v ,. 00.
Fugacity thus serves a very valuable purpose in equilibria studies.
Fugacity for a component i in a mixture can now be defined in terms of
the chemical potential as follows:
/Ll - Pot
~ Po"
+ RT In (fj/ft)
+ RT In (£j/£O) - RT In
Yj
(2-8)
Using these relationships, it can be seen that the condition for equilibrium
can. alternatively, be stated in terms of fugacity. A system is in equilibrium
when the fugacities of a given component are equal in all the phases.
The Equilibrium Ratio
The vapor-liquid distribution coefficient, commonly known as the vaporliquid equilibrium ratio or the equilibrium vaporization ratio, Kit for a component i, is simply the ratio of its mole fractions in the vapor (Yi) and liquid
(x;) phases at equilibrium conditions:
(2-9)
•
28
Ca, Production Engineering
Pruue Behavior Fundamentau
Equilibrium ratio values can therefore be determined by laboratory equilibrium flash experiments by analyzing the mole fractions of the different components in the vapor and liquid phases.
The PartitJ
PrnlUlT
for a pure component, and
In
'+'1""
In f, /px;
Approach
- -In Z +
K-values can be expressed in terms of partial pressures of the components.
The assumption, of course, is that the gas obeys ideal gas laws and behaves
as an ideal mixture. Therefore, such a concept is only applicable at low pressures, up to about 400 psi.
At equilibrium, the partial pressure of component i in the \"apor phase
(- PYJ) must be equal to the vapor pressure exerted by its presence in the
liquid phase (- P.'IX,). Thus, at equilibrium:
So, K, - p,;/p
29
I ~ [(1 v) - (1 RT)(ap ,an.)]dv
(2-13)
for a component i in a mixture. where n, is the moles of component i in the
total mixture. K can be expressed in terms of fugacity coefficients as follows:
K• = ",1'/"'\'•
"'r
(2-14)
;rr
where
and
are the fugacity coefficients of component i in the liquid
and vapor phases, respectively, coexisting under equilibrium conditions.
This can be verified, by expanding the right-hand side term of Equation
2-14:
(2-10)
where pvl is the vapor pres.~ure of component i at the equilibrium pressure
and temperature conditions.
T,h,is ~pproach is very useful as a practical methoo for determining the
eqUlhbrium constants, but has limited applicability.
- (YiP)/(x,p) since
rr .. f[ at equilibrium
- }'i/x, - KI
T~
Fugacity !.pprotu:h
Flasb Calculations
Non-ideal behavior can be accounted for by using the fugacity coefficients. The fugacity (or activity) coefficient, "'" for a component i is defined
as the ratio of its fugacity, f" to its partial pressure. p,:
with Iim.."', "" 1
p-u
These calculations involve solving simple material balance equations for
multiphase systems in order to establish the phase compositions as well as
amounts upon equilibrium separation. In oil and gas systems, we generally
have a two-phase oil-gas phase breakup. Water is assumed immiscible in the
liquid oil (oleic) phase, and miscible only in the gaseous phase where its
presence can be quantified by Dalton's law of partial pressures.
Consider F moles of a hydrocarbon mixture of composition {Zj} enters a
separation unit. At the operating conditions of the separator, it splits into L
moles of liquid of composition {XI}, and V moles of vapor of composition
{YI}' Then, by the law of conservation of mass:
(2- 11 )
F?r a gas phase, the partial pressure, Pi = YiP. To enable definition of a liq~,d fugacity coefficient, an equivalent hypothetical partial pressure concept
IS used, and liquid phase partial pressures are expressed as I~ _ x,p.
Fugacity coefficients are commonly written as:
In
v -In f/p -
I:
F-L+V
[(v/RT) - (lIp)]dp
- Z - 1 -In Z - (lIRT)
L [p - (RT/v)]dv
•
and
(2-12)
--~~>r.
no
Fz; - LXI + VYI for each component i
. . . .__________________________________. . . .___
j"
30
Cal Production Engineering
Phase Behavwr Fundamentals
Changin~ to a unit mole basis, F - I, for simplicity:
L+V-
howe\'er. are different. It is eas)' to envision that for a stream F for which V
is very small, any error in the calculation of V will be far more detrimental
(2.15a)
and
z, - Lx, + Vr, - Vx,(L, V + K)
31
(2· 15b)
to accuracy as compared to an error in the calcuJation of L. For such a system. it will therefore be necessary to solve for V using Equation 2-16 using
very rigorous com'ergence criteria (that is, use a very low error tolerance),
and then obtain L by difference. Similarly. for predominantly gas systems.
Equation 2-17 would provide better accuracy.
Thus. we get
Applications
VX, .. z,J(LIV + K)
Reservoir Behavior
and
Figure 2-6 shows a p. T phase diagram for a naturally occurring hydrocarbon fluid of a known composition. Consider four different reservoirs,
with this same fluid, but with different initial conditions denoted by 1;, 21t
3;, and 4;. The vertical lines represent the pressure decline in the reservoir at
constant temperature. The curved lines represent the pressure and temperature chang~ imposed upon the reservoir fluid as it flows upward through
the well bore. and both pressure and temperature decline to the wellhead
producing conditions. The subscripts sand r denote surface and reservoir
conditions, re;pectively.
Reservoir 1, occurring above the bubble-point curve, is called an undersaturated oil reservoir. It is also called a black oil reservoir, depletion drive,
~Ived gas drive, solution gas dri . . e, or internal gas drive reservoir. Cas is
The following additional relationships must also be satisfied:
1:" x,- 1:"J
,-)
I
and
Thus, the amount of vapor, V. can be calculated as follows:
Condensole
V-
"
"
V 1: y, - 1: [~I(Ll KV + I)J
,-I
I-I
R."rvol.,
(2·16)
U liquid, L, is desired. it can be calculated as follows:
L- L
1:"J x, - 1:" [~I(KVIL + I)J
1-
I_I
Equations 2·16 and 2-17 require a trial and error type of solution scheme.
Both these equ~tions are equivalent, and one has the choice of using either
one; knowing either L or V is sufficient, since L + V-I (Equation 2-15a).
From the standpoint of obtaining an accurate solution. these equations,
Temp"Olure -
Figure 2-6. A typical pressure-temperature phase diagram for a reservoir fluid.
10
32
Ga, Production Engineering
PhDse Behodor FllIIdamerltals
produced at thesur[ace conditions (1, is in the two-phase region), but no gas
is formed in the reservoir untiJ the pressure reaches the bubbJe--point pressure. Typically. higher API gravity oils release greater amounts of gas since
they contain larger amounts of lighter components. Below the bubble point.
the COmposition of the reservoir flUid starts changing. The free gas liberated
. Iying a dissolved gas
COR< 2 ,()()() scf /51 b are I,'kel)' to have T t > T R, Imp
drive resen·oir.
in-.~itu eventually begins to (Jow toward the well bore in increasing quantities with
goe:;
up. reduction in pressure. The producing gas-oil ratio (COR) therefore
ReserVOir 2, occurring in the two-phase region, is an oil reservoir with an
initiaJ gas cap. With declining pressure, COR increases, and the reservoir
flUid Composition changes.
Reservoir 3. OCCurring in the retrograde region, is a gas condensate reservoir. On pressure reduction. liquid begins to condense at and beyond the
dew-point Curve, Since it clings to the pore spaces in the resenoir, a Critical
saturation has to be bUilt up before it can flo\.\.- toward the weJlbore, Thus,
the producing COR (at the surface) increases, The intermediates that condense out of the gas are verr valuable and their loss is a serious affair. How_
ever, as pressure is reduced further, the liquid begins to revaporize into the
gaseous phase, This revaporization aids liquid recovery and, assuming that
the '''''"voi, flUid oomposition oonstant, may lead to a decline in the producing GOR at the su,face, The """"'oi, fluid oomposition, howeve"
changes as retrograde condensation OCCUrs: the p- T phase envelope shifts to
the right, increasing retrograde liqUid condensation into gas, This retrograde 'ross" is greater for a greater shift of the p_ T phase envelope to the
right, lower reservoir temperature, and higher abandonment pressure.
ReserVOir 4, OCCurring in the single-phase gas region, is a true gas reservoir. It is generally known as a wet gas reservoir if 4 is inside the moo-phase
J
region, Or as a dry gas reservoir if 4. is in the single-phase gas region. In this
reservoir type, the reservoir (point 4,) is aJwars in the single-phase gas region,
of the pressure. So, the reservoir fluid maintains a constant
composition since there is no change of phase in the reservoir.
The prodUCing COR for a reservoir is an exOOlent indication of the reservoir tYPe. Cenerally, a reservoir is claSSified as a gas reservoir if the
GOR> 100,000 scflSib, "an oil """"'oi, if the GOR < 5,000, and as a gas
condensate reservoir if the GOR is between 5,000 to 100,000 scf/stb.
The relationship between the critical temperature, T , and the reservoir
t
OCCUrs or
temperature, T R, determines whether retrograde condensation
not. For retrograde condensation to OCCur, the reservoir temperature must
be in between the Critical temperature and the cricondentherm. ReserVoir
systems in Single phase with a surface COR::> 10,000 scf/stb are likely to
have a high C, fraction, and consequentJy, a low T • Expect retrograde cont
densation for such reservoirs, Reservoir systems in single phase that exhibit a
~
regardJ~
I
I
33
bon Production and Separation
Hydrocar
f 'I'res depends upon the
nd,surface .aCI hase
I , gas and oi I Wit
'h a
d' of the producing weII a
The ""gn
'rod ced' gas 0.1,0< tM-P
h d a bons
ature of the fluid bemg p
uf 't Since the inte,mediate y coc , I
n.
COR and the presence 0 \\-a cr. ts it is highl) desirable not to ose
the most valuable
- uid as possible fcom the p,oduced
g",e~ften
~:m
''Ompon~J'
d~gn~e::~ ;;rat;~nal
~e:s~'~~,~:
to the gas, andhto
optimization of
h d arbons For tees
'I'b .
parameters m
);e::t ph"'; behavio, and gas-oil
the
of the p«>;. ce the phase relationsh,ps ace a unc uipment that is op"mum
fluid, we can nevee ,eall,
it for the "avmge"
all conditions.
The
onlf'h
f.lI~:r
to
cha~e
the installation at some POlOt
ed
the life 0 t e Ie ,
d so
expect
over
icalJy
attractive
to 0 .
where it may become econom
(m :io~u07
d~:OO
d~~~",(
oompositio~
u~d",
oond,"~n
Processing and Transport
G
as
,
nds from the gas so that the g:"
It may. be n""""",)' to remo,'e heaVIer
"
tede pressure- temperature changesI10
does not condense liquids upond ahnhCd'PI"ang s)'stems. 10 enable suc~ c~dslcu a·ng an
an
be k
LlqUl aecune fo,
; ; ; in the lines,
in the piping
:,',:,,,,,, of the instability caused by
and are genmll, undes"a e
f p,""ure and tempeca'ure,
'cs
changes
occurring
as
a
befunc"on
t~
ne'"
the
phase
envelope
boun
a~,
eq
uipment must never
opera
ature or composition can cause IS. ressure temper
,
where small changes 10 p
i~
vapor-liquid ratio,
proportionately large changes
:~ensrr:~~:::'t::="po;nt
cum~ate
s)~te~s,
~~~;~~~a~;:;"ure
ph~.::
P''''';''
. Engmccnng
,
. and Enhanced Oil Recovery
ReserVOir
.
h as reservOir
. reserve estimates,
Reservoir engineering calculahons, su~ rs require reliable phase behavpredictions, and simulations uSin~,ooalmih~~ i~ miscible enhanced 7~"'y
ior data. Nowhere is it more ,cn IC
urate hase equilibrium re atJontechniques, where highly deta'~dede :::g::f conltions, The perfbe0rm~n~l~f
'
be known over a WI
, 'ected fluid to
mLSCI .
. fluid The injection
ships musthorls depends upon the ability of the InJ
these met
, 'bTty with the ..,.,vo"
,
, 'b ' m
or be able to generate mLSC1, I I , ts dictated solely by phase eqUlh nu .
fluid must be tailored to reqUiremen
•
3'
Gas Producti()n Enginnring
Phose Behavior FrmdafflCfllais
Tt: - molar a,·erage boiling point o( mixture, OR
~ - mole (raction of 100"'-boiling component
Prediction of the Phase Envelope
To accurately predict the phase envelope for a muiticomponent hydrocarbon system such as oil or gas is almost impossible. Experimental means must
be used, since imprecise results can be quite dangerous to use in the innumerable planning. desi~, and operational problems. However, it becomes
\'ery necessary to use correlations and predictive methods in many instances
where such studies cannot be readily performed.
A'i a bare minimum. an accurate compositional analysis of the reservoir
fluid is essential. Estimates of the critical point. the cricondentherm. and
cricondenbar can then be used in conjunction with ,,'apor-liquid equilibrium
calculations for bubble-point and dew-point curves to generate reasonable
phase equilibrium curves. Sometimes, only a portion of the phase curves
rna)" be required.
The calculation prooedure is quite tedious. The mixture composition.
pure component critical temperatures, and normal boiling points are require(l. Values for T b can be calculated using a mixing rule, or obtained
from laboratory measurements. One proceeds by taking two successive components. calculating their T, and T p values, then adding one component at a
time and calculating the Tt and T p values for this new mixture until all the
components ha,·e been included. Grieves and Thodos (1963) report maximum errors of less than 5% in cricondentherm, but significantly larger errors up to 13 % for cricondenbar temperatures. Such a correlation is dif£icult
to use, and the results are not very reliable.
Critical Point
Cricondcntherm and CriCQndenbar
Grieves and Thodos ( 1963) presented the following equations for the prediction of cricondentherm temperatures:
(2-18)
Many different studies have focused on the problem of characterizing hydrocarbons for predictions of their physical properties. Watson and Nelson
(1933) and Watson et al. (1935) characterized the chemical makeup of petroleum mixtures using the boiling point and specific gravity. They defined
the Watson characterization factor, K. as follows:
and
(2-22)
Tt/T; ""'
(T~Tb
- l)(e6 31<.,
~38)
- OAI8x, + 1.256
for 0.55 < XI < 0.925
(2-19)
For estimating cricondcnbar temperatures, Grieves and Thodos (1963) suggest the following equations:
T piT: - (TbiT b
-
l )(e4 .l.ht
362)
+ 1.008 for 0 < x,< 0.7
(2-20)
and
Tp/T;" (T~Tb - 1 )(e633'r51~) - O.l65~
for 0.7 < Xi<O.925
where
35
+ 1.116
(2-21)
T t - cricondentherm temperature of the mixture, OR
Tp - cricondenbar temperature of the mixture, OR
= pseudocritieai, pseudocricondenbar, or pseudocricondentherm temperature, whichever applicable. of the mixture, OR
T b = nonnal (atmospheric) boiling point o( the mixture, OR
T:
If 51 units are used, with Th in K (Kelvin), the right-hand side of Equation 2-6 should be multiplied by 1.21644 ( - 1.81.3). K defines the relative
paraffinicity of a hydrocarbon fraction. A typical range would be from 10.0
(highly aromatic) to 13.0 (highly paraffinic). Several useful relationships
have been found using the Watson characterization factor ((or example.
Watsonet al.. 1935: Smith and Watson, 1937: Simon and Yarborough, 1963:
Riazi and Daubert. 1980: Whitson. 1983).
Thus, physical property correlations based upon the boiling point and
specific gravity ha'·e been used for a long time. and have proven to be very
reliable. DiHerent correlation parameters have been proposed. Most of these
can be expressed using the (ollowing generalized equation:
8-
where
aT!: y
8 - the property
T b - normal or cubic-average boiling point, OR
..,. - specific gravity at 14.7 psia and GOOF
(2-23)
•
36
Phase Behavw,. Fundamentals
Cal Production Engineering
If I:r_l Z;/K t < l.O, the system is in the single phase all-vapor region.
For critical pressures and temperatures, the constants a, b, and c, deter.
mined by Riazi and Daubert (1980) and Whitson (1983), are as follows:
-a-
b
24 278i
3.12281 x 10'
2.41490 X IOu
0.58848
- 2.3125
- 3.86618
8
T,. R
Pl. psia
p,. psia
-c0.3596
2.3201
42448
If both I:r.l KjZj and I:r.l Zt/K j > 1.0, the system is in the two-phase region.
Both r;r_1 KjZt and I:r.1 z;. K,-t.l.O.
for Tb < 850 0 R
for Tb > 8500 R
An efficient procedure to predict a bubble point is to find the pressure (or.
alternath·ely, the temperature) at which r;r_1 K,Zt '"' 1.0 at a given temperature (or pre.sure). A ~rit:!. of !luch points ,",Quid then (;Oll5titute the bubblepoint curve. A similar procedure can be used to reconstruct the dew-point
curve.
The maximum de\'iations were found to be 10.6 %, 9.3%, and 13.2 ""' , respectively. for these three cases (Whitson, 1983),
Bubble-Point and Dew-Point Curves
The bubble point may be defined as the p,v,T condition at which an all·
liquid s}'stem releases the first (infinitesimally small) drop of gas. Signaling
the entry into the two-phase region. Thus, at the bubble point. the total
mixture composition, {zd, is just equal to the liquid composition. {XI}. Since
the sum of the mole fractions equals unity, it is clear that for the gas phase
released at the bubble point, r:r_l YI is equal to l.0, and in all regions where
gas is not present, this sum will be less than 1.0. Thus, at the bubble point:
"
"
"
~),- ~ K,x( - E KIZt '"' 1.0
1.. 1
,.,
,I
Q uestions aDd Problems
l. Given the pressure and temperature, is it possible to specify the number of phaSd for: (a) water, and (b) a mixture of alcohol and water?
2. Name the type of phase diagram required for the following cases:
(a) a single-component fluid being used for heat transfer in a nuclear
reactor.
(b) a hvo-component gas being compressed for storage as liquid.
(c) a multi-component gas to be transported in a pipeline.
(d) design of an oil-gas separator.
3. What is the state of a substance at: (a) its critical point, and (b) above
its critical point?
4. Define fugacity. Show that the fugacity of a substance must be equal in
all phases in which it may exist at equilibrium.
5. Construct a p,T phase diagram for the following mixture:
(2-24)
At the dew point, the appearance of a liquid phase just begins for an allvapor spitem. The system composition. {Zt}, is equal to the ....apor composition. {y,}. Also, for the just released liquid phase. the sum of the component
mole fractions equals unity. Therefore:
" x, - ~
"
~
I
J
I_I
y,IK, -
"
~ ~I K, -
1.0
37
(2-25)
I_I
Equations 2-24 and 2-25 can thus be used to predict the bubble-point and
dew-point curves, provided K-values are known for all the components as a
function of pressure and temperature. A typical procedure would involve
calculating the quantities Er.1 K1Zj and Ep.1 z,/K, at different pressures and
temperatures. The state of the system can be determined b)' applying the
following rules that are true for vapor-liquid systems:
Component
mole %
Th , OF
C,
C,
Co.
65
20
15
- 258.7
-127.5
96.9
'"
Assume the C 3 .. fraction to be identical to n-C5 • The requ ired hydrocarbon equilibrium ratios (K.values) can be taken from Figures
4-25 through 4-51 in Chapter 4.
6. From the phase diagram constructed in problem 5, determine the cricondenbar and cricondentherm temperatures. Compare these with
the ones obtained using Grieves and Thodos' relationships.
If Er. I K,Z; < 1.0. the system is single-phase all-liquid.
I
-
38
GO! Production Engineering
References
Campbell, J. M., 1984. Gas Conditioning and Processing, Vol. 1. Campbell
Petroleum Series, Normar.. Oklahoma, 326pp.
Crieves. R. B. and Thodos, C., 1963. "The Cricondentherm and Cricondenbar Temperatures of Multicomponent Hydrocarbon Mixtures," Soc.
Pet. Eng. /., 3(4, Dec.}, 287-292.
Riazi. M. R. and Daubert, T. E., 1980. "Simplify Property Predictions,"
Hydr. Proc., 59(3, March), 115-116.
Simon, R. and Yarborough. L., 1963. "A Critical Pressure Correlation for
Cas-Solvent-Reservoir Oil Sy~tems," J. Pet. Tech .. 15(5, May). 556-560.
Sm~th, R. L. and Watson. K. ~1., 1937. "Boiling Points and Critical Properties of Hydrocarbon Mixtures," Ind. and Eng. Chem., 29(12, Dec.).
1408-1414.
Stalkup. F. I., 1978. "Carbon Dioxide Miscible F100ding: Past, Present, and
Outlook for the Future," J. Pet. Tech., 30(8, Aug.), 1102-1112.
Stal.kup, F.. 1.,1983. Miscible Displacement. Volume 8, SPE Monograph SeTIes, SocIety of Petroleum Engineers, Richardo:;on, Texas, 204pp.
Watson, K. M. and Nelson, E. F.. 1933. "lmpro\'ed Methods for Approximating Critical and Thermal Properties of Petroleum Fractions." Ind.
and Eng. Chern., 25(8. Aug.), 880-887.
Watson, K. M., Nelson. E. F., and Murphy, C. B.. 1935. "Characterization
of Petroleum Fractions," Ind. and Eng. ClJem., 27(12, Dec.), 1460-1464.
Whitson, C. H., 1983. "Characterizing Hydrocarbon Plus Fractions," Soc.
Pet. Eng. /., 23(4, Aug.}. 683-694.
3
Properties of Natural Gases
Introduction
In designing gas production, processing, transport, and handling systems
a complete knowledge of gas properties is crucial. For this reason, much research has been done in the measurement and prediction of hydrocarbon
fluid properties. The area of property prediction continues to attract significant attention from researchers who seek to optimize design and control of
gas and oU systems. The current trend is to develop mathematical equations
for implementation on computers, rather than the traditional engineering
charts and tables, because with computers it is far more efficient to solve
equations than to interpolate in a huge domain of possible parameter values,
whereas the opposite is probably true for humans.
Equations of State
AJI fluids follow physical laws that define their state under gi"en physical
conditions. These laws are mathematically represented as equations. which
are consequently known as equations of state (EOS). These equations essentially correlate p. V, and T for any fluid and can be expressed, on a unit
mole basis, as:
¢(p,v,T) - 0
For practical purposes, this form is rearranged to yield a desired parameter,
v ~ ¢(p,T). Many different empirical EOS's have been developed over the
years, and I will only mention the most basic and widely used among these.
39
•
Gas Production Engineering
Properties oj Na/ural Gases
Ideal Cases
too;'~e cont~Pt ~f an ideal gas is a hypothetical idea, but it serves as a useful
a gas ~:!h7c~ tthee':;::w::!::~ gas ~~avior. An ideal gas is defined as
tion between th
I I
P) negllgtble volume; there is no interac_
betw
th . e dOlO ~u. es. that is, no attractive or repulsl\;e forces exist
een em. an collISIOns between the molecules
I
.
plying no energy loss on collision At I
are pure }" elastiC, imexhibit an almost ideal behavior The 'd o~ pr~u~ (.:S 400 psi) most gases
can be stated as follow:;;
.
I ea gas aw
at applies to such gases
pV - nRT
The deviation from ideal behavior is greater for heavier gases because of the
larger size of their molecules. Most gases compress more than an ideal gas at
low pressures, whereas the opposite is true at high pressures. From an appli~
cation standpoint, all equations of state for real gases must be regarded as
essentially empirical in nature, since they attempt to correlate this non-ideal
behavior using empirical parameters.
The Corn preiMbi/ity Fador Approach
To correct for non-ideality, the simplest equation of state uses a correction
factor known as the gas co'l1pressibility factor. Z:
(3-1)
where p and T are the absolute
d
number of moles and V ;~ 'he P""'I ure an ~emperature of the gas, n is the
.
""
vo ume OCCUpied by the
R h
of proportionality in Equation 3-1 is called h
.
gas., t e constant
value of R can be easily dete . 'ed f
~ e universal gas constant. The
mole) of an .
.
rmm
rom t e fact that 1 Ibmole (pound> gas OCCUpies 378.6 ft1 at 14.73 psia and 60°F (5200R).
R - pV'nT - (14.73 x 378.6)/(1 x 520) "" 10.732 (psia ft1)/(lbmole OR)
Thus, if p is in psia T is in OR and V' . ft1 t h
R is 10.732 psia-ft1:lbmole-0R' I 51 IS.IO "h en t.h~ appropriate value of
V' .
. n
umts,w erepISm kPa T"
K
d
IS 10 m-', the value of R to use is 8.314 kPa-mJ'"kgmole-K.'
IS In ,an
Behavior of Real Cases
In general, gases do not exhib't 'd al beh .
tion from ideal behavior can bel I e -, __~Vlor. The reasons for the deviasumma.1L.C'.! as follows;
1. Molecules
for even a spa~ S\'Stem
ume.
.
. such as gas, occupy a £jnite vol2. Intermolecular forces are exerted bern'een the
these forces are:
molecules. Some of
• !i'ec:rostTa'hic forces. also called Coulomb forces, betv.·een ions and
po es.
ese are long-range forees.
• [~d~ced fO.rees between a dipole and an induced dipole, for examp e In a mlXture of a polar and a non-polar gas
• Attraction/repulsion fo
h' h
.
short distances ani T~ w IC a~ generally exerted over very
I
y.
ese forees eXISt even for a perfectly non~
po ar gas such as argon.
3. Molecular collisions are never perfectly elastic.
41
pV
=
nZRT
(3-2)
The Z-factor can therefore be considered as being the ratio of the volume
occupied by a real gas to the volume occupied by it under the same pres<>ure
and temperature conditions if it were ideal. This is the most widely used real
gas equation of state. The major limitation is that the gas deviation factor,
Z, is not a constant. Numerous attempts have been made to define the functional dependence of Z on various other parameters that define the state of
the system, and se\'eral correlations are available for the Z-factor as a result
of these studie;. More complex equations of state that do not represent the
deviation through the Z·factor, but through other correlation constants, are
often used to derive quite precise Z~factor values that can be used in Equation 3-2.
\an der \\aals Equation
This equation is probably the most basic EOS and, though seldom used
today, it serves as a conceptual basis for understanding and developing other
equations. It corrects for the volume occupied by the molecule; in a gas, by
using v - B as the true gas volume. instead of v; and loss in pressure exerted
2
by the gas due to attractive forces and inelastic collisions, by using p + Alv
as the true pressure.
(p + A/")(v - 8) - RT
(3-3)
where A and B are empirical constants. This equation serve; as a good approximation only for low pressures. It can also be written as:
.. _ (RT
+ Bp)v'/p + (A/p)v - AB/p - 0
(3-4)
•
'2
Propntie6 oj Natural Cases
Go, Production Engin«ring
Waals equation, which makes it applicable in developing gencral correlations in terms of reduced variables.
or, in terms of the Z·factor as:
Z3 _ Z2(1
+ SpiRT) + Z Apl(RT)2 - ABp'l/(RT)3 - 0
43
(~5)
p .. RTd + (B"RT - ~ - Co/r.)d Z + (bRT - a)d J + aad6
At the critical point, the three roots of the cubic equation in v (Equation 3-4)
are identical. Thus. if \'~ represents the critical volume, then at the critical
point:
(3-6)
+ (00'11')[(1 + ,d') exp( - ,d')]
(3-10)
where a. b, c. a, -y, ~. Bo. and Co are constants for a gi\"cn ~as_ d is the
molar density (lbmole/ft3), and p, T are the absolute pressure and temperature. respectively.
Comparing Equations 3-4 and 3·6. it can easily be shown that:
Redlich-Kwong Equation
(3-7)
Redlich and K\\'ong (1949) proposed the following equation:
An alternative procedure for obtaining the values for A, B. and R is to use
the fact that the critical isotherm, that is, the curve relating pressure and
volume al the critical temperature. must show an inflexion point:
(3-8)
These conditions are known as the Van der Waals conditions for the critical
point. The first and second partial diHerentials of Equation 3-4 with ~pect
to v would yield the results shown in Equation 3-7 upon substitution of parameter \'aJues relevant to the critical point and use of Equation 3-8.
Van der Waals equation may be written in the reduced form by substituting the values for A. Band R from Equation 3-7 into Equation 3-3:
RT
A
P .. v - B - '}"Q.~(" + B)
where A and B are constants. Other details \\ill be discussed later.
The Redlich-Kwong (RK) equation, along with modifications by
Zudke\'itch and Joffe (1970) and Joffe et al. (1970) (ZJRK). and by Soavc
(1972) (SRK), is widely used.
(3-9)
•
PeJlg-Robin!lOn Equation
Another \..idely used equation is the Peng and Robinson (1976) (PR) equation:
RT
A
p- - - \" - B v(v + B) + B(,·
thill, [po + 3/,,][3v, - lJ - ST,
(3-11)
B)
(3-12)
where A and B are functions of temperature. Note that the RK and PH equations cannot be written explicitly in the reduced form.
Benedict- "ebb-Rubin Equation
A General Form for Cubic Equations of State
This equation was developed by Benedict et al. (1940) for describing the
behavior of pure, light hydrocarbons. It has found a lot of application in
computing thermodynamic properties and phase equilibria for gases due to
two reasons: it gi\'es sufficient accuracy for natural gases, since natural gases
are a mixture of light hydrocarbons for which this equation was originally
developed; and it can be written explicitly in the reduced form, like Van der
Martin (1979) showed that all cubic equations of state can be represented
in the following general form:
RT
arT)
ofT)
p - -;- - (v + ~)(v + -y) + ... (v + ~)(v + -y)
(3-13)
.
Go.! Production Engineering
Propertiet of Natural GaUl
where cr and {) are functions of temperature, and R and l' are constants.
Coats (1985) presents the following equivalent form of Martin's equation,
with {) .. 0:
Zl + [(rn, + ffi2 - 1)8 - IJ Z2 + [A +
- (m, + m,)(B + I)B) Z
- (AB + ffilffiZBZ(B + I)) .. 0
where
ffi,ffi ZB2
(3- 14)
A ..
r:r. r:r _ x,xkAi~
(3- 15a)
B ,.
q -l
xiB)
(3-15b)
(I -
ojk)(AJAS)~
(3-15c)
A Jk
..
I
I
A) - 0., PrJi1~
(3-1Sd)
B, .. Obi Prj' T fJ
(3- 15e)
The Ojk are the binary interaction coefficients, symmetric in j and k with
Ojj - O.
Theoretically, O. and 0b are universal constants, Q<~ and [}g, determined by
making the EOS satisfy Van def Waals' criteria at the critical point (Equation 3-8). The values of m and flg for some commonly used EOS's are as
follows:
RK and SRK,
PR,
n: - 0.4274802. !li: - 0.08664035
n: - 0.457235529, !li: - 0.077796074
In practice, however, O. and Ob are treated as component. and temperaturedependent quantities, O.i(T) and Obo(T):
RK: 0.1 .. miT ,.p"\ and Ob! ..
og
SRK: Oaj" 0<,.11 + (0.48 + 1.574w, - 0.176w~)(1 - TJ'-!i)]2, and Ob'" O!:
PH: 0 .... ~1 + (0.37464 + 1.54226w; - O.26992w1)(1 - TJ'!i)]2, and
0" - !li:
The acentric factor (w), first proposed by Pitzer (1955), is a measure of a
flLLid's deviation from the law of corresponding states (see the section on
compressibility factors). It is defined as:
(3- 16)
45
where p.,. is the vapor pressure of the f1LLid at a temperature of o. 7Te • and Pc
is its critical pressure. As expected, w is equal to zero for noble gase;: like
argon, and is close to zero for gases like methane.
In the$e equations, putting m, .. 0 and ffi2 .. 1, yields the RK or SRK
equations. For the PR equation, m, = 1 + ~!i, and m2 .. 1 - 2<15.
Equilibrium is achieved when the fugacities for any component i are
equal in both the liquid and vapor phases. Fugacities can be calculated using the following relationship for the fugacity coefficient, derived using
Equation 2-13 (Coats. 1985):
In
~,
- In (fiP") - B,(Z - 1)IB - In(Z - B) + [AI(m, - m,)BJ[(2IA)
,
. ,.E, A"x, -
Bi B]ln [(Z + mzB)/(Z + m,S))
(3-17)
A Typical Solution Method for Cubic Equations of State
The input data include the overall composition of the mixture, {Zj}. and
the critical pressure (Pci), temperature (Tti), acentric factor (w,), and critical
compressibility factor (1.,,;) for each component i.
The objective is to determine for F moles of the feed of composition {z.:}:
the moles of liquid (L) and the moles of vapor (V) generated, and the composition of these liquid ({xil) and vapor ({y,}) phases that exist in equilibrium at any given pressure (p) and temperature (T). Referring to Equations
2-15 through 2-17, it is clear that if the equilibrium vaporization ratio, K..
for each component i is known. we can achieve the objectives. Thus, the
problem can alternatively be conceptualized as being that of obtaining very
precise values for K, using an equation of state.
The calculation procedure is iterative. A value is assumed for the distribution coefficient (K.) and the equation of state is then solved with this initial
guess, Kr. The EOS solution yields a new value, Kr + " which is then used as
the new guesstimate. This procedure is repeated till convergence is reached,
within a specified tolerance. between the estimate, Kr, and the solution,
Kr· I. A good initial guess for the distribution coefficient is very advantageous in obtaining faster convergence. A reasonable guess can be obtained
from the following equation. which has been used extensively (Wilson,
1969; Peng and Robinson , 1976):
K; - (lip.,) exp [5.3727(1 + wJ(1 - liT.,))
(3-18)
This equation was obtained by assuming that the fluid obeys Raoults' law
and that the logarithm of the reduced vapor pressure of each component i is
•
••
47
Properties oj Natural Gases
Ga.s Production £Ilgille€ring
Table 3·'
Physical Constants lor Typical Natural Gas Constituents·
a linear function of the reciprocal reduced temperature (Peng and Robinson.
1976).
Using the K-values from Equation 3-18. flash calculations are carried out
for the mixture (see Chapter 2) to calculate L. V, {Xi}. and hi}' Equations
3--15{a-e) are';olved next. Equation 3-14, a cubic equation in Z. can now be
sol\'ed to determine its roots. Since it is a cubic equation, it can have either
all real roots. or one real root and two imaginary ones. The gas Z-factor is
taken as the largest real roo!, when the equa.tion is wived with coefficients
corresponding to gas. Equation 3-14 is solved again with coefficients A. B
corresponding to the liquid phase. The smallest real root is taken as the liq-
Compound
uid Z-factor. These Z values are required in Equation 3-17.
II-C~'1
Equation 3-17 is sol ....ed to determine fugacities in the \'apor and liquid
phases. If the.<\e are equal in both phases for all the components (on an individual basis), com'ergence has been reached. Otherwise, the new Ki values
are determined usin~ the ratio of the fugacity coefficients (see Equation
2-14),
Sewral modifications have been proposed by different investigators to improve the rate of convergence, or to impro\'e the accuracy of prediction in
general or for various special cases. The ~VNR (minimum variable Newton-Raphson) method presented by Fussell and Yanosik (1978) and Fussell
(1979) prO\ides imprO\'ed comergence and is more reliable than the method
of successive substitution previously discussed. Since this is an area of acti\'e
research, the reader can refer to published work in this area for specific
methodologies and developments.
i·~1!
Critical Pressure and Temperature Determination
For pure components, physical property data are readily available. Table
3-1 shows critical temperatures (T...;), pressures (Pc.:). and other useful properties of typical components in hydrocarbon fluids. For mixtures, Kay's mixing rule can be used to find the effective critical properties:
(3- 19)
where Pp..., T po: are the pseudocritical pressure and temperature, respectively,
for the mixture, and r! is the mole fraction of component i in the mixture.
These properties are termed "pseudo" because they are used as a correlation
basis rather than as a very precise representation of mixture critical properties.
Equation 2-23 in Chapter 2 can be used to predict the critical properties
of a hydrocarbon fluid from its normal boiling point and gravity. IT the composition oflhe gas, {y;}. is not known , Figure 3-1 may be used to determine
eH,
C:II;.
C.J l~
n_C,H,g
i-C,H ,(
n·CJ-I"
II-C,H,o
n-CJi"
n-C,lh,.
n-CwHu
N,
CO,
II;>
0,
II,
H~O
Molecular
Weight
Critical
Pressure
(psia)
16.()43
30,070
44_097
38124
58,124
667.8
707.8
616.3
72.151
72.151
86.178
100.205
114.232
12.8_259
142.2.86
28_013
44,010
34.076
488.6
490.4
436.9
396.S
300.6
332.0
3040
493.0
1070.9
1306.0
737.1
188.2
3203.6
31.999
2_016
18.015
550.7
.529, I
Critical
Temp.
(-R)
Cnt. Comp.
Factor
(2.)
Acentric
Factor
(w)
343_1
549,S
665.7
765.4
734 7
0.289
0_28."
0.281
0.274
0.283
0.0115
0.0908
0.1454
0.1928
0_1756
S45.4
828.8
913,..\
972.5
1023,9
lOiO,-l
111l,8
0,262
0,2510
0.2.273
0_2957
0._
227.3
547,6
672.4
278.6
59.9
1165_1
0,273
0,264
0.263
0.259
0,251
0.247
0.291
0,274
0.266
0.292
0.3(\4
0.230
0.3978
0.4437
0.4902
0.0355
0.2250
0.0049
0.0196
- 0.2234'
0.3210
Eykman Mol
Refraction" •
(EMR)
13,984
23.913
34.316
44.2-13
44.741
55.267
55.302
65_5iS
7S.Si5
86.193
96.529
106.859
9.407
15,7SO
19.828
8.49.5
,"'"
,
• From Edmister and Lee (19&1J_
•• I'rom McLeod and Campbell (1969)
, "" _ 0.0 w.ed in moot condatkm>
the critical pressure and temperature from the gas gra\·ity. Corrections may
be made for the presence of non-hydrocarbon oomponents: Thomas et .al.
(1970) took data from Figure 3-1 and other sources to obtam the followmg
relationship:
Ppc _ 709.604 - 58.718 "f,
(3-20a)
T pc" 170.491 + 307.344 "fit
(3-20b)
where "fl is the gas gravity with respect to air. Thomas et al. recommend the
use of this equation in allowable limits of up to 3% H~, 5% Ni , or a total
impurity (no n-hydrocarbon) content of 7%, beyond which errors in critical
pressure exceed 6%. It should be noted that the gas gravity method of obtaining pseudocritical pressures and temperatures is not very acc:urate. 1£ ~he
analysis of the gas is available, it must be used in accordance With EquatIOn
3-19.
..
.9
PropN'tie3 of Natural Gases
Ga., Producl/on Engineering
Find the gas gravity. Also, find the critical pressure and critical temperature for this gas using (I) Kay's mixing rule, (2) Brown et al.'s method, and
(3) Thomas et al.'s equations.
Solution
~omp.
c,
c,
C,
n-C 4
i-C 4
n-e,
i-e.,
Co
C,.
N,
M,
...iL
16.043
0.9300
0.0329
0.0136
0.0037
0.0023
0.0010
0.0012
0.0008
0.0005
0.0140
3O.0iO
44.097
58.124
58.124
72.151
72.151
86.178
128.259
28.013
k
667.8
707.8
616.3
550.7
529.1
488.6
490.4
436.9
332.0
493.0
To
343.1
549.8
665.7
765.4
734.i
845.4
828.8
913.4
1070.4
227.3
M .. E y,M 1 ,. 17.54
"-5
-••
The gas gravity 'Y& - 17.54/28.97,.. 0.6055
-,
••
~
1. Ppc" I: YIPd - 664.47 psia
•
Tpt - I: YiTe; _ 356.93 OR
~
2. From Figure 3-1,
u
0
g
••
..
·
"
PI'" - 670 psia
Tpt - 360 OR
Applying the correction factor for 1.4 % N2,
!'po • 670 - 5 • 665
v"'~ GUVlfY
"
"'I~' \
"
Figure 3-1. PseudocriticaJ properties of miscellaneous natural gases and condensate flUids. (After Brown at aL, 1948; courtesy of GPSA.)
!"ia
T,,' 360 - 5.355 OR
3. Using Equation 3-20a:
!'po - 709.604 - (58.718)(0.6055) • 674.05 ps;a
Example 3-1. The analysis of a sweet gas, in mole%, is known to be as follows: N2 .. lAO, CRt .. 93.0, CtHe" 3.29, <4Ha .. 1.36. Il-C.H IO .. 0.37, iC.H 10 " 0.23, n-~HI2" 0.10, i-~I!" 0.12. Cefi14 .. 0.08, and ~HI6+
.. 0.05. Assume the ~ + fraction to exhibit the same properties as n-Cg.
Using Equation 3-20b:
T,,' 170.491 + (307.344)(0.6055) • 356.59 OR
,
50
Propertie! of Natural
GO,f Production Engineering
51
Gas~
The Gas Compressibility Factor
Several different correlations are available for this important parameter.
The basic correlations use the corresponding states concept. According to
Van dec Waals' law of corresponding states, the physical characteristics of a
substance are a function of its relative proximity to the critical point. This
means that the deviation from ideal beha\ior of gases is the same if they are
located at the same state relative to their critical state. Thus the relevant
temperature and pressure values that express the departure of a real gas
from ideal behal-ioc are the reduced pressure, p" and the reduced temperature, T.;
Z - £(p"T,)
(3-21)
where p, ... piPe
T, -
TIT~
~
IO:!
For gas mixtures such as natural gases, the reduced parameters are denoted
as pseudoreduced temperature Tp. ( = TIT pc), and pseudoreduced pressure,
Ppr ( -
f
•
ni:':
-
p/ppc).
The correslX'nding states concept is more applicable to substances with
similar molecular structure, such as neighboring hydrocarbon comlX'nents
of a similar paraffinic type. than to widely dissimilar substances. For more
complex mixtures. it is more appropriate to consider the compressibility factor as a function of an additional parameter, t:
Z - £(p"T" ()
~ •
u
"
(3-22)
This additional parameter, t, is any term that can characterize the mixture
behavior, particularly the discrepancy resulting from the assumption in
Equation 3-21. Among several alternatives, the two most widely used are
the critical compressibility factor, z." and the acentric factor, w. Z-factor
correlations using z., as a basis have been used for a long time; different
charts are made for different values of z., for manual calculations. The acentric factor. w, has become very popular because it gives good accuracy. Most
equations of state and other computer-generated solutions use the acentric
factor. In addition, the Eykman molecular refraction (EMR) approach by
McLeod and Campbell (1969) is of interest and is described here.
Standing-Katz Compressibility Chart
Figure 3-2 shows the Standing and Katz (1942) correlation for Z as a function of Ppr and T pr for sweet (non-H~ or COt containing) natural gases. The
"
•
P~fUOO ~EOu(EO
...
Figure 3-2. Compressibility lactor lor natural gases as a function of reduced
pressure and temperature. (After Standing and Katz, 1942; courtesy of SPE 01
AIME.)
applicability of Equation 3-21 is assumed, and Kay's mixing rules are used
for gas mixture properties. This chart is generally reliable for sweet natural
gases with minor amounts of non-hydrocarbons such as N2 •
Wichert and Aziz (1972) proposed a correction factor, E, to extend the applicability of the Standing-Katz Z-factor chart to sour gases:
52
53
Properties oj Natural Case:!
COl Production Engineering
These modified values for the critical pressure (~) and temperature (Tp.,.)
are used to calculate the values of reduced pressure and temperature that
will give a valid Z-factor for a sour gas from the Standing-Katz correlation.
Example 3·2. For the gas composition given in Example 3-1, find the compressibility factor at 2,000 psia and 200°F using the Standing-Katz Z-factor
chart.
Soilltion
From Example 3-1,
-
o
u
Ppc: = 664.47 psia
~u
Tpc - 356.93 OR
So,
ppr - 2,OOO/664.4i - 3.010
T,. - (200 + 459.67)1356.93 - 1.848
Using Figure 3-2, the compressibility factor Z
g
0.905.
Example 3·3. Find the compressibility factor at 2.500 psia and 650 0 R for a
sour gas with the following composition in mole%: CH 4 = 89.10,
C 2H6 = 2.65, C3HS - 1.90. n·C,H IO - 0.30, j·C4H ID = 0.20, N2 = 0.65.
CO 2 ,,, 1.00, H 2S - 4.20.
Solution
PER CENT H,S
Camp.
Figure 3·3. Pseudocriticai correction factor, t, for sour gases. (Atter Wichert and
AzIZ, 1972; courtesy of Hydrocarbon Processing.)
C,
C,
C,
(3·23)
where A is the sum of the mole fractions of H:zS and COt, and B is the mole
fraction of H 2S, in the gas. Figure 3-3 is a graphical representation by Wichert and Aziz (1972) of Equation 3-23. This method uses the correction factor, f, to correct the pseudocritical temperature (Tp") and pressure (Ppe) determined by Kay's rule, as follows:
T;''' TI'l' -
t
n-C~
•
i-C 4
N,
CO,
H,S
..1L
..&.
TN
0.8910
0.0265
0.0190
0.0030
0.0000
0.0065
0.0100
0.0400
667.8
707.8
616.3
550.7
529.1
493.0
1070.9
1306.0
343.1
549.8
665.7
765.4
734.7
227.3
547.6
672.4
A - 0.0400 + 0.0100 - 0.0500, and B - 0.0400
(3-24)
, - 120[(0.052)'9 - (0.052)' '] + 15[(0.042)" - (0.042)"] - 10.402
•
Propertia oj Natu ral
Gas Production Engineering
Ppr - !: hPc:i - 696.96 psia
Table 3-2
Correl.tlon Equations tor the Standing-Katz Z-tactor Chart·
Reduced
Pressure
p, Ringe
Between
Appl}ing the Wichert and Aziz correction,
TPc - 371.77 - lOAD - 361.37 oR
Reduced
Tempertlture.
T, Ringe
Between
'OS and 12
1.2 + and 14
1.4+ and 2.0
2.0 + and 3.0
and 1.2
1.2 + and 2.8
12 + and 1.4
14+ and 2.0
2.0+ and 3.0
2.8 + and 5.4 lOS and 1.2
1.2+ and 1.4
1.4 + and 2.0
2.0 + and 3.0
5.4 + and 15.0 1.05 and 3.0
0.2 and 1.2
J>;o - (696.96)(361.37)/[371.77 + (0.042)(10.402)(1 - 0.042)]
- 676.69 psia
'05
1',. - 2,500'6i6.69 • 3.694
Tp,
..
6501361.37 - 1.799
Using Figure 3-2. the compressibility factor, Z - 0.90.
Curve-Fits fo r the Standing- Katz Correlation
Gopal (1977) found straight line fits for the Standing-Katz chart of the
form:
Z - p,(AT, + B) + CT, + D
Example 3-4. For the gas composition given in Example 3-1, find the comprasibility factor at 2,000 psia and 2OQ°F using Gopal's method.
From Example 3-2,
p,. - 3.010
Equations
1.6643T, 2.2114) - 0.3647T, + 1.4385
0.5222T, - 0.8511) - 0.0364T, + 1.0490
0.9969
p,1 O.I39JT, - 0.2988) +
~I O.0295T, - 0.0825) + O.OOO9T,'· 0.9967
p,( -1.35iOT. + 1.4942) + 4.63IST, - 4.7009
~I O.lilIT, - 0.3232) + O.5869T, + 0.1229
~( O.0984T, - 0.2(53) + 0.062IT, + 0.B580
~I 0.0211T, - 0.(527) + 0.0127T, + 0.9549
p,(-0.3278T, + 0.4752) + 1.8223T, - 1.9036
p,(-0.252JT, + 0.3871) + J.6087T, - 1.6635
p,( - O.0284T, + 0.0625) + 0.4714T, - OJXHl'
p,1 O.OOHT, + 0.0039) + 0.0607T, + 0.7927
p,( 0.711 + 3.66T,)-!*"'
- 1.637-'(0.319 T, + 0.522) + 2.071
~(
p,(
o.ooorr,' . .
Equation
Number
,
I
3'
",.
6
7
8
'"
Ill'
11
12
13
• Mt.". CopaJ (l9i7). Coomsy of Oil and eo.. }tnmur/
• 1"hc.e !emu rna' be 'gnom!
b For a "ef) slight 100 In IOCC\1rat'Y. E'I'. 3 and 4 and 9 and 10 <'tin. ~;'f:'l~. be replacoed b). th"
(3-25)
where A, B, C, and D are correlation constants (see Table 3-2). Th irteen
equations of this type were found to suitably represent the Standing- Katz
chart, with average errors on the order of 0.6%, and maximum errors up to
2.5%. (Gopal (1977) does not report any statistical parameters for the error:
it is the author's deduction from the reported results only.) Wichert and
Aziz's (1972) correction factor for sour gases is applicable. Since it attempts
to curve-fit the Standing-Katz chart and uses the same mixing rules, its applicability is also subject to the same limitations as the Standing- Katz chart.
The major advantage of this method lies in the fact that it is not trial and
error type.
So/lltion
55
Gtl.fU
~
folla..ing ''''0 equahoru'
Z _ p,10.0657f, - O.\iSII .. 00009 T: .. 09968
Z _ p,C-O.23&( T.... 0.3695)'" lASH T, - l4SBO
Prrif:'f1Ibiy we this equation for p, up to 26 onl). fur p, _ 2.6 + Eq. 9 ",ill g;"f:' slightl~ brttr, rt:Sults
At.... pn:f.".abl~. we Eq. I for 1.08 :i T, ::; 1.19 and p., ~ 14
Tpr
=
1.848
From Table 3-2, the applicable equation is:
Z
PP,( - O.0284Tpr + 0.0625) + OA714T P' - 0.0011
• (3.010)[(-0.0284)(1.848) + 0.0625] + (0.4714)(1.848) - 0.0011
- 0.900
=
Compressibility Factors from Equations of State
Several authors have reported results using d iffe rent equations of state.
An interesting comparison of the various techniques used is provided by Takacs (1976). Yarborough and Hall (1974) used the Starling-Carnahan equation of state to arrive at the following equation:
z-
0.06 1 25(p,.Jp,T~) ""p{ - 1.2(1 - 1 T~)']
(3-26)
•
.6
Gu Production Engineering
where the reduced density, p" is calculated by trial and error from the fol lowing equation:
!
p, + P.
(1
+
3
~
P. - p, - (14 76 ·' T
p,)3
+ (90. 7/T po -
.
242 . 2.' ~
'po
- 9 76 'T! + 4 58/'T"3 )p'
•
I
pr
•
' P"
+ 42.4'Gr) p ~tI8 . 2II2 Tp<'
(3-28)
where the reduced density was defined as:
to be 0.270
have been reported
by him),
but
It
The Eykman Molecular Refraction (EMR ) Method
Dranchuk et al. (1974) presented an eight-factor trial and error type of
equation for Z-factor using the Benedict-Webb-Rubin equation of state.
Zc was assumed
p. > 1.0, very large errors have been reported (Dra~chuk ~d Abou-Kassem , 1975). Thus, these correlations should be used WIth caution. The ~ccu­
rac), of the Copal (1977) method in t his region is not apparent f~om hlS ~
::7n~:\~!~~e a~;:b~~~~:.n
(3-27)
Pr ., z.:p,/(ZT.), and
57
Properties oj Natural G6&es
This method, deyeloped by McLeod and Campbell (1969), uses a rorrelat ' n between the EMR of a gas or liquid and its properties such as molecular
W ·gbt density· and critical properties. A different mixture com b·ma t·Ion
wei ,
,
r
'btl
rule is used, and the method also requi~ the use of a dir erent compres.o;l ity chart.
T he Eykman molecular refraction . E~t R. is defined as foHows:
EMR - [(n' - 1)I(n + O.4)](Mlp )
w here
(3-29)
and the correlation constants AI through Aa are: 0.31506237, - 1.04670900,
- 0 .57832729, 0.53530771 , -0.61232032, -0.10488813, 0.681570001 , and
0 .68446549, re.pectively.
Dranchuk and Abou-Kassem (1975) developed the following equation
from the Starling equation of state:
(3-31 )
n "" refractive index of the gas or liquid using Sodium-D Yf'llow
light
M - molecular weight
p - density in gm fcc
The Eykman molecular refraction index, EMRI , defined. as
EMRI - EMRIM - [in' - 1)I(n + O.4 )llp
•
(3-32)
is also used for correlation purposes. McLeod and Campbell (1969) found
the following empirical relationship between EMR and M for normal paraffin hydrocarbons:
+ (A, + A,IT, + A,1T;)p1 - A,(A,/T , + A,1T1)p1
EMR '"" 2.4079 + 0 .7293 M + 0.00003268 M2
(3-30)
w here the reduced density is given by Equation 3-30 as before.
By fitting Equation 3-29 from the Starling equation of state to the Standing-Katz correlation using more than 1,500 data points, Dranchuk and
Abou-Kassem (1975) found the values of the eleven coefficients Al through
All to be, 0.3265 , - l.0700, - 0.5339, 0.01569, - 0.05165 , 0.5475,
- 0.7361 , 0.1844, 0 .1056, 0.6134, and 0.7210, respectively.
The Wichert and Aziz correction for sour gases (Equations 3-23 and 3-24)
is applicable to aU these methods using equations of state. It is clear that all
the EOS methods involve a trial and error type of solution scheme. The accuracy of these methods is within 0.5 % , but for the region where T. _ 1.0,
l
(3-33)
Alternatively, M can be expressed in terms of EMR for normal paraffin hyd rocarbons as follows:
M ,. - 3.2971 + 1.3714 EMR - 0 .00008156 EMR2
(3-34)
U the molecular weight, M, is not known , the EMR may be determined
from the density p using the EMR versus pi plot shown in Figure 3-4.
McLeod and Ca:npbell found that EMR correlates very well with the
critical properties of hydrocarbons and also the non-hydrocarbon~ generally
associated with natural gas. Figures 3-5 and 3-6 show the correlations determined by them. The curve fit equations indicated in Figures 3-5 and 3-6
may be used, instead of the figures , ror p rogramming purposes. In the EMR
58
Cas Production Engineering
.t'1~
,
i
~
.~
u
IJ UPUllm.UI. IlU1'UU.O
,/ . ..c,....c u
(PCU:
•
;: g ,;::,
~
,
2 ' 51 S! i st:::2
~
0
~ ~ ~
!
.rl~ a
I
(II - ""1· , , _ 0.0-
.. "
O.ll
....."
" 1.00
==" 0.'"
~
o.~.
'.M
.. "
0.'0
Figure 3·4. Eykman molecular refraction (EMR) versus p2, (After McLeod and
Campbell, 1969; courtesy of Campbell Petroleum Series.)
"
",J>''',
F · ... ~'..
f
I
'.
./
V
r- " - / m,
./
..
','
I
c
~.
I
I - IT,", • O.'UI. 0.00'111
"
I
I
I
IIJonJon
EVKMAN MOL!CULAR REFRACTION
,
Pil '
•••
o.ou<
I
I
(>0 .....
~""
•
,.
~
'.>0
O.~I
..
~# ,.
/'
•••
1
0 •• ,
-:;::. /~
1.10
Al'I O$jIlC ·USSj
V,;_
/'"" l".-
'.M
' .H
%: ~ ~~ ~ ~
W
J
•• M
~
>0
'JI ,II
•. w
/
V
I
III - .,. ":1' CD"
'j I V 1/;;1 1/
Ij 'l, 1/ VI; VI V
~ .~ /
~ 1/
'i ~ /j % V/
~)
.0 ;::::: :;:::: /;:;
59
Propertie& of Natural Gases
IJII
-
I
..I ..I
Figure 3-6. EMR versus TJ pc correlation. (After Mcleod and Campbell, 1969;
courtesy of Campbell Petroleum Series.)
>0
M
....V
W
V
~
c_
eo"
,
~"
~
..
>.
rI-~
m,
" V
IY
19",,"_
~"
•
•I• O.I't'
~.
..
,.1. u •
i-
,,,, -
./
M
~
V
~
M
~r
1.0
Ll_
1f",(Pc)O.~. '.IK. 0 . _ 1111 · 0.00107' (rMA)1
_
-
'.
EYI(.MAH NJL[CULAlI REfRACTION (EAA)
Figure 3-5. EMR versus TJp~ 5 correlation. (After McLeod and Campbell, 1969;
courtesy of Campbell Petroleum Series.)
versus T./p~·.\ plot (Figure 3-5), both the hydrocarbons as well as non-hydrocarbons lie on the same correlation. In the EMR versus T.,Ipc plot (Figure
3-6), two different correlations were found for two categories of components: N2, CD it H2S, and H2 lie on curve I: and all normal hydrocarbon
components lie on the upper curve 2. The two curves intersect at a value
corresponding to C I .
So, for gases containing any non-hydrocarbon components, it is necessary
to divide the mixture into two groups: C h N1, CO 2, H2S, and H2; and hydrocarbon components ahove methane. that is n-C z+. An n-component gas
mixture is thus treated as a pseudobinary mixture in this method. The calculation procedure is as follows (Campbell . 1984):
1. For each of the two groups of components, find the EMR j as follows:
(3·35)
where Xi! is the normalized mole fracti on of component i in the group j
it belongs to, and EMRI is its EMR value determined from Table 3-1.
For fractions such as C, ~, the EMR value can be directly determined
using Equation 3-33 if the molecular weight is known, or using Figure
3-4 if the density is known . The normalized mole fractions , Xi!' are calculated as:
,
60
Propertit!$ oj Natural Ca.Jt!$
GaJ Production Engineering
EZDmplt> 3·5. For the gas composition given in Example 3-3, find the compressibility factor at 2,500 psla and 650 0 R using the EMR method.
XjJ - X!IX!
where X, is the sum of the mole fractions of all the components in
group j.
I
61
2. Using Figure 3-6 (or the equations indicated in Figure 3-6), find the
value (or (ATc!P,,)1 and (AT c!Pe)2 for the two groups. The total mixture
(AT..tPe)mill is calculated as:
(ATJP,)m" - X,(ATJp,,, + X,(ATJ p,,,
Solution
Comp.
"
0.0005
0.0100
0.0420
0.8910
0.9495
N,
CO,
H,S
3. Determine BTdp~5 from Figure 3-5 (or the equation indicated on Figure 3-5) for the total mixture using the EMRmiJ for the total mixture
calculated as follows:
4. Using the mixture ATe/P, and BTel p~·5 values. solve for the critical
pressure, Pc, and critical temperature, Te. In English units, A and B
are 1.0, whereas in the metric or 51 system of units, A .. 0.0124 and
B - 0.1495.
5. Calculate the reduced pressure and temperature. Finally, the compressibility factor. Z, is found from Figure 3-7.
C,
X, -
0.0265
0.0190
0.0030
0.0020
0.0505
C,
C,
n-C 4
i-C 4
X, -
~
0.00685
0.01053
0.04423
0.93839
0.52475
0.37624
0.05941
0.03960
EMR
9.407
15.750
19.828
13.984
23.913
34.316
44 .243
44.741
EMR I - 1: xJjEMR, - 14.2297
•
From Figure 3-6.
.
.
(AT Jp,,, - 0.50
(ATJp,,, - 0.94
So,
o.
(ATJp,) •• - (0.9495)(0.50) + (0.0505)(0.94) - 0.. 522
o.
EMRm" - (0.9495)(14.2297) + (0.0505)(29.8596) - 15.019
o.
From Figure 3-5,
o.
(BTJp1') - 14.90
1.0
1.0
3.0
4.0
S.O
REDUCED PRESSURE, POI
Figure 3-7, Compressibility lactor chart lor the EMA-method. (After Mcleod
and Campbell, 1969; courtesy 01 Campbell Petroleum Series.)
'.0
In English units being used. here,
A-landB - 1
62
Properties oj Natural Gases
Cal Production Engilluring
63
Thus.
(T'-""Pc)mix - 0.522
So,
p~~ - 14.90/0.522,. 28.54 implying that
p< - 814.76 psia
T - (0.522)(8 14.76) - 425.30 o R
Using the ,aJu~ of critical pressure and temperature as pre\iously determined.
Ppt =
2.500/814.i6
T p.
650':425.30
-
=
=
3.068
1.528
Using Figure 3-7. the compressibility factor Z _ 0.835.
Figure 3-8. Generalized compressibility factors ZO as a function 01 reduced pressures and temperatures. (After Salter and Campbell, 1963; courtesy of SPE of
AIME.)
The Stewart. Burkhardt, and Yoo (SBV) Method
Stewart, Burkhardt, and Voo (1959) presented a mixing rule (or pseudo- I
critical pressure and temperature:
T"" - Kil], and Pp<: - Tpo/J
where
J-
-"--',
•
..
(3-36)
(1/3)Er., y,(T.,Ip~)1 + (213){Er.1 YI(T.,JPc)p~)2
K - Er.1 Yl(T..J~5)1
'
The pseudocritical pressure and temperature from this equation are then
used in Pitzer's (1955) charts, extended by Satter and Campbell (1963), to
determine 7Y and Zl (Figures 3-8 and 3-9). Z is calculated as follows:
.
•
(3-37)
,
--
•.
-
......
--- -----
'-
.,
----
_._........
Figure 3 9 Generalized compressibility factors Z' as a function of reduced pressures and temperatures. (Alter Satter and Campbell, 1963; courtesy 01 SPE of
AIME.)
This is one of the best available methros for hydrocarbon mixtures and has
proven to be \'ery accurate.
I
'"
Gas Production Engineering
Properties oj Natural Gasel
PER CENT
where 1:f.1 refers to a summation over all components i except CO 2 . The
value of T determined from Figures 3-1 Oa and b is then used to correct the
ppc and Til<' calculated from Equation 3-36 as follows:
'" !==t==i==t==!=t==!=t==+=Ci"':'::jON{IOXlDE
•
'0
'"'0
~
•~ 20
•
!:
S
,
Figure 3·10•. Multlpole
factor. r. versus acentric
factor, w. for CO 2 concentrations up to 50%. (After
Buxton and Campbell,
1967; courtesy of SPE of
"
,
101-+-:
'0
>
o
T;"-Tp<- riA
2'
•"
0.'
ACENTRIC FACTOR,"
•
•o
'0
AIME.)
t- -
Figure 3-10b. Multipole
factor, T, versus acentric
lactor. w. for CO 2 concentrations greater than
50%. (Alter Buxton and
Campbell, 1967; courtesy 01 SPE of AIME,)
•
•
!:
5
-
....-:: V
. / /' V
,/
V ./
t; 20
:
•
10
.5
.--
~
.-- .. '0
-
'0
>
0'
ACENTRIC FACTOR, ..
0,
(3-39)
where T;" and p;", are the corrected values for pseudocritical temperature
and pressure. rcspecth'ely. and A ,. l.0 for English units, A = 1.8 if metric
units are used. The;e corrected \'alues are used. as in the SBV method, to
determine the pseudoreduced pressure and temperature. and 'l!l and Zl from
Figures 3-8 and 3-9. Finally. Z is determined using Equation 3-37.
Example 3-6. The analysis of a sour gas, in mole%. is known to be as follows: CH 4 = 56.1. CzHe - 20.6, CJHs - 5.3, CO 2 = 15.0, and H 2S - 3.0.
Find the compres.~ibility factor for this gas at 3,000 psia and 3OO"F. Use the
Buxton-Campbell method because the CO 2 content is high.
Solution
..l!...
To
B:i.
T~p,
(T~E')"
Tjp~·5
-""-
C,
C,
C,
CO,
0.561
0.206
0.053
343.1
549.8
O.ISO
H,5
0.030
547.6
672.4
667.8
;07.8
616.3
10iO.9
1306.0
0.51361
0.77673
1.08012
0.51108
0.S14i5
0.71667
0.88132
1.03929
0.71490
O.ili46
13.2727
20.6645
26.8145
16.7284
18.0025
0.0115
0.0908
0.1454
0.2250
0.0949
Com~.
665.;
The Buxton·Campbell Approach for COz-Rich Gases
E ),,(To!p,,) - 0.59749
Sour gas correction methods described earlier have been developed for
sour gases containing H 2S and CO 2 , For gases that have a high CO 2 content
but a low H~ content, these methods have not been found to be satisfactory.
To extend the applicability of the SBV method to sour gases rich in CO 2,
Buxton and CampbeU (1967) pro'v;de a correction factor known as the
multipole oorrection factor, 1', as shown in Figures 3-10a and b. It corrects
for the deviation in the critical pressure and temperature due to the pre;ence
of CO 2, The effective acentric factor, "'~, for use in Figures 3-10a and b is as
follows:
E )'i(Tclfpci)O ..5 * 0.76744
1: y,(To/pd") - 16.1914
1: )'1(0)1 -
0.06946, and E
YI"'I
for all components except CO 2
So,
K - 16.1914
w, - (1i(1 - YcoJI 1:1., )''''',
(3-38)
J-
(''')(0.59749) + (~,)((0.76744)'1 - 0.59181
,,,
0.03571
,
Properties oj Notural Cases
Cm Protirlction Enginl"ering
66
T,
K21J - (l6.1914)2fO.591BI _ 442.98°R
PI'< *" T.
l'sin~
J-
Supercompressibility Factor
In several applications such as gas flm\ measurement, the factor l/ZO-~
appears very frequently. It is called the supcrcompressibility factor, F'p~.
442.9810.59181 - i48.52 psia
Equation 3-38,
FJ" - 1 'Zll_~. or F"p.. - I Z
w, - [11(1 - 0.150)110.03571) - 0,0420
In reservoir engineering applications, one must often relate reservoir vol.
urnes to surface volume:!.. The formation volume factor. BOl_ defined as the
ratio of the volume Ottupied by a given mass of gas at resenoir pressuretemperature conditions to the volume occupied at standard (surface) conditions, is generally used. If V denotes the volume at reservoir pressure p and
temperature T. and V"" denotes the volume at standard pressure p" and temperature T.." then:
4.3
So,
442.91\ - 4.3 I
T';':
=
Pl~'
"" 748.52(438.68 .......12.98) ,.. 74l.25
438.68' R
p~ia
B~ ..
Thus,
Ppr"
(3-4 1)
Cas Formation Volume Factor
From Figure 3-lOb.
T -
V'V.., - (nZRT"p)/(nZ",BT ..,/p...)
(3-42)
- (p.ZT)I(pz.,T.)
30001741.25 - ·1.047. and T p,
From Figure 3·8, ZO
=
67
=
759.671438.68
0.880, and from Figure 3·9. Zl
=
=
1.732
In oil-field practice, generally the standard conditions are taken to be 14. i3
psia ( - p",) and 60°F ( .. T ..,). At these conditions,
can be assumed to be
unity. B~ therefore becomes:
z...
0.250
Therefore. Z .. 0.880 + (0.250)(0.06946) .. 0.897
Bg - 0.0283 ZT P ftl/scf
The expansion factor, E. is simply the reciprocal of the formation volume
factor, Bg . Thus. E is given by:
Some Z-Factor Related Properties
Cas properties that can be derived from the Z-factor are
(3-43)
ga_~
density, supercompressibility. gas formation volume factor, and expansion factor.
E - (pz., T .)1 (p,.J:T)
- 35,30 p ZT ",flft'
(3-44)
Gas Density
Example 3-7. For the sweet gas given in Example 3-1. find: density in
lbmlftl, and formation volume factor, at 2,000 psia and 200°F.
Using the gas law. the density of a gas, Pt;, can be calculated as:
Pt; .. Mv .. pMIZRT
(3-40)
Solution
where \1 is the molecular weight of the gas. If p is in psia. T is in OR, and R
is in (psia ftl)/(Ibmole OR), then PI is in lbm/ftl.
From Example 3-1. the moleculaI weight M - 17.54
•
68
Gas Produclkm Engl'leering
.9
Proper-tier oj Natural Case:!
At 2,000 psia and 2OO°F, from Example 3-2, the compressibility factor
Z - 0.905
The pseudoreduced compressibility, Cp.. is thus given by:
<;. - c,p,. -
From Equation 3-40,
P, _ (2.000)(17.54)/[(0.905)(10.732)(459.67 + 200)] - 5.475Ibmft'
From Equation 3-43.
2- _.!. [az]
p,.
(3-48)
z ap,. T'"
Differentiating Equation 3-29 with respect to pseudoreduced pressure, we
get:
~
_ap, - (0.27fT,,) [ I .Z - (p"iZ 1az]
oPpr
oPr.
B, - (00283)(0.905)(459.67 + 200)/2.000 - 0.008448It'/sc£
The derivative. iJZlopp., in Equation 3·48 can be expressed as follows:
Compressibility of Gases
az _ az ap,
Compressibility of any substance is a measure of the change in its volume
upon changes in pressure. It can also be considered as a measure of the
change in density with pressure. Gases exhibit high compressibility, which
makes the storage of gas under pressure a common occurrence.
The isothermal compressibility, c, of any substance is defined as:
c -
Using the ideal gas law, (OV loph '" - nRT/If. and the compressibility (cJ
for an ideal gas can be expressed as:
(plnRT)( - nRTip2) - 1 P
(3-46)
Thus. the compressibility of an ideal gas is simply equal to the inverse of the
pressure. With increasing pressure, the compressibility decreases. For a real
gas:
CR'
aPr
ZT p.op,
[
cg
,.
I
I [az]
PpcPPT - ZPpt- iJpl'" T pi"
az
apr'
•
I + O.27r,.aZ] az _ 0.27 az
ZZ"fp.oPT opl'" ZTp.oPr
Thus
I
OZ _ 0.27
(aZ!ap,)
)
'ap,. ZT," \ 1 + (p,IZ)(aZlap,)
0.27!
0",' P" - Z'T"
- (plnZRT)nRT[(lIp)(aZlop) - ZIP']
Or, in terms of reduced variables:
Z2'f p,op,
Rearranging this equation results in:
is given by:
- lip - (1IZ)(aZfap)
(p,,,IZ') az]
aPr'
~ 0.27 az _ !0.27 p"az)
1
c, -
oPp.
Substituting for the derivative. oZlop"" in Equation 3-48, the reduced compressibility can be written as follows:
V _ nZRTlp ,nd (aVfaplT - nRT[(lIp)(aZlap) - Zfp']
and the compressibility.
aPr
~ (az) (0.27fT,,) [liZ -
(3-45)
- (I V) (aVlaplT
c, _ -
oPp.
(3·47)
(aZfap,)
I + (p,fZ)(aZlap,)
)
(3-49)
Using the Z-factor equation derived from the BWR equation of state by
Dranchuk ct al. (Equation 3-28), MaHar et al. (1975) evaluated the derivative iJZlop, as follows:
iJZliJpT - (AI + A2/Tp' + ~/'f3p<) + 2(~ + AsIT pr)p, + 5~p:1TI""
+ (2A,p,rr,,)(1 + A,p1 - AM) .,p( - A,p~
(3-50)
70
Properties oj Natural Gases
Gas Production Engineering
10.0
Figure 3·12. cfT,
as a function of
Figure 3·11. CrT,
as a function of reduced temperature
and pressure in
the range 1.05 ~
T,~I.4,
and
reduced lemperature and pressure
in the range 1.4"
T,,3.0, and 0.2~
Pr~ 15.0.
(After
Mallar et at, 1975;
O.2~
p," 15.0. (After
Mattar al ai., 1975;
courtesy of the
courtesy of the
Journal of Canadian
Petroleum
Technology.)
Journal of Canadian
Petroleum
Technology.)
10
71
•
•
0 .01 Ll..ll.LU.u
0.2
10.0
'0
P.
P.
For hand calculations, Mattar et al. (1975) also presented this correlation in
a graphical form as shown in Figures 3-11 and :J..12.
From Example 3-2, at 2,000 psia and 20(P F.
Ppt - 3.010
T p,
Example 3·8. Find the compressibility for the sweet gas given in Example
3-1 at 2,000 psia and 200°F.
-
1.848
From Figure 3·12,
cp,T pr
-
0.620
Solution
Thus,
From Example 3-1,
pP., - 664.47 psia
c,. - 0.620/1.848 - 0.3355
~ _ Cp.lpp( _
0.33551664.47 '" 0.000505 psi-I
72
Proper-lies oj Natural Ga.fel
Gos Production Engineering
73
Viscosity of Gases
The viscosity of a fluid, a measure of its resistance to flow, is defined as
the ratio of the shear force per unit area to the local velocity gradient:
• - (FIA)/(dv/dL)
The viscosity. p., as defined is called dynamic viscosity. In addition, the ratio
of the dynamic viscosity of a fluid to its density, known as kinematic viscosity (p), is also used in many flow problems:
" ,., /lJp
Viscosity is usually measured in centipoise:s (cpl, with 1 cp equal to 0.01 go'
(em sec). or 6.72 x 10 4lbm/(ft sec). The most accurate method of determining viscosity is obviously to measure it for a given fluid under the desired
conditions. This, however, is not generally possible, Some common methods
for predicting gas viscosity are described briefly here.
Figure 3-13. Viscosity of paraffinic hydrocarbon' gases at1.0 atmosphere. (After
Carr at aI., 1954; courtesy of SPE of A1ME.)
Carr et aI. Correlation for Natural Gascs
The Carr et al. (1954) correlation requires only the gas gravity (or the molecular weight) for determining viscosity. It is the most widely used method
for determining the viscosity of natural gases. The correlations were presented in graphical form, as shown in Figures 3-13. 3-14, and 3-15. Figure
3-13 is used first to calculate the viscosity at one atmosphere pressure and
any given temperature. Corrections for non-hydrocarbon components N 2 ,
CO 2• and HgS are provided. The effect of these components is to increase the
viscosity. Then, Figure 3-14 or 3-15 can be used to correct for pressure. Figures 3-14 and 3-15 use the corresponding states principle to present
" - f(p"T,).
Examplt: 3·9. Find the viscosity for the gas given in Example 3-1 at 2,000
psia and 200°F.
•
•
~
·!
,
Solution
From Example 3-1,
M - 17.54, and the gravity 1"1 - 0.6055
Figure 3-1 4. Viscosity ratio versus pseudoreduced temperature. (After Carr et
aI., 1954; courtesy of SPE of A1ME.)
Properties of Nalurol G08e$
Gas Production Engineering
75
From Figure 3·14, the pressure correction,
So, the gas viscosity at 2,000 psia and 200°F,
" _ (1.25)(0.01293) - 0.0162
cp
Viscosity from Single-Component Data
1
~
;
,
.
If the analysis of a gas is known, it is possible to calcu1ate the viscosity of
the gas mixture from the comIX'nent viscosities. First, the viscosity is determined at one atmosphere (or any "low" pressure) and the given temperature
using the Herning and Zipperer (1936) mixing rule:
~,
(3-51)
where
Yl" mole fraction of component i in the gas mixture
pure component viscosity at 1 atmosphere pressure and the ..
temperature of interest
#lIp =
Figure 3-15. Viscosity ratio versus pseudoreduced pressure. (After Carr al ai.,
1954; courtesy of SPE of A1ME.)
From Example 3.2, at 2,000 psia and 2OQ°F,
p" -
3.010
T p,
1.848
-
From Figure 3-13,
J4111 -
The viscosity can be corrected to the desired pressure by using Carr et al.·s
reduced pressure and temperature correlations of Figures :J..14 and 3-15, or
any of the several other such correlations available. Lohrenz et al. (1964)
found the chart by Baron et a1. (1959) useful since it provides a good range
of reduced pressure and temperature. The differences among these charts
are, however very minor (Lohrenz et al., 1964).
Figure 3-16 shows the pure component viscosities as a function of temperature for some common natural gas constituenl~. Single component viscosities at 1 atmosphere pressure, 14]110 may also be calculated using the following relationship developed by Stiel and Thodos (1961):
0.0128 cp
14]1t! - 34 X 1O -5T ,Il{U./t!t for Tri
The gas has 1.4 % N:/:, for which the correction factor (to be added) from
Figure 3-13 is 0.00013 cpo Therefore, the corrected viscosity at 1 atmosphere,
14], -
0.0128 + 0.00013 - 0.01293 cp
14]et - 17.78
where
x
(3-52.)
< 1.5
1O -~(4.58Tri - 1.67)5!8/ tit for Tri
> 1.5
(3-52b)
(3-53)
76
Gal Production Engineering
Tn - reduced temperature for component i
T c:t - critical temperature in K
Pa - critical pressure in atmospheres
M, - molecular weight
Note that units of K for temperature and atmospheres for pressure must be
used in Equation 3-53. Equations 3-52a and b are valid for pressures in the
range of 0.2 to 5 atmospheres. The average error was reported by Stiei and
Thodos (1961) to be 1.83% and 1.62%, respective1y, for Equations 3-52a
PropeTliQ of Natural Gases
77
Exampk 3·10. Find the viscosity for a gas with composition, in mole%, of
o
C 1 ... 90.5, C 2 - 7.2, and C 3 - 2.3, at 3,000 psia and 540 R.
Solution
Come·
~
M,
Jl£L
Tn
'M1''
BIL
0.90S
0.072
0.023
16.043
30.070
44.097
667.8
707.8
616.3
343.1
549.8
665.7
4.0054
5.4836
0.0110
0.0092
0.0082
and b.
C,
C,
C,
Lohrenz et a!. (1964) report that this method gives an average error of
4.03% for the gas mixtures tested by them.
The J.lli\ values are from Figure 3·16.
r:
M =
YIM! - 17.697
Ppc = 1: YiPe! - 669.50
T pc
=
6.6353
r:
psia
YiTe; - 365.31 "R
So,
p,. - 3,000/669.50 - 4.481
T" - 540/365.31 - 1.478
E YiM?·:S,. 4.1723
1: I'lpYiMf"5 - 0.04476 cp
Therefore,
1'1,"
0.04476/4.1723 - 0.01073
From Figure 3-15. the pressure correction,
,,.
I~
200
TEMPERATURE, OF
Figure 3-16. Viscosity of some natural gas constituents allow pressure. (Aller
Carr el at, 1954; courtesy of SPE 01 AIME.)
.,
Thus,
.. - (1.95)(0.01073) - 0.0209 cp
•
78
Proper/in oj Natural Casel
C(U Production Engineering
x ~ 3.5 + 9861540 + (0.01)(17.697) -
Lee et aI. Correlation For Natural Gases
Lee ct a1. (1966) provide an analytic expression for viscosity that can be
used for programming purposes:
p.~ -
K exp(Xpk)
3.5 + 986/T + O.OIM
y -
2.4 - 0.2X
5.50290
Y = 2.4 - (0.2)(5.50290) - 1.29942
Using Equation 3-54, the gas viscosity at 3,000 psia and 540"R is:
(3-54)
'" _ (0.011278)exp[(5.50290)(0.188l4''''''')J - 0.0211 cp
where K _ 10. 4 (9.4 + O.02M)TU
209 + 19M + T
x-
19
and p.~ is in cpo p~ is in gicm1, T is in oR. Equation 3·54 reproduced experimental data with a maximum error of 8.99% (Lee et aI., 1966). The problem with this method is that it does not correct for impurities such as N 2 •
CO 2, and H 2S.
Specific Heat For Hydrocarbon Gases
One of the basic thermodynamic quantities is specific heat, defined as the
amount of heat required to faise the temperature of a unit mass of a substance through unity. It is an intensi\'e property of a substance. It can be
measured at constant pressure (cp), or at constant volume (c...), resulting in
two distinct specific heat values. In terms of basic thermodynamic quantities, molal enthalpy (h) and molal internal energy (u), the specific heats. cp
and c;. can be written as:
(3-55)
Example 3·11. Find the viscosity for the gas given in Example 3·10 at
3,000 psia and 54QoR using the Lee et a1. method.
and
Solutio"
(3-56)
From Example 3-10,
M - 17.697. Ppr:Z 4.481
T pr
-
1.478
From Figure 3-2, the compressibility factor,
Z - 0.78
From Equation 3-40, the gas density,
P, - (3,000)(17.697)1(0.78)(10.732)(540) - 11.745Ibmlft'
- (11.745)(1.601846)10-' _ 0.18814 glcm'
r\ow.
K - 10 -'[9.4 + (0.02)(17.697)](540")1
[209 + (19)(17.697) + 540J - 0.011278
where h is the molal enthalpy (Btullbmole), u is the molal internal energy
(BtuJlbmoie). c p is the molal specific heat at constant pressure (BtutlbrnoleOR), and c; is the molal specific heat at constant volume (Btullbmole.°R).
Using Maxwell's relationships, it can be shown that:
c -
C, _ -
P
T (aplaT)~
(op/ovh
(3-57)
For an ideal gas, where pv - RT, Cp and c; are a function of temperature
only. Furthermore, the right side of Equation 3-57 becomes equal to the gas
constant R. Therefore, for an ideal gas:
c,-c,-R
(3-58)
Note that the units for <;. and c.. are Btu/(lbmole OR) in Equation 3-58. So R
must be expressed in the same units:
R _ 10.732 (lbt ft")f(in. 2 Ibmole OR) x 144 in. 2/ft! x (11778.2) Btu/(lbf ft)
_ 1.986 Btu/(lbmole OR)
•
80
Cas Product/on Engineering
Propertia oj Natural Gases
81
and for a temperature range of 0 to 6OO°F:
A _ 3.7771, B - - 0.0011050, C - 7.5281, D - 0.65621,
E - 0.014609, F - 0.0
.ol--t--+- •
Thomas et al. (1970) report average errors of 1.01 % and 1.37 % for the
temperature range 0_200° F and 0_600°F, respectively, with Equation 3-59.
The effective mixture specific heat at low pressure, ~, can be determined
more precisely using Kay's rulE":
(3·60)
where the cp; for some common constituents of natural gas can be obtained
from Table 3-3, or the data by Thuloukian et al. (1970) shown in Figure
3·18.
•
0.06 006 010
02
0,4
0.6 0,8
Figure 3·17. Generalized plot for the heat capacity difference, c p - c.... versus
Ppr and Tpo' for real gases. (After Edmister, 1948; reprinted from Chemical Eng;neers' Handbook, 1973; courtesy of McGraw-Hili Book Co.)
For a real gas, c., and c.. are functions of both pressure as well as tempera.
ture. A real gas equation of state can be used to determine the right side of
Equation 3-57, and thus the difference between c., and c... Knowing either
one of Cp or c.. the other can then be detennined. Figure 3-17 shows a gener-
alized plot for the heat capacity difference, c., - c., versus p, and T,.
Cp
Determination
The low-pressure isobaric heat capacity, cp, can be determined primarily
by two methods: using the gas gravity, if the gas comp05ition is not known;
and using a weighted molal average (Kay's rule), if the gas composition is
known.
Hankinson et al. (1969) give the following relationship for calculating ~
in Btu/ (lbmole oF), from the gas gravity, 1'g, at any temperature T (oF):
~ - A + BT + C'Y, + D'rl + E(T'YJ +
Ff2
V V
..,
(3·59)
where for a temperature range of 0 to 200°F:
A - 4.6435. B - - 0.0079997, C - 5.8425, D _ 1.1533, E _ 0.020603,
F - 9.849(10 ')
..
"
..
..
..
/'
,
I
,
,
••
•
"
/'
,: ,." ,
•i •• •
---
V
V1
,
/
/
A'~
r/
V
J.-
I
,.,
..
..
•
,
"
....
••
..
..
• :~~
, F'
..
••
• • _ _ _ _ .- ~
.,- ,- ,- ..
,,"""..._
..
..'Vr)17
~
,
~
Figure 3-1B. Heat capacity of gases at 1 atmosphere, C:' as a function of temperature. (After Touloukian et at, 1970; courtesy of lFl/Plenum.)
Table 3-3·
Molal Heat c.pacrty (Ideal-Gas State) , Btuf(lb mOl-oR··)
0.,
Chemical
formula
Ga.
wt
CII,
16.043
26.008
28.054
30.070
O·F
WF
60*F
100·F
1SO-F
200*F
823
8.42
10,22
10.02
12.17
IUl.5
10.71
10.72
12.U5
8.9,5
"I<
11 41
13.78
II ,SS
12,09
14.63
15.7.5
18.17
16.80
19.52
17.85
20,89
250*F
300·F
9.64
11.90
12.76
15.49
18.88
22.25
25.73
24.Q1
25.73
29.39
10.01
12.22
13,41
16.34
42.081
44.097
9.68
9.33
11.44
13.63
15,65
14.69
16.88
IU6
10.33
10,16
12.32
14,90
17,13
56.108
56.IOS
56.108
58. 124
58. 124
17.96
16.54
111.84
20.40
20.80
19.59
18.04
2023
22.15
22.38
H).91
111.34
20.'j(]
22.51
2272
21 18
1!).5-t
21.61
22.74.
21.04
23.!)S
25,77
2.4.08
25,81
24,26
22.53
24.37
27.59
'1:7,SS
72.151
72.151
24.94
25.64
27.17
27.61
27.61
28.02
29.·12
29.71
31,60
31,116
33,87
33.99
29.23
36.03
36.08
c.H.
c.H"
78.114
86.178
100.205
16.41
30,)7
18.41
32.78
34.96
38.00
20.46
35.37
,1.01
2245
37,93
44.00
24.·16
40,45
46.94
26.34
12.94
49JII
28.15
45.36
52.61
Nlll
17.031
8.52
8.52
18.78
33.30
38.61
8.52
6.95
8.00
6.95
8.01
6.97
6.99
7.00
'O:J
8.52
6.97
8.07
8.53
6."'
7.98
1i.52
6.00
8.53
28.964
6.95
6.95
6.86
8.09
6.96
6.95
703
6.96
6.01
UTi
6"
6.94
6.99
8,12
712
8.111
8.27
6.96
'00
6.97
7,01
8,17
7,17
6.98
6,97
fj,46
7.01
9.81
8.53
7.03
8.23
723
7.00
6.98
855
703
Methane
Ethyne (AMylene)
Ethene (Eth)lene) •
Ethane
C~H~
Propene (Propylene)
C;H.
I'ropo~
C~I!
I-Butene (Butylene)
rlf-2-Bulene
fro"s.2-Bulene
iw-Butane
A-Butane
L,o-Pentane
A-Pentane
C,II,
C,II.
C,H.
C,lI lo
Benzene
n·lieul'ie
"-Heptane
Ammonia
Air ..
Water
Ol')'gen
Nitrogen
lI ydrogen
Il ydrogen sulfide
Carbon monoxide
Carbon diol'ide
C, II.
C,I I,
C,HI~
C~HII
..........
~
~
C,1I 1t
G,1I 11
H,o
18.015
31.999
28.013
2.016
34.076
28.010
44.010
0,
N,
II,
11,5
CO
CO,
6.78
8.00
695
8.38
6.H7
8.11
6.96
8.76
8.70
II I;;
2300
6.97
6.95
8.36
699
956
9.29
19.89
23.56
'1:7,16
25.47
27.07
3 1 II
30.90
"••
."
i
~
5
•
•'"
"'•.
~.
•
"
38.14
38.13
10.05
• Comley of Ca~ P,OCleI5OI"S Supp1i<:,.. As•.,d.tlon
•• Da~a !IOO1'Ce: Selfded ...1..... or p.operti... of hydrocarboru. "I'! Iler.earch "roJee! 44. F.'''''pt'n'lI' "AI.:' Kec.IMn ~"d K~, Thrr",odyno",J~ Propt"ftlr" of Ilk Wiley,
3rt! Prlntlnl( 194; MAmmon!.'- "d" R. Crab]. 'lhe-rmod)·nomlc P"'p.·rtle. of AmlllurI;. at "'!d' 11,mperlh""" and !'.... un ... IH. l'ro.-ns1"II.. April lOS;}
MHrd...., Sulfide.
M
J, R \\est.
C~m.
£nll:. I'rotl.reQ. 44,287. 19-1.'1
.
-/;;'''OJ
(O!:
1i-:l
p
-
0.
i3
o
- •
"N.-'"
~ o""c;·~
~~ It>Q.. :::.._.
n ~
n
.... .... 0
~~Sg­
.
_.3
-.
:I
<r.I :l
a
(]>
10>
_
0. III
_.
-if.J' "8
o:ll~~
<p
::tI
~
§ ~
'< .-
s·
•g.
_
~~i § -:l
iJQ~c~g-
3w~!i"·
3'~.c°
e..(O~cg-'
til &; 3 g ::I.
c:lr;;·c.~
-~ if Ii. '< ~
:::r'c",g'=;
(i' jI!1 -;::
?r
5'
::rf5..~ft:r
r;;'
0'" (!)
(\>
oZ_ 3
- ._a
:;;g~..r
:l_"'o.~
--:
-<~a.CTIIl
,.... ;I> '<
....
a~i=f3
2;-5·8;E. ~
~
111 III
0
.c:l .....
co. ....
e..
c
-.
o :I
1Il"C _~
:l
~
-
0
0'<..:::
...
no'
• - c
1;;'
~ n
III
e:t;.",~
.... III
o
3
11
=
n::T,<
c 2 0-
n
~ III
- It'ro
n
......
E.[-l~
10> •
::r 3
S -:l g :;-
p ".
- l\.
0 ..,
...
.
"
.
c- 3 6Q' 5'
C:IIlCo.
_.
.... til
~
....
~
-<;.;l~
Vi' :::.. ::; ~
;:I
< c
it
...
-0
~=.lf_.~
- ... "'"""o.
::I&;"()::Ic:
gO' I
!:;'..r
0'
c _. ..n. ...
;::: ::J
~
is..
<is -0 r;'
r~ti .:-l~ ~~ ~~
(i'
~~;, 03~
. "'.8 0
.".
~ 0 [
o ~
5·
-
"T ::I
-. 0'
~
.......
."
0
0
."
w-"<0 <0
~I»~
.,--_.
o~ ·
g!ll~
.
.l'l.C,' C, -C;. elll fig ·moIeW K I
->w
0-
~o-
,
9..m9.
"o.~
n3~
o
ob
0
o
0
o
N
po.
•
•
!t'0N~
~~
o
0
.I
•
N
•
:ejijii~
... . "0
:I:W·
, (11 (/I
_.
=0°
!!'
.. ~
~iiia.
~~~
,,::'\:~
~
~:"
0
~~,,=.~
,-,,,,,\:
0
:
0
,
!
~.-3
~
"
0
() ::i" ::: ~ :~~ ,,~~~~~ ~
_0._
-, ~ ><~" ~~~~~;:; ~
3."
... ~ 8
o
•
-' :~"'.'Rk!
2,,,~
0:~~
Qii03
• • g-
N
o
o
-~
c
~
!,CD~
, ()"
0_
..0
g,
"
3~o
(i'-
_~~".,
.~ •
9
",.
",3
,·0
,
O~
;;
0
0
1
,,~' ~ "'~ ~ ~0 :::" =-~ J;
\~ )...". '-" '0"~'>J." ~",,'-'9~ I~~
o '" ,-so ~ ~~'.'
.<?
......
-<;
:~I
,
*"
-.
0
~~
.'"
I
I I
~!!t
,"
0."
ll·
,Jl-".Jf...
S
J
""
..
u
...
'I>.J
,,"~~"
,\'\,,'''1\
~~
,,:\ \
1// /I ~,;
I 1
{
5
~
1:'
i
"
~
1:
•
Properties oj Nglurai Go.IQ
Go.! Production Engineering
cumbersome method and is subject to limitations of non-hydrocarbon gas
content of less than 7 %, a reduced temperature greater than 1.1, and a reduced pressure between 0.4 and 15.
Example 3-12. Find ~ for the gas given in Example 3-10 at 540 R
using (1) gas gravity method of Hankinson et al.. and (2) the gas
analysIS. Use the value for cp from the gas analysis method to find '1> and c
at 3,(X)() psia and 540 0 R fOT this gas.
'
From Figure 3-19, at Pvr - 4.481, and T pr
tion,
(c,
-~)
-
85
1.478, the specific heat correc-
- 6.5
0
(80.33~F)
Therefore,
c, - 9.046 + 6.5 - 15.546 BtuI(lbmole OR)
•
from Figure 3-17,
Solution
(c, - "') - 7.0
From Example 3-10,
Therefore,
M - 17.69i
c" .. 15.546 - 7.0 - 9.546 Btu{(lbmole OR).
PI" ., 4.481
T p,
""
1.478
,
The gas gravity,
'YK =
17.697128.97 '" 0.6109
From Equation 3-59,
~
- 4.6435 + ( - 0.(079997)(80.33) + (5.8425)(0.6109)
+ (l.l533)(0.6109') + (0.020603)(80.33)(0.6109)
+ (9.849)10"(80.33') - 9.075 Btul(lbmole OR)
2.
0;:.
Comp.
JL
~
Btu/~lbm
C,
0.905
0.072
0.023
16.043
30.070
44.097
0.530
0.425
0.425
C,
C,
0;:.
oF)
Btu/(lbmole oF)
8.503
12.780
18.741
!he CPI values in Btu/(lbm oF), obtained from Figure 3-18, are converted
IOto Btu/(lbmole oF) by multiplying by the molecular weight, Mh in IbmJ
lbmole. Thus,
cp -
I: y~ .. 9.046 BtuJ(lbmoJe oF) .. 9.046 Btu/Qbmole OR)
1b find cp and c.,:
-
QuesOOm .... Pmblems '"
1. A gas pipeline consists of a lO-mile long 12-in. ID pipe section in series
with a 20-mile long section of 8-in. ID. How many Mscf of gas must be
removed to blowdown this gas pipeline from an average pressure of
1,500 psia to an average pressure of 300 psia? Assume that at the prevailing temperature of 85°F the gas has a compressibility factor of
0.95 at 1,500 psia, and 0.85 at 300 psia.
2. We have a sweet gas of known composition: N2 - 1%, C l - 89%,
C 2 .. 5 %, and C 3 + - 5 %. Assume the C 3 • fraction to be equivalent
to n-C~. Find: (i) the gas gravity, and (ii) the pseudo-critical pressure
and temperature for the gas.
3. For the gas in Problem 2, find the gas compressibility factor at 1,200
psia and 95°F using all the applicable methods given in Chapter 3.
4. A sour gas is known to have the following composition: N2 - 8.5%,
H 2S .. 5.4%, CO 2 ,,, 0.5%, C l .. 77.6%, G.! .. 5.8%, C 3 .. 2.0%, nC 4 .. 0.1 %, and j,C4 - 0.1 %. This gas is being sold at a contract pressure of 1,000 psia at 120°F. What is the error introduced in the calculation of the sales volume by assuming Z .. 0.85? Use the best
estimates of Z-factor from the available corre1ations.
5. For the gas given in Problem 2, find the viscosity and compressibility
at 200 psia and BO°F.
6. For the gas given in Problem 4, find the viscosity and compressibility
at 800 psia and 65°F.
•
Gas Production Engineering
References
Baron, }. D., Roof. J. C., and Wells. F. W .• 1959. "Viscosity of Nitrogen.
Methane. Ethane, and Propane at Elevated Temperature and Pressure,"
/. Chern. Eng. Data, 4(3, July), 283-288.
Benedict. M .• Webb, C. B., and Rubin, L. C .. 1940. "An Empirical Equation for Thermod}'namic Properties of Light Hydrocarbons and Their
Mixtures," }. Chem. Phys., 8(4, Apr.), 334-345.
Bro~Ol. C. C , Katz. D. L., Oberfell, C. B., and Alden. R. C .. 1948. NaWral Gawline and \'olatile Hydrocarbons. NCAA. Tulsa. OK.
Buxton. T S. and Campbell. J M., 1967. "Compressibility Factors for Lean
Natural Cas-Carbon Dioxide Mixtures at High Pressure," So('. Pet. Eng.
1.,7(1, M".), 80-8£.
Campbell, J. M .. 1984. Cas Conditioning and Processing. \'QI. 1. Campbell
Petroleum Series, Norman, Oklahoma, 326pp.
Carr, N. L., Kobayashi, R, and Burrows, D. B., 1954. "Viscosity of Ilydrocarbon Cases Under Pressure," Trans., AIME, 201. 264-272.
Chemical Engineers' Handbook, 1973. R. H. Perry and C. H. Chilton
(eds.), McCraw-Hili Book Co., New York, 5th edition.
Coats, K, H., 1985. "Simulation of Cas Condensate Reservoir Performance," }. Pet. Tech., 37(10, OcL), 1870-1886.
Dranchuk, P. M. and Abou-Kas.sem. J. H .. 1975. "Calculation of Z-Factors
for Natural Cases Using Equations of State," J. Cdn. Pet. Tech .• 14(3.
July-Sept.), 34-36.
Dranchuk, P. M., Purvis, R. A., and Robinson, D. B., 1974. "Computer
Calculation of Natural Cas Compressibility Factors Using the Standing
and Katz Correlation," Inst. oj Petr. Tech. Series, No. [P 74-008.
Edmister, \V. C., 1948. Petrol. Rejiner (Nov.), p. 613. Cited reference on
page 3-238 in: Chemical Engineers' Handbook, 5th ed., 1973, edited by
R. H. Perry and C. H. Chilton, McCraw-Hili Book Co., New York.
Edmister, W C., 1950. Petrol. Engr. (Dec,), p. C-16. Cited reference on
page 3-237 in: Cllemical Engineers' lIandbook. 5th ed., 1973, edited by
R H. Perry and C. H. Chilton, McCraw-Hili Book Co., New York.
Edmister, W C. and Lee, B. I., 1984. Applied Hydrocarbon Thermodynamics, Vol. 1. (2nd ed.) Gulf Pub!. Co., Houston, Texas, 233pp.
Fussell, D. D. and Yanosik, J. L., 1978. "An Iterative Sequence for Phase
Equilibria Calculations Incorporating the Redlich-Kwong Equation of
State," Soc. Pet. Eng. J., 18(3, June), 173-182.
Fussell, L. T., 1979. "A Tcchnique for Calculating Multiphase Equilibria,"
Soc. Pet. Eng. J .. 19(4, Aug.), 203-210.
Cas Processors Suppliers Association, 1981. Engineering Data Book, 9th edt
(5th revision), CPSA, Tulsa, Oklahoma.
Properties oj Natural Ca.rer
87
Copal. V. N., 1977. "Cas Z-Factor Equations Developed for Computer," O.
and Cas J., 75(32, Aug. 8). 58-611.
Hankinson, R. w., Thomas, L. K., and PhiUips, K. A., 1969. "Predict Nat·
ural Cas Properties," Hydr. Proc., 48(4, Apr.), 106-1OB.
Herning, F. and Zipperer, L., 1936. "Calculation of the Viscosity of Technical Cas Mixtures from the Viscosity of Individual Gases," Gas U. WasserJach 79(49), 69.
..
.
Joffe, 1., Schroeder, C. M., and Zudkev.itch, D., 19!0. "Vapor.hqUld Eq~l­
libria with the Redlich-Kwong Equation of State, AIChE J., 16(3. May).
496-498.
Lee, A. L., Conzalez, M. H., and Eakin, B. E., 1966. "The Viscosity of
Natural Cases,"]' Pet. Tech., 18(8, Aug.), 997-1000.
Lohrenz, J., Bray, B. C., and Clark, C. R., 1964. "Calculating Viscosities of
Reservoir Fluids from Their Compositions," J. Pet. Tech., 16(10, Oct.),
1171-1176.
Martin, J. J., 1979. "Cubic Equations of State-Which?" Ind. and Eng.
Chen!. Fund., 18(2, May), 81-97.
Mattar, L., Brar, C. S, and Aziz, K., 1975. -'Compressibility of Natural
Cases," ]. Cdn. Pet. Tecll., 14(4, Oct.-Dec.), 77-80.
McLeod, Wand Campbell, J. M., 1969. "Prediction of the Critical Temperature and Pressure, and Density of Natural Cas," Proc, 48th Ann.
Com). NGPA (Nov.), Nat. Cas Process. Assn., Thlsa, Oklahoma.
Peng, D.· Y. and Robirson, D. 8., 1976. "A New 1\..o-Constanl Equation of ..
State," Ind. and Eng. Chem. Fund. 15(1, Feb.), 59-64.
Peng, D.- Y. and Robinson, O. B., 1976. "Two- and Three-Phase Equilibria
Calculations for Systems Containing Water," Cdll. J. Chern. Eng., 54 (6,
Dec.), 595-599.
Pitzer, K. S., Lippman, D. Z., Curl, R. F., Jr.. Huggins, C. M., and Peterson, D. E., 1955. "The Volumetric and ThermodynamiC Properties of
Fluids. II-Compressibility Factor, Vapor Pressure, and Entropy of Vaporization," J. Am. Cllem. Soc., 77(13, July 5).3433-3440.
Redlich, O. and Kwong, J. N. S., 1949. "On the Thermodynamics of Solutions. V-An Equation of State. Fugacities of Caseous Solutions," Clu:m.
Reviews 44, 233-244.
Reid, R. C., Prausnitz, J. M., and Sherwood, T K., 1977. The Properties oj
Gases and Liquids. (3rd eeL), McCraw-Hill Book Co., Inc" New York,
688pp.
Satter, A. and Campbell, J. M., 1963. "Non-Ideal Behavior of Cases and
Their Mixtures," Soc. Pet. Eng.]., 3(4, Dec.}, 333-347.
Soa\'e, C., 1972. "Equilibrium Constants from a Modified Redlich-Kwon~
Equation of Slate," Chem. Eng. Sci. 27(6, June). 1197-1203.
Standing, M. B. and Katz, D. L., 1942. "Densit}' of Natural Cases," Tram.
AlAtE, 146, 140-149.
os
Ga, Production Engineering
Ste\\-:~,
w. E., Burkhardt, S. F., and VOO, D., 1959 "Pred' .
cntlcaJ Parameters for Mixtures" P
.
lchon of PseudoKansas City, MO.
' aper presented at the AIChE Meet. ,
Sti~;ULp~:~~,h~~hii'.,1~1: ~j,V~~r5~f Nonpolar Cases at Nor-
Takacs. C., 1976 "Co
.
M d r
tions," O. and
/.~i:(57.~.a~). ~_~~puter Z-Factor Calcula-
Th~mas,
Gas
L. K.,
~ankinson. R. W., and Phillips. K. A. 1970 .. Det
;:;;__ ~!5~COUstiC Velocities for Natural Cas," J. Pet.' Tech.',
.
22(7~r~~~;~
4
Gas and Liquid Separation
To~ou~a.n, Y. S.. Kirby. R. K., Taylor, R. E., and Lee T Y
SpecifIC Heat-Nonmetallic liquids and Case;:" T~ 'h' ~., 1970.
~tll!3 oj Matter, IFIIPlenum , Nev.. York City 6'
OP YSlCal PrapWichert E and Aziz K 1972 ..
.' .
.
. " . CaIcuJahon of Z's for Sour Cases" H d
Proc.,.51(5,
May), 119-122.
• Y r.
Wilson, C. M., 1969. "A Modified Redlich-Kwon E
.
plication to General Physical Data Calculatio~s "q~atlOn of State, Ap-
Ya::~:;~ ~~ ~;~:l~~h National ~eet., Clevel~nd,ab~i~0~1!~~!;eZ+Factors'" 0
d G ' J' R., 1974. How to Solve Equation of State for
Z dk . h'
. an
as., 72(7, Feb. 18),86-88.
uu e;~c , ~'. a~d }~ffe, }., 1970. "Correlation and Prediction of Va r+
16q(1 J EqUlhbna WIth the RedJich-Kwong Equation of State" A/ChI:;
, an.), 112-119.
'
.,
Introduction
Only rarely does a reservoir yield almost pure natural gas. Typically, a
produced hydrocarbon stream is a complex mixture of several hydrocarbons. intimately mixed with water, in the liquid and gaseous states. Often,
solids and other contaminants are also present. The produced stream may be
unstable, with components undergoing rapid phase transitions as the stream
is produced from a several hundred feet deep reservoir with a high temperature and pressure to surface conditions. It is important to remove any solids
and contaminants, and to separate the produced stream into water, oil, and
gas, which are handled and transported separately. Cas and liquid separation operations involve the separation and stabilization of these phases into
saleable producU. Generally, intermediate hydrocarbons in the liquid state
fetch a higher price; therefore, it is desirable to maximize liquid recovery.
Field processing of natural gas includes:
1. Gas and liquid separation operations to remove the free liquidscrude oil, hydrocarbon condensate, and water, and the entrained solids.
2. Recovery of condensable hydrocarbon vapors. Stage separation, or
low temperature separation techniques are used.
3. Further cleaning of the gas and oil streams after separation.
4. Gas dehydration processing to remove from the gas condensable water
vapor that may lead to the formation of hydrates under certain conditions (see Chapter 5).
5. Removal of contaminants or otherwise undesirable components, such
as hydrogen sulfide and other corrosive sulfur compounds, and carbon
dioxide (discussed in Chapter 6).
This chapter describes gas· liquid separation and gas cleaning techniques.
89
•
90
Gas Production Engineering
Separation Equipment
Separators operate basically up:m the principle of pressure reduction to
achieve separation of gas and liquid from an inlet stream. Further refine~ent ?,f the gas ,and liquid streams is induced by allowing the liquid to
stand for a penod of time, so that any dissolved gas in the liquid can escape by the formation of smaU gas bubbles that rise to the liquid surface:
a~d remo\;ng the entrained liquid mist from the gas by gravity settling, impmgt:mt:nt , ltntrifugaJ action. and other means. Turbulent flow allows gas
bubbles to escape more rapidly than laminar flow, and many separators
therefore have sections where turbulence is induced for this purpose. On the
o~her hand, fOr the removal of liquid droplets from the gas by gravity setthng, turbulence is quite detrimental to removal efficiency. Thus, the design
of a separator comprise<; different modules assembled to achieve different
functi?ns in a single vessel. Equilibrium is attained in the piping and equipment JUst upstream of the separator, the separator il<;elf serving only as a
"wide" spot in the line to refine the vapor and liquid streams resulting from
this basic separation.
To efficiently perform its separation functions, a well designed separator
must (Campbell, 1984; Beggs. 1984):
1. Control and dissipate the energy of the wellstream as it enters the separator. and provide low enough gas and liquid velocities for proper
gravity segregation and vapor-liquid equilibrium. For this purpose, a
tangential inlet to impart centrifugal motion to the entering fluids is
generally used.
2. Remove the bulk of the liquid from the gas in the primary separation
section. It is desirable to quickly achieve good separation at this stage.
3. Have a large settling section. of sufficient \'olume to refine the primary
separation by removing any entrained liquid from the gas, and handle
any slugs of liquid (usually known as "liquid surges" ).
4. Minimize turbulence in the gas section of the separator to ensure
proper settling.
S. Have a mist extractor (or eliminator) near the gas outlet to capture and
coalesce the smaller liquid particles that could not be removed by
gravity settling.
6. Control the accumulation of froths and foams in the vessel.
7. Prevent re-entrainment of the separated gas and liquid.
8. Have proper control device; for controlling the back-pressure and the
liquid level in the separator.
9. P~vi~e reliable equipment for ensuring safe and efficient operations.
ThIS Includes pressure gauges, thermometers, devices for indicating
CO$ and Liquid Separation
9'
the liquid level, safety relief valves to prevent blowup in case the gas or
liquid outlets arc plugged, and gas and liquid discharge ("dump'')
"alves.
__________________
T~nx-~~o~f=
SC~p=a~'~at~o~~~___________________
Separators can be categori7.eci into thf('(> hasic ty-pe;: certicoJ, hnriuUltal
(single-tube or double-tube). and spherical. Selection of a particular type
depends upon the application, and the economics. Ad"antages and disadvantages for these separator types are cited from Campbell (1955).
Vertica1 Separators
The wellstream enters the vertical separator (Figure 4-1) tangentially
through an inlet diverter that causes an efficient primary separation by
three simultaneous actions on the stream: gravity settling, centrifugatioll,
and impingement of the inlet fluids against the separator shell in a thin film.
The gas from the primary separation section flows upwards. while the liquid falls downward into the liquid accumulation section. A conical baffle is
provided as a separation between the liquid accumulation section and the
primary separation section to ensure an undisturbed liquid surface for
proper liquid le\'el control and release of any dissolved gas. The smaller liquid droplets that are carried along by the upwards rising gas stream are removed in the centrifugal baffles near the top. Finallh a mist extractor at the
gas outlet removes any entrained liquid droplets from the gas in the micron
size range. The liquid particles coalesce and accumulate, until they become
sufficiently heavy to fall into the liquid accumulation section.
Adl."antage3
A vertical separator can handle relativel), large liquid slugs without carryover into the gas outlet. It thus provides better surge control, and is often
used on low to intermediate gas-oil ratio (COR) wells and wherever else
large liquid slugs are expected. Vertical vessels can handle more sand. A false
cone bottom can be easily fitted to handle sand production. Liquid level
control is not as critical in a vertical separator. The tendency of the liquid to
revaporize is also minimized, because less surface area is available to the liquid for evaporation. It occupies less floor space, a particularly important
advantage for operations on an offshore platform where floor area is at a
premium.
•
92
Gas Production Engineering
Ca. and Liquid Separation
HORlZONTAL LOW PRESSURE SEPARATORS
,
-_
.._----,-------,--,------
--
ST""'GAIIO ACCUSOIIIf.1
._._--_
......
,-,------... ...........--..... _._._--.------,------.,----,,--'--._-
93
.......1 .. ' ... - 1 "-"" ... _
... _ _ " -
""
, 0., _ _ .. 10' _ _ ....... _
............
~,
,
,
.......
----
0I"ll0N""'- "CCUI04IIU
-~
Figure 4·1. A conventional vertical separator. (Courtesy of HTI-Superior, a Berry
Industries Company.)
DiMulvantagn
Vertical \'~ are more expensi\'e to fabricate, and also more expensive
to transport to location. A vertical separator for the same capacity is usually
larger than a horizontal separator. since the upwards flowing gas in the ver.
tical separator opposes the falling droplets of liquid.
Horizontal Separators
These separators may be of a single-tube (Figure 4·2) or a double-tube
(Figure 4-3) dt5ign. In the single-tube horizontal separator, the wellstream
upon entering through the inlet, strikes an angle baf£1e and then the separator shell, resulting in an efficient primary separation similar to the vertical
,-_._-'--..-,---'--,---'-..---_-. ,-,---_
.. _---_ . ._---_-..._,,_O<......... __ .. ,___.....
STAN DUD ACCUSOIIIES
~,
,
' .....1 .. ' ... - -
....
'0. ... _
,
-----__ -
Of'flONAI. ACC(.A(NUQ
-~
.....
.
Figure 4-2. A horizontal single-tube separator. (Courtesy of HTI-Superior, a
Berry Industries Company.)
separator. The liquid drains into the liquid accumulation ~ion, via horizontaJ baf£1es as shown in Figure 4-2. These baffles act as Sites for further
release of any dissolved gas. Cas flows horizontally in a horizontaJ separator. It strikes baffles placed at an angle of 45° , thereby releasing entrained
liquid by impingement. A mist extractor is usually provided near the gas
out1et.
In the double-tube type. the upper tube acts as the separator section,
while the lower tube merely functions as a liquid accumulation section,
Thus the double-tube separator is similar to a single-tube separator, but
with ~ greater liquid capacity. The liquid generated in .the primary separation section near the inlet is immediately drained out mto the lower tube.
The wet gas flows through the baffles in the upper separator tube at hig~er
velocities. AdditionaJ liquid generated is drained into the lower section
through the liquid drains provided aJong the length of the separator.
•
94
Cas Production Engineering
Gas alld Liquid Scporatum
95
INL[f
OIVERT(R
""""
" .....
'M
-
I NlU
Liquid level control is critical for horizontal separators, and the surge
space is rather limited. They are much harder to clean. and are therefore not
advisable to use where the well produces a lot of sand. They occupy a lot of
space. The space requirements. however. can be minimized by stacking several of these on top of each other for stage separation operations.
Spherical Separators
Figure 4-3. A horizontal double-tube separator.
G"~k
p ...", ••
2~G~"~W~';'"~===I(~~~V.'''
F'fe ....,. 0'011'0
O.. -"",.IiJlngPlpe
The spherical separator is designed to make optimum use of all the known
means of gas and liquid separation such as gravity, low velocity. centrifugal
force, and surface contact (Craft et a!.. 1962). An inlet flow diverter spreads
the entering wellstream tangentially against the separator wall. The liquid
is split into two streams that come together after going halfway around the
circular vessel wall and then fall into the liquid accumulation section. Liquid droplets from the gas are removed mostly by the velocity reduction imposed upon the gas inside the vessel. A mist extractor is used for the final
removal of smaller liquid droplets in the gas (see Figure 4-4).
Adlxmtagf!ll
FluidtuU"..,I~IOf
Spherical separators are very inexpensive, cheaper than either the vertical
or the horizontal separators. They are \'ery compact, and offer better cleanout and bottom drain features than even the vertical type. Spherical separators are applicable to well streams with low to intermediate GOR's.
Disadmlltagn
Figure 4-4. A spherical low-pressure separator. (After Sivalls, 1977; courtesy of
C. A. Sivalls and the University of Oklahoma.)
Liquid Ic,,'el control is critical to the spherical separator performance.
They have very limited surge capacity and liquid settling section. Because of
the limited internal space, it is difficult to use a spherical separator for threepha'iC (gas-oil-water) separation.
Adcolltaga
.H?rizo?tal separators have a much greater gas-liquid interface area, perImttmg .hlgher gas velocities. They can, therefore, handle large gas volumes
eco~omlcally and efficiently. They are cheaper to fabricate and ship than
vertical separators. They are also easier and cheaper to install and service.
~orizo~tal separators minimize turbulence and foaming. For a given capacIty, ?onzontal separators are smaller and cheaper than vertical separators.
~oTl.zontal separators are almost always used for high GOR wells, for foammg well streams, and for Uquid-Iiquid separation (SeW, 1984).
Separation Principles
The several different techniques applied for separation processing can be
broadly classified into two categories: mechanical separation and chemical
separation techniques based upon thermodynamic vapor-liquid equilibrium
principles. Mechanical separation includes several techniques that will be
discussed later in the section on gas cleaning. In separators, the mechanical
•
96
CO.! and Liquid Separation
GeM Production Engineeri'lg
separation methods that are applied are of three types: centrifugal action,
gra\"ity settling, and impingement.
97
where Cd - drag (or friction) coefFicient
P.. - gas density
v - droplet velocity
Centrifuge Separation
2. The force F., due to angular acceleration, given by:
Consider a centrifuge of radius R2 , height h, and inner shaft radius Rj, as
shown in Figure 4-5. Feed enters at a volumetric rate q. As the centrifuge
rotates at an angular speed w, the heavier liquid droplets are thrown outward to the centrifujOte walls as shown in Figure 4-5. The residence time t for
the fluid in the centrifuge is given by:
t ... centrifuge volume/volumetric flow rate of
At equilibrium conditions, the sum of forces on the droplet must be equal to
zero. Therefore, the two forces Fd and F., acting in opposite directions must
be equal in magnitude. So:
nuid
- .(H! - Hf)h!q
where PI ,. liquid density
(4-1)
GAS
0
•
•
• •
• •
•
•
•
•
•
•
0
•
0
liquid film
•
F,
~
n
1
J
h
•
• •
.,
v2 _ 4~P1W2R
.2~
3Cd P..
Therefore,
i dont think using this is right here, since 4 lines above,
equilibrium is assumed, which means velocity would be
constant, while here, velocity is a funtion of R and R is
clearly changing. :(
Figure 4·5. Forces acting on
a particle in a gas stream in a
centrifuge .
FEED
(4-2)
Separating the variables,
and integrating, we get:
2(Hj' - HI') - 2(d,p,)" wtl(3CdP~"
al rOI. q
Solving for t:
In the analysis that follows, it is assumed for simplicity that the liquid droplets are spherical, with a uniform diameter d p • The area A projected by a
droplet is therefore equal to (T/4)~. As shown in Figure 4-5, there are two
forces acting on any droplet at a radius R:
(4-3)
Substituting for t from Equation 4-1 into 4-3:
1. The drag force, Fd , due to friction, given by:
.(HI - H!)h _ (HI' - HI ')(3C""J"
q
(dpPl)o·:sW
•
98
CO! and Liquid Separation
Gas Production Engineerillg
Solving for the droplet diameter ~:
Solving for the droplet velocity, v:
d\;' _ (R!' - R!')(3C dPJ"q
.h(R! - Rl)pP
dp
(4-5)
'w
'" 3(R~ s - RP)2CdPfl2
72h2(R~ _ Rj)2PIW2
(4-4)
Equation 4-5 for the droplet velocity is often written as:
(4-6)
Equation 4-4 gives the size of the smallest droplet that can be removed b\
the centrifuge. Thus, to decrease the droplet size d p that can be removed, w~
have three options: decrease q, which is not quite feasible; increase the
height. h. of the centrifuge; or increase the rotational speed, w, of the centrifuge. To achieve good separation in a centrifuge, it is therefore essential to
have as large a centrifuge column as possible, and to operate the centrifuge
at as high a speed as possible.
In practice. centrifuge separation involves using several relatively small,
standard-size cyclones in parallel. Centrifuges (or cyclones) perform best
when the gas flows at a constant rate and pressure for which the equipment
has been designed. At lower rates, separation is poorer, whereas higher rates
lead to an excessive pressure drop through the centrifuge or cyclone. Properly operated, centrifuge separation can usually handle liquid droplets
down to a size of about 2 microns.
This is known as the Souders-Brown equation. The constant K relates to the
liquid droplet diameter and the drag coefficient, and is called the separation
coefficient.
FEED
;>
01 role
I.
f'"
L
I
h
~
I
Figure 4·6. Forces acting
on a particle in a gas
stream in a gravity settling
chamber.
The residence time for the droplet in a separation chamber of circular
cross-section, with length L and diameter h, as shown in Figure 4-6. is given
by,
t - (.h'L)l4q
Cravity Settling
Consider a liquid droplet of diameter d" suspended in a gas stream flowing at a rate q. The forces on the droplet are:
1. Force Fit due to
gravit)~
99
(4-7)
The velocity v at which the droplet falls in the vertical direction is given by:
v - dh/dt
given by:
Upon integration.
v _ hit assuming a constant \'
where g - acceleration due to gravity, and
2. Force Fd due to friction, given by:
Substituting for t from Equation 4-7 and rearranging, we get:
q _ (.hLl4) v
Substituting for v from Equation 4-5 into Equation 4-7b:
At equilibrium, Fd - F,. Therefore:
(4-8)
•
100
Ca, ProdlJCtion Engfnurlng
Thus, to allow smaller droplets to settJe, we must maximize the height hand
length L.
Gravity settling can effectively remove liquid droplets of size greater than
about 80 microns. For removing smaller particles, the required chamber size
becomes too large for any practical application.
Impingement
In the impingement process, gas with entrained liquid particles strikes a
surface such as a baffle plate, or wire mesh. The gas flows around this flow
obstruction. but the momentum of the liquid droplet tends to mOve it
straight ahead and impinge and collect on the surface. In practice, the flow
direction is altered several times to achieve better gas-liquid separation.
The design parameters for an effective impingement surface are the distance across the flow path necessary to stop the liquid droplet, since this determines the size of the impingement surface needed to remove droplets up
to a given size: and the pressure drop resulting from the flow of gas through
the impingement medium. The impingement surface size can be determined
using laws governing the £low of particles suspended in a fluid, such as the
terms derived in Equations 4-2 and 4-5 for the particle velocity in a centrifuge and a gravity settling chamber, respectively. The pressure drop caused
by the impingement media is also of concern, because a greater pressure
drop is synonymous, in engineering terms, to higher compression costs for
the gas.
Impingement techniques can handle liquid particles of size greater than
about 5 microns.
Factors Affecting Separation
As is true for all vapor-liquid equilibrium processes, gas-liquid separation
is affected by the separator operating pressure, temperature, and the composition of the fluid feed to the separator. From the general phase diagrams
for naturally occurring hydrocarbon mixtures, such as those in Chapter 2, it
is clear that as the pressure increases, or the temperature decreases, there
will be greater liquid recovery, up to a point referred to as the optimum.
Vapor-liquid equilibrium flash calculations will yield the optimum pressure
and temperature quite easily. From a practical standpoint, however, it may
not be possible to Operate at this optimum point because of the costs involved. operational problems, or enhanced storage system vapor losses.
Generally, with increasing pressure, the gas capacity of the separator increases. The reasons are the effect pressure has on gas and liquid densities,
Gas and Liquid Separation
101
actual flowing volume, and the allowable velocity through the separator.
With increasing temperature, the separator capacity usually decreases, due
to the effect of temperature on the flowing volume and gas and liquid densities.
In actual oil-field practice, economics is the foremost concern. The idea is
to maximize the income from a given wellstream. The type of separator chosen, the operating conditions, and the product mix (gas versus oil), all are
subject to an economic analysis. In addition, the product sales specifications
must be considered. For example. it is usually desirable to produce more liquid because it sells at a higher price in most cases; however, doing so may
strip the gas of its intermediate components to an extent that it may not meet
pipeline specifications for the energy (or Btu) content per unit volume.
Controlling the Operating Conditions
The two parameters that can be controlled are the pressure and temperature. For pressure, back-pressure valves are used. Limitations in separator
operating pressure are imposed. by its obvious relationship to the wellhead
pressure and the transmission line pressure. The wellhead pressure, in turn,
relates to the flowing characteristics of the well, while the transmission line
pressure requirements are usually fixed by its design. One of the goals, ~
sides vapor· liquid separation considerations, is to minimize gas compression
expenses.
Temperature control is usually available to a certain extent. The wellstream flowing temperature is generally higher than the usual separator operating temperatures, and the wellstream therefore, has to be cooled to the
desired temperature. The most widely used cooling method is the simultaneous pressure and temperature reduction by expansion of the wellstream
through a choke (Joule-Thomson effect), although other cooling methods
such as heat exchangers, cooling towers, and refrigeration, are also used. In
the final analysis, it is really the economics that determines whether the
wellstream should be cooled, the extent to which it should be cooled, and
the cooling method applicable.
Separator Design
The design aspects encountered by a petroleum engineer only involve
choosing the correct separator size for a given field installation. Separator
sizing is essentially quoted in terms of the gas capacity, and the liquid capacity of the separator. Other parameters, such as pressure drop through the
separator, are specified for a given design by the manufacturer and are beyond the scope of the present discussion.
•
Ga., and Liquid Separation
Cal Production Engineering
102
103
where A - cross-sectional area of the separator, f~
D _ internal diameter of the \'~ , ft
Separator Design Using Basic Separation Principles
Cal Capacity
The Souders-Brown relationship (Equation 4-6) has been traditionally
used for calculating the gas capacity of gas-liquid separators:
where vll
'"
Note that the gas velocity v. is based upon total separator area , and it is
therefore more appropriate to refer to it as the superficial gas velocity. The
gas capacity at standard conditions (14.7 psia and 60°F) , qg,." gener~lly reported in units of MMscfd (million standard cubic feet per day), is thus
given by:
allowable gas velocity at the operating conditions, fllsee
PI - liquid density at the operating conditions. Ibm/ft'
PI - gas density at the operating conditions. Ibm/ftl
<lgsc ""
K - separation coefficient
The separation coefficient, K, is an empirical constant given as follows
(Craft et a1., 1962; Sivalls, 1977):
Separator type
Range of K
Vertical
0.06 to 0.35
Horizontal
0.40 to 0.50
Spherical·
Most commonly used
K value
0.117 without mist extractor
0.167 with a mist extractor
0.382 with a mist extractor
such as bubble cap or trayed towers for dehydration and desulfurization
units, and for sizing mist eliminators. The K values given by Sivalls (1977)
for these are as follows:
K - 0.35
K "" 0.16 for 24 in. spacing.
K ,. 0.18 for 24 in. spacing.
q, - Av, - (./4)(D')K ((PI - pJ/P.I"
Equation 4-9 or 4-10 can be used to calculate the separator diameter required to handle a given gas rate, or to calculate the gas rate that a separator
of a given size can handle. The area of the mist extractor required, Am. can
be obtained as follows:
(4-11)
where v", is the gas velocity through the mist extractor, determined using
Equation 4-6 with K _ 0.35 for mist extractor (wire mesh type).
Liquid Capacity
The liquid capacity of a separator depends upon the volume of the separator available to the liquid, and the retention time of the liquid within the
separator (Sivalls, 1977):
W - 1440V LIt
Using Equation 4-6, the gas capacity at operating conditions, CIg, in
ftl/sec is given by:
(4-9)
(4-12)
where W - liquid capacity, bbl/day
V L - liquid settling volume. bbl
t _ retention time, min (1440 is the conversion factor to convert
bbllday into bbl/min)
The liquid settling volume, V L , can be calculated as follows:
• The gas capacity of spherical separators ill based upon the capacity of the mist extractor.
(4-10)
where <u:s<- - gas capacity at standard conditions, MMscfd
p ,. operating pressure, psia
T ... operating temperature. OF
Z _ gas compressibility factor al the operating conditions
0.35 with a mist extTaetoT
Besides calculating the diameter of the separator required for a given gas
capacity, the Souders-Brown relationship can also be used for other designs
Wire mesh mist eliminators
Bubble cap trayed columns
Valve tray columns
2.40D'Kp(PI- pJ'.'
Z(T + 460)p~S
VL
-
0.1399D2h for vertical separators
•
""
VL
Cas arid Liquid Separation
Cal Production Engineering
-
O.1399i)2(U2) for horizontal si.ngle-tube separators
VI - O.1399IYL for horizontal double-tube separators
VI. - O.04660l(D/2)O,S for spherical separatorswhere h - height of liquid column above the bottom of the liquid out1et in
the vertical separator, ft
L - separator length (height), ft
For good separation, a sufficient retention time, t. must be provided.
From field experience. the following liquid retention times ha ....e been suggested by Sival1s (1977):
Oil-gas separation
High pressure oil-water-gas separation
Low pressure oil-water-gas separation
105
6 ft and standard horizontal separators of diameter less than 26 in. are available and have been used successfully.
High-pressure separators are generally used for high-pressure, high gasliquid ratio (gas and gas condensate) wells. In this case, the gas capacity of
the separator is usually the limiting factor. Low-pressure separators, used
generally for low gas-liquid ratio at low pressures, are subject to the opposite
constraint-they require a high liquid capacity. The separator chosen must
satisfy both the gas as well as liquid capacities. Also, the liquid discharge (or
dump) valve should be designed for the pressure drop available and the liquid flow rate (Sivalls. 1977).
Note that as the gas-liquid ratio (C LR) increases, the retention time t decreases. The volume of the separator occupied by gas, V c, is given by:
1 min.
2 to 5 min.
5 to 10 min. at > lOO°F
Vc - V - VI.. - V - Wt
10 to 15
15 to 20
20 to 25
25 to 30
because VI.. - Wt by Equation 4-12.
min.
min.
min.
min.
at
at
at
at
goOF
BOoF
70°F
60°F
where V - total separator volume
vc
is also given by:
Vc =
cut -
W,CLR·t
Some of the basic factors that must be considered in designing separators
are (Lockhart et aI., 1986):
1. The length to diameter ratio, LID, for a horizontal or vertical separator shou1d be kept between 3 and 8, due to considerations of fabrication costs, foundation costs, etc.
2. For a vertical separator, the vapor-liquid interface (at which the feed
enters) shou1d be at least 2 ft from the bottom and 4 ft from the top of
the vessel. This implies a minimum vertical separator height Qength)
016 ft.
3. For a horizontal separator, the feed enters just above the vapor-liquid
interface that may be off-centered to adjust for a greater gas (or liquid)
capacity as needed. The vapor-liquid interface, however, must be kept
at least 10 in. from the bottom and 16 in. from the top of the vessel.
This implies a minimum horizontal separator diameter of 26 in.
In practice, novel design techniques violate these rules of thumb by providing additional features. Therefore, standard vertical separators less than
• Spherical separators are generally operated at half-full of liquid conditions; the relationship
mentioned assumes this cue. Also, the \'olume is increased by a factor of (0,2)0$ because
spherical separators have greatet rurge capacity due to their Ulape.
•
Therefore:
W,CLR·t,. V - Wt
On rearranging:
V
t
~ cW~(=Go-'LR~+~I)
Thus, for a fixed separator volume V and liquid capacity W, as CLR increases, retention time t decreases.
E:ram,lJe 4-1. A separator, to be operated at 1,000 psi a, is required to handle a wellstream with gas flow rate 7 MMscfd at a GLR - 40 bbllMMscf.
Determine the separator size required, for: (1) a vertical separator, (2) a horizontal single-tube separator, and (3) spherical separator. Assume a liquid
(oil + water) density of 52 Ibm/ft3, ideal gas with gravity ., 0.80, an operating temperature equal to 110° F', a retention time t - 3 min., and 112 full of
liquid conditions.
106
Ca, Production Engineering
Cas and Liquid Separation
Solution
D - [0.466065/0.35?' - 1.15 ft
Cas density, P, - pM/ZRT - (lOOO)(2B.97)(0.8)/(I)(JO.73)(570) _ 3.789
IbmlCtl
D' _ q,.Z(T + 460)p1'
PJ"
~
(7)(1)(570)(3.789''')
K(2.40)(IOOO)(52 - 3.789)"
- 0.466065 K
For a retention time t of 3 min., the liquid settling volume required for each
separator type is (Equation 4-12):
v, -
WtlI440 - (40)(7)(3)/1440 ~ 0.583 bbl
1. For a vertical separator with mist extractor, K - 0.167. Therefore, the
diameter of the vertical separator required is:
D - [0.466065/0. 167? ,
The liquid capacity,
The liquid capacity. VL
-
O.0466IY(D/2)O!l - 0.583
Therefore, D .. [(2'>~)(0.583)10.0466]1
pacity requirements.
From Equation 4- 10:
2.40Kp(p,
107
VL.t<
~ 1.67 ft (~
3_.5 ..
2.27 ft based upon liquid ca-
So, a spherical separator of diameter 2.27 £t ( .. 27 in.) is required.
Sepa rator Design Using Actual Separator Performance Charts
The Souders-Brown relationship provides only an approximate approach.
A better design can usually be made using actual manufacturers' field test
data that account for the dependence of gas capacity on the separator height
(for vertical) or length (for horizontal). Field experience shows this dependence that is not accounted for by the Souders-Brown equation. Figures 4-7
through 4-14 show the gas capacity charts for various separator types as a
function of their si~ and operating pressures. For horizontal separators. a
20 in.)
O.1399IJ2h '"' 0.583
•
Therefore. h - 0.583/[(0.1399)(1.67 2)] = 1.49 ft. Thus, the minimum
separator length of 6 Ct should be used. The LID ratio .. 6/1.67 .. 3.6
So, a vertical separator of size 20 in. x 6 ft is required.
2. For a horizontal separator with mist extractor, K .. 0.382. Therefore.
the diameter of the horiwntal separator required is:
0 .. [0.466065/0.382]03 .. 1.10 ft ( .. 13.20 in.). Thus, the minimum separator diameter of 26 in. ( ,., 2.17 (t) should be used.
The liquid capacity, VL .. 0.1399!)2(Ll2) .. 0.583
The,efore, L - (2)(0.583)/[(0.1399)(2.17~1 _ 1.77 ft. The LID ,,_
tio .. 1.77/2.17 - 0.816, which does not satisfy design criteria. For a
minimum LID ratio .. 3, separator length required .. 3 X 2.17 .. 6.5
ft.
So, a horizontal separator of size 26 in. x 6.5 ft is required.
3. For a spherical separator with mist extractor, K .. 0.35. Therefore. the
diameter of the spherical separator to handle the required gas capacity
is:
Figure 4-7 . Gas capacity of vertical low-pressure separators. (After Sivalls,
19n; courtesy of C. R. Sivalls and the University 01 Oklahoma.)
lOS
Ga, and Liquid Separation
G/U Production Engineering
109
..•
•,
•
•
•
,
",
"
~
..,•
,
•
-~.,~
•
~:
.,
•
•
,
",
Figure 4-8. Gas capacity of vertical high-pressure separators. (After Sivans,
19n; courtesy of C. A. Sivalls and the University 01 Oklahoma.)
correction has to be made for the extent of liquid (one-quarter fuji, onethird full, or one-halI full) in the liquid section as shown in Figure; 4-10 to
4-12.
The actual liquid settling volume, VL • for standard separators can be determined from their specifications given in Tables 4-1-4-11. Figures 4-15
and 4-16 are the sizing charts for the liquid capacity of horizontal singletube separators, based upon a liquid retention time of I min. Corrections for
retention times other than 1 min . are linear. and are shown in these charts.
Such charts are useful because they take into account the worlcing pressure.
Example 4·2. Repeat Example 4-1, using actual manufacturers' field test
data, and assuming II.. full of liquid conditions.
~
1-~'
~
,•
••
•"
V
• I•
·I
.,~~
•
• J
.,."
,
V
"
_.... -............. ....
,•
,
,.
1C1O
,.,..,
_Il00100
$00 .. _ _ " ... _
lOCI
,/100
....
,
WI
-
,
"
,•
Figure 4·9. Gas capacity 01 vertical high:pre~sure separators. (After Sivalls,
19n; courtesy 01 C. R. Sivalls and the UncverSlty 01 Oklahoma.)
Solution
1. From Figure 4·8, a JO·in. x 5-ft vertical separator is required. From
Table 4.4, VI... _ 1.76 bbl, which is greater than the required VI... of
0.583 bbl. Hence, use a 30 in. x 5 £t high. pressure vertical separator.
2. From Figure 4. 11, a 12 in. x 10 ft horizontal separator is required,
assuming l J4 full liqUid conditions.
Liquid capacity from Figure 4·15 is (380)(0.33) = 125.4 bblJday,
wh~reas (7)(40) .. 280 bblJday liquid capacity is required.
Choosing a size of 24 in. x 5 £t from Figure 4-15, the liquid capacity is
(720)(0.33) .. 237.6 bbl/day, which is still insufficient.
(Iext continued all page 114)
•
110
Gas Production Engineering
,•
••
..
:;--I VlA:""
.
-•..•
m
•,•
..
,•
:;::"iI•
•
,•
.' . .
Figure 4-10 . Gas
capacity of horizontal
low-press ure
separators (After
Sivalls, 1977; cour·
tesy of C. R. Sivalls
•
,
,
••,
•
•
•
Oklahoma.)
.
•
•
•
••
•
•
...
••
•
II ....
:"'-""1
lil ...
"1 ...
' IjAiI
ott'. ~t
"
"
C",
• . • •1iI
,
,"
.~
'j ,-
• 1
.
•
,
,
••
I
I
,
" "
'"
,
... ~
,,
XI U 1IO
---,.""-•
H
J
••
•
I •
Fig u re 4-12. Gas
capacity of horizon-
tal high-pressure
separators. (After
Sivalls, 1977; courtesy of C. R. Sivatts
and the University of
and the University of
Oklahoma.)
i
,I
ill
~.
J
;::; :,i"!
,~: ;,
•
.
/;
40 10 .. "'....,'00'''',.
"
.
t'o
I
,
Sivalls, 1977; courtesy of C. R. SivaJls
and the University of
Oklahoma.)
low-pressure separators. (After Sivalls,
1977; courtesy of C.
R. Sivalls and the
University of Okla-
Ill:
•
•
,
i~
~
>7
;~
%
~'-
~
IfAII
:.: ~P'
~
/,
,
---.... _-
"
~
,
homa.)
•
•
•
i
I
J
,
;;;;r::::
"
,
~
;
I
• J!
•
":: .... ' / I
capacity of spherical
Figure 4-11 . Gas
capaCity of horizontal high-pressure
"
;.;
Figure 4-13. Gas
separators. (After
11l
Ga.s alld Liquid Separation
.
II,
, ,
.•
•,
•
•
•
•
,
,
•
•
.
,
p ---
"•
•,
.,
••
,
~~
,,~
•
•i
•
•
,'1---,•
•
"
,
..
•
/'
,
•
,
" • •• •
---.-
10 . . . . . . . . ,go
,
'"
'IO 100
:roo
IJ
112
113
Ga! and Liquid Separation
Cos Productwl'I Engineering
,•
•
••
•
•
•
•
--'
Figure 4·14. Gas
capacity of spherical
high-pressure separators. (After Sivalis,
19n; courtesy of C.
R. Sivails and the
University of Oklahoma.)
»
;j;
i:
1-.I
,
•
,
" i
•
• 'j
•
•, I
,•
,
high-pressure separators.
(After
1"
.'
,~
,
Figure 4-16. liquid capacity of horizontal single-tube
•
,
.~
.~
,
!
I
Sivalis, 1977; courtesy of C. A. Sivans
and the University
of Oklahoma.)
i
~f~ !
</ ,
,,~
j
,
,
I
,
,
,
•
'j
,
-
,L-f;-H.-;!;;--'!;--±.k-~----,h-b-h-!W
*"'
,
I.
100 . . _
"""---
.... _ _ ' .... 'OIII
uid capacity of hor-
;,
izontal single-tube
high-pressure separators
(After
11 ....
,'0
•
--. " ,,'.
>.
Figure 4-15. liq-
Sival1s, 1977; courtesy of C. A. Sivalts
and Ihe University
of Oklahoma.)
"""
.
--,._-Table 4-1
Specifications 01 Standard Vertical Low-pressure Separators"
• roo>.
J
u
.... T,'-
,_wi"
•
~,
.>.....
"
.,.
• >,
'
.......
......
',If.!.
~I.l
:::1
::q
---
I-I
Working
Pressure,
p.'
24'
x 5'
24" X i1l2'
30" x 10'
36" x S'
36" X 7112'
36" x 10'
'25
'25
'25
'25
'25
48" x 10'
4S" xiS'
60" x 10'
60" )( IS'
60" x 20'
• After S" .11•• urn.
12'
'25
'25
'25
'25
'25
Inlet and
GIS Outlet
Conn .
011
Outlet
2" Thd
2" Thd
3" Thd
4" Thd
4" Thd
4" Thd
2" Thd
2" Thd
6" F1g
6" F1g
6" F1g
6" F1g
6" F1g
Conn.
3" Thd
2" Thd
3" Thd
4' Thd
4" Thd
4" Thd
4" Thd
4" Thd
4" Thd
Standard Valves
011 or
011 and WIIter
,>
'"'"
'"
'"'"
'"
,"
,"
2"
3"
GIS
Shipping
Weight,
I.
"'"
2"
,>
IlSO
2"
2"
2000
2000
'"
,"'"
,"
2350
2"
3"
3"
2700
3400
,,00
'200
6400
7600
Table 4· 3
specifications of Standard Vertical High Pressure Separators '
Table 4"2
Sen llng Volumes of Standard Vertical Low"pressure Separators "
(125 psi WP)
Size,
Dia x Ht
Sen Ung Volume, bbl
Oil-Ges Septlrlltors
OU-Gas-Water Septlralors "'
Z4"~5'
0.65
24-x7 1f1
30" x 10'
110
l.01
2.116
36" "
un
1.82
3.75
;j'
36" X ,112'
36" x 10'
48" x 10'
48- x 15'
60- x 10'
60- xiS'
00" x 20
•
115
Gas ond Liquid Seporation
Qu Production Engineering
114
'63
".
2.4)
304
5.6i
5.48
10.06
14.44
16.OB
12,93
18.64
7.&6
9.23
12.65
15.51
Mt~,
Si<ilh. 1977
,- Thtal ... ttling 'vlume b usually split ~"cn bet" ... n oil and
".tt.
(text continued from page 1(9)
ChOOSing the next available size of 20 in. x 10 ft from Figure 4-15, the
liquid capacity is (980)(0,33) - 323.4 bbllday, which is sufficient. The
same result could alternatively be obtained from Table 4-8, where the
smallest horizontal separator size with a VI. greater than 0.583 is 20
in. x 10 ft for a 1/4 full of liquid condition.
Hence, use a 20 in. x 10 ft high-pressure horizontal separator.
3, From Figure 4-14, a 30 in, diameter spherical separator is required.
Liquid settling volume, VL • from Table 4-11 is only 0.30 bbl, whereas
0.583 bbl is required. From Table 4-11, the smallest spherical separator with a VI. greater than 0.583 is of diameter 42 in.
Hence, use a 42 in. diameter high-pressure spherical separator.
Working
Pressure,
psi"
Inlet and
Gas Outlet
Connection
Standard
Liquid
Vel ve
16- x 5
16- x 7111'
16- x 10'
1000
2- Thd
2' Thd
~. Thd
20- x 5'
2O-x7 112'
20- x 10'
24"x5'
24- x 71/z'
24- x 10'
3O"xS'
1000
3 F1,
3- FIg
3- FIg
3- FIg
I'
I'
I'
I'
I'
I'
I'
I'
I'
Siza,
Dis x HI
30')(
1000
3- FIg
3- FIg
1000
711~'
30' x 10'
36' x i112'
36' x 10
36" x 15'
42- x 7112'
42- x 10'
42" x IS'
4S- X i112'
4S" x 10'
48" xiS'
54' X 71/2'
54" x 10'
54-x 15'
00- x 7112'
00- x 10'
50" xiS'
00" x 20'
4' FIg
4 - JollZ
4" FIg
1000
4" FIg
4" FIg
4" FIg
1000
1000
1000
1000
66"
6'
6"
6"
6"
FIg
FlI;(
FIg
FIg
FIg
FIg
6" FIg
6- FIg
6" FIg
6" FIg
6" FlI;(
6' FIg
6' ~1g
I'
I'
I'
I'
I'
I'
""
"
"
""
2'
2'
2'
""
"
2'
Shipping
Weight,
I.
1.100
1.200
1,500
1.1lOO
1.000
',200
2,500
2.850
3.300
3,200
3.650
4,200
5.400
6.400
8.700
i,700
9.100
12.000
10,400
12.400
16,400
12.300
14,900
20.400
li.5OO
00,500
26,500
32,500
• After SI,.lb. 19TI.
., O~r st_nda,d "orl::ing pn'\.>U .... i"IU_ble a", 230. 500. 600. lroo. 1440. 1.500. and 2000 psi
enable accurate metering of the proouced hydrocarbons,· constitutes the
last separation stage. Therefore, as shown in Figure 4- 17, a two-stage se~a­
ration includes one separator and one stock tank, a three stage separation
means two separators and one stock·tank, and so on.
Stage Separation
\Vhen two or more equilibrium separation stages are used in series, the
process is termed ··stage separation." The storage tank, also called stock tank
because it is generally kept at standard conditions (14.7 psia and 6(PF) to
• This III not always true. The prftSUre csn be controlled, but the storage tank temperaturf' is
subject largel)' to the preo.ailing atmospheric temperaturf'. and It is too expe~,'e to hn-t or
0001 the contents of the tank to OO"F. Modern digital metering devices can easll)' correct for
tempera ture or pres!iure.
•
Cos ond Liquid Sep6rotio n
Gas Production Engineering
116
•. •.. -
- .... "
...
,...
........,
-
--
1'0("
.~
TWO
STAGE
S'P"RATION
'='
We"
-00.,
.......
..",.-..
differential liberation is approximated quite closely by using a few separation stages (two, three, or four). The latter process, where the pressure is
reduced in very large steps. is termed "flash liberation." Flash vaporization
also differs from differential vaporization in another respect: in differential
vaporization, the \'apor is removed as it is formed , but in flash vaporization,
the liquid and vapor are kept in intimate contact until equilibrium is
achieved . For this reason, flash vaporization is also termed "equilibrium vaporization" or '-nash equilibrium vaporization," whereas differential vaporization is called "diHerentialliberation."
Table 4·4
Settling Volumes of Standard Vertical High-pressure Separators'
(230 to 2,000 psi wP··)
THREE
STAGE
SEPARATION
Size,
Die x HI
....
,.
Uoac _ .....
."
~
6
-,,-- ._.
l- •..
~.-
n_.,
'"
=
fOUR- STAGE
SU'ARATIOH
~
ALTERNATIVE
ARRAM""!NT
"on
_r_""
."
FOR THRfE-STAGE
S' ..... IU.TlOM
~
Figure 4-17. Schematic diagrams for stage separation.
Readers who have a background in phase behavior will immediately recthat liquid recovery is enhanced on using a greater number of equihbnum stages for separation. This same principle is employed in designing
columns 'With mu1tiple equilibrium trays for separation purposes (Chapter
5). The ideal separation process is one in which the pressure is reduced infinitesimally at each stage. requiring an infinite number of stages. Such a process, termed "differentiailiberation," would maximize the IJquid recovery
and yield a more stable stock tank liquid. In practice, this is not feasibl e and
~gn~
117
16"x5'
IS" x 7 1/2'
IS" x 10 '
20" x S'
20' x 7 1/!'
20' x 10'
24 'x5'
24' X 71/8'
24 ' x 10 '
30' x 5'
30" x 71/2'
30" x 10 '
36" x 71/1'
36" x 10'
36' xiS'
42" x il!l'
42" x 10 '
42 ' xiS'
48" x 71/2'
48'x 10'
48" x 15 '
54' x illt'
54' x 10 '
54" x IS '
50' )( 711t'
50" x 10'
60" x 15'
60" x 20'
•
••
,
"
Senling Volume, bbl t
Oil-Gel-Water Separalors tl
Oil-Ges Separators
0.27
004\
0.51
O.H
0.65
0.82
0.66
0.97
1.21
1.13
1.64
2.02
2.47
3.02
4.13
3.53
4.29
5.80
4.81
5.80
7,79
633
;.60
10.12
8.08
9.63
12,73
15.31
0.44
0.72
0 ....
0.71
1.15
1.48
1.05
1.68
2,15
l.7S
2.78
3.54
4.13
52'
i.45
5.SO
i.32
10.36
7.79
9.i8
13.76
10,12
12.65
17.70
12.73
15.83
22.03
27.20
Arm Si ••IIs, 1m
St.nd..d ... orking p""""'_ ".il.bI" • .., 230. 1iOO. IIXlO. 1200. 1440. 15OO •• nd 2000 psi.
8 ....,.;1 on lIXlO psi WP Rp'T~tO"
Tot.l ~tlinl ""lume b u.u.Uy ,plit ,....,0 "","wCCT! oil and .... t~r,
,
118
119
Cru and Liquid Separation
Gas Prodl.K'tion Engineering
Table 4-6
Settling Volumes of Standard Horizontal Low-pressure Separators(125 psi WP)
SetHing Volume, bbI
Size,
••
"
:>
~
-
1!
•c
~
•
~
~
~~
o=~
c
•
•e.
. . . . . . . . ..,M"':...
...
........................
lh Fun
,,, Futl
'/4 Full
24' x 5'
1.55
24' x 71lt'
24' x 10 '
'.22
'.89
0.89
12S
I.Si
0.59
0.86
I 12
0 ..
1.36
1.77
2.59
3.79
4.71
6.85
7.47
Ole )( Length
31)")(5'
2.48
1.43
30" X 11/1'
354
4.59
6.71
9.76
'Q.I
3{)'x 10 '
. .. . . . .. .. . .
........................... ..,MM!,.
is
36' x 10'
36" x iS'
48" x 10'
12.24
17.72
19.50
28.06
36.63
48" x IS"
60" x 10'
6O'x IS'
60' x 20'
2.66
3.88
5.66
7.07
10.26
1l2-l
16.23
21.21
10.82
14.16
• After S;,-.Us, \977
Two-stage separation is desirable for wellstreams with low gas-oil ratios
such as low-API gravity oils, and low flowing pressures. Three-stage separation is most applicable to wellstreams with intermediate to high gas-oil ratios (intermediate-API gravity oils), and intermediate flowing pI"e$ures.
Four-stage separation is used for high gas-oil ratio (high-API gravity) wellstreams, and high flowing pI"e$ures. Four-stage separation is also used
where high-pressure gas is needed. From an et.'Onomic standpoint, a threestage separation is usually optimum for most oil-field operations. Sivalls
(1977) reports that the actual increase in liquid recovery for three-stage separation over two-stage will vary from 2 to 12 %, depending upon the wellstream composition, and the operating pressures and temperatures. However, additional recover ies as high as 20 to 25 % have been reported for some
., _ c
1:I.!!O
c_-
_ 0
¥
• •
c.
c
c;;
-e8
--------_ ._ ---
ill Ii i:Hl:!Hl Ii ill ::Hl Ii i!Hi
cases.
For the complex mixture of hydrocarbons produced from an oil well , precise stage separation calculations are very difficult and require the use of a
computer. For practical purposes. it is quite satisfactory to use other shortcut methods and correlations that yield acceptable results. The simplest of
these methods assumes an equal pressure ratio between the stages for optimum performance (Campbell, 1984):
r _ (PllpJl
where
D
(4-13)
r _ pressure ratio
n _ number of stages ( text contilllJed Oil 1)age 123)
•
GaJ and Liquid SqxJr(Jtion
Gas Production Engineering
120
Table 4-7
Specifications of Standard Horizontal High-pressure Separators'
SIu,
OI.:It Ht
12:l!~' :It
1)
Worttlng
Inlet and
Preu.ure,
GIl. Outlet
Connection
....
,
1000
12114 ":It 71/1
12·lI,- )( 10'
16" x 5
16 " x 7 llt"
16"
:It
10
2O"xS'
20-
x
1000
1000
2"
2·
2"
3-
Thd
Thd
Thd
F1g
3" F1g
7112'
20" x 10
24" x 5"
24' x j llt'
24"xl0
24"x 15
30" x 5'
30" x ill~'
30" x 10 '
30" x 15
36" x 71/2'
36" x 10'
36" xiS'
36" x 2(} '
42' x illt'
42"x 10'
42" xiS'
42" x 20 '
1000
48"x71I2'
1000
48' x 10'
4S" xiS'
48" x 20'
54' x 71.12'
54"x 10'
54" x 15
54" " 2(}'
50" x 71/2'
00' x 10'
60" x IS'
50" x 20'
2- Thd
2' Thd
Z" Thd
1000
1000
1000
1000
1000
3" F1g
... F1g
4' F1g
4" Fig
4" Fig
.. " F1g
.. " F1g
.. " Fig
.. " F1g
6" F1g
6" F1g
6" Fig
6" F1g
6" F1g
6" Fig
6" Fig
6" Fig
8" Fig
S" Fig
S" Fig
S" Fig
S' FIg
S" FIg
S' F1g
S' f1g
S' J.1g
S' .1g
S" FIg
S" F1g
Standard
Liquid
Val ve
I'
I'
I'
I.
I'
I'
I'
I'
I'
I'
I'
I'
I'
I'
I'
I'
,.
,.
,.
2'
2'
2'
2'
,.,.
,.
,.,.
,.,.
,.
2'
,.,.
,.
2'
2'
Table 4-8
Settling Volumes of Standard Horizontal High-pressure Separators'
(230 to 2,000 psi WP**)
Shlppll"lg
Weight,
I.
1.100
1.200
1.300
1.400
1.i50
2,100
1.800
2.300
2.900
2,200
3.000
3.8110
5,400
3.200
4.3110
5.500
7,800
6,100
7.500
10,200
12.000
8.200
9.900
13.400
16.900
10.900
12.700
17.500
22,100
13,400
16.000
21.200
26.400
16.700
19.900
26,400
32,900
, AIter S"IIIs. 1977.
• • Other st.ndard ""<>ficin!! praru<a .,·.iI.hIt- Ire m. 500. 600. 1200. 1440. 1500 . • nd 2000 psi
121
Size
Ois :lt Len
12lf," x 5'
12¥.- :It 7
1231, - x 10'
L,Iz'
16" :It 5
16-:It 7 l l!'
16" x 10
2O" x 5'
20" x 7 112'
20" x 10'
24° x 5
24")( 71!2'
24" x 10'
24" xiS'
30" x 5
3O"x71!2'
30" x 10'
30" x 15'
36" x 7)!2'
36" x 10'
36" x i S'
36" x 20'
42" x 71It'
42" x 10'
42" x IS'
42"x20'
4S" x 71/t'
48" x 10 '
48" x IS
48")( 20'
54" X 7112'
54 " x 10'
54'x 15'
54"x20'
60" x 7112'
60' x 10'
00' x 15'
00"x2O'
Settling Volume, bbl t
lh Full
0.38
055
0,72
0.61
088
113 Full
11. Full
0.22
0.32
0.42
0. 15
0.21
0.28
0.24
0.34
0.3.5
0.50
0.66
0.55
0.79
"'
0.98
I.'"
1811
0.44
IOJ
145
,..
0.83
'.63
1.52
2.21
1.39
1.96
2.52
3.65
2.8i
3.68
5.30
6.92
3."
5.119
7.30
9.51
5.32
6.n
9.67
12.57
6.87
8.7 1
12,40
16.08
860
10.86
15.38
19.90
lIB
3.S1
2.43
3.40
4.3i
6.30
4.99
6.38
9. Ii
11.96
6.93
8.83
12.62
16.4 1
9.28
II 77
16.74
21 il
]2.02
15.17
12.49
27.S1
15.05
18.93
26.68
34.44
• After Sh·.IIs, 1977.
•• StAn<brd worl<inll; pn:ssUmI .".iI.bk
, Ba....J on 1000 p5i WI' ~r.tor
a~
230. 500.600. 1000.
I~.
14-40. 15OO.nd 2000 pIoi
0.38
0.54
O.iO
0.55
0.i8
0.01
1.47
0.91
1.29
1.67
2.42
1.90
2.45
3.54
4.63
2.6 1
3.35
4.83
6.32
3.51
4.49
6.43
'.38
4.49
5.73
S.2O
10.68
5.66
7.17
10.21
13.24
•
Gal and Liquid Separation
12l!
(text continued from page 119)
Table 4·9
Specifications of Standard Spherical Separators·
Diamtlt.r
Wor1ling
Inlet and
Standard
Shipping
P,esaure,
Gas Outlet
Connection
liquid
Weight,
I.
p.'
,.
Valve
".".
'"
".
".
4" Thd
4' Thd
4" Thd
!!SO
, >1,
3" F1g
2"
2
6'
2' Flg
2" f1g
"'1/:
2'
3' F1g
,.,.
,.
54-
"'.
,..
24-
IIX)!)' •
30·
42'
]
1000
1300
1700
1100
14lX.
3400
.
]300
].
1400
]BOO
].
". F1g
".
00·
,.3·
4 - F1g
6' F1g
• Aher Sin]"_ 1!)7i
,- Othl:r ,tand.rd "",k"'l!: prrsm ..... \ail.hl~ K.... SOO.IlOO. 1200. 1440.
2O(X).
2800
3700
,100
Kilt! 3000 p<i.
Table 4·10
Settling Volumes of Standard
Spherical Low-pressure Separators'
(125 psi WP)
Size,
Settling Volume,
00
001
PI - pressure at the first (or high.stage) separator
p. _ pressure at the stock tank
Thus, P2 .. p,r"-l, P3 - P1 r"-2, and in general, the pressure p, for separator
stage i is given by:
100
(4-14)
Pi '" p,r"-i-tl
Note that Equations 4·13 and 4·14 bear no relationship with the magnitude
of separation (Le, the Iiquid,vapor ratio).
Whinery and Campbell (1958) studied three-stage separation for ~"eral
different t)'pes of wellstreams. Figure 4·18 from their work shows the rela·
tionship between the pressure at the second stage and stock· tank liquid recover)'. From an empirical analysis of these results, Whinery and Campbell
(1958) derived simple relationships to calculate the optimum pressure in the
second stage for a three·stage separation. They found that two cases can be
specified:
1. For streams with specific gravity> 1.0 (air .. l.0):
p, _ ApI""" + (A - 0.057)10.0233
••
•. ~ ,
O.ii
1.02
•
.
•
•
,
•
Table 4·11
Settling Volumes of Standard
Spherical High-pressure Separators'
(230 to 3,000 psi WP)"
Size,
Settling Volume,
00
••P
123
~,"
I1i ') ~.,
,.
- ~~
~
"-
..
"'
•
"--...
•
•
~,' ,~"
0.'"
•
• Arkr SinU•. 1977.
,- Standard ",o.-kinJj: I',,*UmI .v.H.bl~ Ire 230 • .500.000.1000, 1200, lHO. 1.500. 2000. and 3000 psl
• Sued on 1000 pM WI' ..."..rator
<C',
g
•
221)
•
•••• ••
0.15
0.30
054
133
J7,
(4-15)
,
DIU"'"
..
•
,UGE
~_
~
'---
~USl""l."'"
...
SECOND Sl.G[ '''USUIII[, 'SI.
ow
-
Figure 4.18. Relationship between second·stage pressure (psia) and stock·tank
recovery (gaI/MMscf). (After Whinery and Campbell, 1958; courtesy of SPE of
A1ME.)
Gos and Liquid Separation
Co! Production Engineering
2. For streams with specific gravity < 1.0 (air .. 1.0):
p, - ApI '" + (A + 0.028)10.012
Whiner)' and Campbell found that composition could be expressed in
terms of the specific gravity of the feed and the mole% of C I + C2 + Ca
components in it, asshown in Figure 4-19. Example 4-3 illustrates the calculation procedure.
Example 4·3. For a wellstream haVing a composition shown as follows,
find the optimum second-stage pressure for a three-stage separation, if
PI ,., 800 psia. Use the \Vhinery-CampbeU method, and compare the result
with the equal pressure ratio assumption.
,
••
~
z
2
z
~
•
•
Tn
,
I //
I
.
I
I
-•
I
"z '
•
•"z
8 '
C~
C,
C,
C~
C,
r:
16.043
30.070
44.09;
58.124
0.35
0.25
0.15
0.10
0.08
0.04
0.03
C,
c,.
Mol. wt., M,
)'1
(C,)
;2.151
86.178
128.259
YiM , ... 38.626
Therefore. the specific gravity with respect to air
Mole% C I + C 2 + C 3
From Figure 4.19, A
:z
-
38.626128.9; - 1. 33
0.35 + 0.25 + 0.15 - 0.;5
0.43
Using Equation 4-15 for wellstream gravity> 1.
g
? 7
s
p, _ (0.43)(800""") + (0 .43 - 0.057)/0.0233 - 58.18 p'ia.
019
../ It ,4
I ~~ ItJ. l "
III / ,/
The EqtMd Pr~re Ratio Cmw. Using Equation 4·13. the pressure ratio
with n - 3 - 1 = 2 is r - (800;)4.7)12 = 7.3;7
From Equation 4·14 , P2 ,. (14 .7)(7.3772 " 2. I) - 108.44 psia.
:1:1
This example illustrates that the equal pressure ratio assumption is far
from precise. Even the Whinery-Campbell method is only an approximation. Wherever possible, flash calculations using equations of state must be
carried out for determining the amounts of vapor and liquid that will be
reco\'ered, and the composition of these vapor and liquid streams from the
separators.
I
.,
Mol. fr. ,
MOL" C I + Cz + C)
rr I
I", r. .l 1/ I
J~
•
I'~ "'Til I
,
Solution
Comp o
where PI, P2 ... pre!mJl"eS in the first and second stages, respectively (the
third stage is assumed to be the stock tank at standard conditions of 14 ; psia and 6(}0 F)
A - a function of the stock tank pres..~ure and the system composition
125
,.
,.,
,.•
PSU[OD -S PECIFiC GRAVITT or rEED, DIMENSIONLESS
Figure 4·19, Relationship between A
and pseudo-specific
gravity 01 leed
(T .. 80°F) . (Aller
Whinery and Campbell, 1958; courtesy
of SPE of AIME .)
Low Temperature Separation
Low-temperature separation (LTX) units are based upon the principle
that lowering the operating temperature of a separator increases the liquid
recovery. Besides recovering more liquid from the gas than a normal. tem-
•
126
Ga! Prodllctian Engilleeririg
Gas and Liquid Separation
127
perature .separator, LTX units have another advantage: they are able to dehydrate the gas. frequently to pipeline specifications.
A low.temperature separation unit comiists of a high-pressure separator.
one or mOre Pressure-reducing chokes·. and heat e:tchange equipment.
When the high-pressure wellstream is expanded by pressure reduction
through a choke. the temperature is also reduced. This irre\'ersible adiabatic
(no e..~change of heat with surroundings) simuJtaneous pressure and temperature reduction process is called the Joule-Thomson Or throttling effect. The
heat content of the g:as remains the ~ame across the choke. hut it.;; temperature and pressure are reduced,
The choke is mounted directly at the inlet of the high-pressure separator,
so that any hydrates formed downstream of the choke fall into the bottom
settling section of the LTX unit. where they are heated and melted by the
heating coils provided. The wellstream enters the separator at a low temper_
ature and pressure. and a better separation results. A rorrelation by the Cas
Proces.soI'\ Suppliers Association (CPSA) to determine the temperature drop
through the choke for a briven pressure drop is shown in Figure 4-20. E:tampie 4-4 illustrates the procedure for using this correlation.
Examl)/e 4-4. AD. 7 gravity gas, at 150°F is expanded through a choke. so
that its pressure i~ reduced by 2,000 psi. What is the temperature drop if the
initial pressure is: (1) 4.000 psia, and (2) 2.500 psia~ (3) What is the final
temperature if the gas is initially at 4.000 psia and 150°F and the pressure is
reduced to 200 psia.
Salution
1. From Figure 4-20, for an initial pressure _ 4,000 psia and a pressure
drop - 2.000 psia, the temperature drop _ 380F.
2. From Figure 4-20, for an initial pressure _ 2,500 psia and a pressure
drop - 2,000 psia, the tempel'ature drop _ 86.SoF.
3. From Figure 4-20, for an initial pressure _ 4,000 psia and a pressure
drop - 4,000 - 200 - 3,800 psia, the temperature drop" 1320F.
~
~
•
§
J,
.!
!,
,
,•••
"
..
,
§
.. ,,,,,
••
•,•
8
. . fIP
,,••
"
· ,•
§.
,#.
l
".
It
i
t
•
0 '
j!
~i~
..
If
~
!
o .. e~
'!
hi -.
Example 4-4 iJlustrates that the cooling process is more effective for gases
at high pressures, where a large pressure drop can be provided to the gas in
an LTX unit. As a rule of thumb, at least a 2,500- to 3.000-psi pressure drop
must be available before an LTX unit can be considered for use. Otherwise,
it may not be economical.
1
-
I
I 6 -5
• •• •• •
v v •,
v•
'i
i' "
il~
"
'I
'I
t,
"
~
!
"
~
0
~
"
I.
~~-!
'...
!(;; oeRli!~51
~l
JS B.
~
!I
~
."
!
!
.·. . --1•
!
i
~'
,'#.
,, •
•
Therefore, the final temperature _ 150 - 132 _ 180F.
• A choke is essentially an orifice plate, with a specified hole slu, fo r controlling the rate of
flow or reducing the pressu~ of the flowstream.
"
. ..
~
•
•
•
•
•
,
128
Ga.! and Liquid Separation
Ga" Productwn Engineering
The lowest temperature at which an LTX unit can be used is governed by
the properties of the material used in its construction. Generally, carbon
steel is used, for which embrittlement occurs below a temperature of
- 20' F. For this reason. LTX units in an oil field are usually operated only
in the temperature Tange of 0 to 20°F.
Gas Cleaning
where
P,.
129
v - terminal velocity of the falling particle, ftJsee
a - acceleration on the particle. ft/.sec!
d.p - particle diameter, ft
Pp - density of the particle, Ibm/ft1
I'g - density, Ibmiftl. and viscosity, Ibmift-sec. respectively, of
the fluid through which the particle is falling
The drag coefficient, Cd. and the exponent n in Equation 4-17 are as follows
(Lapple, 1984),
Cas cleaning is important for pipeline transmission systems in order to reduce operational problems. and to maximize their operating efficiency. It is
even more important in other instances, such as for gas .~torage, and for sales
to consumers. Cas cleaning is also neces'iary to prevent solution/catalyst
contamination in downstream processes on the gas, such as dehydration and
sweetening. Some of the cleanup occurs initially at the wellhead by such
means as drips, filters. and syphons. Another phase of cleanup is carried out
in the gas.liquid separators. Further cleaning is generally required before
the gas arrives at a processing plant, and before any processing is begun. A
clean gas transmission averages about 2 Ibm/ MMscf particulate matter in
the gas.
Cas cleaning involves the removal of two types of materials: (1) gross sol·
ids and liquids, called "pipeline trash," and (2) minute solids (particulate
matter) and liquids (aerosols). Pipeline trash is also referred to as sludge,
and is essentially anything in the flowing stream that is not gas. Pipeline
trash consists generally of liquids such as heavier·end liquid hydrocarbons,
water, chemicals (amines, glycols, methanol) carried o\'er from processing
operations, and solids such as drilling mud, pipeline scale, other dirt picked
up by the gas during production and transport operations, and gas hydrates.
Pipeline trash collects in the sags and low spots in the pipeline, and its removal is absolutely necessary, Particulate matter and aerosols are much
more difficult to remove because of their ultra·small particle size, They are
carried over by the gas as suspended solids/liquids.
Flow reiQme
Nile
Laminar
Intermediate
Turbulent
0.3-10'
10'- 2(1{}')
<0.3
Law
Cd
n
Stokes
Intermediate
Newton
24.0
18.5
1.0
0.6
0
0.44
where the Reynolds number, N R~, for the case of particles suspended in a gas
is defined as being equal to d"vpjI;lpK' The equations derived earlier for cen·
trifugal separation (Equation 4·2) and for gravity settling (Equation 4·5)
can be verified as being applicable to the turbulent flow regime.
The Reynolds number is controlled largely by the particle size, ~, since
other factors vary within a relatively small range for a given application.
Thus, Newton's law would be applicable to larger particles that would
~ a higher Reynolds number. This can be understood in physical terms ..
by visualizing that larger particles fall so rapidly that they create considerable turbulence. For intermediate size particles, some turbulence is gener·
ated, and the intermediate law is used. Smaller particles settle much more
slowly, a laminar flow regime is maintained, and Stokes law is used to calcu·
late the settling rate.
A!; we proceed to smaller particle sizes, smaller than about 3 microns,
Stokes law is no longer valid. The particles are now so small that they slip
between the gas molecules at a rate greater than that predicted by Stokes
law. The Cunningham correction, K." is used to correct the settling velocity,
vStok"", from Stokes law:
General Equation for Particles Suspended in a Gas
(4-18)
The well known general exp~ion for the terminal velocity, v, of a part!·
cle railing through a fluid under the influence of a force that exerts an acceleration a on the particle, is written as:
\. -
4ad n+ l (p
[
P
P
-PJ]
3CdI';p~
n
H2-"1
(4-17)
This is called the Stokes-Cunningham equation. The correction K., is deter·
mined as follows:
(4-19)
130
Gas Production
"~nglnt!e,;rlg
where M - molecular weight of the gas
R - gas constant, 1,546 ft-Ibfl lbmole- °R ( .. 10.732 psia-ft'/lbmole- ' R)
T .. temperature in oR
K.:! .. dimensionless proportionality factor
g. .. conversion factor ( .. 32. 17 Ibm-ftdbf-sec2)
Gas and Liquid Separation
•-. •-.
METHODS
FOR
PARTICLESIZE
For particles smaller than 3 microns, a random motion , known as Brownian mO\t:m~nt , abo bt!g1ru to occur. Its effect is superimpc.l.\ed upon the particle settling velocity. and for particles under 0. 1 micron, Brownian mo,,'ement becomes the dominant phenomenon. Since gas cleaning is never really
pursued to such levels. Brownian motion will not be discussed here.
ANALYSIS
1. The incoming particles bypass the cleaning element and enter the out·
flowing clean gas stream. This is the most common problem.
2. The pressure differential becomes too high, leading to rupture or dislodgement of the cleaning element.
3. The cleaning element may become so impregnated that it interrupts
the flow completely.
Proper maintenance is therefore essential for these devices.
Some common gas cleaning methods, besides the gravity settling and cen·
trifugal methods discussed earlier, are described below.
There are several types of impingement separaton as shown in Figure
4-22. The mist extraction section in an oil and gas separator uses impinge-
_PARTICLE DIAMETER, MICRONS
•
•
.b.~~L.'~i~ ""L.
"'--"""4
E.ECTIOMLIC.IIOSCO"~
4~M~---:.~n>M~
=t
1--..-.'"' . ".-. . .- - -
I - ~~ •• ~ ,,~,.,.,.~ - -
'1i~"u!ITY
.~
f.-....cu, C""NYU
......
•• _
EQUIPMENT
~
. _-- -
- ....
- --f----
IU .. MU
."._l..
u"c~o
.. rUJ.(.t..,,(U,
.. .... -
nOYM
'UI.UTgRS
"~v"l~S
I
~.HCTOItI
I
nTnlN~
CEMU ....... ----.
_
I----<
-t."-,,,,lns
......
_
,
".1l~
. ,~
_~
I
{N ....U.
--- ----
--.,OUIO
'OC~fD
~_N
(fI:
"'C,"'CA. _
u.r~I.nNOC'
-.... . .. _--_.
----- -- --
o"".j TO l'U
CC"HII.C"o,10
OF
GAS'CLEANIN G
••
"'ClIOlcor,_
.".-,~
UIOIIHIO
TYPES
-
"
~ • - It.. -1-...
Cas Cleaning Methods
There are several different techniques for separating liquid and solid particles from gas, such as gravity settling, centrifugal action, impingement.
filtration. scrubbing, and electrostatic precipitation. Figure 4-21 shows the
range of applicability of these methods in terms of the size of the particles
that can be removed. Note: I micron,. 10- 4 cm.
Maintenance requirements are generally proportional to the removal ca·
pability. Thus, methods with greater particle removal capability usually require more elaborate maintenance schedules. In cleaning methods that use a
physical separation device (cleaning element. demister, filter. etc.), once the
cleaning element has accumulated to its capacity, there are three possible
results, all of which are detrimental to the cleaning process (Curry, 1981):
~•. -
ro-
.,•
131
l"CI[M;O
••
, ...'t~1
..... ' ' 'C' '.11O" _
I •• ',"CjU'OU'
I
'.'C'it
_ O (. . . .
r
_
. . . . . . TOIl1
~"C"""CI.~--I
r--<
··~r·
..
---.I
Agure 4-21. Gas cleaning methods and their range of application. (Data from C.
E. Lapple, 1984.)
ment methods of two basic types: wire· mesh pad and vane-type mist extrac·
tors.
A wire-mesh separator consists of a 4- 6 in. thick pad of fine wire (diameter of 0.003-0.011 in.) knitted into a mesh fabric with a high void volume
(97-99%). The pad is mounted in a horizontal position, with the vapor
flowing upwards. Liquid droplets impinge on the wire and collect and c0alesce with other droplets, until their size becomes large enough to drop
downwards through the void spaces. The droplets then cling to the bottom
of the wire-mesh by surface tension forces. Here they coalesce again to a
bigger size, until they become sufficiently large to overcome surface tension
132
Gal Production Engineering
=>
Non..
FlO ..
GO! and Liquid Separation
0..
'~
Ira,q'l
'"
,<I
'"
'"
133
and the force resulting from the upward flow of the gas. A flow velocity of
5-10 ftfsee provides maximum operation efficiency (Curry, 1981 ). A higher
rate would flood the pad and lead to re.entrainment of the liquid, whereas a
lower rate may permit the liquid to circumvent the pad and avoid impingement. A mist extractor should not be used where the gas has a high concentration of solids, since this may block the flow of gas and result in high pressure drops across the pad. For liquid droplets, wire-mesh pads are efficient,
can remove droplets down to 4 microns in size, and have a high handling
capacil}'The vane-type design uses an intricate array of metal plates, called vanes,
with liquid collection pockets. The vane-type mist extractor is mounted such
that the gas stream flows horizontally through the vanes. During this flow, a
change in direction is induced several times, resulting in a centrifugal action
that aids the primary impingement separation mechanism in removing the
finer liquid droplets entrained in the gas. The liquid droplets are forced into
the liquid collection pockets, out of the gas flow path. and drain out by
gravity. The pressure drop across a vane-type mist extractor is very small. it
can handle solids in the flowing gas stream. and can remove droplets down
to about 40 microns in size.
Another development of interest is the fiber mist eliminator. This uses a
packed bed of fibers between two concentric screens. Liquid mist collects on
the fiber surface as a film , which is moved horizontally by the gas, and
downwards by gravity, into the liquid collection area. Fiber mist collectors
offer extremely high collection efficiencies up to 99.98%, and can handle
mists smaller than 3 microns (Brink, 1963).
Botlln
Filters
",
'"
'"
'>I
1/'
Flgu,! 4-22. TypeS,OI impingement separators. (After Perry and Green (eds.),
ChemICal Engm86fs Handbook, 1984; courtesy of Mc-Graw Hill Book Co.)
These have been traditionally used to remove solid particles by using a
filtration medium that allows only the gas to pass through. Bag filters, using
woven fabric or compressed felt fabric as the filtration medium, are widely
used. But these materials break down in the presence of liquids. Synthetic
materials such as glass fiber overcome this disadvantage. Even with these
synthetic materials, liquid separation with filters is always a problem. Liquid particles find their way through the filter pad and coalesce on the downstream side of the pad in the form of a liquid film. The gas passing through
this film leads to the formation of bubbles, which disintegrate and are reentrained in the gas.
A scrubber is defined as any equipment that uses a liquid to aid the removal of particles from a gas. It is similar to a separator, except that a scrubber is designed to separate only small volumes of gas and liquid, and it may
•
134
Gas and Liquid Separation
Ca, Production Engineering
use some fluid such as oil to more effectively remove particles from the gas.
Unlike separators, surge capacity is neither necessary nor provided. A scrubber, although similar to a separator, must never be used for gas-liquid separation in the field, where even a reJatively dry gas well may produce some
liquid surge and lead to severe separation problems. They may, however, be
used as secondary separation devices.
The three types of scrubbers used in gas cleaning operations are: dry
scrubbers, oil-bath scrubbers. and cartridge-type scrubbers. Dry scrubbers
are similar to centrifuges. using centrifugal force to effect the separation of
solids and liquids from gas. Oil-hath scrubbers are extensively used. They
cause solid particulate matter to impinge on a surface constantly flushed
with oil, and cling to it. The circulating oil washes the dirt down into a settling chamber, where the dirt settles down by gravity. Clean oil l~ recirculated. It is important in an oil-bath scrubber to ensure that the oil is clean.
and that the proper le...·el of oil is maintained. A less-than-clean oil or too low
an oil level will reduce cleaning efficiency. whereas a high oil level will
cause carryover of the oil into the gas. Dry and oil-bath type of scrubbers
can be effective down to almost a 4-micron particle size.
The most efCecth'e scrubbers are the cartridge-type scrubbers (Curry,
1981). They use cleaning cartridges stacked in parallel, in difCerent configurations, that can remove solid particulate matter down to a size of 0.3 micron. For liquid removal, mist extractors are also provided sometimes. Cartridge scrubbers, however, require constant maintenance and cartridge
replacement, and are more expensive than oil-bath and dry scrubbers.
Ehctric Prropitoton
These units induce an electrical charge that attracts particulate matter. A
strong electrostatic field is provided that ionizes the gas to some extent. The
particles suspended in this partially ionized gas become charged and migrate under the action of the applied electric field. The gas is retained for a
long enough time for the particles to migrate to a collection surface.
Currently, the application of electric precipitators to large volumes of
high-presc;ure gas is quite limited. in the future, though, these pollution-free
devices may prove to be more useful.
Flash Calcu1ations
Two-phase flash calculation techniques were described in Chapter 2. This
section describes some methods that can be used to accelerate convergence
to the correct resu1t. The nomenclature used here is the same as in Chapter
2. F moles of feed with a composition {z;} split into L moles of liqu.id with a
135
... n {.} and V moles of vapor with a composition {YIl· For simplic-~~~
. are carn~
ity, it is assumed in the present discussion that flash calculatiOns
out on the basis of a unit mole of feed (F - 1). Thus,
F_I_L+V
and
Fz; - z; - LxI
+ VYI
Also" ). and x, are related by the equilibrium ratio, K,:
Determination of Equilibrium Ratios
To enable flash calculations, the equilibrium ratio. K, is required. Experimental values for the particular system are the most reliable source for Kvalues. The next best thing is to use equations of state for consistent predictions. For manual calculations. K-value charts are also useful, though they
may not be very accurate.
.
.
The calculation of K-values from equations of state has been discussed to
Chapter 3. These methods are used for implementation on. a comput,er, .and
provide internally consistent values for all thermodynamiC properties In a
convenient form.
The chart method for estimating K-value:s is subject to an important constraint: K-values have been found to exhibit some dependence on the mixture from which they are measured, and therefore there is no single K-value
chart that is superior for all possible mixtures that may be encountered. A
sharp distinction exists in K-values for the same components in a nat~ral gas
liquid versus a crude oil. ThEre differences among K-values for dIfferent
mixtures have been characterized by the concept of conoergence pressure,
which represents the composition of the vapor and liquid phases in equilibrium. Convergence pressure, at a given system temperature, is defined as
the pressure at which the K-values of a fixed-composition system conver~e
toward a common value of unity. Thus, convergence pressure for a system IS
the pressure (at the given system temperature) at or beyond which va~~­
liquid separation is no longer possible. This is similar ~o the concept of cr~~­
cal pressure, and quite often the convergence pressure IS taken to be the cntlcal pressure of the system at the given temperature.
Figures 4-24 through 4-50 show the K-value charts for H 2S. Nz, and hydrocarbons C, through C,o for convergence pressures of 1,000 psia and 3,000
psia. It can be seen in these figures that at relatively low pressures, K-values
are almost independent of convergence pressure: at higher pressures approaching the convergence pressure, K-value:s are very sensitive to convergence pressure.
•
13.
Gal Production Engineering
Gal and Liquid Separation
137
For CO 2• the K-value can be calculated from methane and ethane K-values as follows (CPSA, 1981):
1Ct.<>, -
(K c,
Kc,)"
The convergence pressure Pk. required for selecting the appropriate K-value
chart, has been found to be a function of two parameters-temperature and
the liquid phase composition. Temperature of the system is generally
known, but the composition of the exit liquid stream from the vapor-liquid
separation is not known in advance (v.'e are trying to determine both the
vapor as well as liquid stream compositions using K-value data). Therefore,
the procedure for determining the convergence pressure is iterative. as described in the following (CPSA, 1981):
1. Assume a liquid-phase composition. The total feed composition may
be used as a first guess if no better estimates can be made.
2. Identify the lightest hydrocarbon component which is present at least
0.1 mole% in the liquid phase.
3. Calculate the weighted average critical pressure and temperature for
the remaining heavier components in the liquid to form a pseudo-binary system. A shortcut approach good for most hydrocarbon systems
is to compute the weighted average critical temperature only.
4. Trace the critical locus of the binary on Figure 4-23. When the
averaged pseudo-heavy component of the binary is between two real
hydrocarbons, an interpolation of the two critical loci must be made.
......-
(tm continued on page 164)
.,--
i
•
I
12.00CI
(
r:-
~
-- .-
,'
~
Q
•
,~
••
~ ....
1"
.
~'< ..
•
ll'
-- -- -Q
I I I '1 I
~
"
'""-"-- '"
Figure 4-23. Convergence pressure PIc of binary hydrocarbon mixtures. (From
Engineering Data Book, 1981, courtesy of GPSA.)
PRESSURE. PSIA -
Figure 4-24. Equilibrium ratio, K, for methane for a convergence pressure of
1,000 psia. (From Engineering Data Book, 1981; courtesy of GPSA.)
138
Go., Production Engineering
GO! and Liquid Separation
13.
•
PRESSURE, PSI... -
Figure 4-25. Equilibrium ratio, K, for ethylene lor a convergence pressure 01
1,000 psla (From Engineering Data Book, 1981; courtesy 01 GPSA.)
PRESSURE, PSI"'-
Figure 4-26. Equilibrium ratio, K. for ethane for a convergence pressure of
1,000 psla. (From Engineering Dat8 Book, 198'; courtesy of GPSA.)
140
Ga" and Liqldd Separation
Gas Production Engineering
141
1-
•
PRESSURE, PSI" -
Figure 4·27. Equilibrium ratio, K, lor propane lor a convergence pressure of
1,000 pSla. (From Engineering Dat8 Book, 1981; courtesy of GPSA.)
PRESSURE, PSI"Figure 4-28. Equilibrium ratio, K, for propylene for a convergence pressure 01
1,000 psia. (From Engineering Data Book, 1981; courtesy of GPSA.)
142
Gas Production Engineering
Gas and Liquid Separatioll
.
,.5;
,
-.
,
143
"1'"
,
~~
~.
,
,
•,
~'"
'"'"
,,'
l~0::
I'..
II
,
·
K-'
• K
I.
f-C
,p..,
,
N.
IS;
""-
,
It"
1IIc
,
r'·,
..
"
."
,
,
,
.
.
......
,,
PRESSURE, PSIA-
Figure 4-29. Equilibrium ratio, K, for iso-butane for a convergence pressure of
1,000 psia. (From Engineering Data Book, 1961 ; courtesy of GPSA.)
·
;:
•
I
PRESSURE, PSIA -
,:
,@
.,
Figure 4-30. Equilibrium ratio, K, for n-butane for a convergence pressure of
1,000 psia. (From Engineering Data Book, 1981 ; courtesy 01 GPSA.)
144
Gos and Liquid Separation
Gas Production Engineering
,
, ,
,
,
,-PSl~ - :
,
,-
145
,
~W
,
,
,
I - •.
I·j I'
.
l
1,
~~
I
,
llif".,;
~ ::--;'-,l'>'l":---- ~
,
,
'~.'
I;
,
,
,
;:::
_I
I
,
,
•
K
f'.,
lb N.
"I,, "
t/
,
1
,
,
,
I"
"t
I"
. It---:
+r-
l!.~i+
III,', '
"
'i l,"
..
hi
PRESSURE, PSI A -
--
Figure 4,- 31, Equilibri~m ratio, K, for I·pentane for a convergence pressure of
1,000 pSla, (From Engm98ring Data Book, 1981 ; courtesy of GPSA.)
•
.
,
,
,,'
.. -..
i~
:
_I~~:.
PRESSURE, PS tA -
Figure 4-32. Equilibrium ratio, K, for n-pentane for a convergence pressure of
1,000 psia. (From Engineering Data Book, 1981 ; courtesy of GPSA.)
•
146
Gas Production Engineerillg
Gas and Liquid Separation
'[
PRESSURE, PSIA -
Figure 4-33. Equilibrium ralio, K, for hexane for a convergence pressure of
1,000 psia. (From Engineering Data Book, 1981; courtesy of GPSA.)
147
..
PRESSURE, PSIA-
Figure 4-34. Equilibrium ratio, K, for octane for a convergence pressure 01
1,000 psia. (From Engineering Dara Book, 1981; courtesy of GPSA.)
148
Gas Productioll Engineerillg
Gas and Liquid Separatioll
149
- 0<, 1 , , ( . "....... ,
, ... ,~..(., Ole ........... '
... -'-
..
• "-S._.... ""'_"--
-.,,,, ,,,,,,,
-~.-
..._........
- ....." 'A_'
.... -_"-_c-""'.
•
PRESSURE, PSIA -
PRESSURE. PSIA
Figure 4-35. Equilibrium ratio, K, for decane for a convergence pressure of
1,000 psia. (From Engineering Data Book, 1981; courtesy of GPSA.)
Figure 4·36. Equilibrium ralio, K, for hydrogen sulfide for a convergence pressure of 1,000 psia. (From Engineering Data Book, 1981; courtesy of GPSA.)
150
Ga, Production Engineering
Gos and Liquid Separation
151
•
PRESSURE. PSI" ----
Figure 4-37. Equilibrium ratio, K, for nitrogen for a convergence pressure 01
1,000 pS18. (From Engineering Data Book, 1981; courtesy of GPSA.)
Figure 4-38. Equilibrium ratio, K, for methane for a convergence pressure of
3,000 psia. (From Engineering Data Book, 1981; courtesy of GPSA.)
152
CQ~ Production Engirlf'ering
Cal and Liquid Seporation
153
PSI' _
_ I
:3! . ' "
··~······
tmt
..
K· '11
I~,
•
" .
,,,.
II
II
PRESSURE, PSIA _
PRESSURE, PSI"'-
Figure 4·39. Equilibrium ratio, K. for ethane for a convergence preSSure of
3,000 pSla. (From Engineering Data BOOk, 1981; courtesy of GPSA.)
Figure 4·40. Equilibrium ratio, K. lor propane for a convergence pressure of
3,000 psis. (From Engineering Data Book, 1981; courtesy of GPSA.)
'5<
Gas Production Eng/neering
Gal alld Liquid Separation
155
•
PRESSURE. PSIA-
PRESSURE, PSIA-
Figure 4-41 . Equilibrium ratio, K, for iso-butane 'or a convergence pressure of
3,000 psia, (From Engmeering Data Book, 1981; courtesy 01 GPSA.)
Figure 4-42. Equilibrium ratio, K, for n-butane for a convergence pressure of
3,000 psia. (From Engineering Data Book, 1981, courtesy of GPSA.)
156
Gas Production Engineering
Gas and Liquid Separation
157
•
PRESSURE. PSI ... -
Figure 4,-43. Equilibrium ratio, K, for i-pentane for a convergence pressure of
3,000 pSla. (From Engineering Data Book, 1981; courtesy of GPSA.)
PRESSURE, PSI"Figure 4-44. Equilibrium ratio, K, for n-pentane for a convergence pressure of
3,000 psia. (From Engineering Data Book, 1981; courtesy of GPSA.)
158
Gos Production Enf(inf'f'ring
Call and L/qutd Separation
159
•
PRESSURE, PSIA -
Figure 4....5. Equilibrium ratio, K, for hexane lor a convergence pressure of
3,000 psia (From Engineenng Data Book, 1981; courtesy of GPSA.)
PRESSURE, PSI"
Figure 4·46. Equilibrium ratio, K, for heptane for a convergence pressure of
3,000 psia. (From Engineering Data Book, 1981; courtesy of GPSA.)
Cal and Liquid Separalion
160
161
•
PRESSURE. PSI"
Figure 4-47. Equilibrium ratio, K, for octane for a convergence pressure of
3,000 psia. (From Engin99ring Data Book, 1981; courtesy of GPSA.)
PRESSURE, PSI ...
Figure 4-48 . Equilibrium ratio, K, for nenane for a convergence pressure of
3,000 psia. (From Engineering Data Book, 1981; courtesy of GPSA.)
162
Gas P,aduction Engineering
Cas and Liquid Separation
163
•
PRESSURE, PSI .... -
PRESSURE, PSI ....
Figur e 4-49. Equilibrium ratio, K, for decane for a convergence pressure of
3,000 psia. (From Engineering Data Book, 1981; courlesy 01 GPSA.)
Figure 4-50. Equilibrium ratio, K, for hydrogen sulfide for a convergence pressure of 3,000 psia. (From Engineering Data Book, 1981; courtesy of GPSA.)
164
Cas Production Engineering
Gas and Liquid Separation
165
(text continued from poge 136)
5. Read the convergence pressure P1 at the temperature corresponding to
that of the desired flash conditions.
6. Using Pl from Step 5, together with the system temperature and pressure, obtain K-vaJues for the components from the appropriate convergence-pressure K-value charts. Interpolate for convergence pressure between the charts. if necessary.
7. Make a nash calculation with the feed composition and the K.values
from Step 6.
8. Repeat Steps 2 to 7 until the assumed and calculated PI< check within
an acceptable tolerance.
F1ash Calculation Methods
Simple Trial and Error ScMme
This is the simplest method. A value of the vapor-liquid ratio is assumed.
Using this (V/L)al in Equation 2-16 (or 2-17) along with the appropriate
component K values, a new V (or L) is obtained. The value of L (or V) is
obtained by difference (L - 1 - V). [f this calculated (V/L)c is equal to the
assumed (V/L).t within a specified tolerance. the assumption was correct.
Otherwise. a new value (V/L)a2 for the liquid-vapor ratio is assumed as follows:
This method is similar to the simple trial and error scheme just outlined.
The only difference is in assuming a new value at the end of an unconverged
lrial (Lockhart et aI., 1986),
(V/L)" - (V/L), + [(V/L), - (V'L)• .J
Thus, the new assumed value of VIL is made as far beyond (VIL)e as (VIL)e
is beyond (V IL)d' This scheme gives a much better convergence rate.
Lockhart·McHmry Method
Lockhart and McHenry (1958) proposed a method that reduces the number of trials required for flash-equilibrium calculations for multicomponent
mixtures significantly. In this method, a multicomponent mixture is treated
as a pseudo-binary mixture with a "'light'· component, and a "heavy" component. Components with a K value greater than 1.0 are grouped into the
light component, and those with a K value less than 1.0 are grouped into the
heavy component.
Consider I mole of a multicomponent feed with a mole-fraction Zj of the
light components, and zt, of the heavy components. The total number of
components in the mixture is n. with n1 number of light components and nh
heavy components. In this technique, a parameter v· is defined as follows:
V· - z,/(1 - Kh) - z,,/(K,.- I)
(V'L)" - (VIL),
This procedure is repeated till convergence is reached. After one or two
iterations, it becomes quite obvious whether the system is predominantly
gaseo~ (V < 0.5), or liquid (V > 0.5). For a predominantly gaseous system,
Equatton 2.-16 is used to calculate V, and L is obtained by difference
whereas if the system is predominantly liquid, Equation 2-17 is used and
is obtained by difference. The use of either Equation 2-16 or 2-17 is entirely
analogous; the only difference is in the accuracy of the results.
.Lockhart (1983) has made an important observation regarding the use of
tlus method: the value of the calculated L, as compared with the assumed
L. gives the direction of the correct L. Thus, if at an assumed value of Ltv
of 0.5 the calculated (Ltv)c < 0.5, then the correct UV will be less than (LI
V)c' H the calculated (LlV)~ > 0.5, then the correct LlV will be greater than
(L/V)c' Of course, if the calculated (UV)" '"' 0.5 exactly for an assumed L/V
of 0.5. then convergence has been reached.
where Kh and Ktdenote the K4 values for the heavy and light components.
respectively, in the binary mixture. The K· parameter is defined as follows:
V
K· -
K* _
Ez,
E(z,/K,)
for (V) ...umed
-
1
EZi
_ I for (V) ...um«l- 0.5
E[z,/(K, + I)l
K· - (UV) [EZ, - 1] 10'
ELx(
(V)~",,", - 0.5 to 1
•
166
Ga. and Liquid Separalion
Ga! Production Engineering
KO -
L,V
(E7;!!:VyJ - 1
for (V)-.-d - 0 to 0.5
The summation E in these relation.'ihips represents the subtotals O\'cr all
pure components i for the light component and the heavy component, as the
case may be. Thus, in calculating Ktfor the light component, the summation E is done for i - I to "I' Similarly. for a Kh calculation, the summation
E is carried out for i - I to nh'
For different values of V...1Om«J, V· is calculated. At convergence,
V' - V-.-:!. Alternatively. a graphical method can be used.. where tv.·o
lines are plotted on a Cartesian graph: (1) V' versus V .......... and (2)
V' _ V--.I' The intersection of these two lines gives the correct answer.
A Note on Flash Calculations for Stage Separation
For an isothermal flash calculation, the separator temperature is known,
and is kept at a constant value by suitable heat exchange devices in the separator. The trial and error flash calculation procedure involves determining
the separator pressure. If there is no heat exchanger, or the temperature is
not known, an adiabatic flash calculation is made, involving a double trial
and error: one for separator pressure, and another for the temperature. Usually, a separator pressure is chosen, and trial and error done for a corresponding separator temperature that makes the feed enthalpy equal to the
product enthalp)'. A reasonable separator temperature is assumed, and flash
calculations are made exactly as for an isothermal case.
-."..
Questions and Problems
1. Describe the three major components of oiJ-water-ga.~ separators.
2. What happens to separation quality and the separator when-
167
(c) low COR well producing oil, water, and gas?
(d) heavy, waxy crude (GOR can be assumed to be low for heavy
oils)?
(e) gas condensates with a hydrate problem?
(f) nearly dry gas at high pressure?
4. A 20 ft x 10 ft 1,000 psi
w.P.
(working pressure) horizontal separator
used on a well
with a gas flow rate of 9 MMscflday and a line pressure of 500 psig? If
a gas back-pressure valve were put on the separator, what pressure
should it be set at to handle the gas flow rate?
5. Design a vertical separator, with a mist extractor, that can handle 6.66
MM.scflday of a 0.80 gravity gas. The oil gravity is 45° API, operating
pressure is 400 psia, and the operating temperature is 60°F. Use ba~ic
separation relationships for this design, and compare the results WIth
SivaJls' charts.
6. A gas field delivers 13.4 MMscflday of a 0.68 gravity gas and 300 bblJ
day oil with a 50% water cut. For an operating pressure of 1.000 psig
and temperature of 8O°F_
is operated at 112 full-of-Iiquid conditions. Can it be
(a) Determine the ID of the spherical separator required to accommodate the liquid and gas, assuming a retention time of 5 min.
(b) How much more gas can be flowed through the separator without
worrying about the gas capacity?
7. A 1.25 gravity gas condensate stream at 1,200 psia and 110°F is to be
separated into oil and gas using a three-stage separation.
(a) Assuming that the mole % C) + C 2 + C 3 in the gas is 80%, what is
the optimum second-stage pressure?
(b) Choose and design the appropriate separators for each of these
three stages.
8. Describe the applicability of the various gas cleaning methods in natural gas production and processing.
(a) the gas flow rate exceeds the allowable rate through the separator?
(b) the liquid flow rate exceeds the allowable rate through the separator?
(c) mist extractor becomes plugged?
(d) the wellstream produces slugs of liquid (oil and water) into the
separator?
3. What type of separator(s) should be used for(a) offshore production platform?
(b) high COR well, with liquid surges?
References
Beggs, H. D., 1984. Gas Production OperatiQ1ls. Oil & Gas Consultants International, Inc .. Tulsa, Oklahoma, 287pp.
Brink. J. A., Jr., 1963. "Air Pollution Control with Fibre Mist Eliminators,"
Cdn. J. Chem. Eng., 41(3, June). 134-138.
Campbell. J. M., 1955. "Know Your Separators," O. & Gas J., 53(45, Mar.
14),107-111.
168
Ga! Production Engineering
Campbell, J. M., 1984. Gas Conditioning a11d Processing, Vol. 2. Campbell
Petroleum Series, Norman, Oklahoma, 398pp.
Craft, B. C., Holden, W. R., and Craves, E. D., Jr., 1962. Well Design:
Drilling and Production. Prentice-Hall tnc., Englewood Cliffs, New Jer"'Y, 571 pp.
Curry, R. N., 1981. Fundamentals oj Natural Gas Conditioning. PennWell
Pub!. Co., Tulsa, Oklahoma, 118pp.
Cas Processors Suppliers Association, 1981. Engineering Data Book, 9th ed.
(5th revision), GPSA, Thlsa, Oklahoma.
Ikoku, C. U., 1984. Natural Gas Production Engineering. John Wiley &
Sons, Inc., New York, 517pp.
Lapple, C. E., 1984. Cited reference in: Chemical Engineers' Handbook ,
by R. H. Perry and D. W. Creen (cds.), 6th ed. McGraw-Hili Book Co.,
Inc., New York, pp. 5-63.
Lockhart, F. J., 1983. Personal communication.
Lockhart, F. 1., Chil ingarian, G. V., and Kumar,S., 1986. "Separation of
Oil and Cas," in: Surjace Operations in Petroleum Production, Vol. 1, by
G V. Chilingarian. 1. O. Robertson, and S. Kumar, Elsevier Scientific
Publishing Company, Amsterdam.
Lockhart, F. J. and McHenry, R. J., 1958. "Figure Flash Equilibrium Easier, Quicker This Way," Petro Refiner, 37(3), 209-212.
Petroleum Extension Service, 1972. Field Handling oj Natural Gas. 3rd ed.,
Univ. of Texas Press, Austin, Texas, 143pp.
Sivails, C. R, 1977. "Fundamentals of Oil and Gas Separation," Proc. Cas
Conditioning ConL, Univ. of Oklahoma, 3lpp.
Whinery, K. F. and Campbell, J. M., 1958. "A Method for Determining
Optimum Second·Stage Pressure in Three-Stage Separation:' /. Pet.
Tech. , 10(4, Ap'. ), 53-54.
5
Gas-Water Systems and Dehydration
Processing
Introduction
Water vapor is the most common undesirable impurity found in natural
gas. By virtue of its source. natural gas is almost always associated wit~ water, usually in the range of 400-500 Ib water vapor/MMscf gas. The pmoary
reason for the removal of water from gas is the problem of gas hydrate formation. Liquid water with natural gas may form solid, ice-like hydrates
that plug flowlines and lead to severe operational probl:ms. Oth~r reaso~
for removing water are: (I) liquid water promotes corrOSiOn, .pa~hc~larly In
the presence of H2S and CO 2; (2) slugging flow may result If liqUid water
condenses in the flowlines; and (3) water vapor reduces the heating value of
the gas. For these reasons, pipeline specifications for natural gas restrict the
water content to a vaiue not greater than 6-8 Ibm/MMscf.
Because most gas sweetening processes involve the use of an aqueous sol.ution, dehydration is often done after desulfurization. Nevertheless, part~al
dehydration. or hydrate inhibition. are commonly necessary at the wellstte
itself.
Water Content of Natural Gases
In order to design and operate dehydration procecoses, a reliable estimate
of the water content of natural gas is essential. The water content of a gas
depends upon:
1. Pressure- water content decreases with increasing pressure.
2. Temperature-water content increases with increasing temperature.
169
•
170
Ga., Product/on Engineering
Gas-Water Systems Gild Dehydratiofl Processiflg
3. Salt content of the free water in equilibrium with the natural gal> in
the reservoir-water content decreases with increasing ~alt content of
the associated reservoir water.
4. Cas composition - higher gravity gases usually have less water.
The terms dete point and deu.:-point depression are wideh- used in deh\"dratian terminology. Dew point indirectly indicates the water content oc" a
natural gas, and is defined as the temperature at which the gas is saturated
with water vapor at a gin'n p~ure. The difference between the dew-point
temperature of a gas-stream-betore-and--after-dehydration i.Halled: the dewpoint depression Consider a gas saturated with water at 500 psia and
lDO'-F. It~ dew point is 100° F. and its water content i.~ approximately 100
Ibm MMscf gas. The gas is to be transported in a pipeline at 60' F. Under
~ipeline conditions of 500 psia and 60°F, the water vapor content of the gas
IS only about 30 Ibm/MMscf. Thus, 70 Ib water per MMscf of gas exist as
free water in the pipeline. If the dew point of the inlet gas to the pipeline i~
reduced to 60 °F, no free water will exist in the pipeline at the pipeline flo\-\
condjti~ns. In other words, the dehrdration facility should give a dew point
depressIon of 100 - 60 = 40°F. In practice, although a dew point depression of 40° F is just suffiCient, a 50°F dew point deprasion may be desirable
for operational safety.
T~le methods a\-aHable for calculating the water content of natural gases
faUlIlto three categories: (1 ) partial pressure approach, valid up to about 60
psia (gases exhibit almost ideal behavior up to 60 psia in most cases): (2)
empirical plots; and (3) equations of state.
Partial Pressure Approach
Assuming ideal gas and ideal mixture beha\-ior. the partial pressure of water in the gas is gi\'-en by p.. - Ph. and also by po.. _ p,X". Thus.
Ph - p..x"
where
(5-1 )
p - absolute pressure of the gas
y..- - mole fraction of water in the vapor (gas) phase
p, - vapor pressure of water at the system temperature
K" -
mole fraction of water in the aqueous (liquid water) phase associated with the gas phase under equilibrium conditions
Since water is almost immiscible in the liquid phase with oil K is usuallv
assumed to be equal to unity. Thus, the water mole fraction i~ the gas,
can be calculated as:
y:,
y", - p-Jp
171
(5-2)
This simple approach has limited applicability at the pressure and temperature of interest in most natural gas production, processing and transport
systems.
Empirical Plots
For engineering calcuJations. empirical plots are widely used. ~umerous
Investigations- ha\"e' resulted in several plots. such as- by McCarthy et al.
(1950), McKetta and Wehe (1958). the Gas Processors Suppliers Association
(GPSA), Campbell (l984a), Robinson et al. (1978), and others. Since. the
real danger in design is to underestimate the water content. all correlations
assume the gas to be completely saturated with water, and most correlations
are designed to slightly overestimate the water content. Nitrogen hold~
about 6-9% less water than methane (CampbelL 1984a). Therefore. nitrogen is frequently included as a hydrocarbon, providing a small safety factor.
McKetta and Wehe COfTf'intiofi for Sweet Case,
The McKetta and Wehe correlation (1958), shown in Figure 5-1, includes
correction factors for gas gravity and formation water salinity. It gives acceptable results for sweet gases.
Robifl1lOn et aI. COfTf'lotwn for Sour Case.
The Robinson et aI. (1978) correlation for sour gases. shown in Figures
5-2 and 5-3, is based upon the SRK (Soave-Redlich-Kwong) equation of
state. The hydrocarbon portion of the gas is assumed to be pure methane.
Robinson et at. found that CO 2 carries orny about 75 % as much water as
H.,s under the same conditions. To reduce the number of \·ariables and
th~reby simplify the graphical representation of the correlation, Robinson et
aI. assumed that this condition was true throughout. Therefore, to use this
correlation, one has to multiply the % CO 2 in the gas by 0.75, and add it to
the % H 2S in the gas to get the effective HzS content.
Campbell's Correintion for Sweet afld Sour Cases
Campbell (1984a) presented a composite chart, shown in Figure 5-4, for
sweet gases based upon earlier charts and other available data. This chart
gives values very similar to the McKetta and Wehe correlation, but dot!S not
include corrections for gas gravity and water salinity.
(tm continued Qn page 174)
,
172
Gaa Production Engineering
CIlS- Water
173
Systems Qnd Dehydration ProceDing
_,....,of_ ...
__ H .... H
,,
I
_.
'll"- ,..,
aa; ~..
i
i
~" -
,
.
l
...
,1
•
•
..
I,
-"-i
s
s
•e,
-..
... ....,......
••
Wilt" e...''''' .1
,.,. ...... ...,oIlI- ,.., ......,
o
o
_.
_
----_---_
------'..........-
o
o
...
Figure 5·1. The McKetta-Wehe correlation for waler content of natural gases,
with corrections tor waler salinity and gas gravity, (After McKatta and Wehe,
1958; reprinted from Engineering Data Book, 1981; courtesy of GPSA.)
100"1. IKo
'0".4 CM..
lO1. M~~04
3D"/. ~,s. lD"Xo CM..
It"/. M~.
0 4O"fo-.s.."'-010
I.
Figure 5-2. Robinson at at correlation tor. water content of sour gases In ~he
300-2,001) psia pressure range. (After Robinson at aI., 1978; courtesy of 0;1 &
Gas Journal.)
•
174
Goa Production Engineering
Gas-\\ater S!lstem.. and Deh!ldratlon Processillg
175
(ted cont/nlled from page 171)
To correct for large acid gas (H2.S and CO 2 ) contents, Campbell (l984a)
proposes a weighted 8\'erage water content, \V, for the gas as follows:
(5-3)
where
\\'HC - water content of the hydrocarbon portion of the
gas from Figure 5-4
•
Figure 5-3. Continued.
W a~ - water content of CO,1 from Figure 5-5
- water content of HzS from Figure 5-6
YHC. YC02' YII~ - mole fractions of hydrocarbon, CO!. and 1-1 25,
WH~"
respecth-ely
••
Wottr content"
natural gos mixturel
Exam"le 5·1. Find the water content of a 0.75 gravity gas at 1,500 psia
and 120°F.
'.... ""'" ~ tr, MIll]
o l00"t.o-
G 11% M.s, ~ 010
G 201.1I,S.1IO"J,0I0
o ." M.s, 7rf. ClIo
O ~1,I.6I'1tx.
I.
T..,.,...",.. •• -f.
Figure 5·3. Robinson at al. correlation for water content of sour gases in the
3,000-6,000 pSla pressure range, and at 10,000 psia. (After Robinson at aI.,
1978; courtesy of Off & Gas Joumal.)
Solution
From the McKctta and Wehe (:orreiation (Figure 5-1), W = 781b H 201
MMscl gas.
Correcting for the gas gravity, the water content, W - (0.99)(78) 77.2 Ib H 20/MMscf gas.
Using Campbell's correlation (Figure 5-4), W - 77 Ib H 2 0fMMscf gas.
Thus, the two methods gi\'e very close resu1ts for most practical purposes.
176
Gas-\\uter Systems and Dehydration Proces.Ting
Co.t Production Engineering
177
Solutim)
1.
\'H{:'"
0.80 + 0.05 + 0.015 + 0.005 + 0.02
=
0.89
YHzS - 0.085
FrQm Figure ~4, \\. He:
,.
67 Ib H20~1Mscf CO 2
From Figure 5-5, W C02
From Figure 5-6, W llti
59 Ib H20 MMscf He ~.as
-
150 Ib H20fMMscf H:S
Using Equation 5-3.
IV ~ (0.89)(59)
:z
+ (0.025)(67) + (0.085)(150)
66.9 Ib HzO/MMscf gas
"00
•
1 1000
!
•
•"
; "'"
.l
! "
;- "
30
•
Figure 5·4. Campbell's correlation lor waler content of sweet gases. (After
Campbell, 1984a; courtesy of Campbell Petroleum Series.)
E%ampl~ 5-2. Find the water content of a gas at 1,000 psia and lOO°F
using (1) Campbelrs methcxl and (2) Robinson et a1. method. The gas composition is as follows: CH 4 - 80.0%, C 2H 6 - 5.0%, C3HS - 1.5%, fIC~HIO - 0.5%, CO 2 - 2.5%, Nt - 2.0%, and H2S - 8.5%.
Figure 5-5. Waler
'00
200
300 400 )00
1000
.........., •• pd.
~ooo
3000
content of C02 In saturated natural gas
mixtures. (After Campbell, 1984a; courtesy
01 Campbell PetrOleum Series.)
178
G~
Productiorl Engin«ring
'0000
liquid equilibrium principles discussed in Chapter 2, Equation 5-2 can be
, ...TiUen for a non-ideal system as:
y. _ I,ll _ (1.11.)(1. I)
!
••
c
·.. lill
~ '000
In practice, the fugacity f used is for the gas stream u;ithoul water vapor
in it. Thus, Equation 5-4 is modified in different ways to account for the
discrepancy. In general. the fugacity coefficients for water at its vapor pressure (t',) and at the system pressure and temperature (Y ..-), and for the gas at
the system conditions (y) are calculated using any equation of state (see
Chapter 3 for further details). The mole fraction of water in the gas (in the
vapor phase), y", at equilibrium conditions can then be calculated as:
sao
••
,"
8
,•
"
::
(5-\)
where f, _ fugacity of water at il~ \·apor pressure and system temperature
f" _ fugacity of water at the system pressure and temperature
f _ fugacity of the total ~as mixture at the system pteS!iure and
temperatun'
i
-i
179
Co!-\\ater Systems and Dehydration Proceaing
(5-5)
100
where
"
>0,
lOOO
Figure 5-6. Water content 01 H~ in saturated natural gas mixtures. Note: Solid
curved Imes ar.e lor pure H2 S only. (After Campbell, 1984a; courtesy of Campbell
Petroleum Series.)
2. Effectiye H~S content .. (0.75)(2.5) + 8.5 - 10.375%
In Figure ,5.2, the line<> for 0% H 2S and 20% H 2S at 1000 psia are very
close together; no line for 10% HiS is shown. By interpolation.
IV - 0.175 bbl'MMrl
- (0.175 bbl!MMrl)(62.4 Ibflt')(5.6146 1t'lbbl)
= 61.3 Ib H2 01 MMscf gas
Equations of State
Equati~n of state met~ods are rigorous, but difficult and expensive to im.
rlement smce they reqUire the use of a computer. Referring to the vapor.
p, "" vapor pressure of water at the system temperature
p ,., system pressure
a, b, c '"" empirically determined constants
•
One such method has been de\-eloped by Sharma and Campbell (1984)
for predicting the water content of sweet as well as sour gases based upon
the EMR mixture combination rules. It has proved to be accurate and reliable (Campbell, 1984a). In this method, first the EMR critical pressure,
critical temperature. and Z factor are determined using the Mcleod and
Campbell method discussed in Chapter 3. Thereafter, the pnx:edure is as
follows:
1. Find the value of the parameter k from Figure 5-7.
Alternatively, k can be calculated using the following equation:
k - (fJI.)(plp.)"""
(5-6)
where the exponent 0.0049 is a semi-empirical constant. The fugaci·
ties, f, and f"., for water can be found from Figure 5-8 (as described in
"ep 2).
Cenerally, fugacities are reported in terms of the fugacity coefficient,
Y. Thus, Equation 5-6 can alternatively be written as:
1'"
Gas-'1.'iller System! and Dehydration ProcQ8ing
Go. Produclion Engineering
181
'I..............
(s- 7)
2. Find the water fugacity coefficient, if",. from the generalized fugacity
coefficient chart shown in Figure 5-8. Note that since i'", represents
the pure component fugacity for water, the criticaJ pre'iSure and temperature for water only are applicable.
3. Using Figure 5-8 and the critical pressure and temperature for the gas
determined from the E~1R method, find the fugacity coefficient "t for
the gas mhture (without water as a comiXlnent) at :oy:.tem p~ure p
and temperature T.
10
0., . . ._
0.0)
•
0.01
0.00'''.
.,.
0.001
.
.'
Figure 5-8. Generalized fugacity coefficient chart. (Alter Edmister and Lee,
1984, from data by A. F. Curl, Jr., and K. S. Pitzer, 1958, Ind. and Engr. Chem.,
Feb. 2.)
O.ooos
4. Calculate the mole fraction of water in the gas (in the vapor phase),
Yw, as follows:
0.0001
200
...
lOOO
''''
"0
Figure 5-7. Constant k as a lunction of pressure and temperature. (After Campbell, 1984a; courtesy of Campbell Petroleum Series.)
(5-8)
where the gas compressibility factor, Z, must be that determined from
the EMR method, since the EMR critical pressure and temperature
were used for calculating the critical properties of the gas.
182
Ga& Production
£n~ineerlng
Gas-Water Systems and Dl'hydration Processing
Example 5-3. Repeat Example 5-2 using the Sharma and Campbell
method.
183
From Figure 5-8, 't ... - (f.'p)", - 0.535 on extrapolation of the T, lines to
T," 0.5.
Solution
Comp.
y,
y,.
EMR
0.8602
0.0269
0.0914
0.0215
13.984
15.750
19.828
N~
0.800
0.025
0.085
0.020
\'1 -
0.930
C,
C,
0.050
0.015
23.913
34.316
n-C 4
0.005
0.7143
0.2143
0.0714
Y, -
0.070
C,
CO,
H,S
9.40i
For the gas (without water), "t - 0.S15 from Figure 5-S for a Pp. - 1.195
andT p,-1.249
Using Equation 5-8. the mole fraction of water is equal to:
y. ~ (0.OOl95)[0.53510.815f"" • 1.371 x 10 '
Now. the density of ".'ater vapor at standard conditions
~ (14. 7)(18.015)/{ (1)( 10.73)(491.67) 1
... 0.050197 Ibm/seC - 5O.197Ibm,l~iMscf
44.243
Thus, the water content of the gas
(1.371 x 10 3 MMscf wateriM~lscf gas)
. (50.197 lb watcriM~tscf \\'ater)
_ 68.S2 Ib H20, ~IMscf gas
EO
EMR~
"" E Y2IEMRj .. 27.59
From Figure 3-6, (T.,IPch .. 0.51, and (T•.ip{"h" 0.88.
Gas Hydrates
So, (T"p,) ••
~ (0.93)(0.51)
+ (0.07)(0.88) - 0.5359
And (EMR) •• - (0.93)(14.47)
From Figure 3-5,
Therefore.
~s
(Tr1p~
+ (0.07)(27.59) • 15.388
5) .. 15.5
.. lS.SfO.5359 .. 28.923, implying that
Ppc" 836.56 psia. and Tpc" (0.5359)(836.56) .. 448.31°R
Thus. Ppr" I,OOOf836.56 .. 1.195, and Tpr" 560/448.31 .. 1.249
From Figure 3-7, the compressibility factor, Z .. 0.837
From Figure 5-7, k .. 0.00195
From Table 3-1, (P,,) ..-atn''' 3,203.6 psia, and (T,,) ...,..... 1,165.1 R.
So, (P,)...,«" 1,00013,203.6 .. 0.3J2, and (T,) ..·.tft" 56011,165.1,. 0.481
Natural ga~ hydrates are solid crystalline compounds, resembling ice or
wet snow in appearance, but much less dense than ice. They are included in
a general class of compounds known as clatllratl'.$, which have a structure
wherein guest molecules are entrapped in a cage-like framework of the host
molecules without forming a chemical bond. ~atural gas hydrates are
formed when natural gas components. notably methane. ethane. propane,
isobutane, hydrogen sulfide, carbon dioxide. and nitrogen, enter the water
lattice (which is looser than the ice lattice) and occupy the \acant lattice
positions, causing the water to solidify at temperatures considerably higher
than the rreezin~ point of water. Enough gaseous molecu1es must enter the
lattice and occupy the voids to stabilize the lattice crystal.
Hydrate formation is governed by the size of the host molecule, and its
solubility in water. Size is an important parameter-the molecule should be
small enough to properly orient itself within the water structure to best use
the available space, and large enough to get entrapped. Smaller molecules.
such as those of methane, can a\'oid entrapment because of their smaller size
and rapid, random moyement. Solubility affects the rate of formation because it governs the availability of the guest molecule to the water.
•
184
Cos Production Engineering
Gas-Water Systerns and Dehydration Processing
Hydrate Formulas
:G
Two types of crystalline structures have been pro~ for gas hydrates.
Smaller molecules, such as methane, ethane, and hydrogen suJfide, form a
body-centered cubic lattice. called Structure I. Structure II is a diamond lattice, formed by larger molecules, such as propane and isobutane. Cas mixtures (orm both Structure I and II type hydrates.
The number of water molecules associated with each molecule of the gaseous component included in the hydrate is known as the hydrate nllmber.
Since different number of guest molecules can enter the water lattice and
stabilize it into a hydrate. no specific hydrate number can be given for tt
particular hydrate. The limiting hydrate number. a theoretical quantity determined using the size of the gas molecules and the size of the voids in the
water lattice. serves as a useful parameter, although hydrate structures are
stable at less than 100% occupancy of the voids. For molecules in Structure
I. the limiting hydrate number is 5.75 for the smallest gases (CII I ). and
7.667 for medium sized gases (CZH6). For the largest molecuJes associated
with Structure II, the limiting hydrate number is 17 (CPSA, 1981). Calloway et al. (1970) report experimental values for methane in the range of 5.8
to B.3, and for ethane from 7.9 to 8.5. Thus, hydrate molecules can typically be represented as:
Methane:
Ethane:
Propane:
lsobutane:
CH 4 • BH2 0
C,H,. BH,O
C,H,. 17H,O
Nitrogen:
Carbon dioxide:
Hydrogen sulfide:
N2 . BH.O
CO,.6H,O
H 2S. BHzO
i-C.H 10. 17H2O
Normal·butane does form a hydrate. but it is very unstable. Paraffins higher
than butane do not form hydrates.
Hydrate Phase Behavior
Figure 5-9 shows the phase equilibrium diagram for a gas-water-h),drate
system. Line ABCD represents the hydrate curve, HFCI is the vapor pressure curve for the hydrocarbon gas, and EBFC is the curve representing the
solid-liquid equilibrium for water (or, the water freezing point curve). The
hydrocarbon gas is assumed Single-component to simplify the phase equilib.
rium representation. These lines delineate different regions in the phase
equilibrium as follows:
1. Hydrates exl~t in the pressure-temperature region above the hydrate
cun·e ABeD. Below the hydrate curve, and to its right. no hydrates
can form.
I
,
I
KYOR0CI0R90H
V~POR PftESSORE
CURVE---...........
~
"
I·
HYQRUE
•
HYDROC ... RBDH
V"'POR
•
'"
:•
•·
•
.
HYO:.l.n
I
LIQlIlD
HYOIIQC4RSQ
I
I
I
IF _ _ -
- -r HYDIU.T(
Figure 5-9. Phase equi-
librium diagram for a
gas-water-hydrate system.
llQlIlD
NTtl-ROCloIIe
•
""... TER
185
WUER
__
-
I
c
I
•
IHI'~~S
I.
I
w... t R
,,
HYQfl~T[
CliRVE
I
I
I
,
I,
,
HYDIIOtJ,lIeOH
V... POR
+
L.- W~lEII
HlDIIOCAR80N
VAPOR
+
'"
,
I
FREEZING
POINl ClIIIV(
"
lZ"F
2. Above the vapor pressure cun'e HFCI. the hydrocarbon exists in the
liquid state.
3. Towards the left of the line EBFC, water exists in the solid form as ice.
On the right of EBFC. water will be in the liquid state. In practice.
the region towards the left of the line EBFC wiJI hard1y ever be encountered. except perhaps in extremely cold areas.
Note that in Figure 5-9. the hydrate cur ....e becomes ....ertical at the point
where it intersects the hydrocarbon ,·apor pressure curve. This intersection,
C, therefore represents the maximum hydrate forming temperature.
Conditions Promoting Hydrate formation
For a gas to be a hydrate former, it must satisfy two criteria: (I) it should
be of the covalent bond type, with molecules smaller than 8 A0 units; and
(2) the gas, when in the liquid state, must be immiscible with watcr. The gas
hrdrate that is formed will be stable if the hydrate is water resistant and no
Van der Waals' forces arise between the hydrate molecules. If these conditions are met stable hvdrate formation is possible under certain conditions
governed by 'the hydr~te phase equilibrium behavior. In natural gas systems, the gases mentioned earlier as being hydrate formers, satisfy these cri-
•
186
187
Gas-Water Systemf and Dehydratioll Processing
Gal Production Engineering
teria. The primary conditions necessary for a natural gas to form stable hydrates can be summarized as follows:
1. Natural gas at or below the dew point with liquid water present. ro..'o
hydrate formation is possible if "Cree" water is not present.
2. Low temperatures. at or belO\\ the hydrate formation temperature for
a gh'en pressure and gas com}X)Sition.
3. Hi~h operating pressures, that may raise the hydrate formation temperature to the operatin~ temperature.
Secondar~
2000
10
factors that aid and accelerate hydrate formation are (CPSA.
7.0
1000
1981),
I High ,e\ocities, or agitation. or pressure pulsations.
2. Presence of a small "seed" crystal of hydrate.
3. Presence of H 2S and CO 2 aids hydrate formation because both these
acid gases are more soluble in water than the hydrocarbons.
20
JOOO
•
-:;;
•
5._
~OO
,•
•
3.0
,•
2.0
•
7110
;300
•
·•
1.0
o. ,
Prediction of Hydrate Formation
Figure 5·10 shows the hydrate forming conditions for natural gas compoReferring to Figure 5-9 it ean be seen that the general procedure for
hydrate prediction would invoke prediction of the hydrocarbon vapor pressure curve (line HFCI). and only the portion BC of the hydrate curve (operating conditions in the region AB are never encountered, and the part CD of
the hydrate curve is a vertical straight line). The hydrocarbon vapor pressure curve can be predicted using any of the several available correlation~.
or equation of state methods disclliSed in Chapters 2 and 3. Correlations for
predicting the hydrate curve are disclliSed here,
nenl~.
0.5
"
0.3
30
0.2
20
O. !
ID!,-__~__""'__""'__""'__:::-__~"
~
~
~
~
Tf"iPtnture,
ro
0
00
90
F
Figure 5-10, Hydrate forming conditions lor natural gas components. (After
Campbell, 1984a; courtesy of Campbell Petroleum Series.)
Approximate\ferhod for SWl'f'1 Gases
As a first approximation. the data presented in the Cas Proce;,SOf<> Suppliers Association (cPSA) charts shown in Figures 5-11 through 5-16 can be
used. These charts do not account for the presence of H 2S and CO 2,
Hydrate formation can be divided into two categories (Ikoku, 1984): (1)
hydrate formation due to a decrease in temperature (or increase in pressure)
with no sudden expansion (or compression), such as in flow strings and surface lines: and (2) hydrate formation due to sudden expansion, Stich as in
flow-provers, orifices, chokes, and back-pressure regulators (sometimes bot.
tom-hole chokes, BHe. are used to avoid sudden expansion, and consequently, avoid hydrate formation). For hydrate formation of type I, Figure
5-11 can be used for predicting the approximate pressure-temperature con-
ditions for hvdratc formation. Figures 5-12 to 5-16 are used for estimating
hydrate fon~ation conditions for situations of type 2. In particwar, Figures
5-12 to 5-16 are used for determininK the permissible expansion. ,vithout hydrate formation, of a gas with a given gravity.
Example 5-4. A 0.685 gravity gas i.~ at 500 psia and l(x)°F. To what value
can the temperature be reduced without hydrate formation?
Solution
From Figure 5-11, hydrates will form at or below a temperature of 54°E
188
Ga$ Product/on Engineering
CQ~·Uat('r
Erampk 5·5. How far can the pressure be lowered without expecting hydrate formation for a 0.685 gravity gas if it is initially at (a) 1,500 psia and
100' F, and (b) 1,000 psia and 100°F.
INITIAL
TfM1fUTUU. OF
,
I
1/
4000
,
•~
1//1/ '/ /
~V:b'/
2000
~/.f
Q. r!l
f1
~ 1000
(b) Refer to Figures 5-12 and 5-13.
1••
'"
'·~me.
Solution
(a) From Figure 5-12 for a 0.6 gravity gas. the intersection of the 1.500
psia initial pressure line with the 100°F irtitial temperature CUT\-'£,
gives a final pressure of 490 psia. Similarly. from Figure 5-13 for
a 0.7 gru\'ity gas, the final pressure is equal to 800 f6ia. By interpolation, the 0.685 gravity gas can be expanded without hydrate forma.
tion to a pressure - 490 + (800 - 490)(0.685 - 0.6)/(0.7 - 0.6)
753.5 psia.
Systems alld Dehydration Processing
,
]
The lOO"F initial temperature curve does not intersect the 1,000 psia
initial pressure line for a 0.6 gravity as well as a 0.7 gravity gas.
•
4
6000
4 000
/
3
/
/
4
/
t
<
~
•
150
ff
J
.,
Hence, the gas at these conditions can be expanded to any pressure
without hydrate formation.
////
Katz et aL ,\(ethod
00"
•
Y>
JOO •
f •...,r pr ........... P""
",l7// t?'
40
•
Figure 5-12. Approximate permissible expansion of a O.6-gravity natural gas
without hydrate formation. (From Engineering Data Book, 1981, courtesy of
GPSA.)
rP' 0/'
ee
4
""'f---/r-:-'+--+++++1+tt---t-t- ~
co
1--....
~
<• zoe 1-,(
/
/
r.~
4
•
,
00
Te"'P"',ahJ,.,
]I)
~-=-,.,
00
The Katz et a1. (1959) method is based upon the principle that the gases
entrapped in a natural gas hydrate resemble solid solutions, because on release during the decomposition of the hydrates, they increase in density. It
uses vapor-solid equilibrium ratios, K,~, first proposed by Carson and Katz
(1942),
f
Figure 5-11. Pressure-temperature curves for approximate prediction of hydrate formation for natural gases. (From Engineering Data Book, 1981 ; courtesy
of GPSA.)
K .. - yfx.
(5-9)
where y - mole fraction of hydrocarbon in the gas on a water-free bas~
X. - mole fraction of hydrocarbon in the solid on a water-free basiS
'90
Gas-Water Systems cmel Dehydration Proces$ing
CD' PrOOtlcljoll Engineering
~
~ NlTLAl
I
f II.
Efro'o'UAtUtf
V
,
j ; ,/,
./
/
~
!
;;i
1
,
,
';'l'/
,
..... j
,,/
,
~
1
Z/
?7
V"
,_."
V
y
i~-
""-
From this de£inition of K,,, it is clear that K" is equal to (XI for gases that are
non-hydrate formers. Thus. for hydrocarbons heavier than butane, K" is
CD. The original method assumes that nitrogen is a non-hydrate former. and
that n-butane, if present in mole fractions less than 5%, has the same K,
value as ethane. Theoretically. this is incorrect, but from an applications
standpoint, e\-'cn using a K,~ equal to 00 for both nitrogen and n-butane
gives acceptable results (Campbell, 1984a).
K" values for components in a gas can be found from Figures 5-17
through 5·22. Hydrates will form when the foUowing equation is satisfied:
(y K, ...:) - 1.0
V/ / v,/
~
1
Figure 5-13. Approximate permissible expansion of a O.7-gravily natural gas
without hydrate formal1on. (From Engmeenng Data Book 1981 courtesy 01
GPSA)
•
•
Er~ I
/1/
,//,V
!
i
,
,
-¥-II
:;0:
,
•
'/
~
~///
~
i
i
'/
,,
'9'
r.'
.:.
.-.........,-
1!oOO 2ODO
•
3OilO
Figure 5-14. ApprOXimate permiSSible expansion of a O.8-gravity natural gas
WIthout hydrate formation. (From Engineenng Data Book, 1981; courtesy of
GPSA.)
This method accounts for H2S and CO 2 • and has proved to be very reliable up to about 1,000 psia. A gas with an H ~S content greater tha!l 20%
can be considered to behave like pure HzS regarding hydrate forming characteristics. To account for gases that contain large amounts of nitrogen,
Heinze (1971) gave the following relationship, valid up to a pressure of
about 5,800 psia:
E" (y,K~)
T
,' ,-~I:cc=­
h" - 0.445
(5-10)
Thus, caJculation of the hydrate forming condition is similar to the dew
point calculation for multi-component gaseous mixtures.
00
where Th - hydrate formation temperature. K
(5-11)
'92
GQ" Product/ou En~illf~mng
CQ"- Water- System" Qnd Dehydration Processing
--
•
INITIAl
TEMf'flAMf
"
a
H!\-1
-~
,
I
•
,
•
.,
.,,
."
,
,,
,,
Y.%
I---
,
/
Ii:'/
n-C~
I
/
H,S
N,
~
,
-
1500
8(X)
101»
IlCX)
f.:"
,
~
l~
11'1.,/
2000 JIXD
~
'.001_.-
At 55°F
-.iL
K'~i
y;lK':>I
~
lI/K,,,,
0.800
0.050
0.DJ5
0.005
0.025
0.065
0.020
1.69
1.23
0.24
0.4734
0.0407
0.0625
0.0
0.0
0.3038
0.0
0.8801
1.61
0.79
0.106
0.4969
0.0633
0.1415
0.0
0.0094
0.4048
0.0
~
;
1>;'- V
,
-
0.28
,,'
,,
/
"" ,., "'" "'"
.........
~
,
to',.,
,
~
I
,
t
At 60°F
CO,
IJ
-l-'
!
Examplr 5-6. The gas given in Example 5-2 is at 500 psia. At what temperature will hydrates form?
Solution
C,
C,
C,
~.,
' ,
, ,
Hf
/
Figure 5·15. Approximate permissible expansion of a O.9-gravily nalural gas
without hydrate formation. (From Engineering Data Book, 1981; courtesy of
GPSA.)
Coml2'
,
/
V
/
,
,
:::--:
~
!::
~
I
,
-\iii
,
I
193
~
2.65
0.21
~
l.J 159
Figur e 5-16. Approximate permissible expansion of a 1.().gravity natural gas
without hydrate formation. (From Engineering Data Book, 1981; courtesy of
GPSA.)
Thus, the hydrate forming temperature corresponding to a 500 psia pressure
is between 55°F and 60°F. Further guesstimates may be made to converge to
the temperature value that makes r: Yi/Kvo;I - 1.0.
From a simple interpolation, the hydrate forming temperature can be calculated as:
T, - 60 - (60 - 55)(1 - 0.8801)/(1.1159 - 0.8801) - 57.5°F
Trekell-Campl)eU Method JOt" /'ligh-Prntnlre Gas
Trekell and Campbell (1966) provide corrections to the Katz et a1. method
to extend its applicability to higher pressures and account for the negative
effect of the presence of non-hydrate forming molecules that are too large to
fit into the voids in the water lattice. The Trekell-Campbell method uses
(text continued on page 197)
19<
COl Proouction Enginunng
Gas- WatN Systems
GIld
Dehydration Processing
195
Figure 5·17. Vapor-solid equilibrium constants for methane_ (After Carson and
Katz, 1942; reprinted from Engineering Data Book, 1981 ; courtesy of GPSA.)
•
,-_....
Figure 5-18. Vapor-solid equilibrium constants for ethane. (After Carson and
Katz, 1942; reprinted from Engineering Data Book, 1981; courtesy of GPSA.)
Figure 5-19. Vapor-SOlid equilibrium constants lor propane. (After Carson and
Katz, 1942; reprinted from Engineering Data Book, 1981 ; courtesy of GPSA.)
...
'97
Cas- Water Systemr and Deh!ldration Procuring
"
08
"o·
t#+
,0,0/rc
OJ
./
",}
02
K
l".l
0
,O~
,0
'I>
,0-
0'
f
oce
008
00-
,01
"
,.,.
,.,.
A"~.. : • . .
"
"
TEMPERATURE of
,
, ,
,
, , , , ,,
, , ,
,, , , ,, , , , ,
,
"
,
0
,.'
,0
.0
8P7,091\
•
0
•
, ,
;::::
::::- v. ; /
,
"
•o
o•
,00
oJ
o
"
, , , ,
, , , ,
,,
' ,
, ,
,
'
,
, , ' ,,
~
I
'"
80
~
-'L1:co
'3 0
(!ext continlled from page 193)
"
Figure 5-20. vapor-solid equilibrium constants for iso-butane. (From EngineerIng Data Book, 1981; courtesy of GPSA.)
J0
iI
10
80
Tempera"". , Of
Figure 5-22. Vapor-solid equilibrium constants for H2S. (From Engineering Data
Book, 1981; courtesy of GPSA.)
./ol,lbetu.
I
.,
",
methane as the reference gas. The additive effect of other hydrate forming
gases, Cz, ell n-C., i·C~, and H~, at different pressures is determined from
Figures 5-23 to 5·28. CO i is ignored. Non-hydrate formers are grouped together into the pentanes plus (C 3 +) group, and their hydrate depression effect is determined from Figures 5-29 and 5-30 as a function of the mole%
pentanes plus, and the mole % pentanes plus on the basis of the gas fractions
from 4 to C~. This latter parameter can be written as:
I I
YC3t
(100 %)
l-Yc\- Yc 3+
, , ,
,
I~
60
Figure 5·2 1. vapor-solid equilibrium constants for CO;2- (From Engineering Data
Book, 1981 ; courtesy of GPSA.)
where YCI' YC3+ - mole fractions of methane and pentanes plus, re;pectively. in the gas.
Figures 5-23 to 5-28 indicate the hydrate forming temperature for methane at various pressures. To find the hydrate forming temperature at any
pressure, the appropriate chart is used to read off the temperature displacement for the gas components as a function of their mole% in the gas. These
temperature displacements are added to the methane-hydrate-forming temperature. U any pentanes plus are present, their effect (negative) is also
added. The sum then gives the hydrate forming temperature at the pressure
of interest. These calculations may be repeated for several pressures to obtain the hydrate curve for the gas.
(tnt continued
OIl
page 204)
•
19.
Ga, Production Engineering
Gas- Walt'T S!lstNru and Dehydration Proces.nng
199
•
,
KYDltATE i'UOICrtOti CKAl.T VOl 6.9 I'!P. {lOOO pd_]
Figure 5-23. Trekell-Campbell temperature displacement chart for hydrate formers al 1,000 pSia. (After Trakell and Campbell, 1966; reprinted Irom Campbell,
1964a; courtesy of Campbell Petroleum Series.)
7
9
:K)
K'(DRAT'! fttOICTION CIV.IlT rOf. D.8 1'1" (2000
II
12
l)
p.tO!
Figure 5. 24 . Trekell-Campbelltemperature displacement chari for hydrate formers at 2,000 psia. (After Trekell and Campbell, 1966; reprinted from Campbell,
1984a; courtesy of Campbell Petroleum Series.)
200
Co, Production Engineering
Cos· Water Synenu and Dehydratwn Processing
,
201
.
,
TEI'IP!lATt/U. OlSPlACEK[IIT. AT. DC
,
TDtPlIATlJU DISPlACIllENt OT.
°c
•
'0
HYDRATE I'UDlCTlOJ( CHAJ.T rOIl 20.1 M" [lOOO poh]
Figure 5~2S. Trekell-Campbetltemperature displacement chart for hydrate formers at 3,000 psia. (After Trekell and Campbell, 1966; reprinted from Campbell,
1984a; courtesy of Campbell Petroleum Series.)
KYDlAT! PUOICTIOll CKAJlT
,01.
27.61'1P. (4000 pol_1
Figure 5-26. Trekell-Campbelltemperature displacement chart for hydrate formers at 4,000 psia. (After Trekell and Campbell, 1966; reprinted from Campbell,
1984a; courtesy of Campbell Petroleum Series.)
202
Go" Productum Engineering
o
TDtNU.nru DlSP1.o\C!HZIIT.o. T
2,
Cos- WaIn SyJteml and Dehydration ProceMing
•
203
"c
•
,
•
o.
o
,
o.
tn'lIRAn PI.l:DU:tION C1tAI.T rot. 34.5,.. ()OOO pd_)
Figure 5-27. Tr~kell-Campbell temperature displacement chari for hydrate formars 815,000 pS18. (After Trekell and Campbell, 1966; reprinted from Campbell,
1984a; courtesy of Campbell Petroleum Series.)
tn'DIA.T! lUOICTIOII C1t.UT
roa
41.4",_ [6000
p"al
Figure 5-28 . Trekell-Campbelltemperalure displacement ?hart for hydrate formers al 6,000 psia. (After Treke!! and Campbell. 1966; reprinted from Campbell,
1984a; courtesy of Campbell Petro/eum Series.)
204
Cas Production Engineering
205
Co.t-Waler Sysleml and Dehydratian Processing
(tert continued from page 197)
,
,,
The Trekell-Campbell method is applicable to gases in the pressure range
TDtPEItATIJU OISPUCDWIT (-6T), DC
of 1.000-6,000 psia.
)',~.(1 00.J
Exampk 5-7. For the gas with composition given below, nnd the hydrate
formation temperature corresponding to a pressure of 6,000 psia.
I-)"L-)'C~'
Soilltion
Comp.
-1L
C,
C,
C,
n_C.
0.810
0.050
0.025
0.Ql5
0.010
0.015
0.025
0.050
1.000
i·C~
C"
CO,
H,S
.c:1T. of
75.60
0.75
4.1
0.25
1.9
-1.17
0.0
0.0
81.43
In this table, the aT values for CI. C 2, C 3, n-C•. and i-C~ are obtained from
Figure 5-28. Note that H~ has a negligible effect on the hydrate fo rmation
temperature at high pressures and is therefore not reported in Figure 5-28.
The value of ()'e,.)(IOO%) / (1 - Ye, - Ye,,) - (0.015)(100) /(1 _
0.810 - 0.015) - 8.57
In Figure 5-30, interpolation is made between the 8.0 and 9.5 lines to get
aT - - 1.17 corresponding to C 5 .. - 1.5%. Thus, the hydrate forming
temperature corresponding to a 6,000 psia pressure is 81.43, or B1.4°F.
••
.,
~
'l--~
,
,,
,
,
•
Figure 5-29. Trekell-Campbell temperature displacement chart for non-hyd.rate
fOfmers (pentanes plus) at 1,000 psia. (After Trekell and Campbel!, 1966, reprinted from Campbell, 1984a; courtesy of Campbell Petroleum Serles.)
M cUod-CompbeU Method for \'ny High Pre&YUre Su:ut Ca.
Table 5-1
For gases alxwe 6,000 psia, the Trekell-CampbeJl approach is not quite
valid. For the 6,000-10,000 psia pressure range, McLeod and Campbell
(1961) propose the following relationship:
(5-12)
where Th - hydrate forming temperature, DR
The KJ values are as shown in Table 5-1. The mole fractions of the components, Yr. are normaJized to the C 1 to C~ content. All other components in
the gas are ignored. The method, therefore, has limited applicability.
~ Values for the Mcleod-Campbell Method for Predicting Hydrate
Formation '
K. VIIlues
Pressure
MP,
41.4
0000
".3
7000
55.2
0000
62_1
9000
!O 000
00.0
C,
Psi.
"933
"096
19246
19367
19489
. After McJ...oood .nd C.mpbell,
""
C,
20806
20 848
20 932
"094
21 105
0,
28
28
28
29
29
38'
700
784
182
200
'-e,
'" 696
n-C.
17 340
30 913
17 358
'" 935
17868
17868
31 109
30 935
17 491
•
206
Gas Production Engineering
Gas-\\ater Synem.y and Dehydration Procnnng
Example 5·8. Repeat Example 5+7, using the McLeod-Campbell method.
207
(~),OC
I'DIP'U.\'IIIJ.! DUP'UoCEHEH'I
0.)
1
Solutio"
YC5·{lOClSj
Compo
C,
C,
C,
n-C 4
i-C 4
C,.
CO,
H,S
v
---'0.810
0.050
0.025
0.015
0.010
0.015
0.025
0.050
-v,
0.8901
0.0549
0.0275
0.0165
0.0110
"
1 - YCl - YC5.
K,
"
18,933
•••
20,806
28,382
17.340
30,696
0.0
0.0
0.0
~
1.0
iS I.'
'.0
m
'.0
E
Using Equation 5-12.
i
u
1.0
T, ~ (3.89)(19,398.78"') _ 541.80 oR _ 81.8 oF.
Note that this compares well with the value of 81.4°F determined using the
TrekelJ-CarnpbeU method in Example 5-7.
EqlUlhlnl of State Methods
Several complex computer solution methods have been developed for predicting hydrate (orming conditions. Most equation of state methods are
based upon the Van der Waals and Platteeuw (1959) statistical thermody_
namic equation for the chemical potential of water in the h}'drate lattice.
The different methods essentially use different intermolecular potential
functions. Van der Waals and Platteeuw (1959) used the Lennard-Jones 12-6
potential. Nagata and Kobayashi (1966) used the Kihara potential that they
showed to be better than the Lennard-Jones model. Parrish and Prausnitz
(1972) expanded the concept of fitting hydrate parameters to develop a generalized method for predicting hydrate dissociation pressures for gas mixtures, using the Van der Waals and Platteeuw (1959) equation and the Kihara spherical core model. Ng and Robinson (1976) have added. another
adjustable parameter to the Parrish and Prausnitz (1972) algorithm to improve prediction of the dissociation pressures for multicomponent gases.
Holder and Hand (1982) presented a modified form of the Parrish and
Prausnitz (1972) model.
'.0
1.0
0.1
0.'
•
o
o
o.~
t.O
I.S
TDG'lUtvU aluactlOll h~r)
1.0
.,
Figure 5-30. Trekell-Campbell temperature displacement chart !or non-hydrate
formers (pentanes plus) in the pressure range of 2,000-10,000 pSla. (After Trekell
and Campbell. 1966; reprinted from Campbell, 1984a; courtesy of Campbell Petroleum Series.)
The complexity of these models precludes further discussion here. These
methods too can at best give only approximate an.ru·ers and should be used
with caution.
Preventing Hydrate Formation
The permanent solution for hydrate problems is dehydration of the gas to
a sufficiently low dew point. Commonly used dehydration methods include
208
Gt» Prodlll:t/on Engineering
absorption dehydration using a liquid dessicant. adsorption dehydration using a solid dessicant, and ~imultaneous dehydration and gas-liquid separation by expansion dehydration.
At the wellsite. two techniques are applicable: (1) heating the gas stream
so that it becomes undersaturated, and maintaining flowlines and equipment at temperatures above the hydrate point; and (2) in cases where liquid
water is present and the flowlines and equipment cannot be maintained
above hydrate temperatures. inhibiting hydrate formation by injecting ad.
dith'es that depress both hydrate and freezing temperatures. This latter
technique is discussed in the following section. Note that in practice. hydrates are a problem only when allowed to accumulate and grow to a size
that restricts or stops the flow. Otherwise, they are of no consequence.
Hydrate Inhibition by Additive Injection
Additive injection is generally required for gas streams from producing as
well as storage wells in order to prevent corrosion and hydrate formation in
the gas gathering and transmission systems. In some cases, gas being injected into a reservoir for st(lrage purposes also requires the addition of certain additives to protect the casing, tubing, and sand face (Curry, 1981).
Types of Additives
The mast common additives are methanol, ethylene glycol (EC), and
diethylene glycol (DEC). Methanol is used the most, because it disperses
well in the gas stream, is readily available in bulk, is the least expensive,
and, consequently, does not require recovery. Methanol, however, can cause
contamination problems in plants. Whereas most additives are recovered
and recycled, methanol recovery is often uneconomical.
Methanol injection is very useful in cases where low gas volumes prohibit
dehydration processing. It is preferable in cases where hydrate problems are
relati . . ely mild, infrequent, or periodic, inhibitor injection is only a temporary phase In the field deVelopment program, or inhibition is done in conjunction with a primary dehydration system.
EC and DEC are used primarily at low-temperature processing plants for
extracting natural gas liquids. The water phase of the process liquid contains the EG or DEC, which can be recovered and regenerated.
Injection Techniques
In the early years, gravity-type injection systems were being used. A gravity injection system consists of a capacity tank, a sight glass, and a valve
Cas-Water Systems Qnd Dellytiration Processing
209
manifold to maintain equal pressure across the chemical and to regulate its
entry into the flowing gas stream. This resulted in a generally sporadic injection and poor inhibitor dispersion, leading to freeze..offs (hydrates formation) during the operations.
To counter these problems, newer systems that feed the additive at a uniform rate into the gas stream. such as the pneumatically powered chemical
injection pumps, have been designed. Continuous injection is also desirable
from the standpoint of field personnel who can then operate on a regular
basis. Further. precise chemical requirements can be predicted and bulk
purchases made at possibly lower costs.
The injection pump is usually of the positive-displacement type, so that it
pumps a constant amount of chemical into the gas stream, regardless of the
pressure of the gas against which it must inject the chemical. Since positive
displacement pumps do not sense any buildup of discharge pressure, a rupture disc is put at the discharge end of the pump. Any brass or copper components in the pump should be avoided, since these metals are subject to
severe physical breakdown in the presence of sour gases. The pump injects
chemical downward into the running end of a vertically installed tee of a
size about one inch. The tee functions as a sort of mixing valve. Metering
devices are installed to permit chemical injection at a proportional-ta-flow
rate, eliminating frequent manual adjustment. As a precautionary measure
in field operations, all valves and accumulator systems where free water
may accumulate are precharged with methanol to prevent hydrate formation.
Prediction of Inhibitor Requirements
The weight percent inhibitor concentration in the aqueous phase, w, reo
quired to lower the gas hydrate freezing point by dOF. is given by Hammerschmidt's equation:
w _ ",(
~;::M!-,-)(l:;coo:;t-)
K+dM
(5-13)
where M - molecular weight of the inhibitor
K - a constant, 2,335 for methanol, 4.000 for the glycols.
Equation 5-13 can be rearranged to calculate the lowering of the gas hydrate freezing point for a given weight percent inhibitor in the aqueous
phase:
d _ =;;:,-;-v.::K-,;"
100M - wM
(5-14)
•
210
Typically, Equation 5-13 would predict injection requirements of 2-3 gallons of methanol per MMscf of gas. In practice, only about 1 to 1.25 gallons
per M\1scf may be required in most cases. Thus, Equation 5-13 is designed
to overpredict chemical requirements so as to yield "safe" numbers. Consequently, the process of inhibition is really quite economical if the minimum
re<luired amount of chemical is injected.. This is usually determined in field
operations by reducing chemical amounts to a point where hydrate fo rmation (freeze-off) begins to occur, and then keeping chemical injection just
s1illhtly above this rate. \.inst predictive techniques arE' no bt-tter than a rule
of thumb; it is advisable to correctly evaluate chemical requirements by
field-testing.
Absorption Dehydration
Absorption dehydration involves the use of a liquid dessicant to remove
water vapor from the ga.~. Although many liquids possess the ability to ab.o:;orb water from gas, the liquid that is most desirable to use for commercial
dehydration purposes should possess the following properties:
1. High absorption efficit::nc),.
2. Easy and economic regeneration.
3. Non-corrosive and non-toxic.
4. No operational problems when used in high concentrations.
5. No interaction with the hydrocarbon portion of the gas, and no contamination by acid gases.
The glycols, particularly ethylene glycol (EG), diethylene glycol (DE C),
triethylene glycol (TEC), and tetraethylene glycol (T.EG), come the closest
to satisfying the<>e criteria to varying degrees. Glycols are preferred because
they offer a superior dew-point depression. with process reliability and
lower initial capital and operating costs. For a lO-MM.scfd plant, soud dessicant will cost about 53% more than a TEG plant, and for a 5O-MMscf/d
plant, it will cost 33% more than TEC (Guenther, 1979). Wherever it can
meet dehydration specifications, economics usuall)' favors glycol dehydration over other processes (GPSA, 1981). The equipment is simpler to operate, maintain, and automate, and plant operation is continuous. Furthermore, glycols can be used in the presence of materials that may foul-up a
solid desiccant, and can be regenerated . Glycols can be used for sour gases,
but acid gas absorption necessitates certain precautions (Table 5-2A).
Of all the glycols, almost all the plants use TEG because of lower vapor
losses and better dew-point depression (Table 5-28). TEG has been success-
211
GaJ-U'tI:ter SyJtem.t and Dehydration Processing
Go" Produclion Enginet'ring
Table 5-2A
Physical and Chemical Properties of Glycols"
Molecular weight
Specific grll,it}' lit 68~F
Spceific weight. Ib.:gal
Boiling point at 760 mm IIg, F
Fn=.ing point. Of
Surface tension at 77" F.
dvnes/cm
Hea't of ,·.porizalion at JOO mm Hg,
Btwlb
Ethylen.
Glycol
Diethylene
Glycol
Trlethylene
Glycol
62,07
I 1155
9_292
387.i
91
106.12
1.1184
9.316
474,4
IR 0
150.17
1.12.55
9.375
47.0
44,8
45_2
3&1
23'
174
"'24'
"
• After Siulb. 19i8_
Table 5-28
Variation of TEG Properties with Temperature"
Temp.,
OF
Sp Gr
Viscosity
50
75
100
125
150
175
I 134
88
56
200
225
250
300
1123
I III
I 101
1.091
LOBO
L068
23
15.5
6.1
6.1
<.0
1,0157
3.1
103<
L'
L5
1.022
Sp Helt,
Btullb -F
0,48:s
6.'"
0.52
0S35
0"
0.57
0585
0.00
0.635
0.65
Thenul
Conductivity,
Btu/(hr Itl - Flit)
0_14
0.138
0.132
0.130
0.125
0.121
0.118
0.113
, Aft.... Siv.lls. 1976,
full y used for dehydrating sweet as well as sour natural gases to effect a
dew-point depression of 40 to 140°F. for operating conditions ranging from
25-2,500 psig and 40_160°F (Ikoku. 1984).
Process Flow Scheme
Figu re 5-31 shows a typical flow sheet ror a glycol dehydration plant de.
scribed in detail by Si\'alls (1976). The wet gas is first sent to a scrubber to
remove any liquid water and hydrocarbons. sand. drilling mud, and other
solid matter. These impurities must be thoroughly removed, because they
•
214
Cas-Water SyslemJ and Dehydratian Processillg
GO! Production Engineering
1. Methanol, absorbed by the glycol along with water from the gas
stream, increases the heat requirements in the regeneration system.
2. High methanol injection rate;, and carryover of slugs of liquid methanol can cause flooding in the absorber and regeneration system.
3. Aqueous methanol is corrosive to carbon steel, leading to corrosion in
the reboiler and still.
4. A methanol recovery unit is required at the water \'apor outlet, because methanol cannot be vcnted directly to the atmosphere due to en·
vironmentaJ hazards.
Any dirt or impurities can contaminate the glycol solution severely. Overheating the glycol can lead to solution decomposition, with both low as well
as high boiling products. The reaction products form a sludge that collects
on the heating surfaces. reducing process eHiciency and in some cases, causing complete flow stoppage. This can be avoided by installing a filter at the
downstream end of the glycol pump.
Glycol becomes quite corrosive with prolonged exposure to oxygen
(GPSA. 1981). For this reason, a dry gas blanket is sometimes provided on
the glycol surge tank. Presence of oxygen in the gas stream, however, mav
require special precautions. Corrosion may also be a problem in the presen~
of acid gases. A low pH accelerates decomposition of glycol. Generally, pH
is controlled in the range 6.0-7.5, measured at a 50·50 dilution with dis.
tilled water, to avoid glycol decomposition (GPSA, 1981 ).
Carryover of liquid hydrocarbons can result in solution foaming. Foam
inhibitors are normally used to avoid such a situation. Removal of all liquids
from the gas is necessary before sending it to the contactor. because these
liquids may, over long periods of time, leave crystalline deposits in the con.
tactor. To prel-'ent condensing of any hydrocarbons in the contactor, the inlet
dry glycol must be maintained at a temperature slightly greater than that of
the gas stream (Sivalls, 1976). Liquid hydrocarbons carried over into the
stripping still cause severe damage. They may lead to vapor flooding in the
reboiler and still due to the increased vapor load. Consequently, glycol will
be carried out of the stiJI along with the gas and water vapor. Heavier-end
hydrocarbons will cause coking in the still and reboiler. and may also hinder
glycol reconcentration.
H~ghly concentrated glycol is very viscous at low temperatures, helow approximately SO°F. A heater may be required, especially in cold climatic conditions where the nowlines may solidify completely. Finally, to ensure good
gas-glycol contact, all absorber trays must be completely filled with glycol
at all times. Sudden liquid surges should be avoided to minimize solution
carry-over losses.
215
Glycol Plant Ocsign (After SivaJIs, 1976)
The primary variables required for the design include gas now rate
(M~tscfd); gas gra\;ty; operating pressure (psia); maximum working pres-
sure in the contactor (psia): gas inlet temperature rF): and outlet water
content required in the gas (Ibm, MMscf). In addition, two criteria must be
selected for the design:
1. Glycol to water circulation rate. Requirements are generally in the
range of 2-5 gal TEC per lb water removed (CPSA. 1981 ); most field
installations use 2.5 to 4 gal TEC'lb H 20 removed (Ikoku, 1984).
2. Concentration of the lean TEC from the regeneration system. This
ranges from 99.0% to 99.9%: most designs use a 99.5% lean glycol
concentration.
The glycol to water circulation rate depends upon the lean glycol concentration, and the number (and efficiency) of trays in the absorber. Lean TEG
concentration is determined by what the regenerator can deliver (which is
primarily a function of the amount of stripping gas supplied to the regenerator), and the permissible lower limit of glycol viscosity the plant and equipment can handle.
Frequently, dehydration requirements are expressed in terms of dew-point
depression. This can be calculated easily as the difference between the inlet
and outlet gas dew-point temperatures. Sometimes. the inlet gas temperature is known, and the outlet gas water content is specified. In either case,
the inlet and outlet gases are assumed to be saturated, and their water content, or dew-point temperature, is determined using any of the available
correlations.
The amount of water to be removed. \V, in Ibmthr, can be calculated as
follows:
IV, - (q/24)(W, - IV,)
(5- 15)
where W I. W ° _ water contents, Ib waterlMMscf gas. for the inlet and outlet gas respectively.
A conversion factor of 24 is used in Equation 5-15 to convert the gas rate q
from MMscfd to MMscf/hr.
I"let Scrubber
The inlet scrubber is generally chosen based upon the operating pressure
and gas capacity. The data shown in Tables 5-3 and 5-4, and Figure 5-32,
may be used for this purpose. Cenerally, a two-phase scrubber with a 7.5 ft
shell height is used.
•
212
Gas Productwn Engineering
--~
L.
_
0
.. ..,
'
--
Figure 5-31. Flow diagram for a glycol dehydration plant. (Afler Sivalls, 1976;
courtesy of C. R. Sivalis and the University of Oklahoma.)
may lead to (oaming. flooding, poor efficiency, higher glycol losses, and
maintenance problems in the glycol-gas contactor (also called absorber). A
mist eliminator is also provided at the scrubber outlet to ensure good gas
cleaning. The clean gas is then sent upward through the absorber, countercurrent to the flow of glycol. The absorber consists of several trays that act
as equilibrium separation stages where water vapor from the gas is absorbed
by the glycol. Glycol usually absorbs about 1 sci gas/gal at 1,000 psig absorber pressure (CPSA, 1981). Absorption is more in the presence of aromatic hydrocarbons.
Dry gas from the top of the absorber is sent through a mist eliminator (to
remove any entrained glycol droplets) to a gas-glycol heat exchanger (shown
as glycol cooler in Figure 5-31) where the gas cools the hot regenerated gly_
col before it enters the contactor. After this heat exchange, the dry gas leaves
the dehydration unit. The cooled glycol enters the absorber from the top.
The wet glycol from the bottom of the glycol-gas contactor is first sent to
a high-pressure filter to remove any solids that may have been acquired by it
from the gas stream. The energy of this high-pressure glycol is then used to
drive the glycol pump, which pumps the dry regenerated glycol to the contactor. This results in a considerable energy savings for the process. From the
pump. the wet glycol flows to a low-pressure flash separator where any dis.
soh'ed or entrained gas is removed. A three-phase flash separator rna}' be
required if the wet glycol also contains an appreciable amount of liquid hydrocarbons absorbed from the gas stream in the contactor. The separated
Co,," Water SysUms aod Dehydratian
Pr~og
213
gas is used either as fuel gas for the reboiler, or is vented to the atmosphere.
Clycol from the bottom of the flash separator is sent to heat exchanger coils
in the glycol surge tank to preheat it by heat exchange with the hot, dry
regenerated glycol from the glycol regenerator.
The preheated wet glycol is then sent to the stripping still, which is a
tower packed with ceramic saddle.type (or other types) packing, mounted
on top of a reboiler. The glycol flows downwards through the packing (that
acts as equilibrium separation stages for glycol-water separation) into the
reboiler Water vapor liberated from the glycol in the reboiler passes upwards through the packing, providing heat and picking up some water from
the wet glycol flowing downwards. The water vapor leaves the unit from
the top of the still column through an atmospheric reflux condenser that
provides a partial reflux for the column (Sivalls. 1976).
In the reboiler, glycol is heated to approximately 350-400°F to reconcentrate it to 99.5% or more. In order to obtain glycol of such a high concentration, it is usually necessary to add some stripping gas to the reboiler (Sivalls,
1976). Using a valve and a pressure regulator, a small amount of gas from
the fuel gas system is injected into the bottom of the reboiler through a
spreader system. This gas aids the removal of water from the glycol by three
mechanisms (Sivalls. 1976): (1) it "rolls" the glycol in the reboiler to allow
any pockets of water vapor, entrained in the glycol due to the high viscosity
of the glycol, to escape; (2) it lowers the partial pressure of the water vapor
in the reboiler and still column, thereby allowing more water to vaporize
from the glycol: and (3) it provides a sweeping action (a combination of absorption of water, and creation of a pressure drop for the water vapor to
flow) to drive the water vapor out of the reboiler and stripping still system.
The reconcentrated glycol is sent to the shell side of the heat exchanger,
which also serves as a surge tank. Here the regenerated glycol is cooled by
heat exchange with the wet glycol stream, and is accumulated for feed to the
glycol pump through a strainer. From the pump, it passes through the shell
side of the glycol-gas heat exchanger (glycol cooler), into the top of the absorber.
Total glycol losses. excluding spillage, range from 0.05 gallMMscf for
high-pressure low-temperature gases. to as much as 0.30 gallMMscf for lowpressure high-temperature gas streams (CPSA, 1981). These losses comprise
mechanical carryover from the contactor, and vaporization losses from the
contactor and regenerator.
Glycol Plant Operational Problems
Methanol, injected at the wellhead for bydrate inhibition. can lead to several operational problems in glycol dehydration plants:
•
218
COl Produt:tlon Engineering
Gal-Water Systeml and Dehydration Procasing
...
•
•
•
"
p
./
"7
/'
:;:;;
.....- I--- :--
V
/' .....- I---
I
i •,••
--
V ~
/'
~
.r~
~~
"~
J
•
•
'p
'V,
V-
~~
/
•
:2
•
-- e-
•
•
.- ~
i
V
/'
10
• ~ :;;
.••
I •V
~
,
,.-00
•
•
I---
~
----- --
. r~
•. ...1
~.!
f0-
.J
- -
~,
,1- DO
,.-00
,:r· o~
'V VV
'V
V
V
V
•
•
~
,
. ~
--
·v
1.....- :--
...
.~
•
~~
-
~~
-••
.~
219
a
~
a
,~
,~
Figure 5·32, Gas capacity of vertical inlet-gas scrubbers, based upon a 0.7.
gravity gas al1000F (After Sivalls, 1976; courtesy of C. A. Sivalls and the Univer-
sity of Oklahoma)
Figure 5-33. Gas capacity of Irayed glycol-gas conlaclors, based upon a .0.7gravity gas at 100° F. (Atter Sivatls. 1976; courtesy of C. A. Sivalls and the Umversity of Oklahoma.)
Clycol·Ga, COl1 tactor
Contactor diameter can be selected using Figure 5-33 for a trayed-type.
or Figure 5-34 for a packed-type design. Gas capacities determined using
Figure 5-33 or Figure 5-34 must be corrected for operating temperature and
~as specific gravity as follows:
••
q - q,(C,)(CJ
where
..••,•
q - gas capacity at operating conditions, MMscfd
qb - gas capacit)' at the base conditions of 100°F for a 0.7 gravity gas, MMscfd
C" C, - correction factors for operating temperature and gas grav-
Ity, respectively, as shown in Tables 5·5 and 5·6 for both
the contactor types
•
,
,
0- 00
.....-
--
V ..... V_
~r;:V
•
..
,,-00
~
1.-0 0
-
, -00
11,.-()!I
'=
10'0.- ()!I
,
,~
0".................. ...,
Additional specifications for contacton; are given in Tables 5·7 through 5-10.
The approximate actual number of trays required in the contactor (for a
tray-typecontactor), or the depth of packing (for the packed-t}1Jecontactor)
Figure 5-34. Gas capacity 01 packed glycol-gas contactors, based upon a 0.7gravity gas at 100°F. (After Sivalls, 1976; courtesy of C. A. Sivalls and the University of Oklahoma.)
•
220
Cal Productioll Engineering
Gas-Water System! and Dehydration Processing
Table 5-5
Temper.ture Correction Factor,
Ct,
for Gas Capacity of Trayed and Packed
Glycol-Gas Contactor.·
"
Opeqtlng temperature
e,
OF
Tnlyed
40
50
00
70
110
90
Pock. .
1.07
106
105
1M
0.93
0."
1.02
".,.;
0.9,
1.01
0.99
100
100
100
110
0.'"
0.98
1.01
1.02
120
,
"
•
I
! •
,•• •
•
,I
°
• After Si\'alb. IQ76
Table 5-6
Gas Specific Gravity Correction Factor, g • tor Gas Capacity of Trayed and
Packed Glycol-Gas Contactors·
e
Gas specific
C,
gravity
Trayed
Packed
0.55
1.14
113
0.00
065
0.70
0.75
0110
0.85
0110
lOB
lOB
104
100
I().!
0.97
0.93
0.00
0.88
I,
-~-
"-
I'--. '.,
{, ,
,
Figure 5-35. ApprOXimate number of trays, or depth of packing,
required for glycol-gas contactors. (After Sivalls. 1976; courtesy 01 C. A. Sivalls and the University 01 Oklahoma.)
---
\
f'..
i'- t-......
~ i'""- "- t--
'"
,
•.
,
221
t::::
w,
..
u',
,
,o
I I I
°
• , •
•
"'-10 ..............' _ " ..... 1((;1" H,O
•
100
0.97
0."
0.91
"r---,---,----,---,----,
0.88
BOTTOM OF COLUMN
• After <ii •• llt, 1976
required, can be determined using Figure 5-35. This figure assumes that the
depth of packing in feet for a packed-type column is equal to the actual
number of trays for a tray-type column. This is only true when I-in. metal
pall rings are used as the packing material in the packed-type contactor.
Corrections for other packing types can be made fairly easily (see, for exam.
pIe, C hemical Engineers' Handbook , 1984), A minimum height of packing
equal to 4 ft should be used.
A more accurate procedure for calculating the number of trays (or the
depth of packing) required is to use the McCabe-Thiele diagrams, widely
used in designing equilibrium separation process equipment. The procedure
for constructing this diagram , shown in Figure 5-36, is as foll ows:
(tert co Fltinlied on page 226)
Figure 5-36. McCabeThiele diagram lor Example 5-9.
."
3
~
"
u
"
~oz
ffi
;
10
. ..
"
..
- - "II. TEG CONCENTRAT ION
"
222
Production Engineering
G(U
GUJ- Wotn
Systems and Dehydration Procesring
223
Table 5-7 Conllnued
Table 5-7
Specifications for Tray-Type Glycol-Gas Contactor.Nominal
Nomina'
Go.
Nominal
WP
Size
CliPKity,
~
DO
MMsc'd ' •
""
12 ....
IS
IS'
2.4
'J :1.
"
"'.
'"
30'
147
W
19.7
00'
26.3
32 .•
40,6
12 1', "
".
lB'
20'
'"
.,.
30'
36'
'"
".
600
00'
]2114"
".
IS'
20'
24'
31)'
36'
".
2.0
32
'.3
5.3
'.3
13,1
]9.2
2i.4
35'
44.05
05,':;.2
""
"
55
.5
143
'12
48'
29.'
39.'
00'
49.3
6U
....
" After
9'
36'
".
,.500
4.0
61
S,,'.JI~.
Ga.
Nominal
Gal Inlet
and Outlet
s",
,.
Glycol Inlet
Glycol
Shipping
WP
and Outlet
Cooler
Weight.
Ib
P~'
00
1000
12.1., .
16"
lB'
s",
,"
s",
,.,
Z' x 4'
2 - x 4'
"'900"
3' x 5'
3' x 5'
3' x 5'
IAOO
,.
I'
Jl. 2'
x 6'
'.000
2,·mO
". x 6'
3,2(X)
11;2"
4' )( 6'
4.400
6'
6'
2'
2'
6' )( S'
6')( S'
6'
2'
2'
6.300
7,700
2'
9,000
l'
3'
,,.>, '
,.
6"
2"
2"
3"
3"
3"
3"
2'
3'
3'
3'
,.,.
3'
,.,.
3'
B'
6'
6'
,.
,.
3'
3'
3'
3'
,.,.
6'
O·
6'
".
." .
112"
,1,'. "
'
] i/2'
11.:2"
2'
,.
2'
1'2"
','
,,",".
'
I'
Pli!"
1112°
2'
,.,.
1976
.. C., Cl[lIIcily bibed un lOO°F. 0,7.p IT, and v....elworking prtSSll...,
'"
x
x
x
x
x
x
x
S"
4'
4"
05"
S"
S"
05"
"" x 6"
4' x 6"
6")(S6" x S"
6" x S"
2")( 4"
2" x 43" x 05"
3" x S"
3" x S°
3" x 05"
4"x64"x66° x S"
6° x S"
6" x S"
"'.
1.100
1.000
1.200
1.500
1,700
2.900
3.900
6.000
7.700
10.000
12.000
105,300
1.100
1.300
1.600
1.800
3,000
4,000
0,300
8,400
11 ,300
13,"00
16,500
S ize
24'
31)'
36'
".
".
54'
00'
'200
123i~"
".
lB'
20'
,.'
""..
30'
36'
....
,..
00'
121,.-
Cliptlcity,
MMscfd"
36'
Size
",.
27.5
37.1
49.6
62.0
6'
6'
6'
,.
j7,S
3.0
4.i
60
i,8
12,0
2'
3'
3'
3'
3'
,.
20'
29.8
"O·
41A
'"SSO
68'
91.1
31)'
Size
3'
3'
3'
3'
00'
20'
SIz.e
5.S
7.3
11,3
18.4
.,.
".
,..
...
CooIN
4.3
3.1
4.9
6.5
8.3
13.3
22.3
32.S
44.3
58.3
74.0
".
lB'
Glycol Inlet
end Outlet
,.,.
_.,-
". Gat e&P"rit)' Ins«! on IOO'F. 07 Ip
6'
6'
,.
2'
3'
3'
3'
3'
,.,.
6'
6'
6'
j(I'
Glycol
G•• Inlet
and Outlet
,"
".
,."
,.,.
2·)(4'
2' x 4'
1.:100
3' x S'
3')(-'>'
3' x 5'
3' x S"
2.100
, 000
11 2'
4'x6'
II l'
2'
.j'
,.,.
1/2 "
3,'4 "
3';4 "
,,..
,.
1112"
lilt"
,.
,.,.
I,Z-
','
,,."
'
"
Ji12"
,.,.
1112°
"
.nd contactor worklnll P""'u...,.
Shipping
Weight,
Ib
x 6'
6' x S'
6' x S"
6" x S"
2" x 4"
2" x 4'
3" x 5"
3" x 5"
3" x 05"
3" x 05"
4" x 6"
4" x 6"
6°xS6"xS6" x S2")( 4°
2" x 4°
3- x S3" x 05"
3"x5"
3°)(05"
4-)(6"
4" x 6"
6'xS"
6' x S"
6" x S"
I./lOO
4.200
5.500
8.500
11.800
16,200
20,200
26,300
'.500
1,900
2,300
3,000
'.900
6,400
10,000
13,JOO
IS,400
23,500
29,000
',000
2,200
2,000
3,500
5,000
7,500
11.700
14.400
"'.000
25,000
32.000
•
224
Gas Production Engilleerillg
Cas- Wafer Systems and Dehydration Processing
225
Table 5·8
Table 5-9 Continued
Specifications for Tray-Type Glycol-Gas Contaetors'
51,.
Stlndard
Shell
00
Height" •
12 4·
10"
lB'
13
13
13
'"
13
24 30'
13
""
,,"
13
13'
1.'3'
Add to
Height
Glycol Cooler
Height' •
For Add.
Tray, el .
9
9
,.."
00"
G..
,
10
2"
13
2'
I.
,.
25
36
53
,
,.,
9'
9
9
9
9'
9
13
42'
Nominal
Standerd
13
,.9'
2
2
2'
13'
9'
2'
15
22
16
2.'
36
5.0
8.2
11.8
16.8
20.9
26.6
32.6
73
00
liZ
137
1000
.!~ndltd
WP
pslg
250
500
Size
00
IOJ..·
12~4 '
W
Shipping
Weight,
2' x 4'
2' x 4'
51lO
2'
112'
2'
12'
"
2'
1i2'
2'
2'
3"
1; .. '
3-
11.'
3" x :5'
3" x 5'
""""
""
,..
2.6
I."
3A
4 .•
,';.:5
I (}l, .. •
12"'.. '
1.5
1().1i.·
12:1/1'
l4"
l6'
IS'
Glycol
Cooler
Size
11
25
3A
22
44
5.5
i.S
1.7
2A
"
3.8
4.8
3'
22"
2'
2'
3'
3'
3"
2'
2'
1liz'
I,~"
1,2'
liz'
li.'
li.'
I"
1/2'
1/2'
2'
lit'
2'
li2'
3'
li.'
• Mtff Siulb, 1976
•• CIlJ capr.ci1r htowd on IOO'F, O.7sp gr. and ,'.....A ""orkinl pn:515llrr
Size
Size
,."
"'"
]C).l< ••
00
81
,..
3.3
,0
5.2
66
8.2
11.8
2.5
3.6
23
,..
1200
}(}1,'••
,..
1231,'
41
5A
6.9
85
12.3
2.6
3.7
45
l().ll ••
,..
12"'"
10
00"
,,"
,."
,,"
600
Capllclty,
MMscfd' •
MM.cfd"
20"
1440
Glycol Inlet
and Outlet
Size
00
,,"
,,"
20"
,."
Nominal
Gas Inlet
and Outlet
Size
Glycol Inlet
and Outlet
,,"
Table 5·9
Specifications for Packed Column Glycol-Gas Contactors'
G..
Gal. Inlet
and Outlet
,,"
{mlf·!ray ro,awctor.
Nominal
c.pecfty,
12Ji.'
• Ahcr S;\.II •. 19711.
•• For
Size
x
x
4'
4'
3' x 5'
x
x
x
x
3- x
3" x
3" x
2'
2'
2"
2'
'"
4'
4'
,.
1lOO
650
1lOO
75"
900
.5.55'
2" x 4"
2' x 4'
1000
151lO
251lO
3' x .5"
650
750
1lOO
950
lloo
5.9
,,"
7.5
9.3
12.7
20"
24"
,","
3"
3"
3"
2"
2"
2"
2"
3"
3"
3"
2"
2'
,"
2"
3"
3"
3"
>,'
3'
3'
2'
2'
2'
2'
l'
1/2'
I'Z'
,,"
x S'
x S'
x 4'
x 4'
x 4'
x 4'
3' x S'
3' x 5'
3' x 5'
>,"
1"
112 "
2'
2'
2'
2"
3'
3'
3'
2'
x 4'
x 4'
x 4'
x 4'
x 5"
x 5'
x 5'
x 4'
liz"
2'
x 4"
1,'2'
2' x 4"
2' x 4"
112 "
li2 "
11~"
li2"
.,"
>,'
:li."
112"
>,"
3' x 5'
3' x 5"
3' x 5"
,,"
I"
Shipping
Weight,
,.
liOO
2iOO
900
1000
1100
1300
1800
2300
3500
1200
1300
1500
1700
2200
2800
4000
1300
141lO
1600
1000
251lO
3100
4500
• Mm S;"a1Is. 1976
" Cas t'apK1t} ~ on IOO"F, 0-', <P IU and r:ontactor "'orLng p ........ rr.
900
11 00
11lOO
1lOO
700
~'
2' x '"
2' x '"
,,"
3'
3"
2"
2"
Glycol
Cooler
Size
Table 5-10
Specifications for Packed Column Glycol-Gas Contactors'
Size,
00
IQJ,I. '
123f, '
l4"
l6"
,,"
00"
""
Standard
Shell
Height
Standard
Glycol Cooler
Helghl
Standard
Contacting
Element"
Glycol
Charge,
g"
0'
7'
7'
I' x 4 '
" x 4'
I ' x 4'
6
9'
9'
9'
9'
0'
,.
• Afu.r Si"a1Is. 1976
•• St.nd.rd oontact;nl
7'
7'
-, "
7'
7'
nrmn.t IJ carboa steel nwtal ptll1
rings of:AU
7
I ' x 4'
8
10
I' x 4 '
I' x 4'
12
14
" x 4'
"
lis~
in 1lt.bl,,_
•
22.
Gas Production Engineering
Gas- Water Systems and Dehydralian Processing
Figure 5-37. Dew
points of aqueous
TEG solutions versus temperature.
(After
Sivalls,
1976; courtesy of
C. R. Sivalls and
the University of
Oklahoma.)
(text corltinued from page 220)
/'/
~
1. Determine the concentration of the rich TEe leaving the bottom of
the contactor:
"
~
(5-16)
where C Roch , C, ...... "" concentrations of rich and It!an TEG, respecti\'ely. expressed as a fraction
PLntn - density of lean TEC solution in Ibm/gal
L... - glycol to water circulation rate in gal TEGllb
water
2. On the McCabe-Thiele diagram, the top of the column is indicated by
the water content of the outlet gas from the contactor, and the concentration of lean TEG. Similarly, the bottom of the column is repre.
sented by the water content of the inlet gas to the oontactor, and the
rich TEG concentration. Draw the operating line as the strai!(ht line
connecting the top and bottom of the contactor column.
3. The equilibrium line is drawn using data shown in Figure 5-37, and
any of correlations for the water content of gas as a function of pressure and temperature. This line represents the water content of the gas
that would exist in equilibrium with the various TEe concentrations.
4. Starting from the point representing the bottom of the column, the
theoretical number of trayx required are stepped off by triangulation,
as shown in Figure 5-36, till the top of the column is reached.
S. Use the tray efficiency factor (or packing factors) to calculate the actual number of trays (or depth of packing) required:
Actual number of trays - Theoretical number of trays/tray efficiency
Cenerall)'. a tray efficiency equal to 25% for bubble-cap trays, and
33.3% for valve trays is used, and the figure for the actual number of trays is
rounded off to the next higher integer value. For the packed-type contactor,
a minimum of 4 ft height of packing must be used.
Reboiler
The glycol circulation rate in gallons per hour, L, in the plant is given by:
L - L. W,(ql24)
(5-17)
...~
~
,
i
I
I
!
:/'
%/' :/'
/./' V./' ./'
/'
/
/./
V/'" V
/.
~
L
~
/
......
,o~
~
...
~
-yP
~
~
~
~
./
~
~
~
./
/'
V
~.
,~
~,~
/'
/'
.,~
~
~
",\
./
/'
./'
/'
./'
V
/'
/'
<" V-/ ' I/'
..-;P
/'
• <"
/'
~
"
•
-"
_M
.
,/
<"
....;:/
-~
-~
>I!..dY<"
-~
_c
/'
/'
/'
/'
/'
V-
•
-~
-~
•
227
,~
n.
,~
,
"
.
.
he heat required in the reboiler (also c~l.led
An approximate calculatIOn of t
be
d
iog the following empmcal
reboiler heat load). Q in Btu/hr, can
rna e us
relationship:
Q - 2,OOOL
(5-18)
hi h- ressure dehydration designs.
Equation 5-18 gives good results fbo°r.r~ atglo:d may be made from the folA more precise estimate of the re I er e
lowing procedure:
(5-19)
Ga.t- Water Systems aFid Dehydration Processing
228
Gas Product/on Engineering
where
QI" sensible heat required for glycol , Btulhr
Q ..... heat of vaporization required for water, Btu.' hr
Q... heat required to vaporize the reflux water in the still, Btu/hr
Qh .. heat loss from the reboiler and stripping still, Btu .'hr
These heat requirements are estimated from the (ollowing relationships:
OJ -
Lpc(T, - T, )
(5-20)
Q. - 970.3(q2.J)(\V - IV")
(5-21)
Qr ..
0.25
(5-22)
Qh ..
5,000 to 20,000. depending upon boiler size
where
Q.. , assuming a
25% reflux
(5-23)
p .. glycol density at the average reboiler temperature. Ibmfgal
c .. specific heat of the glycol at the average reboiler temperature, Btu/Ibm-oF
T J .. temperature of the glycol entering the reboiler, OF
T 2 .. temperature of the glycol leaving the reboiler, OF
970.3 .. heat of vaporization of water (Btu/lbm) at 212°F and 14.7
psia
Stril"nng Still
The diameter (or cross-sectional area) of the packed stripping still for use
with the glycol reooncentrator can be estimated from Figure 5-38 as a function of the glycol to water circulation rate (gal TEGllb water) and the glycol
circulation rate (gal/hr). The size of a strippingstiU is governed by the vapor
and liquid loading conditions at its bottom. The vapor load comprises water
vapor and stripping gas flowing upwards through the still, whereas the liquid load consists of rich glycol and the reflux flowing downwards. Figure
5-38 includes stripping gas requirements, generally in the range of 2 to 10
ft'/gal TEC circulated.
[f a tray-type design is used, one theoretical tra)' is usually sufficient for
most cases (Siva11s, 1976). For a packed-type design, a minimum of 4 ft
packing height is provided, consisting general I)' of l.S-in. ceramic saddletype packing. This height should be increased with increasing glycol recon-
--
....,. ............
I_""QOC:'''''''~'''''
• ... ,~,-
,-,-
llill
.--
~
r_
~
If the size of the reboiler and stripping still is known. the heat loss, Qt.. can
be more accurately estimated using Equation 5-24:
229
....l'
, "
,.,1 ; ......<>
r
•
~.?
0'
Q, - O.24A,(T, - T J
where
(5-24)
A.. - total exposed surface area of the reboiler and still ft i
T. - average temperature (of the fluid) in the reboiler.' of
T. - ambient air temperature (the temperature of the surroundings), of
0.24 - an approximate heat transfer coefficient for the reboiler and
stripping still, Btu/( hr ft 2 oF)
The surface area of the firebox, A (ft2), can be determined as follows:
A - Q17,00Q
(5-25)
where 7,000 Btu/hr-ft2 - estimated design heat flux for direct-fired reboilers
This calculation of A enables determination of the o\"erall size of the reboiler.
r
'-1-
",,
,,
•
•
~
f
,
,
,
,
• - 'ol/'"
••••••
G.............., .........
~
~
-
I US§ §-
Figure 5-38. Stripping still size for glyCOl dehydrators. (After Sivalls, 1976; courtesy of C. R. Sivalls and the University of Oklahoma.)
230
eo, Production Engineering
Gas- Water Systems and Deh ydration PrOCessing
centrator size, to a maximum of about 8 ft for a 1 MM Btuthr unit (Sivalls,
1976). Additional specifications for glycol reconcentrators can be obtained
231
T.ble 5-12
Specifications for St.ndard High-Pressure Glycol Pumps'
using Table 5-11.
Circulation Rala-Gallona/Hour
Pump SpeecI- StrokHIMlnule
Count one stloke for each discharge of pump"
Clycol Circulating Pump
Model
The size of the circu1ating pump required can be determined using the
glycol circulation rate, L, and the maximum contactor operating pressure.
Table 5-11
Specifications for Glycol Reconcentratora ·
R.boller Glycol
Cripaclty, capacity,
Btu/ hr
Reboller
gph" •
7.5,000
7.5,000
125,000
125,000
20
IS')(3',6"
IS" x 3', 6"
6'i/8")( 4'.6"
18")(3',6"
18")(3',6"
6'Vs" x 4',6"
IS" x 5'
18")(5'
IS" x 5'
&~.l6·
24")(5'
IS" x S'
2.4' x 5'
24")(S'
24" x 7'
24")( 10'
30" x 10'
36" x 10'
36" x IS'
42" x IS'
48" x 16'
24")(5'
24")(7'
24')( 10'
30" )( 10'
36' )( 10'
36" )( 10'
36" x 10'
36" x 10'
6'1/~' x 4', 6"
8'11s"x4',6'
8'11s" x 4',6'
S'I/~" x S', 0"
1O.1,~" x 5',0"
l ()li~" x 6'.0"
1211~" X 7', O'
14")( 8'. 0"
1""x8',O"
16"x8',0'
Flash SepiflItor Haat Exch.lnge CoIl
Size,
Die )I Ht.
Size Coli Area, sq ft
12")(
12')1
16" )(
16" )(
IS" )(
IS" x
16" )(
20" x
20" )(
24" x
30" x
30" )(
30")1
4S"
4S"
4S"
48"
4S"
48"
4S"
4S"
4S'
4!1'
4S"
4S"
4S"
Stripping
Stili Size,
Ole. x HI.
35
40
70
00
100
I'"
210
250
3"
<56
456
456
175,000
175,000
250,000
350,000
400,000
500,000
150,000
850,000
1,000,000
Heet Exchanger
Size,
Surge rank
Ole . x Len. Size, 01 • . x Len.
LIt"
l/2"
liS"
lit"
lll"
.,"
III"
:l/~
"
.,"
I"
I"
I"
I"
12.9
12.9
23.3
233
31.1
311
44.6
".8
84.8
82.1
102.6
102.6
102.6
Glycol
Pump
Model
17 15PV
4015PV
4015PV
901srV
9015PV
21015PV
21015PV
2101SPV
45015PV
450lsrV
45015PY
45015PV
45015PV
X 4',
6"
lilt"
I!J.·
Jilt'
2"
2"
'"'"
'"
•
10 12
,.
"
14
20
"
,.
" ...
""
24
2.
3. 32
3436
3840
14 IS
20
26 2B 30
3436 38 '0
1715 PV 8 10
11 IS
IS 20 22
343B 38 '0
.rol S PY
28 28 30
27 31.5 36 40,5 45 49.5 54 48,5 63 67.5 72 76,5 SI &5.S 90
9015 PY
66 79 92 lOS 118 131 144 157 171 184 197 210
21015 PY
166 200 233 266 300 333 366 .00 433 466
45015 PV
""
""
Size, 01•. x HI.
• Afw Si"alls, 1976.
• - 11 is not rooommtndnl II.>
abov.: tahlt
2'.
2',
6'1'8")( 2',
6SI~')( 2'.
O perating pTeSliure, psig
300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
Cu ftJgal at 14.4 and 6O"F 1.7 2,3 2.8 3.4 3,7 4,5 S.O 5.6 6.1 6.7 7.2 7.9 8.3
R.tle. Condenser
6'{$")(
~~.)(
O·
O'
O'
O·
~lItmpt
10 run pump/> al
'I~
1_ or greater than Ihose indlCat"':! in It..,
Gas Consumption
8'11~")( 2',0"
8:118')( 2'.0"
~8")(2',O"
x 2',6"
1()li~")( 2 ,6"
1211,")( 2'.6"
14')(3',0"
1"" x 3', 0"
16'x3',0"
1{).1,~·
Higlt-Pressure Glycol Shipping
Glycol Filter Charge,
WI,
Size
gal
I"
I"
I"
I"
I"
I"
Number
75
75
105
lOS
100
100
2tiO
375
2,100
2,100
2,200
2,250
3,200
3,200
3,700
1175
<,000
<,500
8,500
7,000
7,500
"25
10,000
m
880
990
• Afler Sh.lI.s. 1976
• • CI~ C'&pac!h • Instd on drwJating 2..1 pi TECllb HtO and l.c:onlrolled b)' the' m:.oilC'rC'&pKlty or
pump C'&pKll) ... h~ b .ma.I1n.
Pump Model
High-pressure Filter Low-pressure Filter
Size
Pump
Conn, Stflliner Size
Size
Elements
Elements
315PV
17JSPV and 815SC
40 ISPV and 2015SC
90ISPV and SOISSC
210ISPV and 1001SSC
4501SPV and 200 ISSC
l/4 "
lit'
I"
1·2lw.")(
!J3i~"
1;2 "
Iii"
1i~ "
I"
1 -2Ji~")( 9JI~'
1'2'
lit"
3,', "
I"
(L12"
.,"
I"
I"
11'2"
1·2li.")( 931~'
I"
2.211," )( !J3i~'
I"
Il!2 " 4·21,," )( 9Jr4"
8-2.J.'~' x 9li4-
'"
1;2·
1.'4 "
1"
11'2"
1-3" x IS"
1-3")( IS·
1-3" x 18"
1-3" x 36"
4-3" x 18"
4-3" X 36"
Generally, as mentioned earlier, the glycol-powered pump that transmits
energy from the rich glycol to the lean glycol, is used for glycol circulation.
Table 5-12 by Sh-'alls (1976) shows sizing data for this type of pump. Table
5-12 also gives data on the amount of gas released by the pump as a fu nction
of the glycol circulation rate and the contactor operating pressure. For other
(motor-driven) pump types, such as centrifugal pumps or positive displacement pumps, data supplied by the pump manufacturer may be used .
Glycol Hash Se,)(lrator
The glycol flash separator, used downstream of the pump, should be designed for a liquid retention time of at least 5 min . T he size can be calculated as follows:
V
'OK
LtJ60
(5"26)
,
232
Ga .. Production Engineering
Gas- Water S!ls/ems and Deh!ldration Procesnng
233
where V - settling volume required in the separator, gal
t - liquid retention time, min
and gas gravity are both equal to 1.0. Therefore, the contactor can handle a
gas rate up to 9:l MMscfd and is suitable for use.
E%tJmpl~ 5-9. Size a glycol dehydration plant using Sh'alls' method to
meet the following requirements:
Number of Tra!lS Rt:quin>d i,1 tht: ContactOf'"
Gas flow rate - 20,0 MMscfd
Gas specific gravity - 0.7
Operating Iinf> p~lJT(> - 1,000 psig
Maximum oontactor working pressure - 1.400 psig
Cas inlet temperature ., 100°F
Outlet gas water content - 6.0 Ib H2 0 /MMscf gas
Use a tray-type contactor with bubble-cap trays, and assume the followin~
additional criteria:
Clycol to water circulation rate., 3.5 gal TECflb H20
From Figure 5-35, the actual number of trays required for a 3.5 gal TEGI
lb H 2 0 glycol to water circulation rate and 72° F dew-point depression = 4.5.
Thus, approximately 5 trays are required.
For a more precise determination, construct the McCabe-Thiele diagram.
From Table 5-2, specific gravity of lean glycol at 100°F"" l.111, implying a glycol density - (1.111)(8.34) - 9.266 Ibm/gal
Using Equation 5-16. CRI ~h '" (0.995)(9.266) / (9.266 + 113.5) 0.965'" 96.5%.
Thus. the operating line points are:
Lean glycol concentration - 99.5% TEe
lOp of column: 61b HzO/MMscf and 99.5<'10 TEG
Bottom of column: 61 lb 1l20lMMscf and 96.5% TEe
Solutio"
Data points for constructing the equilibrium line are as follows:
From the McKetta and Wehe correlation (Figure 5-1):
Water content of inJet gas at 1,000 psig and 100° F .. 61 Ib H 20 /MMsd gas
Dew point of exit gas with 61b H 2 0 / MMscf water content _ 28° F
]hus, the required dew point depression
=
100 - 28 _ 72°F
Using Equation 5-15, amount of water to be removed, W t
_
(20 1
24)(61 - 6) - 45.83 Ibm/h,
% TEG
99.6
99.0
98.0
97.0
96.0
95.0
Eqlbm. dew-point temp.
at 100° F (Figure 5-37),
Water content of gas at dew-point
temp. and 1,000 psig (Figure 5-1),
OF
Ib H,OMMrl
-10
12
30
40
47
51
1.1
3.2
6.3
9.0
11.7
13.3
Jllid Scrub"" Size
From Table 5-3, a 36-in. 0.0. vertical scrubber is required for a 1,400psig working pressure. The same result is obtained using Figure 5-32 (with
suitable extrapolation). So, use a 36-in. x 7.5-ft vertical two-phase scrubber, with a 1,440 psig working pressure.
Ccmku;lor Size
From Figure 5-33, select a 36 in. 0.0. contactor with a qb _ 27 MMscfd .
From Tables 5-5 and 5-6, the correction factors for operating temperature
The McCabe-Thiele diagram constructed lIsing this information, as shown
in Figure 5-36, gives the number of theoretical trays required - 1.563.
Therefore, the actual number of trays required - 1.563/0.25 - 6.25, or 7
trays.
This result is not in reasonable agreement with the approximate number
of trays determined using Figure 5-35. It appears that Sivalls (1976) intended this figure for a valve-type contactor column. This is apparent if a
tray efficiency of 0.333 is used to calculate the number of trays required
from the McCabe-Thiele diagram. This gives a tray requirement of 1.5631
0.333 - 4.7, or 5 trays.
•
23.
Ga' Production Engineering
On the,other hand, this discrepancy could simply be a reflection on the
poor quahty of ~e ~rrel~tion shown in Figure 5-35, resulting undoubted.lv
from the apprOXimations m\'oln~d in reducing a multivariable problem to ~
few select parameters.
Reboil" Ileal Load
_.:rom Equation 5-17. glycol circulation rate. L .. (3.5}(61 )(20 '24 ) ..
1 u.92 gal hr.
h om Equation 5-18. the reboiler heat load. Q .. (2 ,000 )
(lTI .92) .. 3.56 x 1()5 Btulhr approximate.
For detailed calculations, assume PC(T2 - T 1) .. 1200. Then , using
Cas- Water Syst.effl8 and Dehydration Proceuing
~mmary
235
of Requirements
Inlet gas scrubber: 36-in. 0.0. x 7.5-ft height, two-phase, 1,440-psig
working pressure.
Glycol-gas contactor: 36-in. 0.0., with 7 bubble-cap trays, 1,440-psig
working pressure.
Glycol pump: Model number 21015 PV, with 28 strokes/min pumping
,peed.
Glycol flash sep.: 2O-in. 0.0., two-phase £lash separator.
Reboiler: 289,OOO-Btu i hr heat load requirements.
Stripping still: 8.2-in . l.o.
Equations 5-20 through 5-23:
Or, in terms of standard size units:
Q, - (177.92)(1,200) - 21.35 x lO' Btu/h,
Q. - (970.3)(20/24)(61 - 6) - 4.45 x 10' Btu/h,
Q, - (0.25)(4.45)10' - 1.11 x 10' Btu/h,
Qh ..
20,000 ,. 2.0 x
l()"
Btuihr
Scrubber: 36-in. 0.0. x 7.S·ft height, l,440-psig W.P.
Contactor: 36-in. 0.0. x 19-ft height, 1,440-psig W.P., with 7 trays.
Reconcentrator: 24-in. x lO-ft., 350,000 Btu/hr reboiler, with 1O.7Sin. x 5-ft stripping still, 1O.75-in. x 2.S-ft reflux condenser.
Flash sep.: 20 in. x 4 ft
Pump: Model number 21015 PV, 28 spm.
Thus, Q .. (21.35 + 4.45 + 1.11 + 2.0)10 1 = 2.89 x lOS Btulhr
Stripping Still
. Using F~gure 5-38, the minimum internal diameter required for the
stiJi - 8.2 10., based upon a 177.92 galihr glycol circulation rate, and 3.5
gal TEe·Ib H 20 glycol to water circulation rate.
Glycol Pum"
Fro~ Table 5-12, pump model number 210IS PV, with 28 strokes/min
pumping speed, is required for a glycol circulation rate of 177.92 gal/hr.
Glycol Flash SeIX1mtor
Usi~g Equ.ation 5-26, the settling volume of the flash separator required
assummg a Itquid retention time of 5 min, i~;
,
v-
(177.92)(5)160 - 14.8 gal - 0.35 bbl
From Table 5-4, a 20 in. 0.0., two-phase separator is required.
Adsorption Dehydration
Adsorption (or solid bed) dehydration is the process where a solid desiccant is used for the removal of water vapor from a gas stream. The solid
desiccants commonly used for gas dehydration are those that can be regenerated and, consequently, used over several adsorption-desorption cycles. Some solid desiccants can dehydrate gas down to 1 ppm or less; these
desiccants are wide1y used on feed streams for cryogertic processing (CPSA,
1981).
The mechanisms of adsorption on a surface are of tv.'o types: physical,
and chemical. The latter process, involving a chemical reaction, is termed
"chemisorption." Chemical adsorbents find very limited application in gas
processing. Adsorbents that allow physical adsorption hold the adsorbate on
their surface by surface forces. For physical adsorbents used in gas dehydration, the following properties are desirable (Campbell, 1984b):
1. Large surface area for high capacity. Commercial adsorbents have a
surface area of 500-800 m2/gm ( - 2.4 x loe to 3.9 x loa ft 2/lbm) .
2. Good "activity" for the components to be removed, and good activity
retention with timeluse. Commercial adsorbents can remove practi-
•
em Production
236
3.
4.
5.
6.
7
Engineering
cally all the water from a natural gas to values as low as 1 ppm (parts
per million).
High mass transfer rate, i.e., a high rate of removal.
Easy, economic regeneration.
Small resistance to gas flow. so that the pressure drop through the dehydration system is smalJ.
High mechanical strength to resist crushing and dust formation. The
adsorbent also must retain enough strength when "wet:'
Cheap. non-corrosive, non-toxic, chemically inert, high bulk density.
and small volume changes upon adsorption and desorption of water.
Types of Adsorbents
Some materials that satisfy these criteria, in the order of increasing cost.
are: bauxite ore, consisting primarily of alumina (Alz03_xHZO); alumina:
silica gels and silica-alumina gels: and molecular sieves. Activated carbon, a
Widely used adsorbent, posses.'>eS no capacity for water adsorption and is
therefore not used for dehydration purposes, though it may be used for the
removal of certain impurities. Bauxite also is not used much because it contains iron and is thus unsuitable for sour gases.
Alumina
A hydrated form of aluminium oxide (A1 20 J ). alumina is the least expensive adsorbent. It is activated by driving off some of the water associated
with it in its hydrated form (A1 z0 J .3H 20 ) by heating. It produces an excellent dew point depression to dew point values as low as - lOO°F. but requires much more heat for regeneration. Also, it is alkaline and cannot be
used in the presence of acid gases, or acidic chemicals used sometimes for
well treating. The tendency to adsorb heavy hydrocarbons is high, and it is
difficuJt to remove these during regeneration. It has good resistance to liquids, but little resistance to disintegration due to mechanical agitation b,the £lowing gas.
.
Gels: Silica Gel and Silica-Alumina Gel
Gels are granular, amorphous solids manufactured by chemical reaction.
Gels manufactured from sulfuric acid and sodium silicate reaction are called
silica gels, and consist almost solely of silicon dioxide (Si O z). Alumina gels
consist primarily of some hydrated form of Al 20 J . Silica-alumina gels are a
combination of silica gel and alumina gel.
Gels can dehydrate gas to as low as 10 ppm (GPSA, 1981), and have the
greatest ease of regeneration of all desiccants. They adsorb heavy h)"drocar-
Gas-Water System8 and Dehydration Processing
237
boos, but release them relatively more easily during regeneration. Since they
are acidic, they can handle sour gases, but not alkaline materials such as
caustic or ammonia. Although there is no reaction with HzS, sulfur can deposit and block their surface. Therefore, gels are useful if the H 2S content is
less than 5-6 % .
Molecular Siet.-ell
These are a cr~-qallint' form of alkali metal (calcium or sodium) aluminosilicates, very similar to natural clays. They are highly porous, with a very
narrow range of pore sizes, and very high surface area. Manufactured by
ion-exchange, molecular simes are the most expensive adsorbents. They
possess highly localized polar charges on their surface that act as extremely
effective adsorption sites for polar compounds such as water and hydrogen
sulfide (see also Chapter 6). Molecular sieves are alkaline and subject to attack by acids. Special acid-resistant sieves are available for very sour gaS$.
Since the pore size range is narrow. molecular sieves exhibit selectivity towards adsorbates on the basis of their molecular size, and tend not to adsorb
bigger molecules such as the heavy hydrocarbons. Nevertheless, sieves are
subject to contamination by carryover of liquids such as oil and glycol. The
regeneration temperature is very high. They can produce a water content as
low as 1 ppm. Molecular sieves offer a means of simultaneous dehydration
and desulfurization and are therefore the best choice for sour gaS$.
Process Flow Scheme
The general flow scheme for solid-bed gas treating processes is shown in
Figure 5-39. The adsorption process is cyclic. For continuous operation, two
beds are used in parallel. Most adsorbents tend to adsorb heavy hydrocarbons, glycols, and methanol, resulting in contamination and a reduction in
desiccant capacity. These components are difficult to remove during regeneration. Therefore, for efficient desiccant performanc.'e and for a longer desiccant life, the inlet gas stream is thoroughly cleaned to remove all liquids
and solids.
The clean gas flows downward during dehydration through one adsorber
containing a desiccant bed, while the other adsorber is being regenerated by
a stream of gas from the regeneration gas heater. Gas flow is downward for
dehydration so as to lessen bed disturbance due to high gas velocity, and
therefore, permit higher gas rates. Regeneration gas, on the other hand, is
sent upward through the adsorber to ensure thorough regeneration of the
bottom of the bed, which is the last area contacted by the gas that is dehydrated. Most contamination occurs at the top of the tower, and by sending
the regeneration gas upwards, these contaminants can be removed without
•
238
CaJ Production Engineering
239
Gel.J- \\-'Olcf Syste/11.t and Dehydration Processing
. some cases, insufficient gas dehydration (GPSA, 1981). U oxygen is c\'en
~::Spected in the inlet gas stream, special design modifications are required.
The Regeneration Cycle
-
"
Gn -
A typical temperature-time plot for a dry desiccant plant is shown in Figure 5-40. It shows the relationship betw(''en regeneration gas te~perature at
the inlet and outlet. and the ambient ji!;as temperature for a tYPlcal8-hr ye..
generation cycle.
"
UN!! 0 ..
INlit
IUI[N[IIIiI.l ION
rowER 2
(O<Y"'II)
•
!.
REGENERATION
GAS COOLER
OUTLET G"-S
FILTER
,
......
To
·•••
:;
••
•
>-•
L1QY",
TWO-TOWER ADSORPTION PLANT
Figure 5-39. Flow diagram for a two-lower solid-bed dehydration plant. (After
Campbell, 1984b; courtesy of Campbell Petroleum Series.)
flushing them through the entire bed. Sometimes, only the inlet (top) part of
the tower is recharged with desiccant, in order to minimize desiccant replacement expense. Desiccant bed may also be rearranged, or the gas flow
direction reversed, to obtain additional desiccant life.
The regeneration cycle consists of t"':o parts: heating and cooling. First ,
regeneration gas heated to a temperature of 400_000°F, greater than the fi.
nal bed regeneration temperature by about SO--lOO°F, is sent to the desiccant
bed. Subsequently, the hot regenerated bed is cooled by letting the regeneration gas bypass, or by completely shutting off, the regeneration gas heater,
This cooling gas is usually sent downward through the bed, so that only the
top of the bed may adsorb any water from this gas, The hot regeneration gas
and cooling gas, after flowing through the bed, are sent to the regeneration
gas cooler to remove any adsorbed water, Thus, the bed acts as a sort of
regenerative heat exchanger.
Oxygen. even in trace amounts, can react with hydrocarbons during the
regeneration cycle, forming water and CO 2 which are adsorbed and lead to,
,,
'.
0"""
"
"
to""
'<
• ....,......"et'
~
.
,'.
"
•
.'
•
".. to''''
SU.ItT 0'
t
'.
...
~.
,_...,...
<
,•
[NO O'
etel[
eyell
,
•
•
Trill •
IIIOIHI
•
.f
•
,
•
•
e,cr. )
Figure 5-40. A typical temperature-lime plot for regeneration gas and dessicant
bed for a solid-bed dehydrator.
Refer to the regeneration-ji!;as outlet temperature curve (curve 2) in Figure
5-40. There are four discrete intervals-A, B. C. and D-in the regeneration C}'cle, with average temperatures of T A, T B. T c. and T D, respectively, as
shown in Figure 5-40. Initially, the hot regeneration gas heats up the tower
and desiccant (from Tl to T2 in Figure 5-40). At about 240°F (T 2), water
begins to vaporize. The bed heats up at a slower rate (the curve Flattens).
because a considerable portion of the heat input is used in vaporizing water
from the desiccant, until point T3 is reached where all the water in the desiccant has been desorbed. The average temperature of water desorption, T B.
is often assumed in design to be about 250°F (see Figure 5-40). Heating is
continued (from T3 to T~ in Figure 5-40) to drive off any heavier hydroca~.
bons and contaminants. For a cycle time of 4 hours or greater, the bed 15
COnsidered to be properly regenerated when the outlet gas temperature has
reached 350_375°F (point T.). The regeneration gas now has a high water
•
240
Gas Production Engineering
(plus hydrcxarbon and contaminant) content. This ends the heating cycle.
and bed cooling is begun. The cooling cycle is Wiuall}' terminated at about
125 ~ F (point T 5) . because any further cooling may cause water to condense
from the wet gas stream and adsorb on the bed.
Although Figure 5-40 is for an S-hr cycle. the relative heating and coolin$!
times shown are t~llical for any cycle above 4 hoo .... (Campbell, 1984b).
Analysis of the Adsorption Process (After Campbell. 1984b)
Figure 5-41a illustrates the movement of an adsorption zone front as a
function of time. In a dry desiccant bed, the adsorbable components are ad.
sorbed at different rates. A short while after the process has begun, a series
of adsorptIOn zones appear. as shown in Figure 5-41b. The distance bet\\'een
sllC<.USivc adsorption zone fronts is indicative of the length of the bed involved in the adc;orption of a given component. Behind the zone, all of the
entering component has been removed from the gas: ahead of the zone. the
concentration of that component is zero (unless some residual adsorbed concentration exists from a previous cycle). Note the adsorption sequence: C L
and C 2 are adsorbed almost instantaneously, followed by the heavier hydrocarbons. and finally by water that constitutes the last zone. Almost all the
hydrocarbons are removed after 30-40 min and dehydration begins. Water
displaces the hydrocarbons on the adsorbent surface if enough time is
allowed. Thus. cycle length is critical. Very short cycle lengths are becoming
increasingly popular. since they can simultaneously control water and hydrocarbon dew points at minimum cost.
Figure 5-41c shows the character of the breakthrough CUf\o'e. The ordinate ClCo is the ratio. at any time. of the mole fraction of a given component in the exit gas to its mole fraction in the entering gas. Thus. C le o is
equal to 0 until the zone front reaches the bed outJet (breakthrough) at time
tb· SubsequentJy, C lc., increases until time teo after which no further primary adsorption can occur. In practice. C/c., becomes greater than 1.0 for a
short period of time when one component is replaced by another. The shape
of this C/c., versus t curve is related to the efficiency of separation. Curve 1.
a \'crtical straight line, represents an ideal case where the movement of the
adsorption zone front is essentially "piston-like," whereas curves 2 and 3 are
for a real case where the adsorption zone front spreads through a finite bed
length. Note that the greater the spread, the more difficult it will be to delineate dry gas from partially wet gas when water breakthrough occurs.
Desiccant pellet size has a pronounced effect on the spread (or length) of
the adsorption zone. As shown in Figure 5-4ld, smaller the desiccant size.
better and sharper is the separation obtained. Hence. the smallest size desiccant possible should be used. subject of course, to constraints of higher pres-
Ca.!'-'\-'Oter Systems and Dehydration Proce&ring
1~r1' tU:\--f~~~Of"il
a!([
<l
'"
0
BED LENGTH
_
241
Figure 5-41. A schematic
representation 01 the adsorption process. (After
Campbell, 1984b.)
h,
(.(
l~r(l?\
<l
'"
0
c,' ' \ c,
BED LENGTH
\1
'
'"
j,2")'
( 'b)2
TIME
(,'
;,'OIPl
OO~
L L4-20 MESH
2 8- LO MESH
3~-6MESH
4
3-8 MESH
1IME-
(,(
sure drops that may result from doing so. Usually a 14-mesh (Tyler screen)
size is used.
Design Variables for the Adsorption Process
The three basic components of an adsorption plant are:
1. Adsorber towers.
2. Regeneration and cooling equipment-depends mainly on the adsorber towers.
3. Piping and equipment-primarily a function of the allowable pressure
drop and the flow scheme desired.
In designing these components, the process variables that must be considered are (Campbell, 1984b):
1. Cycle time/length.
2. Allowable gas flow rate.
3. Desiccant capacity-design capacity as well as the effective or useful
capacity.
•
GaJ·Water Systems and Dehydration Processing
Cas Production Engineering
243
4 Required outlet water dew point.
is proportional to desiccant bulk denSity, and the available area for adsorp.-
5. Total amount of water to be remO\"ed.
tion.
6. Regenm'lon requ;,-ements.
7 Allowable pressure drop.
Adsorber Bed Design (After Campbell, 1984b)
:-':ot all of these \'ariables are independent: some are fixed for any calcula.
tion, and others are \'aried to )ield an optimum design. Cycle time and des.
sicant capacity are the most important variables in designin~ an adsorption
plant.
Cycle Tillie
Varies from less than 1 hr for a rapid cycle unit to greater than 8 hrs. The
cycle time is, of cour<;e, limited by desiccant capacity so as not to exceed
outlet !?:as spedfications. and desiccant bed geometry. Also, the cycle time
must be long enough to permit regeneration and cooling of the tower~ not
currently dehydrating.
Adsorber tower desiWi is gO\'erned by the desiccant capacity. zone length,
water loading (rate of removal of water from the gas). breakthrough time.
and allowable gas f10\\- rate and pressure drop. Relationships for these are
discu~ in tht' <,t'1"}uence they are calculated.
An often-used term in the context of adsorber tower design is the "elocit)"
of the gas based upon bed diameter, known as the superficial gas \·elocity.
\ 'g . It is determined by converting the gas rate at standard conditions, q, to
operating conditions:
(5-27)
where
All desiccants dc~ade in service. their useful life being in the range of I ·4
year<>. Degradation is termed normal if there is a loss of surface area only.
During its useful life, a desiccant exhibits rapid normal degradation in the
initial stages, which then becomes more gradual. A more dramatic reduction in desiccant capacity occurs when the small capillary or lattice openinwo
that contain most of the effective surface area for adsorption are blocked.
This latter process, termed abnormal degradation, is caused by materials
such as heavy oils. amines, gl}'cols. and corrosion inhibitors, that cannot be
remO\'ed by regeneration and effect great reductions in capacity in a vcr)"
s.hort time. No liquid water should be allowed in the inlet gas, since this
generally salty water in the inlet gas will evaporate and fill the bed with
salt.
Some properties of common desiccants are (Campbell. 1984b):
Material
Bulk density
Ibm/ft'
Surface area
m2/gm
Design capacity
Ib H,O/ IOO Ib des.
Alumina
Alumina gel
Silica gel
Molecular sieves
SO-55
52-55
45
43-45
210
350
7SO-83O
4-7
7-9
7-9
9-12
650-800
The design capacity must be such that an economic desiccant life is obtained. Assuming a monolayer adsorption, the potential desiccant capacity
superficial gas velocity. ft/hr
q - gas flow rate at standard conditions. Mt>.1scfd
Z - gas compressibility factor at the operating temperature T (OR)
and pressure p (psia)
D - diameter of the adsorber bed. ft
Vg -
Allowable Call HQW RlIte
This is generally expressed in terms of the mass flow \'elocity of the gas,
the product of its ve10city "'. and density:
(5-28)
where
w _ mass f10\. . ,·elocity. Ibml(hr ft2)
Mit - molecular weight of the gas
For downward flow of gas, the maximum allowable gas mass flow velocity,
w, is given by:
where P, - gas density at operating conditions, Ibm/ttl
Pd - bulk desiccant density, Ibm/ftl
d.p - average desiccant particle diameter, ft
g - aC(:eleration due to gravity ( - 32.2), ftlseci
C - empirical constant in the range of 0.025-0.033
,
244
Co.. Productihn Engi'leerilig
Gas·Water Systems and Deh!Jdratwn Processing
The factor 3,600 converts the mass £low rate from Ibm/(sec ft2) to lbmi(hr
(1;2). Substituting g - 32.2 ft/sec2, w becomes:
w - 20.428.22 [Cp",,.!,,]'''
- (q\\',24) /(.D'·4) - O.0531q\\'•• D'
" -- -;::.-.
V
/'
---
>0
1---
,
where q.. - water loading, lb Hp/(hr ftl)
W, - water content of the inlet gas, Ib H 20fMMscf gas
ZoUt'
SILICA GEL
••
Also known as the rate of removal of water required per unit bed area.
water loadinll can be calculated as follows:
q
"
(5·29)
nat" Loading
245
"
~/ ~-
.
~LE~~-i~£vt:S
- - - f-
--
- r~~ f--"";
..
70
RtLATtvt WATER SATURATlON (l.S.) . t
'"
>00
TEMPERATURE • DC
[.I'ngth
The zone length depends upon gas composition, flow rate, relative water
saturation, and desiccant loading capability. For silica gel, the zone length.
h~. can be estimated as follows (Simpson and Cummin~, 1964):
0'" " 3D "
I'
f....
o. ,
"
"
L
J'-.,'
~
,
",
'0. ,
.0 .
(5·31)
E
where h, - zone length, ft
~
~O .
S, - relative saturation of water in the inlet gas. %
For alumina and molecular sieves, the zone length determined using Equation &.31 is multiplied by 0.8 and 0.6, respectively.
The dynamic desiccant capacity. x" is shown in Figure 5-42a as a function
of the relative saturation of water. The temperature correction factor is
shown in Figure 5-42b. This temperature correction is required for gels and
alumina, but not for molecular sieves.
The use/td desiccant capacity, x, generally less than the dynamic capacity.
K,;, is given by the following empirical equation:
xwhere
x. -
~
o.
J'-.,
•
,
"
"
'"0
.......
'" ~
1\0
120
110
TDlPE .... TUR£ • 0,.
•
'"
Figure 5-42. The eHect of (a) relative water saturation and (b) temperature on
the dynamic capacity of dessicants. (After Campbell, 1984b; courtesy of Campbell Petroleum Series.)
From extensive tests, C · has been found to vary only in the range 0.40-0.52
for a wide range of applications, and an average C· - 0.45 is generally used
for design purposes.
Breakthrough l 'ime
C'x,(h,lh,)
(5·32)
x - useful capacity of the desiccant, Ib H 20/tOO lb desiccant
X. - dynamic capacity of the desiccant, lb H2 0/lOO lb desiccant
C· - an empirical corntant, a function of zone length
The breakthrough time for the water zone formed, I:t, in hours, can be
estimated as follows:
(5·33)
246
Ga.t-Water Systems and Dellydratioll Processing
Ga, Production Engineering
where the factor 0.01 takes into account the units for x (Ib H2.0'' 100 Ib d es..'il·.
can.
t)
Minimum
B~d
From Figures 5-42a and 5-42b,
cant. From Equation 5-32;
x. -
247
(O.9){16) .. 14.4 lb H 2 0 /100 lb deo;ic-
,_ 14.4 - (0.45)( 14.4)(7.094)115 - 11.34 Ib H,OI IOO Ib d",kcant
LhJgth
The ~mount of water that can be removed per cycle by the desiccant. \\'
(Ibm). IS gi .. en by
From Equation 5-34, (h,).," - (127.32)(406.67)1[(11.34)(45)(9)) ~ 11.3 ft
Thus, a 15 ft bed length allows a safety factor. From Equation 5-33. the
breakthrough time is:
... _ (0.01)(11.34)(45)(15117.198 - 10.63 h,
On rearranging this e(luation, the minimum length of desiccant bed reo
quired can be written as:
(h,).oo - (127.321V,)I('PdD')
(5.341
Note that (ht)m", is the distance from the inlet to the front of the water 7.one.
So, if ht is less than the total length of the bed. it means that not all of the
bcd, is being used. From an operations perspective, it is desirable to continue
~nhl the water front reaches the end of the bed, since it prolonl'S desiccant
hfe.
E~am"'f' 5·JO. Design an adsorber for dehydrating 20 MMscfd of a O.i
graVIty ~as at 1.000 psia and 100°F. Assume a two-tower plant using an B-hr
cycle WIth a 15 ft long silica gel bed.
Since the breakthrough time of 10.63 hr is greater than the cycle time of 8
hr, the water zone will not reach the outlet, and dry gas will be produced.
The design. therefore, has a .~afety factor to account for future desiccant
degradation .
Regeneration and Cooling Calculations (After Campbell. 1984b)
Regeneration calculations are done for eo;tablishing the regeneration gas
rate, heating and cooling time intervals, heater load, and condenser load.
These calculations are simply heat balances for various parts of the regeneration cycle. For each interval, the heat supplied by the gas, E i • must be
equal to the heat absorbed, Qj;
(5-35)
Solution
From :igure 5·1, water content of inlet gas - 61 Ib H1 0. MMsd gas.
Assummg all of the inlet water is removed. the rate of removal of wa.
ter .. (20)(6 1) .. 1,220 Ibm/da\".
Therefore, amount water to be removed per cycle, W .... (1.220)(8.'
24) - 406.67 Ibm/cycle.
The gas compressibility factor, Z .... 0.88.
~ume a gas velocity of 1,800 ft/ hr. Then, from Equation 5-27:
D - (1,499.73)(20)(0.88)(560)1[(1,000)(1,800)) _ 8.2118 ft', implying
D .. 2.87 ft. Choose a bed diameter of 3 ft for safety.
Then, V.c .. (1,800)(8.2118/9) - 1,642.36 ftlhr
From Equation 5-30, water loading q" - (0.053 1)(20)(61)19 _ 7.198
Ibmihr-ft2
From Equation 5-31, zone length is given by;
h, - (297.7)(7. 198)',.·1[(1,642.36)''''''(100)' ....) _ 7.094 It
where i represents the interval. In addition. the total cycle time constraint
must also be satisfied:
(5-36)
t.,-t.",+t8+ t C:+ t O
where
t.. - total cycle time, hr
tA , ta, te. to - time spans (hr) for intervals A, B, C, and 0, respectively
For these intervals, the
QI
and E J terms are derived as follows;
Heatingjrom T/ to 1'2 (ltlteroai A ill Figl"..: 5-40)
The total heat load is the sum of the heat absorbed by desiccant, hydrocarbon, vessel shell, inert balls, hydrocarbon desorption, and water. Thus.
the total heat load, QA. is givcn by;
,
248
Q. . -
GIlS Production Engineering
ffidCd(T2 -
Goa- Water S!lstem." and Deh!ldration Processing
Til + mHL~dT2 - T I) + m,<;(Tt
+ mlbclb(T2
-
T I) +
ffiHCHHC
+
m .. c..(T2 -
-
T I)
Til
(S-37)
where m - mass, Ibm
c - specific heat capacity, Btu/(lbm oF), for desiccant (d),
hydrocarbon (HC), vessel shell (5), inert balls (ib). and water
(w)
249
As before, the term for heat absorbed by the vessel shell is multiplied by 0.7
if the ..-,essel is insulated. Energy a..-ailable from the regeneration gas, Ec, is
given by:
(5-42)
Cooling from T4 to Ts (lntert:al D in Fig""' 5-401
The second Jast term in Equation 5-37 represents hydrocarbon desorption
with H lle being its heat of desorption. usually taken to be 200 Btu'ibm . Theterm for heat absorbed by the vessel shell is usually multiplied by 0.7 if the
vessel is insuJated.
Energy a ....ailable from the regeneration gas, EA. is given by:
The total coolin~ load is the sum of the cooling requirements for desiccant, vessel shell, and inert balls. only. Thus. the total cooling load. Qo. is
given by:
(S-38 )
As before, the term for the vessel shell is multiplied by 0.7 if the vessel is
insulated. Assuming that the cooling gas rate is the same as the regeneration
gas rate, cooling available, E[), is given by:
where m'K - mass flow rate of the regeneration gas, Ibm/hr
erg - specific heat of the regeneration gas, Btu/(lhm °1-1
(S-43)
(S-44)
I/eatj"gjro'" T2 to T3 Untf'rOOl B jll Figure 5-40)
The total heat load is the sum of the heat absorbed bv desiccant water
water desorption, \.:essel shell. and inert balls. Thus. the total heat l~ad, Qs:
is given by:
Q8 - m<!Cd(T 3 - T i ) + m"c..(TJ - T 2) + m... H"
+ m,c.(T 3 - T i ) + m;bc,b(TJ - T~)
(S-39)
where the heat of desorption of water, H", is usually taken to be 1,400 Btu
Ibm for alumina and gels, and 1,800 Btullbm for molecular sieves. As be.
fore, the term for heat absorbed by the vessel shell is multiplied by 0.7 if the
vessel is insulated. Energy available from the regeneration gas, Ea. is given
by:
(S-40)
I-Ieatingfrom 1'3 to T4 (lntert:al C ill Figure 5·40)
In this final cleanup step, the total heat load is the sum of the heat abo
sorbed by desiccant, vessel shell. and inert ball~, only. Thus, the total heat
load, Qc . is given by:
(S-4I )
In Equation 5--44, the unknown parameters are the regeneration gas rate,
m<i' and the lengths of time intervals, tA, ta. te, and to. a total of 5 unknowns. The number of equations are also 5: four for the heat balances, and
Equation 5--36, which imposes the total cycle time constraint. For a given
cycle time 4, a solution is thus possible.
Nonnally, however, the maximum heat load occurs in the interval B, and
the minimum regeneration gas rate m" is chosen on this basis. The minimum regeneration gas flow rate and water adsorption capacity must be
enough to handle the water desorbed from the bed in time tB' Therefore:
(S-4S)
where
Wt
total water removed per cycle from the gas being dehydrated, Ibm
\V TB, W TI - water contents of the regeneration gas at temperatures
T Band T I, respectively, Ibm waterfMMscf gas
M.. _ molecular weight of the regeneration gas (usually the
same as the gas being dehydrated)
_
Generally, the regeneration gas rate is about 10% of the main gas flow
rate. The entering gas must be heated from a temperature Tl to T H, which is
chosen in the range 400-6(X)°F. Temperature T4 must be kept as low as possible, and is generally in the range 350_500°F, less than TH by 5O~100°F
•
250
Gas Production Engilleering
Ca,,-Water Sy"temt and Dehydration Processing
(usually 100°1'). Tf; and T3 are generally equal to 230°F and 260 G F. Values
for specific heats needed in regeneration calculations are as follows:
Component
Specific Heat, Btui(lbm F~
Alumina
0.06
Silica gel
Molecular sieves
Liquid water
0.22
0.05
1.0
0.12
V~I )h~1l
The heater load consists of heating requirements for the regeneration ,2;a ...
Thus, the heater load, QII in Btu/hr can be written as:
A condenser is used to cool the regeneration gas after it comes out throu,I{h
the adsorber bed. This cooling is done in order to separate the condensable
components picked up by the regeneration gas from the desiccant bed. Cool.
ing loads should be calculated for all the three inten'als, and the conclcnS('r
then designed to handle the maximum cooling load expected. Generally,
condenser loads are the highest for interva1 B. Condenser loads can be calculated sim ilar to heating loads, taking into account the components in th(·
regeneration gas and their specific and latent heats.
Dehydration by E.xpansion Refrigeration
Dehydration can be achieved by expansion refrigeration when su rHcient
pressure drop is available. In this technique, the gas stream is cooled by adiabatic expansion through a choke. as discussed in Chapter 4 (in the section
on "Low-Temperature Separation"), to temperatures as lov. as OaF. Thi.'
drop in temperature leads to condensation of the water vapor and condem
able hydrocarbons associated with the gas.
Two types of c:tpansion refrigeration techniques are used: one with a hydrate inhibitor to prevent hydrate formation that may result upon expansion
of the gas, and another without an inhibitor.
E:tpansion refrigeration without an inhibitor is used only when the pre.sure drop allows the desired water dew point to be obtained without the
formation of hydrates (CPSA, 1981). An inhibitor must be used if hydrate
formation is expected in the precooler used upstream of the choke. Hydrate.
251
allowed to form at this second stage (choke), and are collected in a low
::perature separator (LTX). In the LTX unit, the gas entrapped in ~e hyd tes is recovered using heating coils to heat the hydrates. These COils are
o;~ used as precoolers for the gas stream: the gas passes throu~ the i~id.e
f the cOils, providing enough heat to melt the hydrates. That IS why It IS
:.oportant to ensure that no hydrates are expected to form a.t this precooli?g
stage for the gas. Also, mist eliminators must never be used In the LTX umt.
since they may be plugged by hydrates.
When hydrate inhibitors are used, the process is similar. except that the
heating/cooling coils are no longer necessary. and are replaced by a gas expansion valve.
Questions and Problems
1. What are gas hydrates? List the factors that promote hydrate formation.
2. List three methods for preventing hydrate formation at wellsites.
3. Name three different types of solid dcsiccant~ used for natural gas dehydration.
4. A sour gas at 1000 psia has the following analysis: N1 = 8.5%.
H2S - 5.4%, CO 2 - 0.5%. C 1 - 77.6%. C 2 ,.. 5.8%, C 3 = 1.9 %, 11C~ .. 0.1%, i-C... 0.1%. and i-C$ '"" 0.1%. What is the water content of this gas at 120°F? Use all the methods applicable and compare
the results.
5. For the sour gas given in Problem 4, determine the hydrate formation
temperature. Use all the methods applicable and compare the results.
6. A TEG dehydration plant is to be designed to dry the follov.-ing gas:
N2 - 1.7%, CO 2 ,,,, 0.3%, C 1 - 65.5%. C~ .. 16.6 %, C 3 = 8.8%, nCo( - 3.0%, i-C. - 1.6 '7~, and f-C s " 0.9%. 1I-C 5 " 0.9 %.
eft" 0.5 %, and C,. - 0.2%. The c,. fraction has a molecular
weight of 140 and specific heat or 70 Btu/Ibm-OF at 300°F. Other relevant data arc as follows:
Gas flow rate - 20 MMscfd
Inlet gas pressure .. 1000 psia
Inlet temperature _ l(X)OF
Required outlet water dew point .. lOoF
GI)'col circulation rate .. 7 gai/ib water removed from gas
Glycol reboiler temperature .. 400°F
Specific gravity of glycol .. 1. 11
Specific heat of glycol .. 0.654 Btu/lbm-oF
•
252
Cos Production Engineerlllg
For this plant, calcuJate the following:
(a) Clycol circulation rate in galimin.
(b) Glycol-glycol heat exchanger load in BtuJhr if a 2,5°F approach is
desired. Assume that the glycol enters the absorber at 125°F.
7 A glycol (TEe) dehydrator plant is to be designed for handJing 13.5
\1Mscfd of the SOUT gas of Problem 4. The glycol circulation tate L~ -4
gal TEG'lb water, lean glycol concentration is 99"'~. glycol spec-ifk
gravity is 1.10. inJet gas temperature is 120 c F, and the absorption
tower uses bubble-cap trays. For an exit water content of 10 IbIMM<,cf
gas, determine the following:
(a)
(b)
(c)
(d)
(e)
Contactor diameter.
Maximum gas rate that can flow in the system.
The actual number of trays needed in the oontactor.
Sensible heat required for the glycol, Btu/hr.
Heat of vaporization required for the water, Btu/hr.
(f) Heat required to va}Xlrize reflux water in the still, Btu/hr.
(g) Reboiler heat load, Btu/hr, assuming heat loss '"' 5000 Btu/hr.
8. It is desired to use glycol inhibition to prevent hydrate formation for
the case given in Problem 7. Calculate the amount of TEG required in
lb/day.
9. ~ework Problem 6 using a two-tower desiccant plant, employing !oilIca-gel on an B-hour cycle. The regeneration gas leaH~ the heater at
55O"F. and the towers are regenerated to a final temperature of 450' F
Assume internal insulation. Determine the following:
(a)
(b)
(c)
(d)
(e)
Internal diameter of the towers required.
Amount of silica-gel required in Ibslcycle.
Regeneration gas rate, MMscfd.
Regeneration heater heat load, Btu/hr.
Cooling load, Btu/hr.
References
Curry, R. N., 1981. Flmdaml!1ltais oj Natural Cas Conditioning. PcnnWell
Publ. Co., ThIsa, Oklahoma, 118pp.
Campbell, J. M., 1984a. Cas Conditioning and Processing, Vol. 1. Campbell Petroleum Series, Norman. Oklahoma, 326pp.
Cal·\.Vater Systeml and Dehydratwn Processing
253
Campbell. J. M., 1984b. Cas Conditioning and Processing, Vol. 2. Campbell Petroleum Series, Norman, Oklahoma, 398pp.
Carson, D. B. and Katz, D. L., 1942. "Natural Cas Hydrates," 1)-a1lS..
AIME. 146. 150-158.
Chemical Engineers'Uandbook. 1984. R. H. Perry and D. W. Green (eds.),
~1cCraw.Hill Book Co .• r\'e\\ York. 6th ed .• pp. 13-27 to 13-35.
Edmister, W. C. and Lee. B. I.. 1984. Applied Hydrocarbon Thermodynamics. Vol. I (2nd ed.). Gulf Publishing Company, Houston, Texas.
233pp.
Galloway. T. J.. Ruska. \V.• Chappelear. P. S.. and Kobayashi, R., 1970.
"Experimental Measurement of Hydrate Numbers for Methane and
Ethane and Comparison with Theoretical Values:· Ind. & Eng. Chern.
Fund., 9(2. May), 237 - 243.
Gas Processors Suppliers Association, 1981. Engineering Data Book, 9th ed.
(5th revision), GPSA, Tulsa. Oklahoma.
Guenther, J. D., 1979. "Natural Gas Dehydration,·' Paper presented at Seminar on Process Equipment and Systems on Treatment Platforms, Taastrup. Denmark, April 26.
Heinze, E, 1971. "Hydratbildung," Lehrbogen 3.13 von der Bergakademie
Freiberg.
Holder, G. D. and Hand. J. H., 1982. "Multiple-Phase Equilibria in Hy·
drates from Methane, Ethane. Propane and Water Mixtures," AIChE J.,
28(3, May), 440-447.
lkoku, C. U., 1984. Natural Cas Prodllction Engineering. John Wiley &
Sons, Inc., New York, 517pp.
Katz, D. L., Cornell, D., Kobayashi. R .. Poettmann, E H., Vary, J. A.,
Elenbaas, J. R., and Weinaug. C. F., 1959. Handbook oj Natural Cas
Engineering. McGraw·HiII Book Co., Inc .. New York, 802pp.
McCarthy, E. L.. Boyd, W. L., and Reid, L. S.. 1950. "The Water Va}Xlr
Content of Essentially Nitrogen-Free Natural Cas Saturated at Various
Conditions of Temperature and Pressure," Trans. AIME, 189, 241- 243.
McKetta, J. J. and Wehe. A. H .• 1958. "Use This Chart for Water Content
of Natural Gases," Petr. Refiner, 37(8, Aug.), 153-154.
McLeod, H. 0., Jr. and Campbell, J. M .. 1961. "Natural Cas Hydrates at
Pressures to 10,000 Psia," J. Pet. Tech .. 13(6, June), 590-594.
Nagata, I. and Kobayashi, R, 1966. "Prediction of Dissociation Pressures of
Mixed Cas Hydrates From Data for Hydrates of Pure Cases with Water,"
Ind. & Eng. Chern. Fllnd., 5(4, Nov.), 466-469.
Ng, H. J. and Robinson, D. B., 1976. "The Measurement and Prediction of
Hydrate Formation in Liquid Hydrocarbon-Water Systems,'· Ind. & Eng.
Chern. Fund., 15(4, Nov.), 293-298.
•
254
GO$ Product/on Engineering
Parrish, W, R. and Prausnitz, J. M., 1972. "Dissociation Pressures of Cas
Hydrates Formed by Cas Mixtures," Ind. & Eng. Chem. Proc D'
& Dell., 11(1), 26-35.
•
ess €$Ign
Petrol.eum Extension Senice, 1972. Field Handling oj Natural Gas. 3rd ed .,
Urn\". of Thus Press. Austin. Texas. 143pp.
Robinson. O. B. and 1'\g, H. J .• 1975. "Improve H\"drate Predictions" Hydraco Proc., 54(12. Dec.). 95-9£:;'
.
.
R~~inson, J. N .• Wichert. E .. :\foore. R. G .. and Heidemann. R. A.. 19ih
Charts
.
Content of
.
Sharma, and Cam~~Il.' J. M .. 1984. Unpublished. Cited reference on p.
143 10: Gas CondltlOlIIng and PrOCessing. Vol. 1, by J. M. Campbell.
. Campbell Petroleum Series, Norman, Oklahoma, 326pp.
Slm~n, E. A. and Cummings. W P., 1964. "A Practical Way to Predict
. SIlica Gel Performance," Chem. Engr. Prog .. 60 (4, Apr.), 57 60.
Slva.U.s. ~. R., 1976. "Glycol Dehydrator Design Manual." Proc. Gas CUll
dltlomng Conf.. Univ. of Oklahoma, 39pp.
Trekell. R. E. and Campbell, 1. M., 1966. "Prediction of the Behavior of
Hydrocarbon Clathrate Solutions." Proc. 151st Meet. of Am. Chern. Soc ..
Petr. Chern. Oiv., Pittsburg, Penn .. March 23-26, p. 61.
Van der Waals. J. H. and Platteeuw, J. C., 1959. "Clathrate Solutions" Advances in ~?~mical Physics, Vol. 2, edited by I. Prigogine. Inte~ience
Pub!., a diVISion of John Wiley & Sons, New York, I-57.
6
Desulfurization Processes
Introduction
With i.ncreasing demands for natural gas, natural gases containing hydrogen sulfide (H 2S) are also being tapped for utilization after purification.
Natural gases containing H 2S are classified as "sour." and those that are
H 2S-free are called "sweet" in processing practice. Produced gases from reservoirs usually contain HzS in concentrations ranging from barely detectable quantities to more than 0.30% (3,000 ppm). Other sulfur derivatives,
besides H 2S, are usually completely insignificant or present only in trace
proportions. Most contracts for the sale of natural gas require less than 4
ppm (parts per million) in the gas. Thus, a sulfur removal process must be
very precise since the initial product contains only a small fractional quantity of suUur that must be reduced several hundred times.
A characteristic feature of all H 2S -bearing natural gases is the presence of
carbon dioxide (C0 2), the concentrations of which are generally in the
range of 1 to 4 %. In gases devoid of HzS. however, such concentrations are
rare. HzS and CO 2 are commonly referred to as "acid gases" because they
form acids or acidic solutions in the presence of water.
Reasons for Removal of HzS and CO 2
Besides emitting a foul odor at low concentrations, H 2S is deadly poisonous and at concentrations above 600 ppm it ca n be fatal in just three to five
minutes. Its toxicity is comparable to cyanide. Thus, it cannot be tolerated
in gas that would be used as domestic fuel. Further, H 2S is corrosive to all
metals normally associated with gas transporting, processing, and handling
systems (although it is less corrosive to stainless steel), and may lead to premature failure of most such systems. On combustion, it forms sulfur dioxide,
255
•
256
Gal I'rodllCtiori Engineering
which is also highly toxic and corrosive. HzS and other sulfur compounds
can also cause catalyst poisoning in refinery prOCt'!SSeS.
CO 2 has no heating value and its removal may be required in some instances merely to increase the energy content of the gas per unit volume.
CO. removal may also be required because it forms a complex. C02·CO~.
which is quite corrosive in the pre;ence of water. For gas being sent to cryogenic plants, removal of CO z may be necessary to pre\'ent solidification of
the CO~. Both the acid gases, H2S and CO!. promote hydrate (ormation ,
and thfO p~n('f' nf (:0; may not be desired for this reason also. However. if
none of these situations are encountered, there is no need to remove CO
Removal Processes
The processes that have been developed to accomplish gas puriCication
vary from a simple once-through ,,,ash operation to complex multiple step
recycle systems. In many cases, the process complexities arise from the need
for recovery, in one form or another, of the impurity (H~S) being removed or
recovery of the materials (process chemicals) employed to remo ....e it.
Like dehydration processes, desulfurization processes are primarily of two
types: adsorption on a solid (dry process), and absorption into a liquid (wet
process). There are a few processes that use other methods, such as the cellulose acetate membranes that rely upon the different diffusion rates for hy.
drocarbon and H2S, and liquid fractionation techniques that exploit the rei.
ative volatility difference. Application of these latter types of processes has
been quite limited.
Both the adsorption and absorption processes may be of the physical (no
chemical reactions involved) or chemical type. These processes may also be
classified into the following categories:
1. Non-regenerative, such as Chemsweet process (~Ianning, 1979), NCA
process (Sun, 1980), and the Siurri~,....eet process (Oil & Cas J.. 1981).
The materials used in treating the gas are not reco,·ered in these pro.
cesses.
2. Regenerative processes ·with recovery as HzS. These include the physical absorption processes (water wash, Selexol, F1uor solvent, etc.). the
amine processes (MEA, DEA, DCA, etc.), hot carbonate processes
(Benfield, Catacarb), Alkazid processes, molecular sieves, etc.
3. Regenerative processes with recovery as elemental sulfur. The HolmesStretford process, and the Ciammarco-Vetroooke process fall in this
category. With growing environmental concerns regarding sulfur
emission, these processes have acquired a prominent role in desulfur.
ization operations.
DesulJumation Proca&et/
257
So many sweetening processes are in use today that it would be ~possib~e to
describe them all in detail here. Some widely used processes wIll be bnefly
mentioned. and some important ones among these will be presented in a little more detail.
Criteria for Process Selection
There are man)' variables in gas treating. which makes the precise definition of the area of application of a gi,·en process very difficult Among c:ev·
eral factors, the following are the most significant that need be considered:
1. The types and concentrations of impurities in the gas, and the degree
of removal desired.
2. Selectivity of acid gas removal required, if any.
3. Temperature and pressure at which the sour gas is available, and at
which the sweet gas is to be delivered.
4. Volume of the gas to be processed, and its hydrocarbon composition.
5. CO2 to H 2S ratio in the gas.
6. Economics of the process.
7. The desirability of sulfur recovery due to environmental problems, or
economics.
Besides CO 2 and HzS, some gases may contain other sulfur derivatives
such as mercaptans and carbonyl sulfide. The presence of such impurities
may eliminate some of the sweetening processes. The concentrations of acid
components are important to consider. Some processes effectively remove
large amounts of acid gas, but not to low enough le"eis. Others remove to
ultra-low values, but cannot handle large amounts of acid components in
the incoming stream economically.
Selectivity of a process implies the degree of removal of one acid gas component relative to another. Some processes remove both H 2S and CO 2 , while
others are designed to selectively remove only HzS. Generally, it is important
to consider the selectivity of a process for H 2S versus CO 2 to ensure desired
extent of removal of these components. For this reason. CO 2 to H 2S ratio in
the gas is also an important parameter.
Operating conditions affect the performance of several sweetening processes. Also, different processes discharge the sweetened gas stream at different pressure and temperature levels relative to the conditions of the incoming stream. Thus, the inlet and outlet conditions desired are significant
Variables to consider. It may be economic in some cases to alter inflow conditions to suit the process, and outflow conditions to meet pipeline requirements.
Some processes are economic for large gas volumes, while others lose their
economic advantage when large volumes of gas are to be treated. Cas com-
•
260
Gas Production Engineering
INLET SOU" IJU
~
DemljurlUltioll PrOCes8n
.
~
l~
~:'" ,m"""~
na"E
4-
p
'"
~
<=
tOO"I~
ttEATIN,!,
11£,1,1(11
ir
4_WilT
1'"
VALVE
•
OUTLET $WEET CAS
I
••
T
C'"
'?
f<
~
261
corrosion and fouling problems are generally minimal. These processes offer
fair to good selectivity. The solvent used is generally recovered by flashing
the acid component-rich solvent (called rich solvent) in flash tanks at successively lower pressures. Thus, little or no heat is required for regeneration or
other purposes. But a sulfur recovery unit is required since these pr~ do
not alter the acid components chemically in an)' manner. Some processes in
this category offer simultaneous dehydration. Most solvents currently in use
have a relatively high solubility for heavier hydrocarbons. particularly unsaturated and aromatic components. These components are very detrimental to the performance of most sulfur reco...ery processes and may yield an
unsuitable, contaminated sulfur as the product. So, for sour gases containing heavy hydrocarbons (heptanes plus) or unsaturated and aromatic hydrocarbons. particular care must be taken during the regeneration step to prevent their entry into the acid gas stream that is to be sent to a sulfur recovery
unit.
Water Wash (Aquasorption) Process
.?
Figure 6·1. Flowsheet for a molecular sieve desulfurization process. (After Fails
and Harris, 1960; courtesy 01 Oil & Gas Journsl.)
Besides regeneration losses. gas is also lost by the adsorption of hydrocarbon components by the sieve. Unsaturated hydrocarbon components such as
olerin~ and aromatics tend to be strongly adsorbed (Conviser, 1965). Molecwar Sle\-~ are also prone to poisoning by several chemicals such as glycols
and reqUire ~horough ~as cleaning methods prior to the adsorption step. The
process reqUires a cyclic operation, since it is batch-type, with a cycle time
0." the order of 2 hours. Initial capital investments are high, and regenerahon reqUires a lot of heat. For gas streams containing CO 2• carbonyl sulfide
may form as shown in the following reversible reaction:
H,s + CO, - COS + H,O
~101ecular, sieves tend to catalyze this reaction. The problem has been studIed extensively, and new molecular sieves have been developed to retard the
COS formation.
Physical Absorption Processes
These processes rely ~pon physical absorption of acid components as the
gas sweetening mechamsm. Because only physical absorption is involved.
This process is effective for high pressure gas, with high acid gas content
and high H 2S to CO 2 ratio. According to Maddox (1982), a water wash operation followed by an amine process is 12 to 15% lower in capital investment, and ahout 50 % lower in operating expenses as compared to a Single
amine unit for an equivalent sweetening job. For gases \\:i.th a high HzS to
CO 2 ratio, the saving5 can be as much as 40 % in investment, and 60 to 70 %
in operating costs.
In the water wash sweetening process, sour gas is sent upward through a
contactor, countercurrent to the water (see Figure 6-2). The partially sweetened gas from the top of the to\... er is sent to further treatment units (typically, an amine unit). The rich water solution from the bottom of the tower
is sent to an intermediate pressure flash tank for recovery of dissolved hydrocarbons. A power recover)' turbine is provided for repressurizing the water
before sending it to a low pressure flash tank where all of the acid gas is
removed, and the lean water obtained is recycled.
Froning et al. (1964) presented calculation procedure:; for estimating the
performance of a water wash and provide data required for such calculations. Their results show that HzS is about three times more soluble in water
than CO 2 , thereby showing that the selectivity of the process is quite good.
Selexol Process
This process uses dimethyl ether of polyethylene glycol (DMPEG) as a solvent. Solubilities in Selexol solvent of HzS and CO 2 and other acid gas com-
•
258
Cos Production Engineering
position should also be considered. since some processes are adversely affected by the presence of heavier fractions. while others may strip the gas of
some of its hydrocarbon constituents.
The desirability of reco\"eringsulfur as e1ementaJ sulfur reduces the choice
considerably. Processes with sulfur recovery have become very important in
America. and will become so worldwide in the near future due to environmental problems caused by sulfur emissions. Sulfur is a useful by.product.
~enerally in good demand by the fertilizer and chemicals industry. Thert...
fort'. in <;t>veral in-.tanCf'S. rulfur recovery may be aUracth'e from an economic standpoint also.
Demlfunzation Processes
259
latter process gives an improved performance, generating a higher removal
efficiency as well as better regeneration.
This process offers advantages of simplicity, and absolute selectivity,
which implies less gas shrinkage because COz is retained in the gas. It is relatively inexpensive. There are several disadvantages, such as difficult and expensive regeneration, excessi\"e pressure losses through the bed, inability to
remove large amounts of sulfur, and suUur disposal problems, since it does
not produce sulfur in a saleable form. Details about this process are avail·
able from various SOllrC't'S such as Taylor (1956). Kohl and Riesenfeld (1985).
and Duckworth and Geddes (1965).
Molecular Sieves
Solid Bed Sweetening Processes
These processes are based upon physical or chemical adsorption of acid
gases on a solid surface. Although not as widely used as the liquid absorp.
tion processes, they offer advantage'; such as simplicity, high selcctivity (onl~
H~S is generally removed), and a process efficiency almost independent of
pressure. These processes are best applied to gases with moderate concentrations of H 2S, and where CO 2 is to be retained in the gas.
The Iron Sponge Process
Sour gas is passed through a bed of wood chips that ha\'e been impregnated with a special hydrated form of ferric oxide that has a high affinity for
HzS. The chemical reaction is as follows:
The temperature must be kept at less than 120°F. According to Kohl and
Riesenfeld (1985), temperatures above 120°F and neutral or acid condition_\
lead to the loss of the water of crystallization of the ferric oxide. The bed
then becomes very diHicult to regenerate. Iron o~de is regenerated by passing oxygen/air over the bed:
The process operates in a batch-type reaction-regeneration cycle. Regeneration of the bed, however, is quite difficult and incurs excessive maintenance and operating costs. Also, sulfur eventually covers most of the surface
of the ferric o~de particles and further regeneration becomes impossible. A
continuous regeneration process has also been developed, where small
amounts of oxygen or air are added along with the sour gas at the inlet. This
Synthetically manufactured forms of crystalline sodium-calcium alumino
silicates, molecular sieves are porous in structure and have a very large surface area. The pores. formed by the removal of water of crystallization, are
uniform throughout the material. Severa! grades of molecular sieves are
available, with each grade corresponding to a very narrow range of pore
sizes.
Molecular sieves remove components through a combination of a "sieving" and physical adsorption process. Because of their narrow pore sizes,
they discriminate among the adsorbates on the basis of their molecular sizes.
The sieves possess highly localized polar charges on their surface that act as
adsorption sites for polar materials. Therefore, polar or polarizable compounds, e\'Cn in low concentrations, are adsorbed on the sieve surface. They
are highJy selective in the removal of H~ and other sulfur compounds from
natural gas, and orrer a continuously high absorption efficiency. They remove water also (a polar compound) and thus offer a means of simultaneous
dehydration and desulfurization. High water content gases, however, may
require upstream dehydration (Rushton and Hays, 1961).
Fails and Harris (1960) conducted several pilot studies on sieves and other
adsorbents. They found that the adsorptive capacity of molecular sieves for
H 2S decreases with increasing temperature, and increases with increasing
H2S/C0 2 ratio. Increasing contact time is favorable to H 2S removal up to a
point, beyond which there is no effect. An optimum pressure of about 450
psia was identified by Fails and Harris, though the effect of pressure was
found to be quite small.
The process flow scheme, shown in Figure 6-1, is similar to the iron
sponge process. The bed is regenerated by passing a portion of the sweetened
gas, preheated to about 400-600°F or more, for about 1.5 hours to heat the
bed. As the temperature of the bed increases, it releases the adsorbed H 2S
into the regeneration gas stream. The sour effluent regeneration gas is flared
off. According to Rushton and Hays (1961), about 1-2% of the gas treated is
lost in this regeneration process.
•
262
Gas Production Engineering
.'
ponents are directly proportiona1 to the partial pressures of these components. The solubility of H 2S is about 10 times greater than CO 2 • and
hydrocarbon solubility is quite small. Heavier hydrocarbons. however, have
greater solubility. and intermediate flashe> are generally required for hydrocarbon remO\:al,
Different Selexol·based processes have been designed and used success.
fuJly. H~'er and Hanis (1970) describe three plants installed for a wide
range of H:zS to CO 2 ratios: one plant for a high HzS to CO 2 ratio. another
for a 10\\ H~ to CO~ ratio. and the third for a ga~ containing large amounts
of both H2S and CO 2 _
Figure 6-3 shows a flow scheme for a low HzS to CO 2 ratio gas. Sour gas,
pretreated to remove an)' solids and free liquids, is dehydrated, cooled to
40"F. and sent to the absorber for a countercurrent contact with Selexol sol.
vent. Rich selexol from the bottom of the absorber is sent, via a surge tank to
remove entrained gas that is recycled back into the absorber. and a power
recovery turbine for pTeSI>urizing the solvent, to a high pressure flash. Most
of the absorbed methane and some of the CO 2 is released in this flash. and iii
recycled to the absorber.
In the second flash stage, most of the vapor reJeased is CO 2 and it iii
\"ented after power recovery. Finally, the Selexol is sent to the low pressure
flash, which is operated at 16 psia, Here, HilS and the remaining CO 2 are
flashed off as the vapor stream, which is vented to the atmosphere.
263
De!tIljurizotlon Processes
~
:~;.
-~:;
-->:
---
h
tlAO IRf'IQ.
-n
..i
I
..1
i~
h
.-l
,lI ~
L .JII""
"--'·~j
1
)
( '''-~"
'"'~
'. '<C.
t
L
Figure 6-3. Selexol'" based plant for a low H2S to CO 2 ratio gas. (After Raney,
1976: reprinted from Hydrocarbon Processing.)
Chemical Absorption- The Alkanol-Amine Processes
The alkanol-amine processes are the most prominent and widely used
processes for HtS and CO 2 remo\>·al, They offer good reactivity at low cost
and good flexibility in design and operation. Some of the commonly used
alkanol-amines for absorption desulrurization are: monoethanolamine
(MEA), diethanolamine (DEA). triethanolamine (TEA), fJ/3' hydroxiethanolamine, usually called diglycolamine (DCA), di-isopropanolamine
(DIPA), and methyldiethanolamine (MDEA), Table 6-1 shows some or the
Table 6-1
Some Characteristics 01 Ethanolamines·
Figure 6-2. A typical water wash process. (After Froning at aI., 1964: reprinted
from Hydrocarbon Processing.)
Amine Type
Chem. Formula
MEA
DEA
TEA
DCA
DIPA
MDEA
HOC~ H..NH J
( H O~ H .ltN n
( H OCJH.)~
II(OCtll.l,.\lll t
( HOC~I.),.\l 11
(HOC 2 H.hNCH,
• MItt Maddo.:. 1982.
Mol. Wt.
61.08
iOS.14
148.19
lOS. 14
133.19
119.17
.
Yap. Presa .•,
100-F, mm Hg
Ret C.paclty
LOS
0_058
0_0063
100
0.160
0.010
0.0061
58
,I
58
46
51
Dewljurlzotion PrOCf!:SM!Jl
Cal Production Engineering
important properties for these six alkanol-amines. Among these, MEA and
DEA processes are the most widely used.
MEA has the highest reactivity, and therefore the highest acid gas removal capacity, and the lowest molecular weight among the amines. Therefore, it offers the highest removal capacity on a unit weight or unit volume
basis, which implies lower solution circulation rates in a sweetening plant.
MEA is chemically stable (minimal solution degradation). The reaction rate
of HtS with MEA is greater than that of CO 2 . The process, however, is con·
~idered to be almost non-selective in its removal capacity for HzS and CO~.
because even the slower reacting CO 2 is rapidly and almost completely re·
moved. MEA is able to remove acid gases to pipeline specifications, and
even beyond.
MEA, however, suffers from relatively high solution losses primarily due
to two reasons: it has a relatively high vapor pressure that causes greater
vaporization losses. and it reacts irreversibly with carbonyl sulfide and carbon disulfide. High vaporization losses put a limitation on the operating
temperatures, which must be kept low. whereas the reactions leading to
buildup of solids necessitate efficient filtration schemes.
DEA is quite similar to MEA. except it is not as reactive, so H 2S removal
to pipeline specifications may cause problems in some cases: its reactions
with carbonyl sulfide and carbon disulfide are slower and lead to different
products, so filtration problems are less: and its vapor pressure is lower.
therefore vaporization losses are less. Thus. DEA can be advantageous to use
in some cases.
TEA has been almost totally replaced by MEA and DEA, primarilv because it has lesser reactivity and problems are encountered in sweetenin'g the
gas to pipeline specifications. DCA has found application in recent vears. It
has the same reactivity as DEA, and a reasonably low \'apor pressu~. DlPA
is also able to treat gas to pipeline specifications, and is used in the Sulfinol
process by Sheil, and the AOlP process. MDEA has received renewed attention because it has a fairly good ~Iectivity for H 2S, so CO 2 can be retained in
the gas: and it offers some energy saving in the regeneration step. MDEA,
however, may not be commercially competitive with other amine processes
(Maddox. 1982).
Solution Concentrations and Reactions
For MEA, an appro:timately 15% concentration (by weight) solution is
generally used. DEA is used in 20-30% or more concentration. DlPA and
MDEA are typically used in 30-50% concentration in aqueous solution,
while DCA is used in the 40-70 % by weight concentration range.
Some plants use a mixture of a glycol and an amine for simultaneous dehydration and desulfurization. Generally. a solution containing 10 to 30'?',
265
by weight MEA, 45 to 85% by weight TEC (triethylene glycol), and 5 to
25% by weight of water is used. This process removes both CO 2 and H 2S
be<;ides dehydrating the gas. At high temperatures, the mixture becomes
very volatile and difficult to handle. Also, the g1}"COI-amine combination
does not dehydrate as well as an independent glycol unit.
The reactions for the ethanolamines, MEA. DEA. and TEA are as follows
(Batt et aI., 1980, Rahman, 1982),
1. Formation of a bisulfide of the ethanolamine on reaction ....ith H 2S.
RNH2 + H~ ~ RNH.S + heat
2. For MEA and DEA, with CO 2, the carbamate salt of the ethanolamine
is formed. TEA does not have this reaction with CO~.
2RNH2 + CO 2 ~ RNHCOi + RNH:i + heat
3. In aqueous solution, with CO 2, the carbonate salt of the ethanolamine
is formed. This is a slower reaction.
General Process Flow Scheme
MEA is usually preferred over DEA because it enables a smaller circulation rate of the solution, although it has a higher vapor pressure with increased chances of greater chemical losses.
The plant is very much like an absorption dehydration system. The main
differences are (Curry, 1981):
1.
2.
3.
4.
5.
The contactor contains man)' more tray sectiOns, up to 20 or more.
A side-stream reclaimer is provided in an MEA system.
More elaborate filtration and heat exchange equipment is required.
Operating temperatures are di£ferent.
The reflux requirements are greater.
The problems encountered arc also quite similar, though in a more severe
form. Some such problems are corrosion, foaming, solution losses. and poor
solution filtering. There are other problems relating to the high vapor pressure of MEA. Solution loading, that is, the amount or level of liquid MEA in
the contactor, is critical. The exothermic reactions in the contactor coupled
with the low boiling point of MEA make solution loading a difficult problem. The presence of sulfur intensifies the corrosion problems by introducing
stress corrosion.
•
266
DelU1JuriUltion Processes
GO! Productwn Engineering
u_.
.................
.........
• ••
..... -
.........
~.
__
...
......
.......- .
_"00'
.........
.......
..-......
~
,.
:1.:;1','1" ......
.
~-'Il'i-"'-"f '
-
"" " ...
"
......-
--..•,.1+-+--,
,,~
.,".......... .
. .............
267
absorb approximately 3.5 to 4.5 seC acid gas per gallon of solution. This can
be used to determine the MEA circu1ation rate in a preliminary design .
Besides its performance, the location of the filtering system is critical to
plant operation (Curry, 1981). An efficient filtration will generally reduce
foaming, corrosion , and fouling of mechanical equipment. Remember that
most filtration problems resu1t not from the failure of the filtration system,
but from inefficient gas cleaning. Full-flow filtration is most desirable, although some plants use side-stream filtration where only a part of the stream
is filtered. Iron suUide (FeS) is the most common solid in MEA systems that
requires filtration. Diatomaceous earth (DE) filters are commonly used to
enable removal of particulate matter up to almost I micron. Another commonly used filter is the disposable element type, but it is quite expensive and
used only where severe problems warrant its usage. Usually a secondary filtration system is installed in paraliel to enable crossover and allow time for
cleaning Of removing a used filter.
.... ",.. ..."" ....
,
Figure 6·4. A comparison of a MEA and DGA system lor treating 100 MMscfd of
natural gas. (After Olngman and Moore, 1968; reprinted from Hydrocarbon Processing.)
A typical process flow scheme is shown in Figure 6-4. There are several
variations, such as the location of the Hltering system , using a packed column instead of bubble-cap or valve-type trays in the contactor and the stripper, etc. A side-stream reclaimer mayor may not be used. The design of heat
exchange and reflux systems var)'.
Sour gas is sent upward through the contactor tower, countercurrent to
the flow of MEA . The rich solution from the bottom of the contactor is sent
to a flash tank where absorbed hydrocarbon gas in solution is vented. A retention time of about 2 minutes is usually sufficient. The flash tank also
serves as a sediment accumulator and provisions must be made for sediment
removal. After passing through a heat exchange with lean solution (which
preheats this rich solution), the rich solution enters the top of the stripper
where it is stripped by steam that is generated by the reboiler. Outcomin~
steam from the top of the stripper is sent to a condensing unit to recover
MEA liquid in a reflux accumulator. The acid gases re1eased at this stage are
flared off. The liquid accumulated in the re£lux is sent to the regenerative
system. Lean MEA accumu1ated at the bottom of the stripper is continuously recircu1ated through the reboiler.
In the contactor (also called absorber), almost 90% of the acid gases are
removed within the first three trays at the bottom. The reactions being exothermic, this resu1ts in high temperatures in the contactor in this region.
Usually a 20 % (by \\-eight) MEA solution is used in the contactOf, which can
Chemical Absorption-The Carbonate Processes
The Hot Carbonate Processes
The basic hot carbonate process uses an aqueous solution of pota~ium
carbonate. A highly concentrated solution is used to improve process performance. Temperature is kept high to keep the potassium carbonate and the
reaction products. KHCO J and KHS, in solution. Both the absorber and regenerator are operated at high temperatures of about 230---240°F, which results in considerable savin~ in heat exchange and heating equipment. The
process requires relatively high partial pressures of CO 2 , and cannot be used
for gas streams that contain only HzS. It is also difficult to treat gas to pipeline specifications with this process.
Among carbonate processes, those containing an activator to increase the
activity of the hot pota~ium carbonate solution are more popular. Some of
these are:
1. Benfield- several activators, usually DEA.
2. Catacarb-amine borates used as activators.
3. Ciammarco-Vetrocoke-for CO2 removal, arsenic trioxide most commonly used; sclenous acid and tellurous acid are also used. For H 2S
removal, alkaline arsenites and arsenates (usually KH 2As0 3 and
KH 2AsO t ) used.
The Ciammarco-Vetrocoke (C-V) process is an important development.
There are several C-V processes for different applications. There is one process for the removal of C02t another for a highly selective H 2S removal and
•
268
Gas Production Engineering
subsequent sulfur recovery, and still another for the removal of both HzS
and CO 2 _
The G-V CO 2 process offers substantial savings in steam consumption for
solution regeneration. The arsenic trioxide inhibits corrosion, and the solution is therefore usually non-corrosive in nature. As for most conventional
carbonate processes, impurities such as carbon disulfide, mercaptans, carlxmyl sulfide, etc., have no detrimental effects on the solution. Jenett (1962)
presented data on the performance of a G- V plant and concluded that it
functioned satisfactorily with minimal problems.
The G-V process for HzS removal produces elemental sulfur of high purity as the by-product. It is a flexible process, and by suitably selecting the
pH of the solution, the arsenite and arsenate content, and the operating conditions, the process can be made to be highly selective for H~ or remO\e
both H~ and CO 2, There are no problems of corrosion, solution degradation, solution foaming, or carryover. The economics of the process are also
quite good (Riesenfeld and Mullowney, 1959). and it can reduce H 2S content
to less than 1 ppm. The process, however, is not able to handle gas streams
with H 2S concentrations greater than 1.5% (jenett, 1962).
Another carbonate process in acth'e use is the Alkazid process. There are
three different alkazid solutions, and consequently. three different processe<i
in this category. Alkazid DIK uses the potassium salt of diethyl glycine or
dimethyl glycine. It is used for the selective removal of H 2S from gases that
contain both H 2S and CO~. Alkazid M uses sodium alanine and is effectivc
in removing both H~ and CO 2 , Alkazid S uses a sodium phenolate mixture
and is applicable to gases containing impurities such as carbon disulfide,
mercaptans, HCN, etc.
Deroljurizotion Processe$
269
alkali; (2) reduction of ADA by addition of h)'drosulfide to ~ carbo~yl
up: (3) liberation of elemental suUur from reduced ADA by IOteraction
~th oxygen dissoh'ed in the solution: (4) reoxid.ation of t~~ red~ced ADA by
air; and (5) reoxygenation of the alkaline solution, provldmg dlSSOh'ed O)(yp~_m
..
Sevcra) possible additives have been tested to Increase the solutIOn capacity for hydrogen sulfide and the rate of conversion of .hyd~osulfide .to elemental sulfur. Alkali vanadates proved to be outstandmg In reducmg hydrosulfide to sulfur. with a ~imullaneous ,alence change of vanadium from five
to four. In the presence of ADA. the vanadate solution can be regenerated to
a five valence state. The reduced ADA is easily oxidized by air.
The circulated solution (also called Stretford solution) consists of chemicals in a dilute water solution as follows:
1. Sodium salt of 2,7 ADA. The 2,7 isomer is preferred over 2,6 because
of the greater solubility of the former.
2. Sodium meta vanadate. This provides the active vanadium.
3. Sodium potassium tartrate (Rochelle salts). ThL-; is used to prevent the
formation of a complex vanadium-oxygen precipitate that removes
vanadium from solution.
4. A sequestering agent to prevent precipitation of metallic ions from
Stretford sol ution, such as Chel 242 PN.
5. Sodium carbonate. Used as required to maintain total alkalinity.
6. Sodium bicarbonate added to reduce the absorption of CO 2 •
The overall reaction of the Holmes-Stretford process is the atmospheric oxidation of H2S to elemental sulfur:
The Holmcs-Stretford Process
This process converts H2S to elemental sulfur of almost 99.9% purity. The
process is se1ective for H~. and can reduce the H 2S content to as low as I
ppm. CO 2 content remains almost unaltered by this process. Operating costs
are lower and the process has better £lexibility in application, that is, it can
be designed for larger pressure and temperature ranges.
The Holmes-Stretford process, a modification of the Stretford process developed by the North Western Cas Board in England, was developed by
Peabody-Holmes. Details on the mechanism of the process, and its performance are reported in several publications (Nicklin et ai., 1973; Moyes and
Wilkinson, 1974: Ouwerkerk, 1978; Vasan, 1978). The process uses an
aqueous solution containing sodium carbonate and bicarbonate in the ratio
of approximately 1 :3. resulting in a pH of about 8.5 to 9.5, and the sodium
salts of 2,6 and 2,7 isomers of anthraquinone disulfonic acid (ADA). The
postulated reaction mechanism invol ..·cs five steps: (1) absorption of H2S in
The reaction , however, occurs in the following steps:
(6-1)
(6-2)
(6-4)
The absorption rate of H~ in solution (Equation 6-1) is favored by high
pH, whereas the conversion to elemental sulfur (Equation 6-2) is adversely
affected by pH values abo"e 9.5. Therefore, the process is best operated
\\.ithin a pH range of 8.5 to 9.5.
•
270
DestllJurizatiml Processes
Cas Production Engineering
The comersion of HzS to sulfur is quite rapid and is essentially a function
of the vanadate concentration in the solution. According to Thompson and
Nicklin (1964) the reaction is second order. In practice, an excess of vanadate
is used in order to avoid overloading of the solution with sulfide and subsequent formation of thiosulfate during solution regeneration.
The reduced vanadate is oxidized by ADA (Equation 6-3). Oxidation of
ADA by contact with air is a fairly rapid reaction. The rate of oxidation can.
however, be accelerated by the presence of small amounts of iron salts kept
in solution by a chelating agent (i\icklin and Hughes. 19i8). In general. a
concentration of SO-I00 ppm of iron combined with about 2,700 ppm of
ethylenediamine tetracetic acid (EDTA) is satisfactory.
The chemicals could conceivably be used indefinitely with only minimal
replenishments for losses that occur in the absorber or within the sulfur n....
cover}' unit. This, however. cannot be done indefinitely because side reactions produce undesirable dissolved solids. These solids are permitted to
build up to extremely high concentrations until eventually some solution
must be discarded. Primarily, sodium sulfate and sodium thiosulfate arE'
formed in reactions such as:
..............
-
-"/._-,., ..
--
- " /...-
-
,.....
Thiosulfate formation may be due to the fact that NaHS has not reacted
with the vanadate (because of insufficient time in the absorber) and there·
fore is carried to the oxidizer to react with oxygen there. If there is air in the
feed gas, some of the undesired material can be formed in the contactor itself. High temperature and pH also favor thiosulfate formation. The di~­
solved solids such as thiosulfate are allowed to build up in the solution to
concentrations upwards of 250,0CI0 ppm. It may take a year or longer after
plant startup to reach this level. At these high concentrations, disposal b~
purging in"olvC$ very little of the active chemical, and hence chemical usage
is kept low.
The effluent stream from the Stretford process, containing sodium
thiosulfate and in some cases sodium thiocyanate, must be treated prior to
discharge. Holmes developed four alternative methods to handle effluents
from this process: evaporation or spray drying, biological degradation, oxidative combustion, and reductive incineration. Of these, the reductive incineration process is the most common since it results in a zero effluent discharge, with all the products from the step being recyclable. The reductive
incineration process cracks the bleed liquor containing sodium thiosulfate
into a gas stream containing H2.S and CO 2 and a liquid stream containing
reduced vanadium salts, all of which are recycled.
271
~I'"
"... / 10
UI " .."" ..
Figure 6-5. Flowsheet for Holmes·Stratford process. (After Vasan, 1978; courtesy of Oil & Gas Journal.)
Figure 6-5 shows the process flow scheme. In the gas absorption section,
gas is first subjected to the inlet scrubber unit to remove any liquids and contaminants that may be detrimental to the process. A venturi-type absorber is
used, instead of the conventional packed bed type, to reduce the size of the
absorption unit and achie\'e a better degree of absorption since it provides a
larger surface area for mass transfer. The outlet scrubber prevents carryover
of any entrained Stretford solution in the gas into the sales gas stream.
The reduced solution from the bottom of the absorber is first piped
through a flash drum in the oxidation section. F1ash vapors may be used as
incinerator fuel , or returned to compressor station and mixed with sweetened gas. Liquid from the flash drum is sent to the oxidation tank where air
from the blowers contacl~ the liquid at the vessel bottom, and sulfur froth is
isolated at the surface. The oxidized Stretford solution goes to the circulation
pump and to the surge tank for recirculation to the absorber.
The sulfur processing section includes a slurry tank and an autoclave for
melting sulfur. Molten sulfur from the bottom of the autoclave is cooled,
flaked. and finally bagged for storage and shipment. The clear Stretford solvent is scnt to the effluent treatment section.
•
272
Gas Production Engineering
DerolfuriUltion Processes
The process is fairly easy to operate. Alkalinity. concentrations, and
amounts of the active chemicals change slowly with time and replenishments need only be done quite infrequently. Corrosion problems are encoun.
tered, just as in any sweetening proce;s. Kresse et al. (1981) provide an interesting discussion on some problems encountered, and their rectification. in
two plants using this process.
.
...
Questioru and Problems
'
.
I \Vhy must H 2S be removed from natural gas? Give at least three reasons.
2. Why is it necessary to remove CO 2 ? In what cases is CO 2 removal not
necessary?
3. What types of desulfurization processes are available for natural gas?
What factors are important in selecting the applicable process?
4. Compare the iron-sponge and molecular sieve desulfurization processes.
5. In what cases arc the physical absorption processes useful?
6. Why are chemical absorption pr~ the most widely used desulfuriza
tion processes?
7. Compare the alkanol-amine and carbonate processes.
8. Which of the processes described in this chapter hold the most promising
future? Why?
References
Batt, W. T., Vaz, R. N., Rahman, M., Mains, C. H., and Maddox, R. N.,
1980. Cas Conditioning ConJerence, Univ. of Oklahoma, Norman, Oklahoma.
Conviser, S. A., 1965. "Molecular Sieves Used to Remove Mercaptans From
Natural Cas," O. & Cas J., 63 (49, Dec. 6), 130-133.
Curry. R. N., 1981. Fundamentals oj Natural Gas Conditioning. PennWell
Publishing Company, Thlsa, Oldahoma, 118 pp.
Dingman, J. C. and Moore, T. E. 1968. "Compare DCA and MEA
Sweetening Methods," Hydr. Proc., 47 (7, July) , 138-140.
Duckworth, G. L. and Geddes, J. H., 1965. "Natural Gas Desulfurized by
the Iron·Sponge Process," O. & Cas]., 63 (37, Sept. 13),94-96.
Fails, J. C. and Harris. W. D., 1960. "PracticaJ Way to Sweeten NaturaJ
Gas," O. & Cas 1.,58 (28, July 11), 8&-90.
273
Froning, H. R., Jacob); R. H., and Richards. W. L., 1964. "New K-Oata
Show Value of Water Wash," lIydr. Proc. & Petro Ref·, 43 (4, Apr.), 125-
Heg.
- ...·er, A. M. and Harris, R. A., 1970. "Selexol Solves High HzS/C0 2
problem," Hydr. Pmc., 49 (4, Apr.), 103--104.
Jenett, E., 1962. "Six Case Studies Throw Light on t~e Giammarco-Vetrocoke Process," O. & Cas I .. 60 (l8. Apr. 30), 72--71.
Kohl, A. L. and Riesenfeld, F. C .. 1985. Gas Purijication'4th ed., Culf
Publi.o.hing Co .. Houston, Texas. RtO pp.
Kresse, T. J., Lindsey, E. E .. and Wadleigh, T., 1981. "Stretford Plants
proving Reliable," 0. & Gas J., i9 (2. Jan . 12),80-87.
Maddox, R. N., 1982. Gas Couditioning and Processing - Vol. 4: Cas alld
Liquid Sweelellillg/ 3rd ed., edited by J. M. Campbell, Campbell Petroleum Series, Norman, Oklahoma, 370 pp.
Manning, \V. P., 1979. ··Chemsweet. A New Process for Sweetening LowValue Sour Cas," 0. & Cas /., 77 (42, Oct. 15), 122-124.
Moyes, A. J. and Wilkinson, J. S .. 1974. "Development of the Holmes-Stretford Process," Tile C1Jemicaf Eugineer (Brit.), No. 282 (Feb. ), 84-90.
Nicklin, T. and Hughes, D .• 1978. "Removing HzS From Cases and Liquids," Chern. Abst., 88, 9427601.
Nicklin, T., Riesenfeld, F. C .. and VaelJ, R. P., 1973. "The Application of
the Stretford Process to the Purification of Natural Cas," Paper presented
at the 12th World Gas Conference, Nice, France, June 1973.
O. & Cas I., 1981. "New Cas-Sweetening Process Offers Economical Alternative," 79 (35, Aug. 31), 60-62.
Ouwerkerk, C., 1978. "Design for Selective H 2S Absorption," Hydr. Proc.,
57 (4, Ap'.), 89-94.
Rahman, M ., 1982. Ph.D. Thesis. Oklahoma State Univ. (May, 1982), Oldahoma.
Raney, D. R., 1976. "Remove Carbon Dioxide With Selexol," Hydr. Proc.,
55 (4, Ap'. ), 73-75.
Riesenfeld, F. C. and Mullowney, J. F.. 1959. Proc. 38th Ann. NCPA Meet.,
April 22-24.
Rushton , D. W. and Hays, W., 1961. "Selective Adsorption to Remove
H,S;' O. & Gas /. , 59 (38, Sept. 18), 102-103.
Sun, Y-C., 1980. "Packed Beds for Best SulFur Removal," Hydr. Proc., 59
(10, Oct.) , 99-102.
Taylor, D. K., 1956. "How to Desulfurize Natural Gas," O. & Cas}., multiple issues of Vol. 54: Nov. 5, p.I2S: Nov. 19, p.2oo; Dec. 3, p.139; Dec.
la, p.147.
•
274
Gas Production Erlgineering
Thompson. R, J. S. and NickJin, T,: 1~. "Le Procede Stretford," paper
presented at the Congress of Association Technique de I'Industrie du Cazen, France.
Vasa~ , S.. 19i5. "Holmes-Stretford p~ Offers Economic H~S R
v I"
Oil t/. .~ Cas J., i6 (1. Jan . 2), 78-80.
- erne a .
7
Steady-State Flow of Gas
Through Pipes
Introduction
Pipes provide an economic means of producing (through tubing or casing)
and transporting (via flowlines or pipelines) fluids in large volumes over
great distances. They are convenient to fabricate and install, and provide an
almost indefinite life span. Because flow is continuous, minimal storage facilities are required. at either end (field supply end, and the consumer end).
Operating costs are very low, and flow is guaranteed under all conditions of
weather, with good control (an installed pipeline can usually handle a wide
range of flow rates). There are no spillage or other handling I~, unless
the line develops a leak, which can be easily located and fixed for surface
lines.
The flow of gases through piping systems involves flow in horizontal, inclined, and vertical orientations, and through constrictions such as chokes
for flow control. This chapter introduces some basic concepts for these flow
type<.
Gas Flow Fundamentals
AI} fluid flow equations are derived from a basic energy balance which,
for a steady-state system (no time-dependence of flow parameters), can be
expressed as:
Change in internal energy + Change in kinetic energy
+ Change in potential energy + Work done on the fluid
+ Heat energy added to the fluid
- Shaft work done by fluid on the surroundings
-0
275
•
276
Steady State Flow of Gas Through Pipn
Gas Production Engineering
Thus, on a unit mass basis, the energy balance for a fluid under steady-state
flow conditions can be written as:
dv' g
dU + - + - dz + d(pY) + dQ - dw, - 0
2g, g,
(7- 1)
where U - internal energy. ft.lbfilbm
\: - £luid velocity. ftlsee
z - elevation above a given datum plane, ft
p - prarure, Ibflft2
V - volume of a unit mass of the fluid, ftJ/lbm
Q - heat added to the fluid, ft-Ibf/lbm
W, - shaft work done by the fluid on the surroundings, ft.lbfllbm
g - gravitational acceleration, ftlsec'l
g., - conversion factor relating mass and weight·.
This basic relationship can be manipulated in several different ways. Com.
monly, it is converted into a mechanical energy balance using the well
known thermodynamic relations for enthalpy (h):
dU + d(pY) - dh - T<h + Ydp
where h - specific fluid enthalpy, ft.lbfllbm
T - temperature, oR
s - specific fluid entropy, ft-Ibfllbm
Equation 7-1 now becomes:
dv'
T<h + Ydp + - + (glg,)dz + dQ - dw, - 0
2g,
For an ideal process, ds... - dQ/T. Since no process is ideal (or reversible).
ds ~ - dQ/T, or:
T<h - - dQ + clio
where I", is the lost work due to irreversibilities such as friction.
• F .. mgll<. In metric (Of 51) units, IN .. (1 kg)(9.8 mlsec")Ig.., implying that g.. .. 9.8 kgm:
(t-; secI) .. 1 N·N. In British units, 1 Ibf .. (I Ibm)(32.17 h /secf)I g.., Implying that
g.. .. 32.17 Ibm fti/lbf sec-t).
277
On this further substitution, Equation 7-1 becomes:
Ydp + dv' + (glg,)dz + clio - dw, - 0
2g,
Neglecting the shaft work
sity, p:
(7-2)
w,, and multiplying throughout by the fluid den-
dp + pd,' + (glg,)pdz + pcll.-O
2g,
(7-3)
All the terms in Equation 7-3 have units of pressure. Equation 7-3 can also
be written as:
6p + p11v' + (glg,)ptu + p61. - 0
2g,
.6p
+ pil.v2 + (gI~)p.6z + .6Pf ... 0
(7-4)
2g,
where .6p, represents the pressure drop due to friction , and is dependent
upon the prevailing flow conditions.
Types of Single-Phase Flow Regimes and Reynolds Number
Four types of single-phase flow are possible: laminar, critical, transit.ion,
and turbulent (see Figure 7-1). Reynolds applied dimension~1 anal}~IS. to
flow phenomena, and concluded that the flow regime that will prevaillS a
function of the following dimensionless group known as the Reynolds number, NRe:
Nae - inertia forces/viscous forces - dvplp.
(7-5)
where d _ (inside) diameter of the conduit through which the fluid is
flowing
v _ velocity of the fluid
p - density of the fluid
Il - viscosity of the fluid
For cross-sections other than circular, an equivalent diameter,
four times the hydraulic radius, Rh • is used instead of d:
<1", defined as
•
278
Go.J Production Engineering
Steady State Flow oj Ca.s Through Pipes
d" ,..
.
4R" .. 4[area of flow/wetted perimeter]
279
(7-6)
For example, for a flow conduit with a square cross-section (a x a):
Cross-sectional area of flow = a 2
•,;
Wetted perimeter - 4a
Thus,
•
-'0
d"
=
4(a 2 /4a) - a
For flow through a casing-tubing annulus, with casing inside diameter
equal to da and tubing outside diameter equal to <ito:
Cross-sectional area of flow =- ('lI"/4)(~ ~
Wetted perimeter
=
r(d.,;
rltz,,)
+ clIO)
.i
•
o
§
Z
•
'" ~
Th verify the applicability of this approach, consider the case of a pipe with
a circular cross section of diameter d:
Cross-sectional area of flow'"' rd 2/4
Wetted perimeter = .,.d
•
•
•
•
•
The units for parameters in the Reynolds number should be consistent, so
that a dimensionless number is obtained. One such consistent set would
have d in ft, v in ft /see, p in Ibm/ftl, and p. in lbmf(ft sec). The dynamic
fluid viscosity /l. frequently given in centipoises (cp), can be converted into
lhm/(ft sec) using the conversion factor of 1 cp - 6.7197 x 1O-~ Ihm/(ft
sec). Thus:
N.. _ d(ft)v(ItJ=)p(lhmlft') _ I 488 d(ft)v(ftlsec)pQhmlft')
.(cp) x 6.7197 x 10-"
.(cp)
(7-7)
For gases, the flow rate is commonly expressed in Mscfd (thousands of standard cubic feet per day). This volumetric rate, q.., (Mscfd), at standard conditions of pressure (p"", psia) and temperature (T"", OR) . can be converted
into mass flow rate, m in Ibm/sec, as follows:
,
Gas Production Engineering
m _ Avp -
(I,OOOq,.)Mp. _ (3.1243
(24)(3,600)z.,RT.
Steady State Flow oj Gas Through Pipes
X
IO-')(q.h,p.
T.
As shown in the Moody friction factor chart (Figure 7-1), flow regime is
related to Reynolds number as follows:
A - cross-sectional area of flow, ft2
M - molecu1ar weight of the gas
R - gas constant (- 10.732 psia-ft3/lbmole-°R)
Poe - pra-;ure at standard conditions, psia
TE - temperature at standard conditions, OR
gas compressibility at standard conditions ( _ 1)
1', - gas gravity (air - 1)
where
~ow
vp - (4)(3.1243 x 1O")q.>,p..,l(T.~d')
- (3.9780 x 1O")q.>,p..,l(f.d')
Substituting for vp in Equation 7-9 for NR~:
_ d(3.978O x lO")q.>,P. _ 59. 1991q.>,P.
T.,d2(J.t x 6.7197 x 10- 4)
T.,dJt
Generally, d is used in inches for most gas flow equations. For d in inches,
N Re becomes:
No. _ 7l0.39(p.(p';a)IT.(OR)]q.(Mscfdh.
d(;n.) -<Cp)
14.4
14.65
14.73
15.025
T." oR
520
520
520
520
(60°F)
(60°F)
(60°F)
(60°F)
71O.39 2..,1T.
19.672
20.014
20.123
20.526
Thus, for most practical applications, the Reynolds number for a gas is
given by:
rote it, very important
where q., is in Mscfd, po is in cp, and d is in inches.
<2,000
2,000-3,000
3,000-4,000 (m 10,000)
>4.000 (0' 10,000)
Friction to flow through a pipe is affected by pipe-wall roughness. However, pipe roughness is not easily or directly measurable. and absolute pipe
roughness t is, therefore, defined as the mean height of protusions in uniformly sized, tightly packed sand grains that give the same pressure gradient
as the given pipe. This roughness may change with pipe use and exposure to
fluids. Initially, the pipe contains mill scale that may be removed by fluids
flowing inside the pipe. The fluids may also increase roughness by erosion or
corrosion, or by precipitating materials that stick to the pipe wall. Thus,
estimating pipe roughness is quite difficult. Usually, absolute roughness is
determined by comparing the observed friction factor to that given in
Moody's chart (Figure 7·1). If no roughness data are available. a value of
l ,., 0.0006 in. can be used. Some typical values for roughness are shown below (Chemical Engineers' Halldbook, 1984):
(7·8)
The factor 710.39p.,JT.., for some common standard conditions is as follows:
p.., psia
NRh smooth pipes
Pipe Roughness
Thus, for a circular pipe of diameter d (ft), vp is given by:
R~
type
Laminar (or viscous)
Critical
Transition (or intermediate)
Turbulent
z.. -
N
281
(7·9)
in.
Type of pipe
i,
Drawn tubing (brass, lead, glass)
Aluminum pipe
Plastic--lined or sand blasted
Commercial steel or wrought iron
Asphalted cast iron
Galvanized iron
Cast iron
Cement-lined
Riveted steel
0.00006
0.0002
0.0002-0.0003
0.0018
0.0048
0.006
0.0102
0.012-0.12
0.036-0.36
Commonly used well tubing and line pipe:
New pipe
12-months old
24·months old
O.OOO5-Q.OOO7
O.(XHSO
0.00175
•
286
287
Steady Slate Flow oj Cas Through Pip/!$
Gas Production Engilleering
Frictional losses for a length dL of pipe are given by (Equation 7-11):
pd!. - (fpv'/2g.d) dL
Substituting for frictional losses:
cally expedient. because an analytic description of the variation of temperature along the pipeline length is rather difficult and introduces some complexity. See last section in this chapter for expressions for temperature
profiles in flowing gas systems. The gas compressibility factor, Z, is made
independent of temperature and pressure by using an average compressibility factor, Z... for simplicity. Integrating over the pipe length from 0 to L
and p~ure PI (at L - 0, at the upstream) to PI! (at L "" L, at the downstream end), Equation i-2S becomes:
Substituting for g.ll densit) p:
p -
pM/(ZRT)
and gas velocity v:
, _ q.
(ZTP.)(~)2
0'.
v can directly be writen as this- in terms of q(sc)
(7-28)
pTJC rd
Any consistent set of units can be used in Equation 7-28. In common units,
with q,., in Mscfd, p in psia, T in OR, d in in., Lin ft, and with R "" 10.732
psia ft1f1b mole- OR and g., - 32.17 Ibm ftllbf-sec2, Equation 7-28 becomes:
we obtain:
_ d _ (_f)( pM )(IfX&Z'T'p!,J d
2g.d
~"'d'
p
ZRT
L
[10'1(3. 000 x
0'.
- I Z~ dp - 8fMTp!,q!,
I dL
R.-'d'g.lt
24) ]'q!, _ (( 10. 732 x
144)(32.17)(1112)'
46.9644
)(It)(
(pi - PI)d')
Pi, ")'gZ.. TfL
Thus,
(7-251
(7-29)
Note that T is constant (or, independent of length) since isothermal flow i~
assumed. Otherwise. an average temperature, T.~, is commonly used in.
stead of T in the previolls relationship. The two types of averages used are
the arithmetic average,
(7-26)
where
q,.,
p..,
T.,
PI
_
_
-
PI! d 'Y~ -
and the log-mean temperature,
T _
Zo.. (7-27)
In practice, both these averages are quite close since temperatures T J and T2
are used as absolute temperatures. Using an average temperature is practi-
f L -
gas flow rate measured at standard conditions, Msc£d
pressure at standard conditions, psia
temperature at standard conditions, OR
upstream pressure. psia
downstream pressure, psia
diameter of the pipe, ft
gas gravity (air - 1 basis)
flowing temperature. OR
average gas compressibility factor
Mocxly friction factor
length of the pipe, ft
Equation 7-29, attributed to Weymouth, is the general equation for steadystate isothermal flow of gas through a hOrizontaJ pipe. Implications of the
282
Steady Siale Flow of COl Throllgh Pipes
Ga.! Production Engineering
From dimensional analysis, it has been deduced that relative roughness, the
ratio of the absolute roughness and inside pipe diameter, tid, rather than
absolute roughness, affects flow through pipes.
283
Thus, the friction factor is independent of pipe roughness in the laminar
flow regime.
rartiolly-Turbuknt and Full!l.Turbulent Singk·Phme Flow
Friction Factor
For convenience, friction factor f' , defined as the ratio of the shear stress
at the fluid-solid interface and the kinetic energy of the fluid per unit volume. is used in computing the magnitude of the pressure drop due to (ric
tion. For steady-state flow in a uniform circular conduit such as a pipe. this
results in the well known Fanning equation:
"PI - 2f' Lpv'I(g.d)
(7·10)
where d is the inside pipe diameter.
Any consistent set of units can be used in the previous equations. In customary units, ~Pt is in psi, L is in ft, p is in lbmfftl, v is in ft/see. d is in ft,
and ~ is therefore equal to 32.171bm-ftllbf-sec2.
Friction factor f' is called the Fanning friction factor. Usually, the Mood~
(also called Blasius, or Darcy-Weisbach) friction factor, equal to 4f' , is used.
In terms of the Moody friction factor, f. the Fanning equation becomes:
"PI - fLpv'/(2g.d)
(7·11
The friction factor includes, besides roughnao>, the flow characteristics of
the flow regime. It is therefore a function of Reynolds number and relatin'
roughnao>:
f - f(N •• , ./d)
For partially-turbulent flow, friction factor is a function of both Reynolds
number and pipe roughnao>. For fully turbulent flow, however, the friction
factor is only very slightly dependent upon Reynolds number (see Figure
7-1) .
Generally, intermediate or partially turbulent flow is included in turbulent flow for purposes of developing correlations. Several correlations have
been reJXIrted for the dependence of friction factors on Reynolds number
and pipe wall roughnao>; only some of the most accurate ones are presented
here.
For smooth pipes, the follOWing relationships are applicable:
f'"" 0.5676
NR~-o.3Irn
for intermediate flow
f - 16 log (N~·~/0.7063) for partially turbulent flow
f-O.~
_ 2 log (NR,f'~/0.628) for fully turbulent flow (prandU's
formula)
(7-14)
(7-15)
(7.16)
f .. 0.3164 NRe- o 2.'5 for NRe up to 1()5 (Blasius formula)
(7·17)
f - 0.0056 + 0.5N Rf-03! for 3,000 < NRt < 3 x 1()6 (Drew. Koo,
and McAdams)
(7-18)
For rough pipes, Colebrook's equation is the basis for most modern friction
factor charts:
Laminar Singk-PhaM Flow
f~" -
The pressure drop for laminar flow is given by the analytic HagenPoiseuille relationship as follows:
"PI - 32,<vLl(g.d')
(7·12)
Equating Equations 7-11 and 7-12:
0'.
64 pJdvp - 64/N IW
(7·19)
For very rough pipes, Colebrook's equation (Equation 7-19) reduces to:
f-U __ 2 log (f/3.7d)
(7·20)
whereas for smooth pipes, Colebrook's equation reduces to Prandtl's equation (Equation 7-16),
Swamee and Jain (1976) have presented an explicit correlation for friction
factors as follows:
fLpv'I(2g.d) - 32,<vLl(g.d')
r-
- 210g [.1(3.7d) + O.628/(N R,J")]
(7·13)
(7·21)
•
Gas Prodllclion Engineering
Steady State Flou: oj Gas Through Pipes
Equation 7-21 is applicable for 10- 8 < f/d < 10
2,
and 5,000 <
Nile < lOS, with errors within 1 % when compared with Colebrook's equa-
tion.
In practice, solutions to the equations presented for friction factors are
cumbersome, so a composile friction factor chart is used. as shown in Figure
7-1.
Allowable Working Pressures for Pipes
It is desirable to operate a pipe at a high pressure in order to achieve
higher throughputs. This is, however, limited by the maximum stress the
pipe can handle. The maximum allowable internal working pressure can be
determined using the following ANSI (1976) specification:
2(, - elSE
Pmu - c\, - 2(, - e)Y
(7-22)
where Pm,.. - maximum allowable internal pressure, psig
t .. pipe thicknes:>, in.
c .. sum of mechanical allowances (thread and groove depth),
corrosion, erOSion, etc., in.
S .. allowable stress (minimum yield strength) for the pipe material. psi
E .. longitudinal weld joint factor (i.e., the anomaly due to weld
seam), equal to l.0 for seamles:> pipes, 0.8 for fusion-welded
and spiral-welded, and 0.6 for butt-welded pipes
this is different from line
do
..
outside
diameter of the pipe, in.
efficency factor (symbol is
Y
..
temperature
derating factor, equal to 0.4 up to 900°F, 0.5
same= E)
for 950°F, and 0.7 for l,OOO°F and greater
Allowable Flow Velocity in Pipes
In most cases, C is taken to be 100 (Beggs, 1984). Su~ituting for C and
the gas density (p .. pM/ZRT), Equation 7-23 can be wnUen as:
Ve ""
100
lOO(ZRT)"
(p~1 ZRT)0's "" (28.97P"rJ05
where 'Y is the gas gravity (air - I basis).
The g!s flow rate at standard conditions for erosion to occur, (q")..,, can be
obtained as foUows:
)(TE)«d')
I(lO(pR)o,
.. ((28.97'YgZT)05 p.., . 4 .
where (qe).," ga~ flow rate for onset of erosion, scf/see
d '"' diameter of the pipe, ft
p ,. flowing pressure, psia
T "" flOWing temperature, OR
R - gas constant ( - 10.732 psia-ftlllbmole..°R)
Z .. gas compressibility factor at pressure p and temperature T
Substituting for p., .. 14.73 psia, T., .. 520 OR. and converting to field units
of d in inches and (Q.:)., in Mscfd. we get:
(qJ••
1,012.435 d' [Y~Tr'
(7-24)
where (q.).., is in Mscfd, d is in inches, p is in psia, and T is in OR.
High flow velocities in pipes can cause pipe erosion problems, especially
for ga5e'l that may have a flow velocity exceeding 70 fUsee. The velocity at
which erosion begins to OCCUr is dependent upon the presence of solid particles, their shape, etc., and is, therefore, difficu1t to determine precisely. The
following equation can be used as a simple approach to this problem (Beggs.
1984),
(7-23)
where v~ .. erosional velOCity, fUsee
p .. fluid density, Ibm/ftl
C .. a constant ranging between 75 and ISO
285
Horizontal Flow
Many pipeline equations have been developed from the basic mechanical
energy balance (Equation 7-3):
dp + (pI2g.)dv' + (g/g.)pdz + pdt. _ 0
Assuming horizontal, steady-state, adiabatic, isothermal flow of gas, with
negligible kinetic-energy change, Equation 7-3 becomes:
dp + pdl ... .. 0
•
2B8
Steady Stole Flow oj Cos Through Pipe!
Gas Production Engineering
"'r.--- L, ---'~I"'-'U I-')i
various assumptions made in the development of Equation 7-29 are as follows:
l. No mechnnical work: It is assumed that no work is done on the gas
between the points at which the pI'eMures are measured. This condition can be satisfied easUy by putting pressure measurement stations
such that no mechanical energy is added (by compressors or pumps)
between these two points.
2.
3.
4.
5.
6.
Reasons for
: pressurelflow rate pulsations
or surges, liquids in the pipeline. variations in operating conditions,
variations in withdrawal or supply rates, etc.
Isothermal flow: This assumption is usually met because buried pipelines are used which are not affected much by atmospheric temperature variations. Heat of compression is also dissipated rapidly, usually
within a few miles downstream of the compressor station. For small
temperature changes, the average temperature given by Equation 7-26
or 7-27 is generally satisfactory.
Negligible kinetic energy change: This assumption is justified because
kinetic energy changes are negligible, compared to changes in pressure, for very long pipelines, such as commercial transmission lines.
Constant (average) gas compressibility factor: This is a reasonable approximation, especially if Z.v i~ computed at the average pressure
given by Equation 7-32.
Horizontal pipeline: In practice, flow is never truly horizontal. Equations developed to account for elevation changes will be discussed in
the section on inclined flow.
Average Pressure in a Gas Pipeline
For an incompressible fluid, the average pressure is simply the arithmetic
average of the inlet (PI) and outlet (P:2) pressures:
p.~
- (PI + Pt)/2
"" _ 0.0775543
.
(T_)(Pj
- If.)d')"
p"" "ygZ.,TfLx
A~,==========~======~B
,- oll..•.-_____ L_C_ _ _ _-<~_l'-'
Figure 7-2. Schematic of a gas pipeline for determining the average pressure.
,Figure 7-3. A plot of pressure versus distance in a pipeline carrying gas. (After
Szilas, 1975.)
and,
"" _ 0.0775543
(7-30)
(T<)(
(pi - P!)d' )"
p.., 'YgZ..TfL(l - x)
•
(7-3 1)
Equating these Equations 7-30 and 7-31 (with the assumption that the difference in Z.v for the two pipe sections is negligible):
~-p~=pi-p~
x
(1 - x)
Solving for p.:
p, •
For a gas, a compressible fluid, this is not true. Consider a pipeline AB
shown in Figure 7-2. Using Equation 7-29 for gas flow, one can derive a
simple formula to determine the pressure at any point C along the pipeline
at a fractional distance x from the inlet end. For a flow rate fk in the pipe.
the following two relationships are true (from Equation 7-29):
289
[1'1 -
x(pl - P!)f'
This suggests a pressure profile as shown in Figure 7-3. The mean pressure is
given by:
-~(p,+~)
3
PI + P2
290
C(u ProdllctiQII Engineering
Stead!J State Flow oj Gas Through Pipe!
Rearranging and multiplying both numerator and denominator by
(PI - p,),
P.. _
~ (PI + PIP, + PlI/PI 3
PI + P2
Panhandle (Panhandle .4.) Equati<m
This equation assumes that f is a function of Reynolds number only as
p,1
follows:
llpl - p;J
-~ (H)
291
f _
(7-32
(7-35)
O.0768INR~-I461
Substituting 10' Il<om Equation 7-35 into Equ.tion 7-29,
------------------",-~~~~~-----------
5.6353821 (T_)(PI - pi "2Oq,." "'''''' d"
where P., - average pressure, psia
PI - upstream pressure, psia
P2 - downstream pressure, psia
q. - (0.0768)"
Therefore, Z., must be computed using Equation 7-32 for average pressurt'.
Several equations for gas flow have been derived from Equation 7-29 as.
suming a friction factor relationship to avoid a trial and error computation.
These equations differ only in the friction factor relationship assumed. As
we have seen earlier, friction factors vary over a wide range with Reynold....
number and pipe roughness. Thus, none of these equations is universally ap.
plicable. In gas field operations, engineers use the equation that best suits
their conditions, or use their own modified versions.
''''''' ~
25.309468
f - O.0321d 1tJ
-,:.,
(T_)(Pi -P!)"(.!.j'' ' ' de."",
p~
Z T L
.'...
-y
(}0730.5
I'g
Thus:
d"""
Z T p$''''''(lj'''''"'
(T_)""'''(PI., .,.
'Y
q., "" 32.6491 p.,
0,07881
(7-36)
!'~
The Panhandle A equation is most applicable to large diameter pipelines, at
high flow rates.
Modifu:d Panhandle
Weymouth proposed the foUowing relationship for friction factor as a
function of pipe diameter d in inches:
----;;;<l
0'.
q.c:
Non-Iterative Equations for Horizontal Gas Flow
Po Z••T..
(Panhandl~
B) EqUlltion
One of the most widely used equations for long transmission lines, the
Panhandle B equation assumes that r is a function of Reynolds number as
follows:
(7-33)
(7-37)
f - O.00359/N~039U
Substituting for f from Equation 7·3,3 into Equation 7·29:
q. _ 31.5027
(T_)(W - P!)d"~"
Pte
"Y,Z."T.,l.·'
The pipeline flow equation is thus given as follows:
(7-34)
This is known as the Weymouth equation for horizontal flow. It is used most
often for designing gas transmission systems because it generally maximizes
pipe diameter requirements for a given flow rate and pressure drop.
q.,
_109.364 (T_)I,,",(PIP!)""'(lj""
d"'
"
p.,
Z."T.~L
'Y
!'i.
00.,
(7-38)
The Panhandle B equation is most applicable to large diameter pipelines, at
high values of Reynolds number.
•
292
Gas Production Engineering
Sleady Slale Flow oj Gal Through
pj~
293
A More Precise Equation for Horizontal Gas Flow: The Clinedinst Equation
! I~~~~~ ~~~~§ §§~~~ ~~I~~ §~~~~ 1l
The Clinedinst equation rigorously accounts for the deviation of natural
gas from ideal behavior (an average gas compressibility factor, Z." is not
used in this method), and the dependence of friction factor, f, on Reynolds
number and pipe roughness, leading to a trial and error solution scheme.
The integral I (PiZ) dp must be evaluated. In order to generalize this evalua.
tion, it is converted into the following:
~I~~~~~ ~~~~§ §§~~S ~~~~~ ~~~~~
~ Inm
um mu um nm
!l~~~~~ ~~~~§ §§~~~ ~~~§~ ~~j§~
~l~~~~~ ~~~~§ §§~~~ ~~§§~ ~~~§~
~I~~~~~ ,~~~§ i§i~~ ~~§!~ ~~~~i
~
-'••"
g-
l(p/Z) dp - l[(p,.p,/Z) p"dp,) - p:" j(p,/Z) dp,
where ~ - pseudocriticaJ pressure of the flowing gas mixture. psia
P. - reduced pressure (p, _ pip",,)
Values for the integral function j(p,lZ) dp, are given in Table 7-1. For this
case, Equation 7-25 becomes:
1",. [1 0" (p,/Z)dp, -
1.. (p,lZ)dp,1- BfMTp!q!.L
~r'd'~ T1.
0
Rearranging this equation, and using common units, with CJ:oc in Mscfd, p in
psia, T in QR, d in in., Lin ft, and substituting for R ( '"" 10.732 psia-ft1l1b
mole- oR) and g., (= 32.17Ibm-ft/lbf_sec2):
~
~
•
il
e
•
0.
..." ' ..
.,
,•• -.:.•
:c .." E
"I N •
_
0
1;
0
~
~
~
J!
~
.!
:i§~~~~ ~~~~§ §§i~~ ~~§~~ §~!~I
"
"
I~~~~~ ~~~~§ §§~~; ~~~~~
I
This is known as the Clinedinst equation for horizontal flow.
I
:lm~~
:I~i~~~ ~~~§§ §§§~~ !~§~~ ~!~I;
"2
,Inm nm §§m um mn
E
"I~~~~~ ~i~~§ §§~~~ ~~~~! ~~~~~
>
The pipeline equations developed here assume 100 % efficient conditions.
In practice, even for single-phase gas flow, some water or condensate may
be present, which collects in low spots in the line Over long periods of time.
Some solids, such as pipe-scale and drilling muds, may also be present. To
account for the reduction in pipeline capacity that will result from the presence of these materials, an efficiency factor E is generally used as a multiplying factor for the flow rate predicted by the flow equations. Only very
rarely does a pipeline exhibit an E equal to 1.0; a pipeline with E greater
than 0.9 is usually considered "clean." Typically, the follOwing efficiency
factors may be encountered (l koku, 1984):
(text continued on page 303)
go to page number 154/326 directly
um mu nm um
' I~~~~~ ~~~§§ §§~~; !~~~~ ~~~~I
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•;;;•,
Pipeline Efficiency
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•
29-4
Gas Production Engineering
Steady State Flow oj Gas Through
Pi~
295
•
III
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Gas Production Engineering
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297
Steady State Flow oj Gas Through Pipes
aBSS
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Ga, Productwn Engineering
299
Steody State Flow of Gal Through Pipel
.
..••
m
m
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/i" ' ~
<
iE ",,
• ,
0
•
.cOB
3~8
oo';:!~i
~
•
--• ••
0
!
n""
~~~
.-~';o03¢
... ""
ig!§i
66000
-,~U::!:S
-~, '" r'~~~
g:s:s:sa
oaiU
§-
mH
•
-•
,• - ll
" .."•
--· ,•
•
0
~
"., i
'S
0
"0
.
~~.
n
.. " " .-.. ....n
~l:!~~g
000
,. ~~
'0
-
~m
•
0
0
•
:;;
--g
,
c
c
"-
~~
Hi ••
;a:5H~
aas8il
8
~
Z
.E
,••
..
>
'.2iae:'!
...........
g:
s: s22222
i: :u:;:
"" ...... g:
~qn:~
300
Cal Production Engineering
Steady State Flow of Gas Through Pipes
"'"S'
md
;gg~~
~QQQ:;
~~r;~~ s!;!~a:;
b l:iS 1;(; 1;15:';00
....;;~;;§;.
,_ ........
~~~~~
g~~~;; iIliHi!l!
... ,- ..........
"'§"'~"
-;-!ig!;!;
<!-o.";;-;:
81:;&00
SI:;SoS
00000
00000
...
~S~~~
..
~~~~;!
S:;1:;8:;
!l!~U
1:;SSSS OSO:;:;
~~~::;::;
......
~~Sbb
~;
_"1"0
- -,S~SSS
§;g
'--·i
O:,;S
~---
-:::-;;;;iiE
):;~~.;a
...,
mH
...
!a$~~
!;I:;::;:;t;
co ..... !S.
:.;;;:t; ... ~ n~ft~i
s~ss
815S::;
",
r···
~!i~
1$."
"'c>~n'"
iiis~~
... - ......
on"''''''''St
nO.
~~!1:~C>
~i*"~
~!'?;:~I!
0'-;'
_0-
-"'''' .....
nm
nm
a:;C;$;>1
!l~:8~
..
"'", .,
8~;21"!;;
lL!!'!
~,
.,
~
~~§
0 ..
-
.m.
-"'"I
mu nm ~~.i
...
nm um ~Tf
i ~ '"ri3i i~
- ...- -"ilT
U.
8Sgg§
~:;~ i !isii i"'~
Hm
mu
.... !
n--..
iili h
!S! .. n. mu ··i"'
j~~§i mH nm nm m.~ 'T§§
H!U
ss
mH mn ..nm.... mn
gggg
""!Ii
U'"
is! hi! il mH hm nm
mH um um §ji§~ i... U
.soh hhii Hm nm Hm ••••• ;ill§
-'T~ !jji~
mn ·"~·i r"r
ll. I nm i§~li h~
H"~ mH
.... w-i~i nm um §on ••••
r'"
.. .. "' .. §
jli~~ mn m.§ nm Hm ihH .'-§
mil n-··
h. mn mu nm nm
~~;;:t§
~S:8""
....... $::iI
S0
,- 0
......
00
l:i:;b!:;S
!-O.~;.';::!~
..,.,,,,,,,,
:::~;~i
bbbSS
l51:;l5bb
~iE~a
bObSS
:g ... ",§ ..
....
d~!!!
~
~m~
. . .. -r:
~
~i~l"!~
§ gg8
;1r.~;:ft
•
0
-
~1=li!;:::~
... '"
'"'-"'I'"
"_0:20-
s ........ ~
000
~!;:"!~
~s
~!E~;;
gS888
;;-
.....
~iii~I'"
Z-:g--:
~-
"'18"' .....
;;«;;;~:;::
U§ •• 888&g
00000
8"'- ....
-:!~!1~
81515153
~~
8g8g8
~rHHH~
88888
!St:R:!!:
.1~:::~;:
~~g~:
-~-~-
..
"'-~-n
.. §
.~;
- ..... 8 ..
......
.,. ..
----~i;!~:,!
~ :38:
=s:
!::~~~~
.
-rr
.. .. ..
.. mu ~~~~i mn
~im Hm mn
i~~"~ um u-·" mu
.....
';SJ;;So
~..,
--
"'~I ~i~!i
~~~!>
S81:;bo
::!;,;g~F:
-~B'i
:,;
SS
";3""
~·i
... _- i
'"
sfiP.HH
Sl:;SSS ~:;oS~ U~.~
~~~§;
.um
301
3 ~:2 ~pl;
~~!:!!:!!!
.~
...
!!!!!!!:!!:!
... "'s ......
•• § -
-8"'1-
~§§§~
~ird~;e
!:!!:!!:!!:!!:!
i:~
liPol8
!!!:!!:!!:!!:
85::e2~
::':::'::.0:::.0::':
•
Steod!l State Flotl-, of Gas Through Pipes
Gas Production Engineering
(text ccmtililled from 1Hlge 293)
Liquid content
gallMMscf
Type of gas
in the flowline
0.1
7.2
600
Dry gas
Casing-head gas
Gas and condensate
E
(£Taction)
0.92
0.77
0.60
For high liquid conten~, ~uch as the pre\;ous case shown above for gas with
condensate, h\:o-phase flow conditions exist. Pipeline efficiency can no
longer represent the complex flow behavior, and different equations that account for two-phase flow must be used (see Chapter 8).
Transmission Factor
Equation 7·29 can be written as:
- pI)d')"(l)'f .'
(T.)(M
Poe
q. - 5.6353821 -
)'gZ.,T.,L
-
The factor (lIf)05 is known as the transmission factor. Several correlations
have been developed for the transmission factor (derived from the friction
factor) , but it remains one of the most difficult parameters to evaluate accu·
rately. Transmission factor, frequently used in pipeline literature, is just an·
other way to represent friction factor and further discussion is, therefore,
unnecessary.
Example 7·1. What is the maximum pressure at which a lO·jn. nominal
size pipe (0.0. _ 10.75, Lo. - 10.02 in.) can be operated? Calculate the
maximum throughput for a 40-mile pipeline of this type. using (a) Wey.
mouth equation, and (b) Clinedinst equation. Assume tId - 0.002,
c.., 0.05. E _ 1.0 (seamless pipe), Y - 0.40, S - 35,000 psi, T... - 100°F,
'" - 0.01 cp, 1, - 0.70. Assume 0.0 psia minimum pressure.
Solution
Pipe thickness. t _ 10.75 - 10.02 .. 0.73 in.
Using Equation 7.22,
0..
_
0
2(0.73 - 0.05)(35,000)(1.0) _ 4,663.92 ps;a
10.75 - 2(0.73 - 0.05)(0.4)
•
3()4
Gas Production Engineering
Steady State f'low of Gos Through Pipes
To provide additional safety, the maximum pressure specification is chosen
as 4,000 psia.
From Figure 7-1, f .. 0.024. From Table 7-1:
"OO
Thus. to calculate the maximum throughput, the upstream pressure,
PI .. 4,000 psia, and the downstream pressure, P2 .. 0.0 psia
jo
Assume T .... 520 oR, p.., - 14.73 psia
o (p,lZ)dp, j '05
From figure 3-1. Ppc ~ 663 psia. Tpc
=
387°R
+ 460)/387 - 1.447
(a) Weymouth equation (Equation 7-34):
_ (3 1.5027)(520/14.73) [
23.
88
23
j'·OJ:!(p,/Z)dp, _ 22.88
o
+ (23.23 - 22.88)(6.033 - 6.0)/(6.05 - 6.0)
-= 23.11
Thus,
From Figure 3·2, Z., ,. 0.74
q",
(P;Z)dp, - 22.
By interpolation:
Using Equation 7·32, p•• - (2/3)[(4,000' - 0)/(4.000' - D)] _ 2.666.6,
psia.
P" - 2.666.67/663 - 4.022, T" - (100
305
q",
f'
(4,000' - 0)(10.02)1"
(0.7)(0.74)(560)(40 x 5,280) J
- 265,206.15 Mrid - 265.21 MMscfd
(b) Clinedinst equation (Equation 7-39):
_ (6,515.2606)(23.11)" _ 202174.39 M",fd ~ 202.17 MM",fd
(0.024)"
'
A second trial is not required because the friction (actor plot in Figure 7-1
shows an almost constant ( in the turbulent region applicable here.
This example shows the differences in results that may sometimes occur
from using different flow relationships. Most of the difference results from
the friction factor values used in the two equations. From Equation 7-33.
we can calculate that the Weymouth equation used an f = 0.01484, whereas
an f = 0.024 was used in the Clinedinst equation.
PrJ" 4,000/663 - 6.033, Pr2 - 0.0, Tpr - 1.447
q", _
(7.969634)(663)(520/14.73) [
[ j : OJ:! (p,JZ)dp, - j: (P,lZ)dp,
_ 6,515.2606 [j"OJ:! ( IZ)d
f05
0
p.
fS
J'
Prjf'
First trial: Assume Ck .. 265 MMscfd
U~ng
Vertical and lnclined Single-Phase Flow of Gas
(10.02)'
(0.7)(560)(40 x 5,280)1 J
Equation 7·9, N.. - (20)(265,000)(0.7)/[(0.01)(10.02)] _ 3.7 x 10'
Neglecting changes in kinetic energy, and assuming that no mechanical
(or shaft) work is done on or by the gas, the mechanical energy balance expressed by Equation 7-3 becomes:
1
dp + Pg dz + fpv dL _ 0
g,
2g,d
(7-40)
Consider the flow scheme shown in Figure 7-4. 8 is the angle of drift from
the vertical, L is the total length of the pipe, and z is the vertical elevation
difference between the inlet (point 1) and outlet (point 2). Land z are related as foUows:
•
306
Cas Prodrlction Engineering
2
Steady Stale Flow of GO!! Through Pipes
I,' 1 + (6.7393
GROUND SURFACE
(ZT/p) dp
X
- 0.01875,",
lO-'fLq!,Z'T')/(zp'd')
307
(7-42)
9
Figure 7-4. Gas flow In an
•
inclined sectlon_
1
L - zlcos 6, implying that dL "" mlcos 8
I
dL - (Liz) dz
Using this relationship between Land z, Equation 7-40 can be written as:
Substituting for gas density and velocity (as described earlier for horizontal
flow):
(_r
_ dp _ [28.97"",][.ll +
)(!:)(I&&z'1Y..)L
ZRT
g. 2g.d z P'ltr'd' j
this (pie)^2 consumed here to change the factor
as 0.81057 ( = 16/(2 x (pie)square)
-
(ZIp) dp
I, 1 + (6.7393 x 10 ·'fLC&Z'T')I(zp'd')
Substituting for cos 0 - z/L.
0',
where the units are: p _ psia: q,. .. ~hcfd; d .. in.; T = oR; and L. z - Ct.
Equation 7-42 is the general equation for vertic,al flow calculatio~. The
left integral cannot be evaluated easily because Z IS a compl~ fun~on of p
nd T and the temperature variation with depth z is not easJiy defmed. The
:ario~ simplifying assumptions made in the evaluation of this integral form
the basis for the different methods that give results of var}ing degrees of ac·
curacy.
.
.
Some methods for vertical flow assume an average temperature, m which
case Equation 7·42 becomes:
(ZTlp) dp
28.97 I'
I'I (gig.) + (0.81057fLq!,Z'1Y..)/(zP'ltg.d')
- - R- I"'lz
(7-4 1)
Almost always, 'Y, is assumed constant in evaluating the right integral in
Equation 7-41. Substituting for p.., ( - 14.73 psia), Till' ( _ S200R), and ~
(- 32.17 Ibm ftflbf.sec2), and converting to conventional units, Equation
7-41 can be written as:
_ O.01875')'gz
TO'
(7-43)
In the left integral of Equations 7-42 and 7.43, the value of the constant is
6.7393 x 10 - 4 • Some authors use a standard pressure, Poco equal to 14.65
psia, in which case this constant becomes equal to 6.6663 X 10- 4 . Still others use Pte - 14.65 psia and diameter din ft. In this latter case, the constant
becomes equal to 2.679 x 10 ,11.
Static Bottom-Hole Pressure (SBHP)
For production and reservoir engineering calculations. the shut·in (or
static) bottom. hole pressure, p.... , is frequently required. In many cases, it
may be difficult or expensive to obtain p..... by gauge measurements. Tech.
niques have, therefore, been developed to calculate SBHP from wellhead
pressure measurements.
For a shut-in well, the flow rate (q or CJ.tc) is equal to zero, and Equation
7-42 simplifies to:
I....
.... (ZT/p) dp - 0.01875,",
(7-44)
Equation 7-44 describes the relationship between the pressure measured at
the surface (or wellhead), P... h, and the pressure P.... at a depth z. Note that
the pipe length L has no effect on the static pressures.
..
308
Ga.r Pmdll£,tioll Ellgineerillg
Steady Stote Flow oj Cas Through Pipe!
At.wag~ T~mlJemtun and Z-Factor Method
~is ~ the simplest method. An average temperature and Z.factor is used
to simplify the left-hand side integral in Equation 7-44:
j
..., (ZlPp.)dPp. _ 0.0187s-,,.
I'ptI
1 + BZ!/~
(6.6663
where B -
Z••T"
jp.. (dp/p) -
"'.
0.0187s-,,z
(7-49)
T."
X
1O-4)~11.
(7-50)
zd~
In Equation 7-50, ~ is the pseudocritical pressure of the gas (gas mixture),
and q., is the rate at 14.65 psia and 520 0 R (instead of 14.73 psia and 520°F).
As stated earlier, a conversion constant of 6.6663 x 1O -~ in Equation 7-50
implies a Pot of 14.65 psia, whereas a conversion constant of 6.7393 x 10-·
(as in Equations 7-42 and 7·43) implies a ~ of 14.73 psia.
For the case of SBHP, the flow rate 'be is zero (or, B = 0), and Equation
7-49 becomes:
Vpon integration.
In p •• _ 0.01875>",
p..h
309
Z.,T1y
0'.
"'"" (ZI
p" ... pwh exp [_0_.O,I-,87"5-,>,,,'J
Z~,TI'
\
(7-45)
Generally, this is written as:
p,r.-...
P .. h &-2
where s - (0.037s-,,,)/( Z,, T ..)
(7-46)
(7-47)
the average temperature, the bottom-hole temperature
(B~;')determine
and the surface temperature should be known In c ••- wh
th
BHT'
k
.
.
-ere e
n~ nown, It can be estimated from the fact that the temperature
gradient IS usually of the order of 0.015 ° F/ft For a static column of
~~
•
.
~M
an m Ie a .. erage temperature is satisfactory to use. For caJculating Z
the
"alaverage press·
llfelSrequired (.Inaddition to average temperature). Thus".a
'ben "ndd er~r type of,solution is necessary. A good initial estimate of 1>.. can
rna e using Equation 7-48:
'S
. 15
(7-48)
......
PI"
)d
PI"
..
_ 0.01875>,.
T
(7-5 1)
Sukkar and Cornell (1955) evaluated the left integral in Equation 7-49 by
numerical integration. They reported re.u1ts in tabular form for reduced
pressure Pp. in the range of 1.0 to 12, reduced temperature T p, of 1.5, 1.6,
and 1.7, and B in the range of 0 (for static) to 20 (flowing). Messer et al.
(1974) presented an extension of the Sukkar-Cornell method, showing its applicability to deep, sour gas wells, and presented the values of the integral in
Equation 7-49 for T p, up to 3, PI" up to 30, and B up to 70. These values are
shown in Tables 7-2(a-m). The case B co 0, shown in Table 7-2a is applicable to SBHP determination .
For computer programming pur~, Messer et al. (1974) have also proposed the following equation to Fit the tabu1ar data:
... (Zl17.)dPp.
-E+ Fpp. +Clnppr
\ 0.21 + BZ2..2
I~
(7-52)
where E, F, and C are regression constants, determined by Messer et al .
(1974) as follows:
For O:s B:s 25 , 10:s pp< s 30, 1.1 s Tp.:S 3,
Tl, -
(1.21216 - 0.015178) T"
Tl. -
(0. 12792 - 0.002268 ) T ~
Sukkar'CornelJ Method
E - (0. 18011 - 0.002628)
- (0.28026 - 0.005528)
also uses an average temperature, but accounts for the varia. This method
.
t~on of Z W1~ pressure. SukJcar and Cornell (1955) converted the basic equation (Equatton 7-43) into the pseudoreduced form :
F - (0.02246 - 0.000438)
+ (0.21463 - 0.002748)
(text continued on page 336)
page number wise bole to 171/326
•
Table 7-2 (a,
Extended Sukkar-Cornellintegral for Bottom-hole Pressure Calculation
~
0
Reduced Temperature for 8 '" 0.00
020
0'"
100
150
200
2.'"
300
J.'"
400
4'"
'.00
,.'"
600
6'"
7.00
7'"
800
8.'"
900
1.1
1.2
1.3
1.4
1.5
1.'
1.7
1.8
1.'
2.0
2.2
0.00l0
00010
0.00l0
0.00l0
o 0010
00010
00010
0./i387
1.3774
l,fIOJ8
L7149
1.7995
0.8582
1.4440
1.7373
L9116
00010
0.00l0
08824
1,5129
18565
0.9017
1.5654
1.9422
2.2U23
2,3996
2,5583
0.9079
1,5781
L9f109
2.2273
2,4.'107
2,59J7
2.7325
2,11515
2.9569
3.0523
3.1400
3.2215
3.2980
3.37OJ
34393
3.5052
35665
3.6297
3,68R9
3.7465
3.8026
38573
3.9108
3%34
40150
0.9082
1.5823
1.9693
2.2397
2.1255
2.2101
2.2882
2,3622
2,4330
2.5013
2.5677
2.6329
2.6971
2.7602
0.8I!97
1.5334
1.8911
2 J3)1
2,3138
24570
2.5162
2.6793
2.7715
2 8558
2,9341
HXl79
3.0781
3,1452
3.2100
3.2727
3,3338
3.3934
3.4516
0.8966
LS514
1.9192
21709
IS7~
0.S719
1.4836
1.11078
2.0157
2.1631
2.2778
2.3746
2,4603
2.5390
2.6128
2.6833
2.7512
28171
28814
2,5442
3.0058
0.00l0
0.9108
1.58119
1.9798
2 25](,
24641
2,6354
2.1798
2.9050
3,0158
3, 1I511
3.2014
3.2924
1947.1
2.0178
2 0689
2.1547
2.2214
2.2872
23522
2.4165
2,4S02
2.5432
2f1OS7
2,t)676
2,7289
2.7896
2,8499
2.0298
28223
2.8336
2.9441
3.0039
3,0630
3.1215
31794
3 ......
12.50
1300
3,02f!O
3.0867
] 14~2
3.3506
3.1260
3.1847
3.2427
3.2999
3.3565
34126
3.4681
3.5231
34068
3.~777
~n
2~ml
3 Jh27
, (,11'1
95"
10.00
1050
1100
11.50
12.00
1:"1
/4 00
100
15.00
15.SO
16.00
16.50
17,00
17,50
18.00
18SO
19.00
19.50
2000
"'"
2_
2.9690
3,2612
3.3 189
3.]763
3,4335
3,4906
3.5474
3.6041
3.6606
3.7170
3.7732
3.8293
3.8853
3.9411
3.9969
24.50
4.0525
4.1080
4.1634
4.2187
4,2739
4.3291
4.384\
44391
"00
44940
"'"
4,5488
2100
21.50
22.00
22.50
23.00
23.50
2400
2600
46036
26.50
27.00
27.50
4.6583
4.7 129
4.7675
4 822{)
48764
4.9308
4.9851
5,0394
21100
211'"
29.00
29'"
30.00
32J69
J.29W
3.5 1Rl
3.5735
3.6285
3.6832
3.7376
3.79 19
3.8459
3.8996
3.9532
4.0066
4.0599
4.1129
4.1658
4.2186
4.2712
4.3237
4,3760
4.4282
4.4803
4.5323
4.5M2
4.6360
4.6877
4.7392
4.7907
4.8421
4.8934
4.9447
4.9958
'.0469
'.0979
5.1488
5.1997
3,6857
3.7391
3,7922
3.8450
3,8974
4.9497
40016
4.0533
4 1048
4.1560
4.207\
4.2579
43086
4.3590
4_
4.4595
4.5095
4.5594
4.6091
46587
47081
4.7575
4.8067
4.8558
4.9()48
4.9536
5.0024
5.0511
,5,1482
5.1966
5.2450
5,2932
2.cX>42
2.2507
US13
2,4898
2.5945
2.6698
2.7484
2.8222
2.8926
2.9603
3.0258
3,0893
3.1612
3.2118
3.2713
3.3296
3.3870
3,4-436
3,4993
3.5543
3._
3.6523
-'-71 ~4
:"I 7.~)\(1
3.8200
3.87 16
3.9228
3.9736
4.0240
4.0740
4.1237
4 1731
4,2221
4.2709
4.3195
4,3678
4.4158
4 4636
45112
4.5586
4.6058
4.6528
4.6996
4.7463
4.7928
4.8391
48853
4.9314
4.9772
5.0230
'.0686
5.1142
5. 1595
, 2048
5.2500
5.2950
5.3400
3 ..5OR7
),5647
36198
3.6741
3,7277
3.7806
3 !02R
.1.S(,-U
3.9354
3.9859
4.0359
4 ....
41346
4.1833
42316
4.2795
0271
4.3744
44214
4.4681
4.5145
4,5606
4,6065
4.6522
4,6976
47428
4.7879
4.8327
4.8773
4,9217
49660
5.0101
5.0541
5.0979
5,1415
5.1850
5,2284
5,2716
5.3147
5.3577
5.4005
23607
2.5125
2.6190
2.7480
2,8449
2,9330
3 0146
HI911
3,1635
3,2324
3."""
3,3623
3,4239
JAII38
3.5·m
3,5993
36552
3.7100
3.76-10
3.8171
38694
~.9211
, 9721
2.6909
2,8052
2.9065
2.9982
3.0828
3.1616
3.2360
3.3065
3.3740
3.4367
3.5012
3.5617
3,6204
3.6776
3.7336
3.7883
3.8420
3.H9JR
3.9467
3.9977
41l-lHO
4.0224
40722
4.12 15
4I7Il2
4.2185
4,2663
4,3138
4J")8
4.4075
4.4538
4.6998
4.5455
4.5909
4.0977
4.14SO
4.1950
4.2428
4 2900
4,3368
4.3830
4.4289
4.4743
4.5193
4._
4.6053
4.6522
4.6959
4.7392
4.7822
4.8250
4.8675
4.9098
4.95111
4.9935
5.0351
5.0764
5.1176
5.1585
5.1993
5.2398
4 6360
46808
4,7254
47f1n
48138
4.8577
4.9014
49449
49882
5W12
5.0741
5.1169
5.1594
5.2019
5.2441
5,2862
5,32K2
5.3700
5.4117
5.4532
'2JlO2
5.3204
5.3605
'.4001
5.4401
5.4797
r
2_
4H~~7
2,6148
2.7561
2.8784
2,9867
3.0645
3.1742
3.2575
3,3355
3.4092
3.4792
3,5460
3.6101
3.6718
3.7315
3.7894
3.8456
3.9OOl
3.9540
4,01165
4.0579
4 IOR4
~
~.I ~HO
II'
4. 1547
4,2 131
4.2609
"'4.3546
l8O
4 4007
44462
4 4913
4.5359
Ogol
4.6239
4.6574
4.7104
4 7531
4,7955
4,8376
48794
4.9209
4.9621
5.0031
5.0438
5,0843
5 1245
51646
5.204-4
5.2440
5.2634
5.3227
5.3617
4.2067
4.2546
4.3018
4.3483
4.3942
4.4395
4.4843
4.5285
4.5722
4.6154
4.6582
47006
4.7425
4.7841
4,8253
4,8662
4.9068
4.9470
4.9869
5.0265
5.0659
5.1050
5.1438
5.1824
5.2208
5.2589
5.2968
5.3345
,- ,5.4393
5.4779
5.5163
5.3720
5.4465
5.4834
5.5202
3,3720
34470
351SO
B6S7
Jt\S04
3.1126
3.7727
38:m!1
38872
3.9421
3.9958
41)·H2
40994
4 14'l~
-l I'IH'I
42472
4.2941
4.3414
43874
44327
4.4773
4,5213
4.5648
4 6017
4.6501
4.6921
4.7335
4.7746
4,8152
4.8554
48953
4.9348
4.9739
5.0128
5.0513
50895
5 1275
5.1651
5.2025
5.2397
5.2766
5.3132
5.3497
5.3859
5,4219
5,4577
5.4933
5.5287
2.4
2.'
2.8
3.0
0.00l0
U.OOOO
o 0010
0.0000
0.00l0
0.9147
1.5966
1.9951
2,2744
2.4900
2.6654
2.8138
2.9426
3.0571
3,1605
3.2557
3.3428
3.4245
3.6012
3.5738
11.9177
1.6059
:!.0063
2.2893
2.5081
2,6863
2.8382
0,9194
0.9206
1,5111
1.6148
2.0151
2.0211
2,)013
2.3100
25234
2.5J47
2.7050
2,7189
28589
2.8152
2,9928
3.0114
3.1119
3.1322
3.2195
3.2413
3.3178
3.3408
34085
3.4325
3.4931
3.5176
3.5722
3.5973
3,6467
3,6723
3.7173
3.7432
3.7844
3.8108
38484
),8750
3 91199
3.9367
3.9690
3.9961
4,0262
2.05&3
4 U814
4,1086
4 1351
4.1622
-I 1872
4.2143
4.2380
4.2650
4 21l7.~
4.3144
-l 1 t~7
-l 1"2.~
0,9218
1.6184
2.0274
2.31o.t
2.5452
2.1134
3.6486
3,7144
),7775
3.6382
3.8969
3,9538
40090
40627
411511
"'"
4 21 ~Il
-l. 'M'
4 .3122
4.3589
4.4047
4.4-497
4 4939
4,5374
4,5802
4.6223
4 6638
4.7048
4.7451
08.50
4.824-4
4 8633
4.9017
4,9397
4,9774
5.0146
5.0514
5.0879
5,1241
5,1599
5,1955
5.2307
5.2656
5.3003
5.3347
'.J688
5.4027
5.4363
'.4697
5.5029
5.5369
2.9699
3.0871
3.193()
3.2899
3.3795
3.4629
3.54 11
3.6148
3.6847
3.7512
3.8148
3,8760
3.9350
3.9921
4,0473
4.1010
4,1532
4,2041
4 2.~"7
J to::' I
4.3494
4.3957
4.4-4 10
4.4855
4.529 1
4,3829
4.4289
44741
45183
4.5617
4.5720
4 6042
4.6141
4.6555
4.6963
4.7365
5.7761
4.11151
4.8536
4.8916
4,9291
4,9662
5.0027
5.0391
5.0750
5.1104
5.1455
5,1803
5,2147
4.2488
5.2826
5.3162
5.3494
5.3823
4.41SO
5.4475
5.4796
5.5116
5.5433
46461
4,5872
4.7276
4.7675
48067
4.8454
4.5878
4 6J02
4.6119
4.1129
4.7532
4.7928
4.8319
4.8704
48835
4908J
4 9211
4 9582
4.9457
4 9969
5.0311
5.0670
5. 1024
5 1374
5 1720
52083
5.2403
5.2739
5.3073
5.3403
5.3780
5.4054
5,4376
5.4695
5.S012
5.5326
5.5638
4.4095
4 .4555
4,5005
45446
,-
28896
3,0274
3.1496
3.2597
33600
3.4H4
3.nSI
3,6181
J 6934
37646
3./i323
3.8969
3,9588
4.0182
4.0755
4,1309
4 ISJ5
42:\66
om
4.1165
4 11lJIl
4. 43 \6
4.4775
46224
45663
4.6094
4,6518
46933
0341
4.7743
UI38
4.8527
48911
49288
4 "'I
49827
'.0029
5.0192
5.0552
5,0392
5.1260
5.1808
5.1953
'.2294
5.2631
'.2965
5.3296
5.3624
5,3950
5,4272
5,4591
5.4903
5.5223
5.5935
5.5844
5,0751
5.1105
5 1455
5.1802
5.2144
5.2483
52819
5.3151
5.3480
,."'"
5.4129
5.4460
5.4767
'.l<l82
5.5394
5.5'704
5,6011
Table 7-2 (b)
Extended Sukkar-Cornell Integral for Bottom-hole Pressure Calculation
P,
0.20
OSO
1.00
I.SO
2.00
2SO
300
3.SO
400
4.SO
'00
'.SO
.00
6.SO
700
'SO
8.00
'SO
'.00
'.SO
1000
10..50
11.00
11.50
12.00
12.50
1300
\3 .'\11
14.00
/4 .50
15.00
15.SO
16,00
16.50
17.00
17.50
18,00
18.SO
19.00
19.50
20.00
2O.SO
21.00
21.50
22.00
22.50
23,00
23.SO
2-1.00
2-1.50
25.00
25,SO
26.00
26,50
27.00
27.50
2800
28.50
29,00
29.50
30.00
1.1
1.2
1.3
1.4
00000
0.0000
0.0000
0.0000
0.0226
01036
0.2121
0.0983
0.3002
0,3741
0.4419
0 ..5014
0,5715
634<;
o
06966
0.7579
08185
08184
09378
09967
1.0551
I 1131
1l7Jl6
12275
2,2841
1·3403
13961
14515
1.S067
1.5616
1616-'
I f>7!111
/
.~Z"""'
/ .5753
1.6261
I 6767
1.7271
l.m5
1,R2n
1 8778
1.9278
1.9711
2.0216
2.0773
2.1269
2.1765
2.2260
2.2754
2,3248
2,3141
2.4233
2.4723
2.5216
2.5706
26196
, 661!5
2,717-1
2,7M3
2,8151
2.Hfl-'R
2,912~
2,1}612
3.0098
30SfW
3,1069
0.0220
0.2052
0.3125
0._
0.4854
0.5594
0.6291
0.6957
0.7601
0.8225
0.8836
0.9431
1.0030
1.0614
1.1191
1.1761
1.2325
1.2883
1.3435
13983
1,4526
1.S065
LS601
1,6133
1,6662
1,1 11111.
/ ,5368
1. 5860
1,635 1
1.6839
1.1326
1.7811
1,8294
1.8117
1.9257
1.9737
2.0215
2.0592
2.1167
2.1642
2.2116
2.2588
2.3060
2.3531
24001
2 .4470
2.4938
2.5406
2.5873
2.6339
2.6805
2.7269
2.7734
2.8197
,2.9123
2.9585
3.00--\6
3.0507
0.0216 00214
0.0954 0.0934
0.1995 0.1954
0.3102
0""
0.4126 0.4133
0.5032 0.5105
0.5847 05983
0.6594
0,6785
0.7294
0.7530
0.7960 0.8229
0,8601
0.8895
09222 0.9536
0,9829
1.0156
1.0423
1.0758
I lOOS
1.1346
I 1578
1.2142
1.2698
13248
1,3791
14328
1.4860
1.5387
1.5910
1,6429
1.694.\
1.J921
1.24!!6
1.3041
1.3687
1.4126
1.4658
1.5182
1.5701
1.6214
1,6721
7·1 ~f.
I ~O3
1.5!!!!3
1.6360
J .6835
11308
1,7778
1,8247
1.8114
1.9179
1,9643
2.0105
2,0566
2.1026
2.1484
2.1941
2,2396
2.2851
2,3304
2,3757
24208
2,4659
2.5 lOS
2.5557
2.6005
2.~52
2,6898
2.7343
2.77811
2.8232
2.8675
29118
2.9560
3.0001
Reduced Temperalure for 8 "" 5.0
1.'
1.7
1.'
1.'
2.0
00000 00000 0.0000 00000
0""" 00000
0.0212
00210
0.0209 0.0201 00201 00205
0.0921
00909 0.0901
0.01194
0.0890
00886
0.1924
0.1901
0.1882
01868 0.1859
0.1850
0,3034
1.5
04124
0.5131
06065
06915
07702
0,n97
0.8440
0.9138
09803
1,0442
I 1058
1 1656
1.2231
12805
1.3361
08560
0.9280
13907
14443
1.4970
1.5490
1.6002
16S09
1.1010
1.722"
I.1SO~
I. T:'~.'
' /<lS
1.5-176
1.59-12
1.6.\05
16S65
1.7323
I.ms
18230
18680
1.9127
1.9573
2.0017
2.0458
2.008
2.1336
2.1773
2.22U7
2,264\
2,J073
2.35113
2.3932
2.4.160
2.4781
2,5212
2,5637
'.6060
2.641'12
2.690.\
2.1324
2.77-13
2.8162
2.8579
2.11996
2.9412
0.3001
04107
0.5144
06101
0,6982
'--~511
1.6035
1.6490
1,6941
1.7389
1.7834
1.8275
1.8714
1.9151
1.9585
2JXl16
2.0446
2.0873
2.1298
2,1722
2.2143
2.2563
2.2981
2 ..U97
2.3812
2.4226
2.4637
2 ~\.I8
2.5457
2.5865
2.6272
2.6677
2.1UM2
2.7485
2.7887
2.8288
2,8689
2.90AA
0.2983
0_
05143
0,6123
0.7029
0.7868
0.8653
09393
0_
1.009S
10620
1 1249
I 1857
1.2447
13020
1.3579
14125
14661
15187
1.5705
1.6214
1.6717
17213
I. 77114
10764
I 1406
l.2024
1.2621
13201
1.3764
1,4313
1.4851
1.5377
1.5894
1.6401
1,6901
1.7393
I 7879
unsx
RIlIll
1.5716
1,6 163
1.6605
1.7043
1.7411
l.5652
1.6 104
1.6553
16999
1,744(1
1.7878
1.8314
1.8746
1.9175
17906
1.8333
1.8756
1.9175
1.9592
2,0005
2,0416
2.0824
21229
2,1632
2.2033
2,2432
2.2828
2.3222
2.3615
2.4005
2.4394
2,4761
2,5166
2,5550
2.59.12
2.6312
2.6691
2,7069
2,7446
2.7821
2.819-1
2.8567
19602
2.CXl26
2.(1-141
2.0Il61
2.12S4
2.1699
2.2112
2.2523
2.29.'2
2Jl40
2.3745
2.4149
2.4952
2,4953
2.5353
2.57~1
2.614/1
2.6S4l
2.69-'11
2.7331
2.772]
2RI14
V\''i(1-I
2,81192
•
0.2965
0,4(}16
OSI40
0.61.18
02954
02943
0.4066
0,4056
0.51311
051}4
0.6147
0,6152
0._ 0.7081 0.7104
0.1927 0,1964
07994
0.8734 0.8785
0.8827
0,9493 0.95511
0.961 I
1,0213
10289
10354
10896 1,0984
I 1060
I 1552
I 1649
I 1734
12182
1,2286
1.2379
1.2188
1,2900
12999
Ll374
1,3492
1.3596
IJ9..I3
14066
14173
14497
14623
1,4733
1..5031
15165
15278
1.5694
1.5808
16081
1,6211
16326
1.6587
1.6718
1.6833
17085
1.7215
1.1330
1,7575
I"..
17817
11«1h7
I ,RIM
I S295
I :i),\2
1(1) ~{'
I 7(, ~
15"'"
1.5794
1,6237
1.6575
1.7108
1.7537
1.7961
1.8382
1.5SS1
1,6290
1.6723
1.7151
1.7575
1.7993
18799
1.9212
1.%22
2.0029
2.0433
2.08.33
2.1232
2.1627
2.2020
22411
2.2199
2,311(5
2.),\69
2.3\151
24'31
2mJ\l
1.8818
1.9224
1,9626
2.0025
2,0<120
2{1812
21201
2.1587
2.1970
2.2350
2.2728
2.31OJ
2,3476
2.3847
2.421S
2.4581
2,49-Ul
2,5.3Ot!
2.5668
2,6027
2.63114
2673'1
2,7(J\I.:!
2,7".w
2.7794
2U14]
2,5(JgS
2.5459
2.~!132
H2O)
2(7)
26941
2.7.'\(17
2.7673
z.s036
2.S399
18407
2.2
0_
1.5988
1.64 17
1 684Il
18020
1.8429
1,8833
19232
1.9628
2.0020
2("",
20m
2.1173
2.1551
2.1926
2.2298
2.2667
2,)033
2.3397
2.3758
2.4117
2.4473
241'127
2,5179
2 5529
2.5877
2.6223
1807Il
I_
1.8862
1.9251
1.9634
2,0013
2,0388
2.0759
2.1126
2.1489
2.1848
2,2204
2,25S7
2.2906
2.3253
2.3597
2.3937
H567
2.o2~]
2.fI\I()<}
26575
2.6R95
2.7212
2,72~0
2,75119
2.7926
1.1256
1.7666
V1275
2A611
2."9.\4
2.5275
2.5603
2.5921)
2.7~211
~
2.4
2 .•
00000
3.0
00000
0.0000
00206
00201
0.0877
0.0814
0.1829
o 1822
0.2914
0,4030
04020
0,5118
0.5112
0.6155
06155
0,7133
0.714(}
0,8051
0_
0.8916
0.8941
09732
0.9765
1,0504
1.0544
I 1236
1 1284
1 1932
I 1987
1.2597
1.2657
1,3234
1.3299
1.3845
I 3914
14434
1,4S06
1,5003
1.5077
15555
1.5630
1.6090 1.5167
16611
1.6687
1.7118
17195
1.1613
1,1689
18097
1,8m
I.S.~69
U!M4
00000
00204
0.0871
o 1816
0.2896
04012
0.5108
0.6157
0.1149
"901
0,5125
06154
0.7121
0.S027
0.8879
09682
1.{1441
I 1162
1 1848
1.2504
1.3161
1.3773
14357
14922
1.5472
16006
1.6526
17034
1.7530
I,SOI5
UI4!N
I IN.'",,
J
I .S899
16335
1.6764
1.7188
1,7(1.}7
~
2.'
0"""
0.02U5
0.0881
o 19]8
0.2926
-
0_
0_
0.9795
I05SO
1 1324
12031
1.2704
1.3349
13967
14561
1.5135
I.""
00204
0_
0.181\
02889
0_
05103
06156
0.7154
0.8094
011980
0,9315
"<04
I 1351
1.2060
1.2137
1.3383
1,4003
14599
1.5174
1.5729
1,6267
16789
1.6226
1.6741
1,7254
l,n49
18231
1,8701
1,8271
I 8742
1.7296
11790
t>
J '/J(I5
J 'I J(iJ
J 92()J
1,6016
1.6443
1.6862
1.7274
1.7619
1.8078
1,8472
1.8859
\.9242
1.9619
1.9992
2.0359
2.0723
2.1082
2.1438
2.1789
2.2131
2.2461
2.2822
2.3160
2.3494
2.3826
2.-1155
2.441'11
2.480.\
2.5124
2.5443
2.5758
2.0072
2.6333
2.6692
16043
I ....
1.6885
1.7296
17tf}9
1.6062
1,6486
1.6902
1.6074
1.60'91
1.6912
1.7320
1,1122
I.S116
'~I
'.6999
2.7304
1.7311
1.8872
1.9252
1.9626
1.1113
1,8109
1.8499
1.8883
1.9261
1.9634
19996
20007
20004
2.0360
2.0721
2,1011
2.1429
2.1777
2.2121
2,2462
2,2799
2,3133
2.3463
2.3791
2,4115
2.4431
2.4756
2.5073
2.5386
2.5698
2,60117
26-'1"
2.66UI
2,6970
2.7221
2,0365
2.0366
2,on4
2.0723
21079
2.1429
2.1775
2.2118
2.2457
2.2792
2.3124
2.3453
2.3779
2.4102
2.4422
2.4739
2.S053
2.5365
2.5675
2,5982
2.6286
2.6589
2.1on
1.18487
,2.7187
18505
1.8888
1.9265
1,9631
2.1425
2.1770
2.2111
2.24-19
2.2783
2.3133
2.3440
2.3165
240M
2,4.j().1
2.4719
2.5032
2.5342
2.5650
2.5955
2,62511
2,6558
2,6857
2,7153
-•
Table 7-2 (c)
Extended Sukkar-Comell Integral tor Bottonl-hole Pressure Calculat ion
Reduced Temperature for 8 '" 10.0
P,
1.1
020
OSO
1.00
I. SO
200
2SO
3.00
3.SO
400
4 SO
'.00
,SO
600
6SO
1.00
1.SO
800
.'"
'00
,SO
10.00
10.50
11.00
11.50
12.00
12.91
11 UO
~
~
ill
1.2
295{)
JlJOO
2.'
2 .•
3.0
0.0000
00000
00000
00000
00000
0.0000
0.0000
00000
0.0000
0.0000
00000
0.0107
0.0479
0.1056
0.1767
0.250
0.3332
0.4102
0,4841
0.5545
0.6217
0.6!!6 1
0.7481
0.8079
0,8659
0.9221
0,9770
1.0305
1.0829
I 1342
1 1847
0.0106
0.0474
0.1041
0.1743
0.2513
0.3302
0,4080
0.4830
0.5547
0.623]
0.6891
0.7522
0,8JJ1
0.8720
0.9290
0.9845
1.0385
1,0912
I 1428
I 1935
1.24]2
1,2920
1,3402
1.)876
1 4l4~
0.0105
O.OHO
0.1031
0.1725
0.2490
0.3278
0,4061
0,4820
0.5549
0.6248
0.6919
0.756]
0.8182
0.8781
0.9360
0.992 1
1.0467
0.0105
0.0468
0.1024
0.1713
0.2475
0.3263
0.4047
0.4812
0.5549
0.6256
0.6934
0.7586
0.8214
0.8819
0.9404
0.9911
1,0522
I 1057
I 1579
0.0105
0.0465
0.1018
0.1703
0.2461
0.3248
0.4035
0.4803
0.5546
0.6260
0.6946
0.7605
0.8240
0.8852
0.9443
1,0015
1,0569
1 1108
I 1633
1.2 145
12645
1.3135
1,3(>16
1.400
0.0\04
0.0104
0.0103
0.0456
0.0994
0.1660
0.2403
0.3184
0.3974
0.4755
0.5517
0.6256
0.6968
0.7654
0.8314
0.8950
0.9562
0.0103
0.0455
l oon
I 0575
I 1104
1 1630
1,2 153
1,2674
1.3 192
1 37118
1 4 ;>~~
~7
,
1.9402
1.9936
2.0469
2, 1000
2, 1530
2.2059
2.2587
2.3113
2 ....
"00
2.'
0.0107
0.0486
0.1074
0.1797
0.2578
0.3364
0.4123
0.41:146
0.5533
0.6 189
0.6818
0.7424
0./1010
0.8580
0.9134
0.9676
21.00
21.50
22.00
22.50
".SO
26.00
26.50
27.00
27.50
28.00
28.SO
29.00
22
0.DI08
0.0494
01098
0, 1837
0.2624
0.3399
0.4135
0.4832
0.5492
0.6122
0.6729
0.7]16
0.71!O8
0.6447
0.8994
0.9531
1.0059
1.0580
I 1094
I 1601
1 2102
1,2598
1.3089
1.3574
] 4n~o
1 4 ~Jl
2.3639
24.50
2.0
00000
2000
2O.SO
" 00
1.9
0.0000
1.8330
1.8867
23.50
1 .•
0.0110
0.0507
0.1132
0.1891
0.2677
0.3427
OA130
OA793
0.542]
0.6029
0.6617
0.7190
0.7752
0,8304
15.00
2300
1.7
0.0000
'.7250
17.SO
1.'
0.0 112
0.0525
0.1 187
0.1968
0,2723
0.3422
OA08O
OA708
0.5315
0.5904
0.6480
0.7045
0.7602
0.815]
0.8697
0.9236
0.9769
1.0296
1.0819
1 13311
I 1852
1.2J63
1.2871
1.3376
1.7191
18.00
18,50
19.00
19.50
1.5
0.0115
0,0561
0, 1292
0.2028
0.2684
0.3300
0.3897
0.4485
0.5065
0.5638
0.6204
0.6765
0.7321
0.7873
0.8421
0,8965
0.9506
14.00
16.00
16.50
J7.oo
1.4
00000
14.SO
15.50
1.3
2.4164
2.mO
2.5733
2.6254
2.6774
2.7294
2.78\3
2.8)32
2.8849
2.9367
2.9883
3.0399
3.0915
3. 1429
3. 1944
3.2458
].2971
3.3484
3.3997
I3R71
14 377
~I
73
1.7711
1.8212
08846
0.9381
0_
10·131
1,0947
I 1458
11964
1. 2466
1 2964
1. 3458
1 W~q
"'Ie
2.13 11
2.18 17
2.2323
l/i216
1.8706
1.9192
1.9675
2.0154
2.063 1
2. 1104
2. 1575
2.2043
2.2826
2.2909
2.3329
2.3830
2.4329
2. 4828
2.5325
2.5822
2.6317
2.6811
2.7304
2.7796
2.8'...88
2.8778
2.9268
2.9757
3.0245
3.07]3
3. 1220
3.1706
3.2191
3.2676
3.3 160
3.3644
2.3393
2.3875
2.4355
2.4834
2.53 11
25788
2.6263
2.6736
2.2973
2.3434
2.3893
2.4350
2.4306
2.5259
2.571 1
2.6 161
2.6610
2.7057
1.8750
2.om
2.0802
21209
2.7680
2.8 151
2.8620
2.9088
2.9556
3.0022
3.0488
3.0953
3.1 417
3. 1880
3.2343
3._
3.3265
1.0729
1.1242
1 1747
1.2245
1.2736
1.3222
I 3"702
I 4171'1
,.
] ·11,1'
I '1)11
1.7965
1.8470
1.897]
1.9472
1.9970
2.0465
2.0958
2.1449
2. 1937
2.2424
1.9266
1.9780
1.Q201
22509
27S03
2.7047
2.8390
2.8832
2.9272
2.97 11
3.01 49
3.0586
3.1022
3.1457
3. 1891
].2324
3.2756
\.8480
1.8960
1.9436
I. _
2.0371
2.0842
2. 1303
2.1762
2.22 17
2.2670
2.3120
2.3567
2.40 12
2.4455
2.4895
2.5333
2.5770
2.6204
2.6637
2.1068
2.7497
2.7924
2.8351
2.8775
2.9198
2.9620
3.0040
3.0459
3.0877
3.1294
3.1710
3.2124
3.2537
1."'-'
1,2834
1.3317
1.3"794
I 4 ~'..o
,.
1.0999
I 15 18
1.2027
1.2525
1.3013
1,3494
1.3967
l .wn
14 ~n
4);<1:
~I'II
L ~ ;!'o-I
I
1.8667
1.9142
1.9612
2.0071
2.0538
18830
1.9298
1.9760
2.0217
1.9001
1.9463
1.9920
2.0372
2.0818
2. 1260
2.1697
2.2131
2.0996
2. 1450
2. 1900
2.2347
2.2791
2.3233
2.3671
2.4107
2.4541
2.4972
25400
25827
2.6252
2.6674
2.7095
2.7514
2.7931
2.8346
2.8760
2.9172
2.9583
2.9993
3.0400
3.0807
3.1212
3.16]6
3.2019
3.2421
2.0669
2. 1117
2. 1561
22000
2.2437
22869
2.3299
2.3725
2. 41 48
2A568
2.4986
2.5401
2.58 14
2.6224
2.6632
2.7038
2.744 1
2.7843
2.8243
2.8640
2.9037
2.94]1
2.9824
l02 1S
30604
3.l1992
3.1379
3.1764
3.2 148
•
~.1--l{,
22560
2.2%5
1.2090
1.2689
1.3078
1,3559
1.4032
]44<)7
")~
".
0.0160
0.1003
0.1676
0.2426
0.3210
0.]999
0.4776
0,5532
0.6263
0.6967
0.7M5
0.8297
01667
0.2413
0,3195
0.3985
OA764
0.5523
0.6258
0.6967
0.7650
0.8307
~(lnl'l
0.1009
0.\687
0,2440
0.3225
0.4014
0.4787
0.5538
0.6262
0.6959
0.1629
0.8273
0.8895
0,9494
1.00')2
1.065]
I 1197
1 1726
12242
12746
1.3238
1.3719
1.4190
1 ~MJ
I.SIOt'
~H'
I
1.4~5 ~
I
1.9121
1.9580
2.0032
2.0478
2.0918
2,1353
2. J783
2.2209
2.2630
1.9227
1.9681
2.0128
2.0570
2. 1005
2. 1434
2. 1858
2.2276
2._
2.3100
2.3505
2.3906
2.4303
2.3407
2.3459
2.3825
2A24 1
2.3868
2.4653
2.5062
2.5468
2.5872
2.6273
2.6672
2.7068
2.7462
2.7854
2.8244
2.8532
2.9018
2.9402
2.9785
3.0165
3.0544
3'()<)22
3.1297
3.1672
3.2045
O.OW
0.0104
0.0458
2.4273
2.4675
2.5074
2.5470
2.5862
2.6252
2.6639
2.7023
2.7405
2.7784
2.8 161
2.8536
2.8908
2.9279
2.9648
3.0014
3.0379
3.0142
3. 1103
3. 1463
3. 1821
2.2690
2._
2 S086
2.5472
2.5855
2.6235
2.66 12
2.6986
2.7357
2.7126
2.8092
2.8456
2.88 18
2.9 177
2.9534
2.981:19
3.0242
3.0593
3.(1942
3.1289
3. 1635
~~.-
1.94]0
1.9858
2.0298
2.0730
2. 11 55
2. 1574
2. 1987
2.2394
2.2795
2.3191
2.3582
2.3969
2.4350
2.4728
2.5 101
2.5471
2.5837
2.6 199
2.6558
2.6913
2.7266
2.7615
2.7961
2.8305
2.8646
2.8985
2.9320
2.9654
2.99KS
3,0314
3.0641
3.0966
].1288
00997
0.8925
0.8940
0.953 1
1.0115
1.0681
1 1228
I 1760
1.2278
1.2783
1.3275
1,3756
1.4227
0.9550
I,OJJ8
1.0106
11256
11 790
1.2309
1.0123
I 1275
I 1810
1.2331
1.2814
12836
1.3901
1.3329
1.3810
1.4280
] .4140
I 4NtR
1 3788
1 4258
I 4719
1 ~ Ult
1. ~51'1J
I ~r.r I
1.9485
1.9927
2.1)364
2.0792
2. 1212
2. 1626
2.2032
2.2433
2.2828
2.3217
I.om
U /t>9
1.9556
I ~/w
1 ......111
0.0990
0.1653
0.2394
0.3174
0,3964
0.4746
0.S511
0.6252
0.6967
0.7655
0.8311
0.8955
0.9566
'-0160
1.0732
11286
11822
I.DO
1 28SO
1.3343
1.3824
1.4294
I 4753
1.5202
, .'IM:?
1.%12 \.965\
2.0053 '20091
2.0432 2.0485 2.0523
2.0857 2.0910 2:0946
2. 1275 2.\326 2. 1362
2. 1686 2. 1736 2. 1TI0
2.7090 2.2138 2.2172
2.2488 2.2535 2.2567
2.2925 2.2956
22880
2.3266 2.3309 2.]]39
2.3600
2.3646
2.3688 2.37J7
2.3979 2.4022 2.4062 2.4089
2.4392 2.4431 2.4456
2A353
2.4723 2.4158 2.4795 2.4819
2,5 11 9 2.S 155 2.5171
25088
2.5449 2.5477 2.5510 2.553 1
2.5806 2.5830 2.5861 2.588 1
2.6159 2.6 179 2.6209 2.6226
2.6508 2.6524 2.6552 2.6568
2.6854
2.5866 2.6892 26906
2.7 197 2.7200' 2.7229 2.724 1
2.7536 2.7540 2.7562 2.7573
2.7R72 2.7872 2.7892 2.7901
2.8206 2.8200 2.8192 2.8226
2.8536 2.8526 2.8543 2.8548
2._
2.8850 2 . _ 2.6867
2.9189 2.9 170 2.9 182 2.9 184
2.95 12 2.9488 2.9498 2.9497
2.9f132 2.980] 2.98 11 2.9809
3.0149 3.0 11 6 3.0 122 3.0117
3.0465 3.0426 3.O·no 3.0424
3.077f1 3.0735 3.0736 3.0728
3. 1089 3. 1040 3.1040 3.1029
1 99911
-
Table 7-2 (d)
Extended Sukkar-Comell Integral lor Bonom-hole Pressure C8lcu a.tlon
P,
0,20
1.2
1.3
1.4
1.5
0."""
0.0000
0,0075
0,0359
00838
0.1453
0.2093
0.27]0
0,3302
0.3874
0.4430
0. 4975
0.5508
0.6034
0.6553
00000
0.0074
0,0345
0.0793
0.1371
0.2008
0,2648
0.3267
0.3862
0.4435
0.4992
0.5535
0.6066
0.6590
0.7105
0.76 13
0.81 14
0,8611
OOIlOO
0.0073
0.0336
0.0765
o 1319
0.1943
0,2587
0.3222
0.3837
0.4431
0.5004
0.5561
0.6103
0.6634
0.1155
0.7666
08170
0.8666
0.9151
0,\1641
1.0121
l.0595
1 1065
I 1530
\ 1992
1.2449
00000
0.lM:J72
0,0330
00146
0,12/12
0.1/192
0.25)3
OJI76
I2'Xn
v.oon
1.00
1000
0.03RS
0.0939
0.1571
0,2162
0,2725
0.3275
0.3818
0. 4355
0.4S87
0.5413
0.5936
0.6454
0._
0.14R2
0.1991
0,8497
0.9000
0.9500
0,9998
]0,50
I.o·m
1.0544
]] 00
I.(l985
I 1475
1 1963
1.1026
I 1506
1 1983
1.2449
1.2458
0.9588
10011
1.0549
1 1024
I 1496
11964
1.2430
l~q:u
!.:!931
1.2~91
I
.,.
I ~ ·lt l ~
1,3899
/.4380
1.4860
1.5338
1.58 15
1.6291
\.6766
1.7241
1.1714
1.8 ]87
1.8659
1.9130
1.3870
J .4337
1.4803
2.00
2,50
3.0n
3.50
''''
'SO
'.00
'SO
600
6.50
7.00
7.SO
8.00
8.SO
'00
'50
]150
12,00
12.50
nuo
,
1400
14 .SO
15.00
15,SO
16. 00
16.50
11.00
I1.SO
18.00
18.SO
]9.00
19.5O
"'.00
2O.SO
21.00
2 ],SO
22.00
"SO
23.00
23.SO
24.00
24.SO
25.00
25.50
26.00
26.50
21.00
21.50
28.00
28.SO
2900
"SO
"'.00
~
0=
1.1
OSO
'SO
Reduced Temperature for B 15.0
1.6
1.7
1.8
1.9
2.0
~
1.9600
2.0070
2,0539
2. 1007
2.1475
2.1943
2.2410
2.2876
2.3342
23807
2.4272
2.4736
2.5200
2."'"
2.6121
2.6590
2. 7053
2.75 15
2.7977
2.8438
2.8899
0.7068
0.7517
0.8082
0,8582
0,1XI78
0.9570
1.0059
0.9 ]02
1.6 189
1.6649
1.3812
1.4268
1.4722
1. 5174
1.5625
] .6073
1.6520
1.7107
1.6966
1.7564
\.1410
\.1853
1.8294
] ,8134
1.9173
1.9611
1.5266
1.5728
1.8020
1.8475
1.8929
1.9382
1.9834
2.0285
2.0736
2.1185
2, 1634
22082
2.2529
2.2976
2.3422
2.3861
2.43 12
1.4756
2.5200
2.5643
2.6086
2.6520
2.6969
2.74 10
2.785 1
2.829 1
1.3802
1.4247
1.4689
1.5129
1.5S66
1.6001
1.6434
1.6865
1.7293
\.1720
1,8146
1.8.\69
1.8991
1,\1412
2,0048
19831
2,0484
2.0918
2.1352
2.17&5
2.2217
2.2648
2.3019
2.J501l
2.3937
2.4366
2.4793
2.5220
2.5646
2.6072
2, 6497
2.692 1
2.7345
2.7769
2.0248
2.0665
21080
2,1494
21906
2.2318
2.2728
2.3138
2.3546
2.3953
2.4360
2.4766
2.5 170
2.5574
0.~805
0.4415
0.5006
0.5579
0.6135
0.6676
0.7205
0.7722
0.8230
0.8729
0.9220
0._
1018 1
1,0653
I 11\9
1 1580
J.2037
1.2490
I:!'JW
.UR-1
1.3825
1.4263
1.46911
1.5130
1.5559
15985
I._
1.6830
1.7249
1,7666
1.8081
1.8493
1.8904
1.9314
1.9721
2.0 127
2.0531
2.0934
2 1335
2 1135
2.2134
2.2531
2.2917
2.3322
2.3716
2.4109
2.4501
2.4891
2.5281
2.5'F77
2._
2.6380
2.6781
2.7182
2.6051
2.6444
2.6830
0'.11.)
00000
o.txXXl
O.OOOU
orxXJQ
OU011
O.U01I
0.0070
O.lwno
0.O.l2~
0.0322
0.0721
0.1236
U 11127
0.24511
0.0071
0.3119
0.0732
o I2.H
0.11157
0.2493
0.31.18
0.3174
0.4393
0.4994
0.5577
0.6143
0.6694
0.7230
0.1754
0.8266
0.8768
0.926]
0.9146
1.0223
0.3102
I 1159
1 1618
\.2072
1.2522
0.3743
0.4369
0.4918
0.5570
0.6144
0.6703
0.1246
0.n76
0.8293
0.8799
0.9295
0.9782
1.0260
1.073 1
I 1J95
1 1653
1.2105
1.2551
12%7
L299~
, '-IU
IQO
I .....
1.3845
14278
1.4708
1.5\35
1,5558
1.5979
1.6397
1.6812
].1225
1.7635
1.80·n
1.8449
1.8RS3
1.9255
1.9655
2.0054
2.04SO
2.0845
21239
2.1631
2.2021
2.24]0
2.2798
2.3184
2.3569
2.3953
2.4336
2.4718
2.5098
2.5478
2.5856
2.6234
2.66 10
1.3862
1.4290
1.47 14
LS134
LS55 1
1.5964
1.6374
1.6181
I.7II!6
1.75117
1 7986
\.8382
1.8176
1.9168
1.9557
1.9944
2.0330
2.0713
2 1095
2. 1415
21853
2.2229
2.2~
2.2978
2.3550
2.3120
2.4089
2.4457
2.4824
2.5189
2.5553
2.59 16
2.6278
•
0.0317
0.0113
omos
0.1220
0.1!104
0.1790
U.2431
0.JU74
0.3717
0.4349
0.4966
0.5566
0.6149
0.6715
0.7256
0.7802
0.11324
0.8835
0.9334
0.9824
1.0J()4
\.0776
O.121l
0.2413
0.3055
0.3699
0.4335
0.4956
0.5561
0.6 149
0.6720
0.7216
0.7817
0.8344
0.8858
0.9360
0 .9852
1.0334
0.0316
0.0703
0.1202
0.1777
0.2397
0.3O~8
II1JJ(16
0.)683
0.4320
0.4945
0.5554
0.6147
0.6724
0.7284
0.7829
0.8360
0.8878
0.9382
0.9876
1.0359
1.003
I 1239
I 1696
1.1271
1.1298
1.1128
1 2 147
1.2592
1.2118
1.2622
1 1755
1.2205
I "lCl.' 1
I lI)OCl
1.3694
1.4319
1.4739
1.5155
1.5567
1.5976
1.6381
1,67113
\.71111
1.7577
\.7970
1.8360
1.8741
1 9132
I 95 15
1.9895
2.0273
2.0649
21024
2. 1346
2.1766
2.2135
2.2502
2.2867
2.3230
2.3592
2.3953
2.4312
2.4670
2.5026
2.5382
2.5736
2.6088
2.3067
2.3418
2.3767
2.4115
2. 4460
2. 4805
2.5148
2.5489
2.5829
0.2)74
(J.)UI2
0.3657
0.4298
0.4928
0.5543
0.6143
0.6726
0.7293
0.7M4
0.11391
0.8914
0.9423
0.9920
1.0407
0.9432
1.0883
0.9932
1.0420
1.01:197
I 1349
1.1364
I 1807
1 1822
1.2270
11711
.l nl
1..114.1
1.3938
1.4356
1.4769
l.S 117
1.5580
1.5979
1.6373
1.6764
1.7150
1.7533
1.7912
1.8288
1.866 1
2.2005
2.2.361
2.2715
01111')
Om8
.l!1lW
1.391 8
1.4339
1.4756
1.5168
1.5575
1.5978
1.6378
1.6773
1.7166
1.7554
21~
"(1.0313
O.()OO.l
0.(.)70
Il.OJII
0.0692
0.1 ]/10
1l.174';
0.2357
0.2<)94
0.3679
0.4281
0.4914
0.5534
0.6138
0.6721
0.7299
0.7854
0.8395
0.8920
1.2048
~ I .t
1.7940
II " ' "
O'_)7U
1.903 1
1.9397
1.9761
2.0122
2.0481
2.007
2. I 191
2. ]542
2.1891
2.2238
2.2583
2.2927
2.3268
2.3607
2.3944
2.4280
2.4614
2.4947
2.5278
2.5607
1.3977
1.4390
1.4797
l.S 198
LS594
1.5984
\.6370
1.6750
17127
1.7499
1.7866
1.82.10
1.851X1
18947
I. 9300
1.9650
1.9997
2.0341
VJMI
21019
2.1355
2.1687
2.2017
2.2345
2.2671
2.2994
2.3315
2.3634
2.3951
2.4266
2.4579
2.4890
2.5200
2.6
2.4
1.2256
1.2698
".'
1.8322
1.8702
1.9079
1.9453
1.9824
2.0193
2.0560
2.0924
2 ]286
2.2
,
1.3984
1.4395
1.4798
1.51%
1.5587
1.5973
1,6354
1.6730
1.7100
1.7466
1.711211
1.8186
1.8540
1.8R89
1.9236
1.9H8
1.99\7
2.0253
2.0586
2.0916
2.1242
2 ]561
2.1~
2.2207
2.2523
2.21B7
2.3 149
2.3458
2.3765
2.4070
2.4373
2,4674
2.4974
°
(IIWJQ
0()(K)9
U.U~1O
0""",
0.1172
Om3
U.2342
0.29711
0.3622
0.4265
0.4900
0.5522
06129
0.672 1
0.7296
0.7855
0.8398
08926
0.9440
0.994 1
1.0430
I 090Jl
I 1375
I 1832
1.2281
1.2720
I .1/~2
1
1~7~
1.399\
\ .4400
141102
1.5197
U5f11
1.5911
1.6350
1.6123
1.7091
1.7455
1.711]4
1.8169
1115 19
2.8
0.0000
00069
0.03!)9
0.""'"
1l.lln7
o 1124
0.2331
0."'"
0.36JJIJ
0.4252
0.4888
0.55 12
0.6121
0.67]5
0.7291
0.7852
0.8397
0.8927
0.9442
3.0
00000
0_
0.0308
0.1J682
0.1161
0.1716
0.2320
0.2952
0.3596
0.4240
0.4877
0.5503
0.6113
0.6708
0.7286
0.7848
0.8394
08925
0.9441
0._
0_
1.0434
I.o·m
l.OOIJ
1.0914
1.1311 1
11839
\.2281
1.2725
1.3156
11380
I 1837
12285
12724
I.JHS
.~7.~
l.l.UX
1.39'11
I 4401
1.3m
I 4400
1. 4802
1.4800
LS I97
1.5585
1.5968
1.6346
1.5194
1.6718
1.7085
17441
1.71105
].8158
L5582
1.5964
1.6)4\
1.67 12
\.7018
1.7439
1.1196
1.8148
1.8496
,_ 119m
1 9549
191:184
2.0217
2.OS46
2.1:»172
2.1196
2. 15 16
2.1834
2.2149
2.2461
2.2171
2.30711
2.3384
2.3687
2.39g7
2.4286
2.45g3
2.4878
\ .85(111
1.8853
1.9195
1.9532
1.9867
20148
2.0525
20850
2] 17]
2.1490
2.1806
2.2119
2.2430
2.2738
2.3044
2.3347
2.3648
2.3947
1.4244
2.4538
2.4831
1.9 180
1.9517
1.9850
2.0179
2.0506
2.0829
2.1149
2.1466
2.1780
2.2092
2.2401
2.2707
2.3011
2.3313
2.3612
2.3909
2.4205
2.4.t97
2.4788
~
Table 7·2 (e)
Extended Sukkar-Cornell Integra' for Bottom·hole Pressure Calculation
P,
Reduced Temperature for 8 = 20.0
1 .1
1.2
1.3
0,20
00000
00000
200
2'"
300
0.0058
0.0294
0.0740
0, 1295
0, 1832
0,23SO
00000
00056
00000
0.'"
1.00
3.'"
02860
0.0055
0,0262
0,0610
0.1071
0.1614
0.2172
0.2725
0.3264
0.]790
0,4305
0.4809
0.5305
0,5794
O,62n
0.6755
0,7221
0.7695
0.8 159
0.8620
0,0055
0,0255
0,0587
0.1030
0.1547
0,2099
0.2657
0,]208
0.3747
0,4273
0,4787
0.5291
0.5786
0.6274
0,6754
0.7228
0.7696
0.8 160
0.8618
0.9073
0.9523
0,9969
\.0412
1,0851
1 12Rl1
11721
I.'"
4.00
4.'"
5.00
5.'"
6.00
6.'"
700
7.'"
800
8.'"
'00
,.'"
10.00
10,SO
I LOCI
11 ,50
12,00
12.SO
noo
r
~
0.]365
0.3865
0.4360
0.4852
0.5341
0.5827
0,6]10
0,679 1
0.7269
0.n45
0,8219
0.8690
0.9159
0.9626
1.0091
1.0554
I 1016
1 1476
1 Iq15
~l
/4.00
14.50
15.00
15.50
16.00
16,SO
17 ,00
17.50
1800
18.SO
19.00
19,5O
2000
20,SO
21.00
21.SO
22.00
22,50
23.00
2J.SO
24.00
24.SO
".00
,,'"
26.00
26.'"
27.00
27.SO
2800
28.'"
2900
29.SO
lO.OO
1,~9
1.3304
1.3759
1,4212
,4665
LSJl6
1.5567
1.6017
1.6467
1.6916
1.7364
1.1811
1.8258
1.8705
1.91 50
1.9596
2,OOU
2.0485
2.om
2.1372
2.1815
2.2258
2.2700
2.3 142
2.]584
2.4025
2.4466
2.4907
2.5347
2.5787
2.6227
0.0272
0.0649
0.1156
0.1712
0.2264
0.2801
0.3]26
0.3841
0.4346
0.4843
0.5335
0.5821
0.6304
0.6782
0.7257
O.ms
0.8 196
0.8661
0.9123
0.9582
1.0089
1.0494
1.0946
11397
llR4h
0.9077
0.95JO
0.9981
1.0429
1.0874
11317
I
17~~
"
'n
1.2739
J.3183
1,3625
1.4067
1.4507
1.4945
1.5383
1.283]
IJ(l68
<5820
1.6256
1.669 1
1.7125
1.1558
1.mo
1.8421
1.8852
1.9282
1.97 11
2.0140
2.0568
2.0995
2.1422
2.1849
2.2274
2.2700
2.3124
2.3549
2.3973
2.4396
2.4819
2.5742
2.5664
2.6666
2.6085
2.7106
2.6507
1.3501
1.3933
\.4363
1.4792
1.5219
1.5645
1 6069
1.6493
\.6915
1.7336
1,7757
1.8176
1.8594
1.9012
1,9429
\.9844
2,0259
2,0674
2.1087
2.1500
2, 1912
2,2324
2.2135
2.3145
2.3555
2.3964
2.4373
2.4781
2.5 189
2.5596
2.6003
1.4
I '." I
1.2579
1.3005
1.3428
1.3~9
1.4267
14684
<50"
1.6
1.7
1.B
1.9
2.0
2.2
2.4
2.6
2.B
3.0
0.0000
0.0000
0.0000
0.0000
00000
0.0000
00000
00000
00000
00000
00000
0,0054
O.()2.IO
0,0572
0.0054
0,0246
0,0561
0.0976
0.1465
0.1999
0.2553
0.3111
0.0053
0,0243
0.0561
0.0958
0.1438
0,1964
0.2514
0.307]
0,3629
0,4177
0,4714
0,5241
0,5756
0.6261
0,6755
0,7240
0.n16
0.8184
0.0053
0.0241
0,0545
0,0945
0,1417
0.]937
0.2484
0,3041
0,]599
0,005]
0,0240
0,0541
0,0937
0,1404
0,1920
0,2463
0,3020
0,3578
0,4132
0.4678
0.5213
0.5738
0.6252
0.6754
0.7247
0.n29
0.s:!02
0.0053
0.0239
0.0537
0.0930
0.1393
0,0052
0,0237
0,0532
0,0918
0,1376
01SN2
0,24]9
0,2972
0,3531
0.4088
0.4639
0.5182
0.5714
06236
0.6746
0.7251
On40
0,8218
0,86lS7
0,9147
0,9599
l.oon
1,0479
I.()IX)!!
IIDI
0,0052
0.0052
0.0235
0,0525
0.0905
0,1354
0,1853
0,2384
0.29]4
0.3492
0.4050
0.4604
0.5151
0.0052
0.0234
0.0522
0,0052
0,0233
0,0520
0,0895
0,1339
]8.12
0.2359
Q,2906
0.).162
0.4021
0.45n
0,5125
0,5665
0,6194
0,67 12
0.72 19
0.n14
0.8198
0,8672
0,9135
0.9589
1.0034
l.o·no
1.5
0.0998
0.1498
O.2O-W
0.2597
0.3154
0,3703
0.4240
0,4765
0,5279
0,5783
0,6276
0,6761
0,7238
o.nos
0.8m
0.863\
0.J664
0.9531
0.9975
1.0414
1.0849
1 12112
I I7IH
0.4208
0,4740
0,5261
0,5n1
0,6270
0.6760
0,7241
0,n14
0,8179
0.8638
0.9091
0.9538
0.9980
1.0418
1.0851
I 12110
17Ut>
1 )116
~ I:
\.2558
1.2541
1.2962
1.3375
1.3784
1.4191
1.4595
1.4997
1.5397
1.5194
\.6190
1.6583
1.6975
0.9083
1.2977
1.3394
1.3808
1.4220
1.4629
1.5512
1,5924
1.6]34
\.6742
1.1149
1,7555
1.7959
1.8362
1,8763
1.9164
1.9563
1,9982
2,0359
2,0756
2 1151
2 1s.lit
2.1939
1.5036
1.5441
1.5844
1.6245
1.6644
1.7042
1.7438
US32
1.8225
1,8616
1.9006
1.9395
1,9782
2,0168
2.0553
2.0937
21319
2.1701
2.~2
2.2002
2.2724
2.3115
2.3S05
2.3895
2.4284
2.4672
2.5060
2.2461
2.2840
2.3218
2.3595
2.3971
2.4146
2.4720
2,5447
2._
1.7364
1.7752
1.8139
1.8523
1.8906
1.9288
1.9668
2.00n
2.(,.t25
2,0801
2,1!76
2.1550
2.1923
2.2295
2.2665
2.3035
2.3404
2.3772
2.4119
2.4504
2.4870
0.1~
0.2445
03000
I '7H-I
11714
I 72.'
0.3559
0,4114
0,4662
0,5201
0,5729
0.6246
0.6752
0.7247
0,n32
0,8207
0,8673
0.9131
0.9580
1.0023
1.0459
1,06!!1I
II.H2
17.111
'I.'
I ~I1H
Inn
12q:>
0.8644
0.9098
0.9545
0.9987
l.o·m
1.085S
1 12112
I
1.2537
1.2948
1,3355
1.3759
1.41SO
1.4558
1,4953
1.53045
1.5735
1.6 123
1,6508
1.6891
1.7271
1.7650
UI027
1.11401
1.8774
1.9146
1.9516
19684
2()2.1O
2.0615
20919
2,1341
2.1702
2.2062
2.2420
2,2778
2.3 134
2.3409
2,3843
2,4195
2.4547
•
O,·USI
0,4594
0,5226
0.5747
0.6257
0.6756
0.7245
O.n25
0.8 195
0.8658
0.9113
0.9561
1.!XXl2
104]8
1.0S68
1 1294
0.B666
0.9123
0.9571
1.1))14
1,0450
l.OH79
I 13U4
1.2542 1.2547
1. 2949 1.2952
1.3353 J.J352
1.3754 1.3749
1.4151 1.4142
1.4544 1.453\
\ ,4935 \.4916
1,5323 1,5298
1.5108 1.5678
10090 1,6054
1.6470 I,().n?
It)g.17 1,6797
1.7222 1.7165
L7595 L7530
1,7965 1.789]
1,8334 1,8254
I.S7OU 1.8612
1.9065 1.8968
1.9428 1.9322
1.9789 1,9674
2.0149 2,0025
2.0507 2.0373
20863 2,0719
21218 21064
2.1671 2.1408
2.1923 2.1749
2.2274 2.2089
2.2823 2,2428
2.2971 2.2765
2.31!8 2.3100
2.J66' 2.3435
24008 2.3768
2.4352 2.4100
2.2549
1.2952
1.3349
1.3743
1.4132
1.4517
1.4898
1.5275
1.5649
1,6020
1,63M
\.6752
1.7114
1.7473
1.7829
1.8183
1.8534
1.8882
1,9229
1,9573
1.9916
2.0256
2,0594
2.0980
2.1265
2,1598
2.1929
2.2258
2.2586
2.2912
2,32 17
2.3560
2.3882
r
~
"
\.2559
\.2957
1.3349
1.3736
L411 8
1.4496
')()2)6
t),0528
')09 11
11.1364
0,11i67
(j,2401
U.2952
O.35!O
0.4068
0.4622
1).5]67
0.5703
()6228
11,6741
11,7244
IIn35
11,8216
0.6216
0.6732
0,7237
O,n3(l
0,8212
11,8687
08684
\J,9148
0.9601
1.0045
1.0481
0.9146
0.9599
1.0043
1,0479
1 ''''~
LlH
r 174~
I Il!!!
0.5689
10908
0.0900
0, 1346
0,1842
0,2371
0,2919
0.]476
0.4034
0.4589
0.5137
0.5676
0,6205
0,6722
0,7227
0.m2
0.8205
0.8678
0,9141
0.9595
L{)039
1.0475
1,0903
1 1,123
1 ,.,ltI
°
10698
J iJI8
"
i 1"4:'
I : \-1'1
J
~I·JI
:1.1(1
,,56-1
\ .2549
U541
11S3<,
1.2463
1.3331
1.37 13
1.4090
1.4462
1.4829
\,5191
1.5549
1, 5902
1.5252
\.6597
1.6938
1.7276
1.761!
1.7942
I.R270
1.8595
1.8916
1,9235
1.9551
1.9K65
2.0176
2.0484
2.0790
2.1094
2.1395
2. 1695
2.1992
2.22117
2.2540
2.2871
2.3 161
\.2':135
1.)322
\.2921\
1.2949
1.3339
U723
].4101
1.4475
\.4869
1.4~
I 5238
1.5603
1.5%4
16121
1.6675
1.1025
1.7372
1,7716
18056
1.8394
1.8730
1.9062
I. 9392
1.9719
2()().l4
2.0367
2.(1687
2.1OUS
2.1321
2.1636
2,1968
2.2258
2.2566
2.2873
2.3\78
2,]481
1.52Q8
1. 5588
1.592·'
l.tl275
1.6623
1.6967
1.7308
1,7645
1.7979
1.8310
1.8638
1.8963
1.9286
1,9605
1.9922
2,02]7
2.0549
2.0858
2.1166
2.147 1
21774
2.2075
2.2375
2,2677
2,2967
2.326 1
1.:\7~
14080
14451
1.4KI7
UI7S
1.5584
UK\?
1 6235
I.M79
1.6919
1.7256
1,7589
L7918
I.R24S
1.8568
1.AA89
1.9206
1.9521
1.9H32
20 142
2,0449
2.0753
2.1055
2.1355
2,16S2
2,I94H
2,2241
2.2662
2.2822
2.3109
I 17.11
\3315
1.3695
1.4071
\44-11
\,4S06
1.5166
1.5522
1.5973
I 6220
1.6563
1.6902
1.7238
1,7570
1,7898
1.!:!22l
I.R545
1._
1.91110
2.9·19]
1,91;04
2.0112
2.0417
2,072(}
2.1020
2.\318
2.1614
2.1908
2.2220
2.2480
2.m7
2.3063
Table 7-2 (f)
Extended Sukkar-Cornell Integ,.1 for Bottom-hole Pressure Calculation
Reduced Temperature for B = 25.0
P,
1.1
1.2
1.3
1.4
1.5
O<ml
00044
O<ml
0.0044
ow
O<ml
O.<ml
OSO
100
ISO
200
2.SO
'.00
'SO
'.00
'.SO
5.00
5.SO
6.00
6.SO
7.00
7SO
800
'.SO
'.00
'SO
O.OO-H
0,0045
0,0219
0,0529
0,0961
0.1 453
0,1952
0,2444
0.2930
0.340!!
0.3879
04345
10.00
10,SO
ILOO
\I.SO
12.00
12.SO
0,02]7
0,0611
01106
0.1598
0.2079
0.2554
0.3025
0.3492
0.3957
0.44111
0.4878
0.53]5
0.5790
0,6241
0 .....
0.7143
0.7591
0.8036
0.8480
0.8922
0.9362
0.9801
0_
0.526]
0.57H1
0,6169
0,66 18
0.7063
0,7506
0._
08384
0.8520
0.9254
09686
om
1.0676
11111
1 0117
1.0545
I 0973
\' \11
\ \',.j,,,
,'1)\
1.0239
1.1979
1.2412
14.5()
1500 1.2844
15.SO 1,3275
16,00 1.3705
16.50 1.4135
17,00 1.4564
17.50 1.4992
18,00 1.5420
18.SO 1.5847
19 .00 1,6274
19.5O 16700
20.00 1.7126
".SO 1.7551
21.00 \.7975
21,SO 1.8400
22.00 1,8824
22.SO 1.9247
2300 1.9670
23.SO 2.00B
24.00 2.0516
24.50 2.0938
25.00 2. 1360
25.SO 2.176 1
26,00 2.2202
26.50 2.2623
27.00 2 . _
27,SO 2.3'61
2800 2.3885
28,SO 2.4305
,.00 2.4724
,.SO 2.5144
30.00 2,5563
J4.oo
~
~
Q
I HIl3
J.2146
1.2668
1.3089
1,3509
1.]928
1.4346
1.4763
L5180
1,5595
16010
1.6424
\.6837
I.72SO
1.7662
1 8073
,......
1.8895
1.9J04
1.9714
20122
2.0531
2.0938
2, 1346
2.1753
2.2\59
2.2566
2.297 1
2.3377
2.3782
2.4186
2.459\
2.4995
0,0211
0.0496
0.0!!1!8
0.1352
0,1846
0.2346
0.2840
0,3]25
0,3803
0.4274
0,4739
0,5198
0,5653
0,6104
O,65SO
0,6993
0.7433
0,7870
0.8303
0.8735
0.9163
0.9590
1.0014
1.0437
1 n~~7
",
I 1693
1.2109
1,2523
1.2936
1.3347
1.3757
1.4166
1.4574
\.4981
1.5387
1.5792
1 6196
1.6597
1.7001
\ ,7403
1.7803
1.8203
1.8603
1,9001
1.9399
1.9797
2.0 193
2.0590
2.0985
21380
2.1775
2.2169
2.2562
2.2955
2.3348
2.3740
2.4132
2.4523
oOW5
0,0477
0 .....
0,1287
0,1769
0,2267
0,2766
0.]260
0.3745
04223
04694
0.5158
0.5616
06069
0,6516
0.6960
1.'
1.7
1 .•
O<ml
00000
00000
0,0043
0,0201
0._
0,0818
0,124\
0,1711
0,2202
0,2702
0.]200
0.369]
041711
0.4656
0.5126
0.55119
06045
0,6-495
0,0043
0,0]98
o,oon
0,0]96
00446
0,07113
0.1186
o 1637
0,2117
0,2613
0.3112
0.3610
0,4103
0.4589
o0,7380
""'"
0.7399
07834
0.8266
0,8695
0.9120
0.9542
0.9961
10HI!
I 079:'
0._
1 1.\
1\1>\
0,7814
0.8245
0.8671
0.9514
0.9930
1 1n43
1 117~~
O,04~4
0.0198
0.1211
0.1670
0.2 156
0,2654
0.]154
0.3650
0,4139
0.4622
0,5097
0,5564
0,6024
06477
0,6924
0.7365
0.7800
0.8231
0.8657
0.9078
0.9-496
0.9910
LO.m
1.072<1
!l:..l
I Ins
I 1934
1.2368 1,2331
' 2766 1.2725
L31 16
1.3161
1,3555
L3505
I.3H92
1.3947
14336 1 4218
14M1
14724
1.5042
L5111
1,5422
1.5496
1.5879 1,5800
1.6176
] 6261
1. 6551
16641
1.7020 1.6924
\.7296
1.7398
1.7667
\.m5
U\036
I 81SO
1,1!404
\.8524
I lf171
1.R898
1.9270 1.9 136
\.9477
1.9SO]
1.9858 1.%41
1.9S64
2.0239 2,0011
2,()618 2.0380 2.0226
2.0998 2,0749 2.0588
2.1376 2.1116 20948
2.1754 2.1403 21307
2,1848 2.1666
2.213\
2,2507 2.2213 2,2024
2.288] 2.2578 2.2..180
2.2736
2.3258 2.2lJ41
2.3632 2,3]()4 2,3091
2._ 2.3666 2._
1 1614
L2021
1,2427
1.2X30
1,3232
1,)632
1.4031
1.4428
I 4823
1.5217
1,5610
, 6002
1.6392
\.6781
1.7169
1.7556
1,7942
1 8327
1.8711
,-
1 1566
, '968
0.5068
0.5539
0,6003
0.6459
0.6908
0,7351
0,77Sf!
0.8219
0.8645
0,9056
0,9483
0.9896
UnO-l
lU7m
1111
11509
\.1904
L2296
1.2685
1,3071
1.3455
1.3836
1.4215
\.4591
14')65
1.53311
1.57U11
1,6076
1.6443
1.6808
1.7171
1.7532
1.7892
1.8251
,8608
1.8964
1.9318
1.9671
2.l1023
20373
2.0723
2.107 1
2. 1418
2.1764
2.2110
2,2454
2.2797
21119
•
1.9
2.0
2.2
2.'
00000
O<JOOO
O.lnlO
00000
0.<.1042
0.0\94
0,0441
0.0771
0.11K{!
0.1612
0.2087
0.2579
0.3078
0.3578
0,4073
0,4563
Q.5(M5
0,5520
0,5987
0.6447
0,6899
0.7344
0.7783
0.8215
0.8641
0.9063
0.9679
0.9891
OJX)42
0,0]93
0,0.08
0.0164
0,1156
o 1596
0,2067
0,2557
0,3055
0.3555
0,4052
0,4543
0.5028
0.5506
05975
0,6437
0.6892
0.7]38
om8
0.82 12
n.8639
0.9061
0,9477
0.(1042
0,0]92
0,0.05
0,0758
0,1146
(J,1581
0,0042
0,0191
(I,o·no
0.0749
o 1131
0,1561
0,2024
O,251J8
0._
04498
049R8
0.547\
05946
06415
0.6874
0.7325
07769
08205
0.8635
0.9058
0.9-475
0.900
I ()2-l()
O,IJOO)
O.IK)42
O.IJlS9
0,0·'21
0.0742
0.1171
(J 1547
0.20m
0.24K8
0.291\2
0.3481
0,3<J80
0,4477
0.4969
0.5454
1)5932
11,6401
1),68112
0.7315
11,7760
I),B198
1J.8628
1J.9052
0.9468
11.9879
1,()283
I (1M')
].0298
I 07111
I llul
1.1496
1.1889
1.2278
1.2663
10295
101'>'1)\
I If;
1 U292
I 1)(,91
I 11189
I 1489
I 1879
1.2265
\.2647
1 1481
11868
1.2252
1,2631
1. 3026
1.3402
1.3775
1.4\45
14512
14876
1.52311
1.5597
\5954
1.7U94
1.7450
1.7011
1,1359
\.770S
],AA56
0.8636
0,9058
0,9475
0._
1.3426
1.3803
1.4178
1.45SO
1.4920
1. 5287
1.5653
1.6016
1.6377
1.6736
1.92{)4
1.9550
1,9895
2.0239
2.058]
2.0923
2. \263
2.160 1
2.19]9
2.2276
2.2611
2.2946
08208
0.9889
1.-
1.7804
\.8156
18507
O,~9
0,2537
0.30]6
0.3536
04031
04525
0.5012
0.5492
115966
0,6428
0.6884
(),733]
(I,77N
I._
1.6308
\ ,8049
1.8392
\.8733
I 'J072
1.9409
1.9745
2.0079
2,0412
20744
2.\074
2.1403
2.1730
2.2056
2,2331
2.2705
(),3004
Ol~O3
I til
3.0
O<JOOO
O<JOOO
00000
O,O(i4;:
0.0189
0,0424
0,0737
0,1111
o 1534
0,1991
0,2470
0,2962
0.3461
0,3961
0,4450
0,4951
0,5437
0:'917
O,6J88
0.6850
0.7.'\04
0.7750
0.8 189
0.8619
0.9043
0,9459
0,0042
0.0198
0,0422
0,0733
0.1104
0.1524
0. 1978
0.2455
0.2946
0.3444
0.39-43
0.4441
0.4935
0.5422
0.5902
0,6374
0,6837
0.7292
0,7739
0.8178
0.0042
0.0187
O.OUO
0.0729
0.1098
0.1515
0.1967
0.2442
0,2932
0,3429
0.3929
04428
0.4922
0.5409
0.5690
0.6362
0.6826
0.7282
0,7830
0,8169
0.8609
08600
0.9024
1,(I(~1
] .0273
I (1(,70
0.9033
0.9449
0.9854
] .0262
I06W
IfI)-
I Tit.:
I
I 1472 1.\459
\.1840
1.1855
1,2234 1.22 \7
\.2588
1,2008
1.2978 1.2954
1.3007
\.33 16
1.3343
1.3379
\ ,3674
\.3705
1.3748
1.4028
1.4062
\4114
1..4377
14476 1.4617
1.4728
\.4767
1.4835
U065
I ~1 14
\ ,5192
\54l)4
1.5458
1.5546
\.5739
1.5799
1.5997
1.6246 16137 1,6071
1.6400
\.6472
1.6592
, 6IIQ.I
\.6726
1.6936
1.7049
1,7 134
\.7278
1,7460 1.7370
1.7617
17(~7
1.7785
1.7955
1,8107
I.IIIKl2
I 8290
1.11115
1.8427
11\623
I.M25
1,8744
1.8955
\.11933
1.9060
1.9285
1.9238
1.9373
1. 9613
\ ,9'i-l2
19939
1.9843
\.9994
2,0264
V1l42
2.0S!!7 2.0301
20909 20607 2.0440
2.0735
2,1229 2.0911
2.10211
2.1548 21213
2.1H65 2. 1913 2,1320
2.1812 2.111 J(J
2.2181
2.2496 2,2110 2. 11191'1
,-
2 .•
2.'
0_
'0,(1
0._
0,9850
1.0253
1.0650
I III_HI
I 14)5 1 1415
1.1441
I 1615 \.\004
\.1827
1.218lJ 1.2177
1,2202
1.2558 1.2546
\,2572
1.2922 ,2909
1.29)7
1.3281 1.3268
\.3298
\.3637 1,3623
L3653
1.3987 1.3973
\.4005
14.\34 \.43\8
1.4353
1.4677
14(197
1,5015 \.4998
\.5036
1.5351 1.5332
1.S373
1,5706 1.5692 1S663
].6011
1.5990
1.6035
1.63]6 1.6614
1.5362
1.6658 1.6635
1.5M5
1.6977 1.6953
1.700~
1.7322 1,7243 1.7267
1.7606 1.7579
1.7637
1,7916 1.7889
1.7949
1.8258 1.8224 L8195
\ .8530 1.8499
1.8565
1,!lg7()
l.fUl33 1.8801
1.9133 \.9100
] 9172
1.9431 1.9397
1.9728 1,9692
\.9769
2.(X)65 20022 19964
2,0359 2.0314 2.0275
2,0650 H)60) 2,0563
2.0940 2.0891 2.0849
2,1228 2.1178 2.1134
2.1462 2.1417
2.\514
2. 17')8 2.1744 2. 1698
,""'"
.
,"
Table 7·2 (g)
Extended Sukkar...comell Integral tor Bottom·hole Pressure Calculation
1.1
I."
200
2,.
300
3.50
4.00
4.50
'.00
,."
.00
'.50
700
7."
8.00
850
9.00
9.50
1000
10.50
lUll)
11.50
12.00
1150
1.2
1.3
1.4
2.'
3.0
0.0000
0.0000
0.0000
0.0000
00000
00000
00000
0.0000
0.0000
00000
0.0036
0.0166
0.0382
0.0676
0,1033
0,1436
0.1869
0.2318
0.2n3
0.3229
O,(lIns
0,0162
0,0371
0,0652
0.0993
o 1381
0.1801
0.2242
0,2693
0.3149
0.3605
0.4059
0.4508
0,4952
0.5391
0.5824
0.6252
0.6674
0.7091
0.7503
0.7910
0,1013
0,11711
0.9106
U'HII7
0,0035
0,0162
O,036!l
0,0035
0,0169
0,0361
0,0632
0.0963
01366
0.1782
0.2219
0.2669
0.3124
0.3580
0 ...t035
0.4486
0.4932
0.5372
0.5808
0.6237
0.6660
0.7078
0,7491
0.71199
O,R302
(J,87()('
U YO')5
U II-'X~
0,0035
0.0161
0,0365
0.0640
0,0974
0,1353
0.1765
0.2199
0,2647
0,3101
03551:1
0,4013
0,4465
0,4913
0,5355
0.5792
0,6223
0.6647
0.7066
0.7480
0.71!S8
O,82Y2
0!i690
U.90114
U.9-'74
0,0035
0,0159
0,0351:1
0,0626
0.()951
01321
o 1725
0.2152
0,0035
0,0157
0,0355
0,0618
0,0937
0,0035
0,0157
0,0353
0,0615
0.0931
0,1292
0.1687
0.2108
0.2545
0.2993
0.3525
0.3981
0.4·05
0,4&14
0.5329
0.5767
o 62()()
0.6627
0.7048
0,7463
0.71173
O,II2n
O,I!676
o 9()7U
0.6612
0,7034
0.7451
(),7!S61
0,11265
0."""
() ()I]57
0,0035
0,0158
0,03.56
0,0621
0,0943
0,1309
0,1710
0,2135
0,2675
0.3025
0,3480
0,3937
0.4392
0.4843
0.5291
0.5712
0.61bR
0.6597
0,7020
0,74]6
() 7847
0.8251
086:'iO
0,90·n
U '1J~1I
n" -'Jo
" W~X4
II
(J,i)SW
n \//1.1:'
1I'11oI:.'S
0.'1-'.11
lI'Jlln
U97W
0.7411
0.71122
0,11227
0.11626
0.9019
09-'06
II.Y7117
, leM
1.02.11
, .11.'
11:.'11(,
1 1l1'!1
1.11171>
! IJJN
1.0618
1.0992
1 1362
I 1729
1.2092
1.2453
1.2610
1.3164
1.3515
1 J864
1.4211
1.4554
1.4896
1.5235
155n
1.5906
1.6239
1.6570
1.6899
1.7226
1.7551
1.787<1
1.8196
1,8516
1.8835
1.9152
1,9468
1,9782
2,0095
2.0407
2.0717
2.1026
2.1334
1.0596
1~79
1.il966
1 09-17
I 1332
116<J.i
1.2052
1.2<W7
1.2757
1.3105
1,3449
1.3789
1.4127
1.4462
1.4794
1.512.1
1.5449
1.5773
1.6095
1.6414
1.6731
1 1311
1 1670
1.2026
1.2377
1.272'1.3067
I 056~
10930
1 1293
I 165\
1,2005
1.2354
\.2700
1.3042
1.3380
I 3714
1.4U45
1.4373
1,'-698
1.5019
\.5338
1.5654
15967
162n
1.6585
1.0547
1.0914
I 1276
I 1633
I 19K7
1.2:'15
1.2(>110
\ U5.lS
11110\
I 121>3
1 I"2U
I 1972
I.HW
1.2665
1.3005
1.3.\41
I 3674
1.4003
I 4329
1.4652
1.4971
I .S2RB
1,5601
1.5912
1.6220
1.6525
1.6828
1.7128
1.7<126
1.7722
1.8015
0.0823
0.8329
0,8747
0,9165
0.9581
0.1264
0.1719
0.2174
0.2625
0.3071
0.3513
0.395\
0.4386
0.4817
0.5247
0.5574
0.6098
0.6521
0.6941
0,7360
Q,m5
0.8181
o8roI
0.9()16
U.942/1
U""""
0.7909
0._
08901
OmOb
0.5527
0.5951
0,6372
0.6789
0,7204
0,7615
0,8026
0,8430
0.8833
0.9234
0.6007
0.6428
0.6846
0.7261
0.7674
0.808S
0.8"94
1 1237
I 1649
15.00
1.2060
15.50
16.00
16.50
17.00
17.50
18,00
18.50
19.00
19.50
\.2471
1.2881
1.3291
1.3700
\.4109
1.4517
1.4924
1.5332
\,5738
1.6145
1.6S51
1.6956
1.7361
\,n66
1.8171
1.8575
I 10Sol
I 1459
I 1862
1,2264
1,2666
1.3067
1,)467
1.3866
1.4264
10912
I 1310
1.1707
1.2102
1.2497
1.2890
1.3282
1.3674
29.SO
30.00
2.'
0.0000
14.00
28.50
29,00
2.4
0,0036
0,0168
0,0390
"50
28.00
2.2
0.0000
1 unn
I 0425
27.00
27.50
20
0.0037
0.0112
0.O-W1
0.0718
0.\103
01531
0.\980
0.2436
0.2891
0.3343
0.3789
0.4230
0.4667
(I9f,:n
26.50
1 .'
00000
'.11!1~
26,00
1.'
0.0037
0.0176
0.0418
0,0755
0.1164
0,1608
0.2063
0.2519
0.2970
0.3416
0.3858
0.4295
0.4728
0.5158
0.5584
U 9710
24 SO
"00
".50
1 .7
0.0000
1 H2J~
I 0(>4"
24.00
1.'
0.0038
0.0184
0.0447
U.911~~
2200
22.SO
23.00
23.50
1.S
0.0000
I 11411
1IIIQ4
21.00
21.50
~
0.0039
0,0199
0,0521
0,0967
0,1422
0,1870
0,2314
0.2756
0.3195
0.3632
0,4067
0,4500
0.49]1
0,5361
0.5789
0.6216
0.6642
0.7066
0.7488
13 Ol)
\\.511
20.00
20.50
~
Reduced Temperature for B .; 30.0
P,
020
0."
1.00
~
1.8979
1.9383
1.9786
2.0189
2.0592
2.0995
2.1397
2.1799
2.22{\1
2.2603
2.3OCl5
2._
2.J807
2.4208
14662
1.5059
1.5456
1,5852
1.6247
1,6642
1.7037
1.743\
1.7824
L8217
1,8610
1.9002
1.9393
1.9785
2.0176
2.0S66
2.0957
2.1346
2.1736
2.2125
2.2514
2.2903
2.3291
2.3679
1.0~1I
1.-
1.0318
11209
1 1598
119116
1.2372
1.2757
1.3140
1.3522
1.3903
1.4282
1.4661
1.5038
1.5414
1.5789
1,6163
1.6537
1.4454
1.4843
1.5231
1.5618
1.6005
1.6391
1.6n6
1. 7160
1.7544
1.7928
1.8311
1.8693
1.9075
1.9456
1.9837
2.0217
2.0597
2.0976
2.1355
2.1734
2.2112
2.2490
2.0226
2.0591
2.0955
2.1319
2.1682
2.2045
2.2868
2.2407
2.3245
2.2769
1.6909
1.7281
1.7651
1.8021
1.8390
1.8759
1.9127
1.9493
1.9860
0,3278
0,3729
0,4175
0.4616
0,5052
0.5483
0.5909
0.6331
0.6749
0,7163
0.7573
0.7980
0,8384
0,8785
0.9183
O.YS711
(19'173
1I.'J'lJI,
ll1.lM
l.()-'~-'
0,0036
0,016--\
0,0375
00672
0.1010
0,1404
01831
0.2275
0.2729
0.3186
0.3641
0.4092
0.4539
0.4981
0.5417
0.5848
0,6273
0.6693
0.7109
0.7520
0.7926
08329
0.8728
0912.l
o 9~1~
n,'I'/I14
1.02'HI
1.0710
1,0673
1.~9
106J4
1 109-1
1.l054
1 1027
1 1402
IIn4
1.2144
1.2511
1.2876
1.3238
1.3598
1.3956
1.4312
11009
1.1382
I 1751
1,2117
1.2481
1.2842
1.3200
1.3555
1.3908
1.4259
14666
1-
1.5019
1.5369
1.5718
1.6065
\.6410
1.6754
1,7(1%
1,7437
I.7m
1.8115
1.8452
1,8788
1.9123
1,9-'56
1.9788
2.0119
2.04J9
2.0779
2.1107
2.1434
2.1760
1.4954
1.5298
1.5MI
1,59S 1
1.6320
1.6657
1.6992
1.7325
1,7657
1.7987
1,8316
0.0692
0,106(}
0,1474
0,1914
0.2367
0.2823
1 0753
1 1139
I 1524
11907
1.2287
1,2666
1.-
1.3419
1.37~
1.4167
1.4538
1.4908
1.52n
1,5644
1,6011
1.6376
1,6740
l.7i03
1,7485
1,7826
1.8186
1,8546
1,8904
1.9262
1.9618
1.9974
2.0330
2.11684
2.1038
2.1391
2.1743
2.2095
2.2446
0.3683
0,4132
0.4576
0.5015
0.5-1-49
0.511n
0,63(11
0.6719
0.7134
0.7544
0.7951
0.8354
0.8754
0.9150
n.9~4-'
I 1475
I 1855
1.2232
1.2607
\,2981
1.3352
1.3722
1.4091
1.4457
14823
1.5187
1.5549
1.5910
1.6270
1 6629
1.6987
1.7343
I. 7698
1.8053
I 1431
1 1606
1.2179
1.2549
1.2917
1.3283
1.3847
1.4009
1.4370
1.4728
1.S08S
1.-
1.5794
1.6146
1.6497
1.684<>
1.9810
2,0159
2.0507
1.7194
1.7541
1.7886
1.8230
1.8573
1.8915
1.92.56
1.9596
1.9934
2.0272
208S4
2.0609
2.1200
2,1546
2.1891
2.2235
2.0945
2.1280
2.1614
2.1947
1.8406
1.8758
1.9110
19460
•
1 ml>s
0_
<}1017~
1.-
1,8970
1 ,92~
1.9618
1.9940
2.0261
2.0580
2.01199
2.1216
2.153]
0.0960
0,1334
0,1741
0.2112
0,2617
0.J069
1.7~6
1.7358
1.7669
1.79n
1.8284
1.85119
1,8891
1.9192
1,9492
197'JO
2.0086
2.03AO
2.0673
2.(1%5
O,25~
0.3046
0.3501
0,3957
0.4412
0,4863
0.5309
0.57411
O,61~
1.J407
I 374.I 4077
"-107
1,4734
1 ~58
I ~379
1.5697
160iJ
1.6326
1.6636
UJ9.-5
1,72S0
1,7554
1,7855
iJ!l55
I.~S2
11047
1.9040
1.9332
1.9672
1.'J910
2,()196
2.i)4S1
2.0764
16890
1.7193
1.7494
1.7792
1.8088
1.8382
1.8674
1.8964
1.9252
1.9538
1.9R23
2,0105
2,0386
2.0666
onoo
0,1697
0,2120
0,2559
0.3008
0.3462
0.)919
0.4374
04826
0.5274
0,5716
0,6152
0.6582
O,71()6
0.7'-23
0.7833
0.1I23R
0.11637
0.9()]()
0.9-117
1.3021
1.3358
1.3692
1.4022
1.4349
1.4672
1.4993
1,5310
1,5625
1,5937
1.6246
1.6552
1.6856
1.7158
1.7457
l,n54
1,8O-tS
1,8341
1.8631
1.8920
1.9206
1.9.-91
1.9774
2.0055
2.0334
2.0612
0.J448
O,39(}.\
0,4359
0,4812
0,5260
0.5703
0,6139
0.6570
0_
1 1<306
18595
1.8AA2
1 9167
1 9.-51
1.9732
2.0012
2.0289
2.0566
Table 7-2 (h)
Extended Sukkar-Cornellintegral for Bottom-hole Pressure Calculation
P,
1.1
0.20
O.SO
1.00
I.SO
2.00
2.SO
3.00
3.SO
4.00
4.SO
'.00
'.SO
600
6.SO
7.00
7.SO
8.00
8.SO
9.00
9.SO
10.00
10.50
11 .00
11.50
12.00
12.50
13.00
BStl
1400
14.50
15,00
15.50
/6.00
16.50
17.00
17.50
18.00
18.50
19.00
19,50
20.00
2O.SO
21.00
21.50
22.00
22.SO
23.00
23,SO
24.00
24.50
2500
25.SO
26,00
26,50
27.00
27.50
28.00
28.SO
2900
29 SO
30.00
0.0000
0.0033
0,0171
0 . ~S4
0.086 1
0.1283
0,1703
0.2 120
0.2536
0.2950
0.3362
0.3773
0.4183
0.4591
0.4999
0.S405
0.58 10
0.6214
0.66 17
0.7018
0.74 19
0.7818
0.8217
0.8614
0.9011
0,9407
0911.03
I 0\97
1,0591
U1985
1.1377
I 1770
1.2162
1.2553
1. 2944
1.3334
1,3725
1.4114
1.4504
1.4893
1,5281
1.5610
1.6058
1,6446
1,68)3
1.7220
1.7607
1.7994
1.8381
1.8767
1.9153
1,9539
1.9924
2.0310
2.0695
2 1080
2,1465
21850
2,2234
2,26 19
2,3003
1.2
0.000l
0.0032
0.0158
0.0387
0.0720
0.1119
0.1538
0.1960
0.2382
0.2800
0.3216
0.3630
0.4040
0.4449
0.4856
0.5261
0.""
0._
0.6466
0.686S
0.7262
0.7657
0.8051
0.....
0.8836
0.9227
0,9617
1.{){X)(,
1.0394
1.078 1
1.1167
1.1552
1.1937
1.2321
1.2705
1.3087
1.3470
1.3851
1.4232
1.4613
1.4993
1.5373
1.5752
1.6130
1.6509
1.6887
1.7264
1.7641
1.8018
1.8394
1.871 1
1.9146
1.9522
1.9897
2.0272
2.0647
2.1021
2,1395
2.1769
2,2142
2.2516
1.3
1.4
0.000l
0.0032
0,0152
0.0361
0,0657
0.1022
0, 1425
0.1844
0.2266
0.2688
0.3106
0.3522
03934
0.4344
0,4752
0.5 156
0.5558
0.5959
06357
0.6753
0,7147
0,7539
0.7930
0.8319
08607
0.9094
09479
0.000l
0.0031
0.0148
0.0346
0.0623
00965
0.1350
0,1759
0.2179
0.2601
0.3023
0.3442
0.3857
0.4270
0.4679
0.S08S
0.5487
0.5888
0.6285
0.6681
0.7073
0.7464
0.7852
0,8239
0.8623
09006
0.9386
{) <)101/,1
II <J7f15
1.0246
1.0627
1,1008
1.1388
1.1767
1,2 144
1.2521
12898
1.3273
1.3648
1.4022
1.4395
1.4768
1.5140
1.55 II
1.5882
1.6252
1.6622
1.6991
1.7360
1.7729
1.111m
1.8464
1.8831
1,9198
1.9564
1.9930
2.0295
2.066 1
2,1025
2. 1390
2,1754
2.2118
1.0143
1.0519
1.0893
1.1 266
1.1638
1.2008
1.2378
1.2746
1.31 13
1.3479
1.3844
1.4208
1.4571
1.4933
1.5294
1.5655
1.60 14
1.6373
1.6732
1.7089
1.7446
1.7802
1.8158
18513
1.8867
1.9221
1.9574
1.9927
2.0279
2,0631
2.0983
2.13J3
2. 1684
1.5
0.000l
0.0031
0.0145
0.0336
0.0601
0,0925
0.1295
0.1694
0,2108
0.2529
0.2951
0.3373
0.3791
0.4207
0,46 18
0.5026
0.5431
0.5832
0.6230
0.6625
0,7017
0.7406
0,m3
Reduced Temperature for 8 - 35.0
1.'
1.7
1.6
2.0
1.'
08559
0.8939
0.\)317
0000l
0.0031
0.0143
0,0329
0.0585
00900
0.1259
0,1650
0,2059
0.2477
0.2899
0.3321
0.3742
0,4159
0.4573
04983
0.5390
0.5792
0.6191
0.6586
0.6978
0.7367
0.7753
08136
0,8517
0.8895
U9271
0000l
0.0031
0.0141
0.0323
0,0573
00879
0,1230
0. 1613
0.2017
0.2433
0.2854
0.3276
0.3698
0.4117
0.4532
0.4944
0,5352
0.5756
0.6156
0.6552
0.6945
0.7334
0.nI9
0.8 102
0.8481
0.8858
0,9232
11 9(,(j,
0.000l
0.0030
0,0139
0.0320
0.0564
0._
0,1208
0.1585
01984
0.2396
0,2816
0.3238
0.3660
0_
04-198
0,4912
0,5822
0.5727
0,6129
0.6526
0.69 19
0.7308
0,7694
0.8076
0.8655
0.8831
O,92U4
{)(jM~
lL'MI4
()
0.9913
1.0340
1.0704
1.1066
1.1426
1.1784
1.2140
1.2494
1.2846
1.3197
1.3546
1.3893
1.4239
1.4584
1.4927
1.5269
1.S609
1.5948
1,6286
1.6623
1.6959
1.7294
1.7627
17960
1.8191
1.8622
1.8951
1.9280
1.9608
1.9935
2.0261
2.0587
2.0912
0.9941
1.0305
1.0667
1.1027
1.1 384
1.1739
12092
1.2443
1.2792
1.3139
1.3484
1.3828
1.4170
1.4510
1.4849
1,5186
1,5522
1.5856
1,6U19
1.6521
1.6851
1.11110
\.7508
1,7835
1.8161
1.8486
0.8171
1'(l067
1.0439
1.0809
1.1178
1,1549
I 191/
1.2275
1.2638
1.2999
1.3359
1.3718
1.4075
1.4432
1.4788
1.5142
1,5495
1.5848
1.6199
1.6550
1.6900
1.7249
1.7597
1.7944
18291
1.8637
1.8982
1.9326
1.9670
H)014
2.0356
2.0698
2.1040
2.1381
1.0017
1.0386
1.0754
1.1120
1.1484
1.1846
1,2207
1.2566
1.2923
1.3280
1.3634
1.3988
1,4340
1.4691
1.5041
1.5390
1.5738
1.6084
1.6430
1.6775
1.7118
l.7461
l.7803
1,8 144
1.8484
1.8824
1.9163
1.9501
1.9838
2.0175
2.051 1
2._
2.1180
•
(j~7.1
1.8810
1.9133
1.9454
1.9775
2.0095
2.~14
2.0732
(J~S~
0.9920
1.0282
1.0642
I.Il999
1.1354
I 1705
1.2055
1.2402
1.2747
1,3089
1.3430
1.3769
1,4105
1.4440
IA773
1.5104
1.5434
1.5762
1.6088
1.6413
1.6736
1.1{)58
1.7379
1.7698
1.8016
1.8333
1.8649
1,8963
1.9277
1.9589
1.9900
2.02iO
2.0519
2.4
2.'
2.6
3.0
0000l
0.0030
0.0137
0,0311
0.0546
0,0834
0,1165
0,1528
0.1916
0,2320
0.2734
0.3153
0.3576
0,3998
04418
0.4836
0.5247
0.5657
0.6062
06462
0.6858
0.7250
0,7637
0,8019
08398
0,8m
0.9141
(1'150
o000l
0.0030
0.0136
0.0309
0.0542
00826
0,1153
0,15 13
0.1897
0.2298
0.2710
0.3128
0.3550
03972
0,4394
0,48 12
0.5227
0.5638
0.6044
0.6445
0.6842
0.7234
0,7621
0.8001
0.8381
08755
1)'112-l
00000
0.0030
0.0136
O,OJ07
0.0537
0,0819
0,1142
01499
0.1880
02279
0.2690
0,3107
0.3529
03951
04373
0,4792
0,5208
0.5619
0,6026
0.6428
06825
07217
0,7604
0.7987
0.8364
08737
U9106
0.0000
0.0030
0.0135
0.0305
0.0534
0,0813
0.1134
0.1487
0.[866
0.2263
0.2672
0.3089
0.3910
0.3932:
0,4354
0.4n4
0.5190
0.5(;)2
0.6009
0,6412
0.6809
0.7201
0.7589
0.7971
0.8349
0.8721
0.9089
J 'qXl
0.0000
0.0030
0.0135
0,0304
0.0531
0"""
o 1127
0.1478
o 1855
0.2250
0.2658
0.3014
0.3495
0,3918
0.4339
04759
0.5175
0.5588
0,5996
0.6398
0,6796
0.7189
07576
0.7958
0.8336
0.8708
0.9076
11'1-17(1
f) ()-l~.1
f) 9~.19
0.9900
1.0261
1.0618
1.0973
1.1325
1.1674
1,2020
0.9869
1.0226
1.0500
1.0931
1.1278
1.1622
0.9848
12364
1.2300
1.2634
\.2966
1,3294
1.3620
1.3944
1,4265
1,4583
1,4900
1,5214
1.5525
1,5835
1.6143
1.6448
1.6752
1,1054
1.7354
1.7652
1.7949
1.8244
1.8537
I.M29
1.9119
I.1.9696
0.0000 0000l
0.0030 00030
0.0139 0.0139
0.0317 0.0315
0.0559 00554
0.11055 0.0847
0,119.1 01182
0.1567 0,1550
0.1962 0, [942
0.2372 0,2350
0.2790 0.2766
0.3211
0.3187
0.3634 0,3610
04{l55 0,4032
0,4473 0,4451
OA~
04867
0.5300 0.5280
0.5707 0S688
0.6109 0.6091
0.6507 0.6490
0.6901
06S85
0.7291
0.7275
0,7677 0.7661
0.8059 0,8043
08438 0.3422
0.8813 0.8797
0918.'1 091611
11
2.2
w
S1
II "'~1~
1.2705
1.3044
1.3380
1.3714
1.4046
1.4376
1.4704
1.5030
1.5355
1.5677
1.5998
1.6317
1,6634
1.6950
1.7264
1.7577
1.7888
1.8198
1.8506
UI814
1.9119
1.9424
19726
2.0030
2.033 1
1.1962
1.9982
1.0205
1.0557
1.0905
1.1247
1.1590
1.1928
1.2262
1.2592
1.2970
1.3245
3166
,3885
,4201
,45 15
,4826
,5134
5440
5744
6()'16
6345
6642
.6937
,723 1
I. 7522
1.7812
1.8100
1.8386
1.8670
1.8953
1.9234
1.9513
1.9791
0.9ln9 0.9812 0,9793
1.0184 1.0\67 \.0\53
1.0536 1.0517 I.OS03
1.0883
10864 1.0849
1.1226 1 1206 1-1191
11566 1.lS45 I 1529
1.1 88() 111164
1.1901
1.2234
1.2212 1.2195
12563 1.2540 1.2522
1.2889
1.2865 1.2847
1.3212
1.3187 1.3168
1.3531
1.3506 1.348S
1.3848 1.3822
1,4162 1.4135 1,4112
1,4473 1.4445 14422
1,4782
1.4752 1,4120
1.S088 1.5057 1.5032
1.5391
1.5360 U333
1.5693
1.S66il 1.5632
1.5957 I-sm
1.5992
1.6288
1.6253 1.6223
1.6583
1.6546 1.6S15
1,6837 1.68Ol
1.6875
I. 7165
1.7126 1.7093
1.7454
1.7413 1.7378
1.1698 1,7662
1.7740
1,7981 1.7944
1.8025
1.8306
1.8262 1.8224
1.8542 1,8502
1.8589
1.8868 1.8820 1,8779
1,9/46 1.9096 1,90S3
1.9422 1.9370 1.9327
1.9696
1.9643 1.9598
"""
Table 7-2 (I)
Extended Sukkar-Comell Integral for Bottom-hole Pressure Calculation
P,
0.20 00000
O.SO 00029
1.00 O.OLSO
I.SO 0.0403
2.00 0.0776
2.SO 0,1170
300 0.1565
3SO 0.1958
4.00 0.2351
4SO 0.2743
'00 0.3133
'.SO 0.3523
6.00 0.3912
6.SO 0.'1300
7.00 0.4687
7.SO 0.0573
800 0,$458
8.SO 0.5843
9.00 0.6227
9SO 0.6609
1.2
1.3
0.0000
0.0000
O,(JO?..8
0.0139
0.0341
0,0028
0.0133
0.0318
0,0582
0.0912
0.1281
0.1668
0,2062
0,2457
0.2851
0.3244
0.3634
04023
0.44\0
0.4795
0.5179
0.5560
0.5940
0,6319
0.0640
1000
10.50
11,00
11,SO
12,00
0.6991
0.7372
0.n53
0,8132
0.8511
0.1005
0.1393
0.1787
0,2182
0,2576
0.2969
0.3360
0.3750
0.4138
0.4525
0.4910
0.5294
0.5677
0.6059
0,6439
0.6818
0.7196
0.7573
0.m9
0.8324
IBO
(),AA~
0_
D,no
n Q~t.X
0907:'
0.7071
0,nt6
0.7819
0.8190
0,851'01
tUN'1
I'~I
II ,lid'
01--1.1'\
L)?'N
10022
1.0398
1.0774
1 1149
r 1525
1 1"'.19
]2274
1.2648
1.3021
1.3395
1.3768
1,4140
1,4513
1,4885
1.5257
15629
1.6001
1.6372
1.6743
1.7114
1.74K5
1.7855
1.8226
1.8596
1.8966
1.9336
1.9705
2.0075
2.0444
2.0!!\3
2.1182
2.1551
2,1920
0.9816
0,0188
1.0558
1.0928
1.1297
0,9667
1.0034
10400
1.0765
I 1129
1 1492
I 1855
1.2217
1,2579
14.00
15.00
15 ..~
J/)I~l
16.50
17,00
17.50
18.00
18.50
19.00
19.5O
20.00
20.SO
21.00
21,50
22,(k)
22.SO
23.00
23SO
,"00
24.50
23.00
23 SO
26.00
26.50
27.00
27,SO
28.00
28.SO
29.00
2950
3000
~
~
Reduced Temperalure for 8 - 40.0
1.1
14 SO
~
II""
1.2034
1.2402
].2769
1.3136
1.3502
0.6696
12940
1.5327
1.S691
].330)
],)659
1.4019
1,4)77
1.4735
1.5093
1.5450
\.6417
1.6780
1.7143
1.7505
1.7867
1.8229
1.8591
1.8952
1.9313
1.9674
2.0034
2.0194
2.0755
2.1114
2.1474
1.6163
16519
1.6874
1,7229
1.7584
1.7938
1.8292
1.8645
1.8999
1.9352
1.9704
2.0057
2,0409
2,0761
2,1112
13868
1,4233
1.4598
1.4963
I._ I."""
'"
1.5
1.6
1.7
1 .•
0.0000
0.0000
0.0000
0.0000
0.0027
0.0129
0.OJ05
0.0551
0.0027
0.0127
0.0296
0,0530
0.0821
0.1156
0.1520
0.1901
0,2292
0.2686
0.3081
0.3476
0,386!1
0.4258
0.4646
0.5031
0,5413
0.5793
0.6 171
0.0027
0.0125
0,0517
0.0798
0.1122
0.1477
0.1853
0.2240
0.2633
0.3028
0.3423
0,3816
0,42{)8
0.4597
0.4983
0.5367
0.5747
0.612S
0.0027
0,0123
0,0284
0.0505
0.0779
0.1095
0.1442
0.1812
0.2]95
0.2586
0.2980
0,3376
0.3170
0.4163
0.4553
0,4941
0.5325
0.5707
0._
0.6500
0,6873
0,7243
0.76] I
0.7977
OSJJI
IlInm
00858
0.1208
0.]584
0.]973
0.2367
0.2762
0.3156
0.3549
0,3939
0.4328
0.47]4
0 ..5097
0,$479
0.5859
0.6237
0.6612
0.6987
0.7359
0.7729
n~66
0,6919
0.7290
0.7659
0.8026
(),8J91
n ~~n~
II
"
n 'JI
0.8098
'I' '.
0,9559
0,9921
1.02112
1.0641
I 1000
\ 1357
I.J 713
1.2068
12422
1.2776
1.3128
13480
1.3831
1.4181
1.4530
1.4879
1.5227
1.5574
1.5920
1.6266
I.MI2
1,6957
1,7301
1.7645
1,7988
l.8m
1.8673
1.9015
1.9356
1,9697
2.0038
2.0378
2.0717
~7'i~
0.0290
1.'
2.0
2.2
0.0000
0.0000
0,0027
00122
0.0279
0,0493
0,0756
0.106]
0.1398
0.1758
0,2JJS
0.2521
0.2913
0.3308
0.3703
0,4097
0,449(}
0.4879
0.5266
0,5650
0.6030
0.0000
00026
00000
0.0026
0.0 120
0.0273
0,6461
0.6833
97203
0.7571
0,7936
0,8299
0,0027
0.0122
0.0281
0.0497
0.0765
0,2074
0.1416
0.1780
0.2159
0.2548
0,2941
0.3336
0.3731
0.4124
0,4516
0.4905
0.5290
0.5673
0.6052
0.6429
0.6802
0.7172
0,7539
0,7903
O.IQM
n.so~'1
II IIO~J
0._
7
II )1111.'
II '~IL'
II
0.9477
098.15
1.0193
1.0548
].0903
J 12S5
I 1607
1.1958
1.2307
1.2655
] .30)2
] ,3349
1.3694
1.4038
1.4381
1.4723
0,9421
0.9778
0.9373
0.9727
1.0079
1.0429
1.0777
1.1123
1 14611
I 1811
1.2152
1.2492
1.2831
] ,3168
] .3504
1.3838
1.4171
1.4503
1.4834
1.5 164
1.5492
1,5820
I.nt46
1.6472
1.6797
1.7120
1.7443
1.7765
1.81186
1.1H06
1.8726
1.9044
1.9302
0.9335
0,9588
1.0037
1,0)85
1.0731
1.1075
I 1417
1.1757
1.2095
1.2432
1.2767
] .3101
1.3433
1,3763
1.4093
1.4421
1.4747
1,5072
1.5396
1.5719
16041
1.6362
1.6582
1.7000
1.7318
1.7634
\.79.50
1.8265
1.8579
1.8892
1.9204
1.9516
1.9826
I."'"
1S4<J6
1.5746
I1,6423
"""
1.6761
1,7098
1,7434
1,7770
1,8105
1,8439
1.8773
1,9107
1.9439
1.977J
2,0103
2,0434
I ,OJ))
].0486
J .0837
1.1187
I 1536
11884
1.2230
1.2574
1.2918
1.3261
1.3602
1.3942
1~281
I 4620
J 4957
1.5293
1.5629
1.5963
1.1'0297
1.6630
1.6962
1.7293
1.7624
1,7954
1,11283
1,1\612
1.11940
1.9267
1.9594
1.9920
2.0246
19680
1 \l996
•
~'Il'il
0.0121
0.0276
0.0488
0.0749
0.1050
0. 13&3
0.1740
0.2113
0,2498
0.2889
0.3283
0.3678
0.4073
0,4466
0.4856
0.5244
0.5628
0.6009
0"",
0.0738
0.1034
0.1362
0,1714
0.2084
0.2465
0.2854
0.3247
0.3642
0.4037
0.4431
0,4819
0,52{)8
0.5593
0.5975
0,6353
06728
2.6
2 .•
0.0000
0.0000
0.0026
0,0119
0.0271
O.04n
0.0730
0,1023
0,1348
0.1696
0.2063
0.2442
0,2829
0.3221
0.3616
0.4011
0,44{)5
0,4797
0.5]87
0.5573
0,5955
0.6334
067\0
0,7081
0,7448
0.7812
0.0026
0,0119
0.0270
0.0473
0.0724
0.1013
0,1335
0.1681
0.2045
0.2422
0,2808
0.3199
0.3594
0.3989
0,4383
0.4776
0.5166
0.5553
0.5936
0,6315
0.0000
00026
2.'
0.6780
0.7150
0,7517
0.7882
n,!Q43
0.6386
0,6760
0.7130
0.7498
0.7862
Q,K!2J
0,7466
0,78JO
0,819n
IUIl7I
!1iWIZ
n H'iSO
US.~4·
II
"
/I,
HINIJrI
06407
,'Il~
0.9310 09287
0.9661
0.9636
1.0009 0.9982
1.0328
\.0355
1.0698
1.0667
1.1039 1.1005
\.1378 1.1341
1.1714
I 11'075
1.2049
12006
1,2336
1.2382
1,2663
1.2713
J .3042
1.2988
1,3311
1.3369
1.3695
1.3633
1.4019 1.3952
1.4J.t 1 1.4270
1.4662
1.4586
1.4982
1.4900
1.5300 1.5213
1.5617
1.5525
1.5834
1.5932
] ,6246
1.6143
1.6559
1.6-*.50
1.6871
1.6755
1.7181
1.7059
1.7491
1.7362
1.7799 1.7664
1.8106 1.7965
1.8412 1.8264
1.8717 1.8562
1.9021
1.K859
1.9325 1.9155
1.9450
1.9627
07099
S~:>7
'K"I,~'
06690
0.7052
0.7429
0,7792
1),11152
II
H~17
'I!'SiO
J.O
0.0000
0.0026
00118
0.0267
0.0118
0.0268
0.0471 0.0468
0,0718 0.0714
0.1005 O.om
0.1324 0.lJI5
0.1667 0,1656
0,2029 0.2017
0.2405 0.2391
0.2790 0,2175
0.3181 0.3166
0.3575 0.3560
0.3970 0.3955
0,4365 0,4350
0.4758 0.4743
0.5148 0.5133
0.5535 0.5521
0.5918 0.5904
0.6298
0.6284
0.6660
0.6673
0,7045
0.7412
0.m5
0.8]34
01490
0,7031
0.7398
0.7762
0,8121
0,8-176
(l ,~.~~I
{) 1<827
0.9228 0.9'201 0,9188 0,9\14
0,9532 0.95\1
0.95n 0.9551
0.9914 0.9891
0.987i 0.9856
1,0228 1,0208 1.0192
1.0251
1.0541 1.0525
1.051\6 1.0561
1.0917
1.089\
1.0870 1.0853
I 1245
I 12111 I 1196 I 1179
I 1541
I 1008
I 1570
I 1519 1 1501
I 1934
I 1S92
I 1862
I 1839 ] 1820
l.llS6 1,2211
1.2180 1.2155 1.2136
1,2528 1.249~
1.2577
1.2469 1.2450
1,2780 1.2760
1.2842
1.2894
1.J(]68
1,3210 1.3153 13116
1.3462 1.3422 1.3395 1,3373
US23
1,3K34
1.3768
1.3727
1.3698 1.3675
1.4143
1.4072
1.4028 13999 1.3975
1.4449 1 4373
1.4328
I 4297 142n
\,4754
\ ,4593 1.4567
14673
I 462.\
1.4970 1.4920 1 4887 1 _
I.S057
1.5265
1.5358
1.5213
15178 1.5151
1,5657
1.5559 1.5503
1.5468 1,5439
1.5954
1.5792
1.5755 JS725
1.S85O
1,6249
1,6041 1.6010
1.5078
1.6139
1,6427
1.6S43
1.6363
1.6324 1.6292
1,6646 1.6606 1.6572
1.6836
Ui713
Ui997
1.6927
1.7126
1.6886 1.6851
1.7415
1.7279
1,7207
1.7164 1,7128
1,7560
1,7484
1.7440 \.7403
1.7703
1.7839
1.7760
1.79fl9
1.7715 1.7676
1.11274
IKI16
1,8035
\.7988 \.7946
1,8308 1.11259 1.8216
1.8557
I.K393
1.8X4U
1,8579 1.8529 18487
1R667
].8849 1.8797 1.8754
1.9120
1.8940
09250
0.9596
0,9939
1.0279
1.0516
\ .0949
I 121!O
"806
I._
l
Table 7·2 (j)
Extended Sukkar-Cornell Integral for 9oHom·hole Pressure Calc'" II....
P,
1.1
0.20
0."
1.00
I."
200
00000
0.0026
0.0134
0.0362
0,0707
0.1016
o 1449
0.1821
0,2193
0.2565
0.2936
0.3306
0.3676
0.40-'5
0.4414
0.4782
0,5150
0.5517
0.5883
0.6248
0,6613
0.6978
0,7342
0.7705
0.8068
1.3
1.4
0.0000
0.0025
0.0124
0.0305
0.0576
0.0912
0.1273
0,1643
0.2015
0.2388
0.2760
0.3131
0.3501
0.3871
0.42]9
00000
0.0025
0.0119
0.0000
0.0024
0,0115
0.0272
0,0494
12 ,50
I' Ull
o &.no
0.4973
0.5]39
0.5704
0.6067
0.6430
0.6792
0,7153
0.7514
0.7874
OR2]]
o R"7<l2
1))1<;'11
0.0522
0.0823
0.1163
0,1523
0.1892
0.2264
0,2637
0.3009
0.3380
0.3750
0.4118
0_
0,4852
0.5216
0,5580
0.5942
0.6301
06664
07023
0,7381
0.TI]8
a 8Il94
II S4--l'J
\ '\ \II
\I 'HS]
U,I('I.\'1
(\I!I'.\l-\
2."
3.00
3."
4.00
4."
5.00
5."
'.00
,,.
7.00
7."
8.00
8,.
900
9."
10,00
10,50
11.00
1I,SO
12 .00
14.00
0,9514
0.9875
15.00 1.0235
15.SO 1.0595
16.00 1.0955
16.50 1.J315
17.00 1.1674
17.50 1.2032
18.00 1.2391
18.50 1.2749
19.00 1.3107
19.5O 1.3465
20.00 \.3823
20.SO 1.4180
21.00 \.4538
21.SO 1,4895
22.00 1,5251
22." 1.5608
23.00 1.5965
23." 1.6]21
24.00 1.66TI
24.50 1.70]3
25.00 1.7389
25.50 1.7745
26.00 1.8100
26.SO 1.8456
27.00 1.8811
27.50 1.9166
28.00 1.9521
28." 1.9876
29.00 2.0231
29.50 2.0586
30.00 2.0941
14.50
Reduced Temperature for 8 = 45.0
1.2
0.0284
o 46()7
0.9306
0.9663
1.0019
1.0374
1.0729
1.1084
1.1438
1.1791
1.2145
1.2497
1.2850
1.3202
1.3554
1.31X15
1.4256
1.4607
1.4958
1.5308
1.5658
1.6008
1.6357
1.6706
1.7055
1.7404
1.7752
1.8101
1.8449
1.8797
1.9144
1.9492
1.9839
2.0186
2.0533
0.9157
0.9510
0.9863
1.0214
1.0565
1.0915
1.1265
1.1614
1.1962
1.2310
1.2658
1.3005
1.3351
1.3697
1.4043
1.4388
1.4733
1.5077
1.542]
1.5765
1.6108
1.6451
1.6794
1.7136
1.7478
1.7820
1.8162
1.850]
1.8844
1.9184
1.9525
).9865
2.0205
w
!l
1.5
0."'"
0.4029
0,4397
0.4763
0.5128
0.5492
0.5853
0,6214
0.6573
0,6930
0.7286
0,764]
0, 7994
n K\47
0.0000
0.0024
0,0113
0.0264
0.0475
0.0738
o 1043
0.1378
0.1732
0,2096
0.2466
0.2838
0,3211
0.3583
0.3954
0.4323
0._
0.5055
0.5419
0.5780
0,6140
0.6498
0.6854
0.7209
0,7562
0,7914
IUC:I, I
lJ ,1>')\
t kl>I.1
0.on2
0.109]
0.1441
0.IS03
0.2172
0.2544
0.2917
0.3289
0.9048
09396
0.9744
1.0091
1.0437
1.0782
1.1126
1.1469
1.1811
1,2153
1.2494
1.2834
1.3173
1,3512
1,38SO
14187
\.4524
1.4860
1.5196
1.5531
1.5866
1,6200
1.6534
1.6867
].7200
1.7532
1.7864
L8195
1.8526
1.8857
1.9187
1.9517
1.9847
0.8961
0.9307
0.9652
0.9995
1.0338
1.0679
1.1019
I 1358
1.1696
1.20]3
1.2370
1.2705
1.3039
1,]373
1.]706
1.4038
1.4369
1.4699
1.5029
1.5358
1.5687
1,6015
1,6342
)
""
1.6995
1.7320
1.7645
1.7969
1,8293
1,8617
1.8940
1.9262
1.9584
1.6
1.7
0.0000
0.0024
0,0111
0.0258
0.0462
0.0716
0.1012
0.1338
0.1685
0.2045
0.2412
0.2783
0.3158
0.3528
0.3900
0,4270
0.4638
00000
0.0024
0.0110
0.0254
0,0452
0.0699
00986
0.1304
0.1645
0.2001
0.2366
0.27]5
0.3107
0.3480
0.3852
0.422]
0.4592
0,4959
0.5]23
0.5686
D."""
05368
0.5730
06090
06447
0,6803
0.7157
07509
0.7MO
OIQm
f) k~'
h
0.8902
0.9246
0.9589
0.9931
1.0271
1.0609
1.0947
1.1283
1.1619
1.1953
1,2286
1.2618
1.2949
1.3279
1.3608
1.3937
1.4264
1,4591
1.4916
1.5242
1.5566
1,5890
1.6212
1.6535
1.6856
1.7177
1.7498
1.7817
1,8136
1.8455
1,8773
1.9091
1.9408
1.8
1.9
2.0
2.2
0.0000
0.0024
0.0109
0.0250
0.0445
0.0586
0.0967
0.1279
0,1614
0.1966
0.2327
0,2695
0._
0.3439
0,3811
0.4182
0.4552
0,4920
0,5286
05649
06009
0,6367
0,6723
0.7076
0.7427
0, 7776
IUll 22
0.0000
0.0024
0.0108
0,0248
0.0440
0,0678
0.0955
0.1263
0. 1594
0.1942
0.2301
0,2667
0.3038
0,3410
0.3782
0.4154
0,4525
04893
0.5259
0.5623
0.5984
0.63-;2
0,6698
0.7051
0. 7402
1)'775 1
00000
0,0024
0.0108
0,0247
0.0436
0.0671
0.0944
0.1248
0,1576
0.1921
0.2278
0.264]
0.3012
0,]384
0.3757
0.4129
0,4SOO
0.""
0,5235
0.5599
0,5961
0.6320
0,6676
0.7029
0,7380
0.7728
O,XlI'J7
Okl'l7)
II
~n~
ill7
() KI(,7
!I X4_h!
) )0(-1 11,
tI
1'-
0.8851
0.9193
0.9533
0.9872
1.0209
1.0544
1.0878
1.1211
1.1542
1.1872
1,2200
1.2528
08809
0.9]50
0.9489
0.9825
1.0160
1.0494
1.0825
1.1155
1.1484
1.1811
1.2136
1.2460
1.278]
1.3105
1.3425
1.3744
1.4062
1,4]79
1.1.5009
1.5323
1.5635
1.5947
1.6257
1.6567
1.6876
1.7184
\.7491
1.7798
1.810]
1.8408
1.8712
1.9016
0.8782
0.9 121
0.9458
0.9793
1.0125
1.0456
1.0785
1.1112
1.1437
J.l761
1.2Q82
1.2403
1.2721
1.3038
U354
1.3668
1.3981
1.4292
1.4603
1.4912
1.52]9
1.5526
1.583]
1.6136
1.64]9
1.6741
1.7042
1.7343
1.7642
1.7940
1.8238
].8534
0.8756
0.9094
0.9429
0.9762
1.0093
1.0422
1.0748
1.1072
1.1394
1.1715
1.2033
1.2350
1.2665
1.2978
1.3290
U599
1.]908
1.4215
1,4520
1.4824
1,5]27
1.5428
1.5728
1.0027
1.6]24
1.6621
1.6916
1.7210
1.7503
1.7795
1.8086
1.8376
1.8664
0.~6
o"'"
0,6759
0,7113
0.7464
0,7K14
{) KIM
!I
) 2854
1.3179
1.3503
U825
1.4147
I_
1.4788
1.5106
1.5424
1.5741
1.6057
1.6]73
1.6687
1.7001
1".7314
1.7626
\.7937
1.8248
1.8558
1.8868
1.9176
•
I.Il8.3O
0.0000
00023
0.0107
0,0244
0.0430
0,0661
0.0930
01229
0.1552
0.1893
02246
0.2608
0.2976
0.3347
0.3719
0.4092
04459
04828
0.5196
0,5561
0.592]
0,6283
06639
06993
0.7343
0,7690
0.87\5
0.9050
0.9382
0.9712
1.0039
1.0]64
1.0685
1.1005
1.1321
1 1636
11948
1.2258
1.2566
1.2871
1,3175
1,3477
1.3n6
14074
1.4371
1.4665
14958
1.5249
].5538
1.5826
1.6112
1.6397
1.6681
1.6963
1.7244
i.7523
1.7801
] .8078
1.8354
2.4
00000
00023
00106
0.0242
0,0426
0.0654
0,0919
0.1215
o 1534
0. 1872
0.2223
0.25113
0.2949
0.3319
0,3692
04064
04436
04806
0,5174
0.5540
0.5903
06262
0,6619
0,6977
0,7323
0,7670
() XHU
d.~
1\.1
.869 1
.902S
.9355
.9684
1.0009
1.0331
1.0650
1.0967
1.1281
1 1592
1 1901
1.2207
1.2511
1.2812
1.3112
1.34()9
1.3704
1.3997
1.4288
14577
1.4865
1.5150
1.5436
1.5716
1.5996
1,6275
1,6552
1,6828
1.7102
1.7375
17646
1,7916
1.8184
2.6
2.8
3.0
0.0000
0.0023
0.0106
0,0240
O.O·U)
0.0648
0,0910
0.1203
0.1520
0.1855
0.2204
0,2562
0.2928
0.3297
0.3669
0,4042
0.4414
0,4785
0.5153
0.5519
05882
0,6242
0,6598
06952
07302
0.7649
II 7IN2
0,4395
0.4766
0.5135
0,5501
0.""
0,6224
0.6580
0,6934
0.7284
0,7630
(l 7974
0.0000
0.0023
0.0105
0.02J8
0.0418
0.0640
0.0897
0.1185
0.1496
0.1828
0.2174
0.2530
0.2895
0.3264
0.3635
0.4008
0,4360
0.4751
0.5120
0.""
05650
0.6210
0.""
0.6920
07270
0.7616
0.7959
" "II.'
OH.IJ.l
IIK!'I'J
0 ....
0.9002
0.9332
0._
0.9984
1.0305
H)623
1.0938
I 1250
11560
I 1867
1.2172
U474
12n4
1.3071
1.3367
1.3660
1.3951
1 4239
1.4526
14811
1._
1.5375
1,5655
1.5933
1.6209
1.6483
1.6756
1.7027
1.7297
1.7565
1.7832
1.8097
00000
00023
0.0105
0.0239
0.0420
0.0644
0.0903
0,1193
0.1507
0.1840
0.2187
0.2544
0.2909
0.3278
0.3650
0402.l
0.8650 0.8635
0.89S3 0.8968
0,9312 0.9297
0.9639 0.%23
0,9963 09946
1.0283 1.0266
I . _ 1.0583
1.0915 1,0697
U227 1.1208
1 1536 1.1517
I 1842 11823
UI46 1.2126
12447 1.2426
1.2746 Im4
1.30·'1 IJ020
1.3337 1.3]14
1.3629 1 3605
1.3919 IJ""
1.4207 1 4181
1.4493 1._
1.4n6 1.4748
1.5058 1.5029
1.5338 1.5308
1,5617 1.5585
] ,5893 l.S86t
1.6168 1.6134
1.644] 1.6406
1.6712 1.6677
1.6982 1.6945
1,7251 1.7212
1.75!8 1.7478
1.7783 1.7742
1.8047 1.8005
Table 7-2 (k)
Extended Sukkar-Comell Integral for Bottom-hole Pressure Calculation
P,
Reduced Temperalure for 8::0 50.0
0.20
0.50
1.00
150
2.00
2.50
300
3.50
400
450
500
5.50
6.00
6.50
7.00
7.50
8.00
850
900
9.50
10,00
10.50
11.00
II.SO
12,00
12,SO
IHO
1:\
w
w
0
~~l
14.00
14.SO
15,00
15.SO
16,00
16.50
17.00
17 .SO
18.00
18.SO
19.00
19,5O
2000
20.50
1.1
1.2
0.0000
0.0023
0.0000
0.0023
0,0121
0,0328
0,0649
0.0111
0.0276
0.0524
0.0835
0.1173
0.1521
0.1873
0.2226
0.2579
0.2933
0.3285
0.3638
0.3990
0.4341
0.4692
0.5042
0,5391
0.5739
0.0997
0.1350
0.1703
0.2057
0,2410
0.2763
0.3116
0,3469
0.3821
0.4173
0.4525
0.4876
0.5227
0,5577
0.S927
0,6277
0.6626
0.6974
0.7323
0,7670
0,S018
n,lnf>5
U
r.- I~
0.9059
0.9405
0.9751
IJYJ97
1.0442
1.0788
\ 1133
1.1477
\.1822
1 2167
1.2511
1.2855
1.3199
1.3542
21.00
21.SO
22,00
22.SO
23.00
13886
23.50
1.5602
24,00
24,50
1.5944
1.6287
1.6629
1.6972
1.7314
1.7656
1.1998
1.8340
1.8882
1.9024
1.9366
1.9107
2.0049
25.00
2S.50
26.00
26.50
27.00
27.50
28.00
28.50
29.00
29,SO
30.00
1,4229
1,4513
1.4916
1.5259
0.6087
0.6435
0.6181
0.7127
0.7473
0,7818
0,8163
n 1'<'111
0.8850
0.9193
0.9536
0.9878
1.0220
1.0561
1.0902
1.1243
1.1583
1.1923
1.2263
1.2602
1.2942
1.3280
1.3619
1.3957
1.4295
1.4633
1.4911
1.5308
1._
1.5983
1.6319
1.6656
1.6992
1.7329
1.7665
1.8001
1.8337
].8672
1.9008
1.9341
1.9678
1.3
1.4
1.S
1.6
1.7
1.8
1.9
2.0
2.2
2.4
2.6
2.8
3.0
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
00000
0,0022
0,0107
0,0:251
0.0474
0.0750
0.1066
0.1402
0.1749
0.2101
0,2454
0.2807
0.3161
0.3513
0.3865
0.4216
0.4567
0,4916
0,5264
0.5612
0.5959
0,6304
0.6649
0,0022
00104
0,0246
0.0447
0.0702
0.0998
0.1322
0.1660
0,2008
0,2359
0.2712
0.3066
0.3419
0.3772
0.4123
0,4474
04823
0.5171
0.5518
0,....
00000
0.0000
0,0022
00102
0.0022
0.0100
0.0233
0,0418
00610
0,0921
0.1222
0.1545
0.1882
0.2227
0.2577
0.2929
0,3282
0.3636
0,3989
0.4340
0.4690
0.0021
00000
0.0000
0.0021
0.0000
0.0021
0.0021
0.0021
0,0021
0.0021
0,0095
0,0216
0.0380
0.0583
0.0820
0.IOS5
0.1375
0.1683
0.2006
0.2339
0.2681
0.3029
0.3380
0.3733
0,6553
0.69'J.I
0.,""
0.7337
0,7680
o 1'022
0.1237
0.1578
II 7')17
n K;"t.
(I II 'In~
0.8704
0.9044
0.9384
0.9722
1.0061
1.0399
1.0736
1.1073
11409
1 1745
U081
U416
1,2151
1.308S
1.3419
1.3753
1._
1,4419
1.4752
I.1084
1.5416
1.5748
1.6079
1.6410
1.6741
1.1<r72
1.7403
1.1733
1.8063
1.8393
1.8722
1.9052
1.9381
0.6209
0.859-l
0.8930
0.9266
0.9601
0.9935
\.0269
\.0601
1,0933
I 1266
I 1595
1 1925
1 2254
1.2583
I 2911
1.3238
1,3565
1.3892
1,4218
1,4543
1,4868
1.5193
1,5517
1.5841
1.6164
1.6487
1.6809
1.7131
1.7453
1.1775
1.8096
1.8li16
1.8781
1.9057
0.0099
00098
0.0098
0"""
0.0096
0.0096
0.0021
0,0095
0.0226
0.0402
0.0622
0.01179
0.1l67
0.1477
0.1804
0.2143
0,2488
0.28]8
0.3190
0.3544
0.3897
0,4250
0,4601
0.4951
0,5299
0.5645
0.5990
0.6332
0,6672
0,7011
0.7347
0.on4
0.0398
0.0615
0.1l1168
0.1151
0.1457
0.1781
0.21\7
0.2461
0.2809
0.3161
0.]514
0.3868
0.4221
0.4573
0.4923
0.5271
0.5618
0.5962
0.6305
0,66J5
0.6984
0,7320
(I,7M4
0,0222
0,0395
0,0220
0.0389
0.0599
0.0844
0.1119
0.1417
0,1734
0,2063
0.2402
0.2747
0.3097
0.3450
0.3803
0,4151
0.4504
0,4855
0,5204
0,5552
0.5897
06240
0,6581
0.6919
0,0218
0.0385
0.0593
0.0835
0.1100
0,1401
0,1714
0.2040
0,2377
0.2721
0.3069
0.3421
0.3774
0,4128
0,4481
0.4832
0.5182
0.5530
0.5875
0,6219
0,6558
0,6897
0,12]2
00382
0.05R7
0.0827
0.1095
0.1387
0.1697
0,2022
0.2356
0.2700
0.3048
0.3399
0.3752
0,4105
0.4458
0.4810
0.5160
0.5508
0,5854
0,6197
0,6537
0.6815
II 1210
0.4395
0.4745
0.5093
0,5440
0.5786
0.6130
0.6413
0,6815
0,7155
0,7494
() 7K1~
0.5386
0,5732
0,6076
0,6418
0.6759
01099
0,7437
(17774
0,0229
0,0409
0.0634
0.0897
0.1191
0.1507
0,1839
0,2181
0,2529
0.2880
0,3233
0.]587
0.3940
0.4292
0.4643
0,4992
0,5340
0,5685
0.6029
0.6372
0,6712
0,7051
0,7JSR
0,7724
OI'lh'l
o II to'1
II
00238
0,0430
0,0670
0,0951
0.1261
0.1591
0.1933
0.2281
0.2632
0,2985
0.3339
0,3692
0_
0.8504
0.8839
0.9172
0.9504
0.9836
,0166
,0495
,0824
1151
1478
I'"
,2129
2453
2m
,3100
.3422
,3743
....
1.4385
1.4704
1,5024
1,5342
1.5660
1.5!n8
1.6295
1.6611
1.6927
1,7243
] ,7558
1.7872
1.8187
1.8500
1.8814
0.S039
0.8443
0.8776
0.9108
0.9438
0.9768
1.0096
1.0423
1.0749
1.1074
I 1398
I 1121
1,2044
1.2365
1.2686
1,3005
1,3324
1.3643
].3960
1,4277
1,4593
1.4908
1.5223
1.5537
1.5851
1,6164
1.6476
1.6788
1,7100
1.7410
1,7721
1,1\030
1834<>
1.8649
!«I~
0.8391
0.8722
0.9051
0.9379
0.9706
1.0031
1.0355
1,0678
1._
1 1320
1 1639
I 1957
1.2274
1.2590
1.2905
1,3219
1.3532
I,31W4
\.4155
1,4456
1,4775
1._
1.5392
1.5700
1.6006
1.6312
1.6617
1.6922
1,7226
1,7529
1.7831
1,8133
1.8435
•
O,7~S~
,
Ill'
0.8347
0.8576
0.9004
0,9331
0.9656
0,9979
1.0301
1.0621
1.0940
1.1258
1.1575
11890
1.2204
1.2517
12829
1.3140
1,3449
1.3158
1._
1.4372
1,4678
1.4983
1.5287
1.5590
1.5892
1.6194
1.6494
1.6194
1.7094
1.7392
1,7690
1 79117
1.S2S4
"
IS7
0,83 17
0,8645
0.8972
0.9297
0.9620
0,9'}41
1.0260
1.0578
1.0894
1.1209
1 1522
1 1834
12144
] .2453
1.2761
1,3067
1,3372
1.3676
1,3979
1,4280
1 4581
14880
1.5178
1.5476
1.5772
1.6068
1.6362
1.6656
1.6948
1,7240
!.7531
1.7821
1.8111
0.""'"
0.0858
0.1138
0.1440
0.1761
0.2094
0,2436
0,2784
0.3135
0.3488
0.3841
0.4194
0.4547
0,4897
0.5246
0.5593
0,5938
0,6280
0.6621
0,6959
0.7295
n,1K!Q
n
II
'hl/l
(1 nl '
0.8290
0.8617
0,8942
0.9265
0.9586
0.8245
0.8510
0.889]
0.9213
0.953\
0.9847
1.0160
1,0471
10779
0.9906
1.0223
1.0538
1.0852
1.1164
1.1474
1.1710
1.2090
1.2395
0.72~
1~K1
1 1086
11390
1 1693
I.199J
1.3001
1.3302
1.2292
1.2589
\,2RR4
1.3177
1.3602
1._
1.3900
1.4197
1.4493
1.4788
1.5081
1.5313
1.5664
1,5954
1,6243
1.6531
l.bRl8
1.7104
1.7]89
1,7673
1.7956
1,3758
1,4046
l.4333
1,4618
1.4902
15184
15465
1.5744
1.6022
1.6299
1,6574
\.6R49
1.7122
1.7394
1.7664
12699
(l1~M
n1~~
f) 1.~2,1
0,0021
0.0095
0.0215
0.0378
0.0579
0.0814
0.1078
0.1365
0.1671
0,1993
0.2326
0.2667
0.3014
0.3365
0.3718
0,4071
0.4424
O.4m
0.5127
0,5475
0.5821
0.6184
0.6505
0.6842
0.7177
0,7509
'I
n
(I ',~P
07/HIj
0,0217
71,7~
0_
0.4439
0.4791
0.5142
0,5490
0,5835
0.6179
0,6.519
0,6857
0.1192
11.822 1 0.8198 11.8178
0.8545 0,(\521
0.8502
0.8866 0.8842 0.8822
0.9!85 0,9160 0.9139
0,950 1 0.9475 0,9454
0.98 14 0.9788 0.9766
1.0125
1.0097 10075
1.0434
1.0405
1.0]82
1,0740 1.0709
10686
I 1043
1 1012
1,0988
1 1345
1 1287
I 1312
1 1644
1 1609
1 1'"
1 1941
1 1905 I 1878
1,2198 1 2171
1.2236
1,2489 1.2461
2528
1.2778 1.2749
2819
,31OS
1.306S
1.3035
1,33SO
.3395
1.3319
.J680
1.3633
1.3601
3....
1.3914
1.388\
4245
1.4193
1.4160
1,4471
,4525
1.4436
,4803
1,4747
1,4711
1,4984
.lOBO
1.5021
.5355
1.5294
1.5256
1,5629
1,5565
1.5526
] ,59t11
] ,5835
1.5794
1.6J72
1.6 \03
1.606 1
1.6441
1.63H9
1.6328
1.6709
1.6634
1.6590
1.6976
1.6R911
1.6!l53
\,7160 1 7114
1.7241
1.7505
1.7421
1.7373
0.8\8]
0,8486
0._
0.9123
0.9438
0.9749
1.0058
1.0364
10668
10969
I 1268
11,..
11858
\.2149
I 2439
1.2726
1.3011
1.3295
1.3576
1.3855
1.4iJ3
1.4408
1.4682
1.4954
1,5225
1.5494
1.5761
1.6027
1.6291
1.6553
1.6815
1.7075
1.7333
Table 7·2 (I)
Extended Sukkar-Cornell Integral for Bo"om-ho~ Pre.sure c.lculatlon
P,
1.1
1.2
1.3
1.4
00000
0.0019
0.0093
0.0232
0.0443
0,0115
0.1014
0.1325
0.1642
0.1962
0.2283
0.2606
0.2928
0.3251
0.3574
0.3896
0,4219
0,4541
0.4863
0.5185
0.5507
0,5828
0.6149
0.""
0,67W
0.7110
0,7429
00000
0,0019
0.0069
0.0215
0.0399
0,0631
0.0913
0.1211
0.1521
0.1837
0.2157
0.2479
0.2801
OJ124
0.""
0.3769
O,409J
0,4413
0.4735
0.5056
0,5377
05698
0.6018
0.6337
0,6656
0.697S
\) ,01)
0.0000
0.IX)l9
0,0101
O,02TI
0.0559
0.0870
0.1189
0.1509
0.1831
0.2153
0.2475
0,2798
OJ120
0.3443
0.3766
0.4066
0.4411
0,4734
0.5056
0.5378
0.5701
0,6023
0.6344
0.6666
0.6987
0,7309
11 76:\11
11 72'n
0.0000
0,0018
0.0067
00206
0,0316
0,0594
0.0851
0.\135
o 1435
0.1745
0.2062
0.2382
0.2703
0.3026
0.3348
0,)671
0.3m
0.4316
0,4637
0,4958
0,5279
0,5599
0.5718
0,6237
0,6555
0,6872
Q,7 IH'J
\3.<;0
tl '7'1<"\
n7'7-l1)
() 761 \
tl15H~
0.8068
0.8387
0.8705
0.9024
0.9342
0.7929
0,8246
0.8562
0.8879
0.9195
0.9510
0.9826
1.0141
1.0455
1.0769
I 1083
1.1397
1.1711
J.2o:!4
\.2337
1.2650
1.2962
1.3274
1.3586
1.3898
1.4210
1.4521
1.4832
1.5143
1.5454
1.5765
1.6075
1.6385
1.6695
1.7005
1.7315
1.7625
1.7934
0,7820
0.8i3S
0.8449
0.8763
0.9076
0.9389
0.9701
1.0012
1,0]23
1.0634
1.0944
1.1253
1 1562
1.1811
1,2179
1,2481
1.2795
1.3102
1.3409
1,3715
1.4021
1.4327
1,4632
1.4937
1.5242
1.5547
1.5851
1.6155
1.6459
1.6762
1.7065
1.7168
1.7671
0.20
O.SO
1.00
I.SO
2.00
2.SO
3.00
3.SO
4.00
4.SO
5.00
5.SO
6.00
6.SO
7.00
7.SO
8.00
8.SO
9.00
'.SO
10.00
IO.SO
11,00
II,SO
12.00
12 .50
14.00 0.8272
14.50 0,8592
15.00 0.8913
15.50 0.9233
16.00 0.9554
16.50 0.9874
17.00 1.0194
\1.50 1,0514
18.00 1.0834
18 ..50 1.1153
19.00 I 147)
19 ..50 1.1792
20.00 1.2112
2O.SO 1.2431
21.00 1.27.50
21.50 1.3069
22.00 1.3388
22.50 1.3707
23.00 1.4026
23.50 1.4344
24,00 1.4663
24.50 1.4982
25.00 1.5300
25.SO 1.5619
26.00 1.5937
26,50 1.6255
27.00 1.6574
27,SO 1.6892
28.00 1.7210
28.50 1.7528
29.00 1.7846
29.SO 1,8164
30.00 1.8482
O. ""'"
0.9977
1.0295
1.0612
1,(1929
1.1246
1.1562
1.1879
1.2195
1.2511
1.2827
1,3143
13458
1.3774
1.4089
1.1.4719
1.0534
1.5349
1.5664
1.5978
1.6292
1.6607
1.692\
1.7235
1.7549
1.7863
1.8177
1.5
Reduced Temperature for 8 - 60.0
1.6
1.7
1.S
1.9
2.0
0.0000 00000
0,oot8 00018
0.0065 00084
0.0200 0.0195
0,0361
0,0351
0.0566 0,0549
0.0808 0,0781
0.1079 0.1043
0.1369 0.1326
0,1672 0.1624
0,1984 0. 1931
0.2301
0.2245
0.2620 0.2563
0.2942 0._
0.3264 0.3206
0.3587 0.3529
0.3910 0,3&51
0.4232 0.4174
0.4554 0.4496
0,4875 0.4817
0.5195 0.5137
05515 0.5457
0.5833 0.5775
0,6151
0,6093
0"" {l6409
()67}15 06725
II 7w I
II 7(1.10
o 1~15 (1 ns~
0.0000
0.0018
00063
0.0192
0,0343
0.0535
0.0160
0.1014
0.1291
0,1583
0.1887
0.2198
0.2515
0.2834
0.3156
0.3478
0,3801
0.4123
0,4445
0.4767
0,5087
0,5407
05725
0,6042
0,6359
0,6674
0,7730
0,8043
0.8355
0,8667
0.8978
0.9288
0,9598
0,9907
1.0215
1.0523
1.0830
1.1137
1 1443
I 1748
1.2053
1.2357
1.2661
0.7613
0.7924
0,8233
0,8542
0.8850
0.9156
0.9462
0.9767
1.(mO
1.0373
1.0675
1.0976
I 1277
I 1576
I 1875
1.217)
1.2470
1.2166
1.3062
1.3357
1.3652
1.39.15
\.4238
1.453\
1.4823
1.5114
1.5405
1.5695
1.5985
1.6274
1.6563
1.6851
1.7139
12964
1.3267
1.3569
U871
1.4173
1,4474
1.4774
1,5075
1,5374
1,5674
1.5973
1.6272
1.6570
1.6868
1.7166
1.7463
0.7667
0.7979
0,8291
0.8601
0.8911
0.9219
0.9527
0.9835
1.0J41
1.0447
1.0752
I 1056
"360
1 1663
"965
1,2267
1.2568
1.2869
1.3169
1.3469
1.3768
1.\.4364
\.4662
1.4959
1.5255
1.5552
1.5847
1.6143
1.6438
1.6732
1.7026
1.7320
0.0000
0.0018
0.0062
0,0189
0.0338
0.0524
0.0745
0.0993
0.1263
0.1551
0.1850
0.2158
0.2472
0.2791
OJJl I
0.3433
0.3756
0.4079
0.4401
0.4722
0,5043
0.5363
0.5581
0.51)98
0,6314
1)11629
0.0000 00000
0.0018 0.0018
0'<X)81
0.0081
0.0188 0,0186
0.0334 0,0331
0.0518 0.0512
0.0734 0.0726
0.0979 0.0966
0,1245 0,1229
0.1529 0.1510
0.1826 0.1804
0.2132 0.2108
0.2444 0.2419
0,2761
0,2735
0.3081
0,3054
0.3403 0,3375
0.3725 0.3697
0,4048 0.402Q
0,5370 0,4343
0,4692 0,4665
0.5013 0,4985
0.5333 0.5305
0,5651
0,5624
0,5988 0.5942
0.6284 0,6257
0,f>S99 0,6571
2.2
2.4
00000
00018
00060
0.0184
0.0326
0.0504
0,0714
0.0950
0.1209
0.1485
0.1775
0,2075
02383
0.2697
0.3015
0.3336
0,3651
0,3976
0.4297
0,4619
0,4940
0,5260
0.5579
0,5896
0,62J2
n 6526
I),MH
00000
0,0018
00060
0.0183
00323
0.0499
0.0705
0.0989
0, I 194
01466
0.1783
0.2051
0.2357
0.2670
0,2986
0,1306
0.3628
0.3951
0,4273
04596
0,4917
0,5237
0,5556
0.Sln3
0,6189
0 6503
f) (''»1('
f) ,6'N J
() (fi 12
U~
f) 7~W
O.n'
II.
"
1171'Jf>
t
0.1505
0.71m
0.8120
0.8425
0.8728
0.9030
0.9331
0.9630
0,9928
1.0224
1.0519
1.0812
1.1104
1 1395
1.1685
1.1974
1.2261
1.2547
1.2832
1.3116
1.3399
1.3681
\,3962
1.4242
1.4521
1.4799
1,5076
1.5353
1.5628
1.5903
1.6176
1.6449
1.6722
0.7457
0.7764
0.8069
0.8371
0.8612
0.8971
0.9269
•
0.7566
0.7876
0.8184
0.8492
0.8798
0.9103
0.9408
0.9711
1.0013
1.0313
1.0613
1.0912
1 1210
1 1507
1 1803
1.2099
1.2393
1.2667
1.2979
1.3271
1.3563
1.3833
\.4143
1.4432
1.4721
1.5008
1.5295
1.5582
\.5868
1.6153
1.6438
1.6722
1.7005
0.7534
0,7843
0.8151
0.8451
0.8762
0.9065
0.9368
0.9668
0.9968
1,0267
1.0564
10860
I 1155
1.1419
1 1741
1.2033
1.2324
1.2614
l.2902
1.3190
1.3477
1.3763
1.4048
1.4332
1..1616
1.4898
1.5180
1.5461
1,5742
1.6021
1.6300
1.6579
1.6856
'q'l
0.9~64
0.9!!58
1.0150
1.1).140
1.0728
I 1015
1 1301
I 1584
I 1867
12147
12.127
1,2705
1,2981
1.3256
l.J530
1.)803
1.4014
1.4344
1,4613
1.4R81
1,5148
1.5413
1.5678
1,5941
1.6204
1.6465
')M I ~
"
'I.'~
~
~
~
2.6
2.S
0.0000 0.0000
0.0017 0.0011
0.0060 0,0079
0.0181
0,0181
0,0321
0,0319
0.0494 0.0490
0.0698 0.0692
0.0928 0,0920
0,1181
0.1170
0,1451
0.1438
0.1736 0.1721
0.2032 0,2016
0.2337 0.2320
0,2648 0.2630
0._
0.2946
0.3284 0.3265
0.3605 0.3586
03928 0.3909
0.4251
0,4231
0,457) 0.4554
0,4894 04875
0,5215 0.5196
0.5534 0.5515
0,5851
0.5832
0,6166 0,6148
U,MIIO
0,6461
(t oM (t,(,77J
" 71ft I /I 7(1.12
3.0
0.0000
0.0017
0.0079
00180
0.0311
0.0487
O.OW
0.0913
0.1161
0.1428
0.1709
0.2003
0.2306
0.2616
0.2932
0.3251
0.35n
03894
0.4211
0.4539
0.4861
0.5181
0.5500
0,5818
0.6133
0,6446
0,6758
0,7()67
0.7482 0,7409 0.1389 0.1374
0.7738 0.17\4 0.1694 0,761'1
0.8042 0.8011 0.7991 0,7982
0.8343 0.8318 0.8298 0,8282
0.8643 0,8617 08596 0.8580
0.8940 0.8914 0.8892 0.8876
0.9236 0.9208 0.9186 0.9170
0.9529 0.9501
0.9478 0.9461
0.9820 0.9791
0.9768 0.9751
10110 1.0080
10056 1.0038
1.0398 1.0:\66 1.0342 1.032~
1.0683
1.0626 \.0607
1.0651
1,0967
1,0933
1.0908 1.0889
I 1214
1 1250
1.1188 1 1168
I 1530 I 1493 1.1466
"800 I 1770 1 \143 1 1721
1.2086 1.2046 1,2018 "995
\.2319 1.2291 1.2268
1.2361
1,2592
1,2562 1.2538
1.2635
1.2908
12862 \,2832 1.2807
1.3179 1.3131
1,3100 1.3074
1.34.18
1,3366 1.3340
1J399
1.3716
1.3664
1.3631 1.3604
1.3983
1,3895 1,3867
1.3929
1.4248
1.4192
1.4157 1.4128
1.4512
1.4454
1.4417 1.4388
1.4775
1.4714
1.4617 1.4646
1.50J6
1.4973
1.4935 1..1903
1.5296
1.5231
1.5191 1.5159
1.5555
1.5407
1.5447 1.5413
1.5813
1.5742
1.5701 1.5666
1,5997
1.6070
1.5954 1.5918
1.6325
1,62~9
1.6205 1,6168
,,4<6
Table 7-2 (m)
Extended Sukkar-Comellintegral for Bottem-hole Pressure Calculation
P,
020
OSO
100
I.SO
200
2.SO
)00
).SO
4.00
4.SO
'00
'.SO
600
6SO
7.00
7.SO
.00
8SO
9.00
9.SO
10.00
10.50
11 .00
II.SO
12.00
IBO
13 nn
\) su
/4.00
/4 ..<;(1
Reduced Temperature for B - 70.0
1.6
1.7
1.8
2.0
1.'
1.1
1.2
1.3
1.'
1.5
0.0000
0.0000
00000
0.0000
0.0000
0.0017
0.0000
0.0000
0.0016
o00I<l
0.0199
0.03&5
0.0016
0,0016
0,0074
00000
0.0000
0.0016
OJID3
O.01n
0.0312
0.0490
0.0703
0,0943
0.1202
0.1475
0.1756
0.2045
0.2337
0.2632
0.0000
00015
00071
0.0165
0,0296
0.0462
O.(XlIS
0,0070
0,0163
0,0291
00453
0.0015
0,0070
0.0161
0,0288
0.0015
0,0070
0,0160
0,0285
0,0443
00660
0.08S4
0._
0.11864
0.1129
0,1391
0.1664
0.1946
0.2233
0,2525
06()t}4
0.1104
0,1360
0.1629
0.1907
0.2192
0.2482
0,2775
0.3071
0.3368
0,3667
0.3965
0.4264
0.4563
0,4861
0.5159
0.5456
0.5752
0,,047
0.3337
0,36)5
0.3934
0.4233
0.4531
0.4830
0.5127
0.5424
0.5721
0.6016
0.~987
0 . 650~
0.0015
0.0072
0.0168
0.0303
0.0475
0.0679
0,0910
0.1162
0.1429
0.1706
0.1991
0.2281
0.2574
0.2870
0.3167
0.3465
0.3764
0.4063
0,4362
0.4660
0.4958
0.5256
0.5553
0.5850
0.6146
00442
O.hJ.~1j
1l(,.~~2
Hf.:!I'('
/l (,i_
o (,:" ,1~
IJ(, ' '1~
o fl.']]
I l l>hH.l
I ! (,t'.~I,
n (, '>4 1--1
II ('5'<;
,,~~
0.7093
0.7388
0.7682
0.7976
0.8269
0,8662
1.0S86
1.Il1<08
I 1175
I 1463
1 1751
1.2039
1.2326
1.2613
1.2899
1.3185
1.3471
1.3757
1.4042
1.4327
1.461l
1.4895
1.5179
1,5463
1,5747
1,6030
1.6313
1.1095
1.1381
1.1667
1.1953
1.2238
1.2522
1,2807
1.309Il
1.3374
1.3657
1.3940
1.4222
1.4504
1.4786
1.5067
1.5341:1
1,5629
1.5909
1.61 89
06977
0.7270
0.7562
0.7854
0.8145
0.8435
0.8724
0.9013
0.9.'100
0.95118
0.91174
1.0160
10445
1.07.10
1.1014
I 1297
1 15SO
1 1862
1,2144
1,2425
1,2706
1.2986
1.3265
06929
0.7222
0,7513
0,7804
0.9 146
0.9437
0.9728
10018
1.0308
1.0597
0.7031
0.7325
0.7619
0.7911
0.8203
0,8495
0,8786
0.9076
0.9366
0.9656
0.9945
1.0233
1.0521
0.6897
0.7189
0.7479
0.n69
0.S058
0.8345
0.8632
0,8918
0.9203
0.9486
0.9769
1,0051
1.0332
Ul612
1.0892
1 1170
1 1448
I 1724
1.2000
1.2276
1,2550
1.2824
1.3097
1.3369
1.3641
1.3912
1.4182
0.6867
0.7158
0.7448
0.7737
0.8025
0.8311
0.11597
0.R881
0.9164
0.9446
0.9727
I.()OO7
1.0286
1.0564
1.11841
I 1116
I 1391
I 1665
I 1938
1.2210
1.2482
1.2752
1.3022
1.3290
1.3M8
1.3625
1.4092
0l1li87
0.024(1
o,om
oom
00625
0,1063
0,1356
0.1651
0.1947
0,2243
0.2540
0.2838
0.3135
0.3433
0.3732
0,4030
0.4328
0.4627
0,4926
0.5225
0.5523
0.5822
0.6121
0.6420
0.6718
1l.7n17
0.0894
0.1175
0.1464
0. 1756
0.2050
0.2347
0.2644
0.2941
0.3239
0.3538
0.4135
0.4434
0.4733
0.5031
0.5330
0.5629
0.5927
0.6226
0.6524
O.6X22
11. 'It.
n .711\
{/7615
079/3
0,8112
0,8510
0.7419
0.7717
0.S014
0.8312
/5.00
15.50
/6.00 08809
/6.50 0.9107
17.00 0 _
17.50 0._
18.00 1,()(]()2
18.SO 1.0300
19,00 1,0599
19.5O 1.0897
20.00 1.1195
20.50 1.1493
21.00 I 1791
21.50 L2089
22.00 1.2387
22.SO 1.2685
23.00 1.2982
23.SO 1.3280
24.00 1,3578
24.50 1,)876
25.00 I 4173
25.SO 1.4471
26.00 1.4769
26.50 1.5066
27.00 1.5364
27.50 1.5661
28.00 1.5959
28.SO 1.6256
29.00 1. 6554
29.SO 1.68SJ
3000 1.7148
• After M......
,~
0.3836
0.8609
0.8907
0,9204
0.9501
0.9798
1.0095
1.0392
1.0689
1.0985
1.1282
1.1578
1.1874
1.2170
1.2466
1,2762
1.3058
1.3354
1.3650
1.3946
1.4241
1.4537
1.4832
1.5127
1.5423
1.5718
1.6013
1.6308
1.6603
1.6898
a!.
(197~);
0.0077
0.0185
0.0345
0,0554
00799
0.1066
0,1346
0.1634
0.1926
0,2221
0.2517
0.28 15
0,31lJ
0.3411
0,3710
oom
()M9~
0.0325
0.0515
0.0742
0,0994
0, 1264
0.1545
0,1833
0,2125
0.2420
0.2716
03014
0.3312
0,3611
0.3909
04208
0,4507
0.4805
0.5 104
0.5402
0.5700
0.5997
0.6294
JU,Wl
<I t.'N \
41 1>1<)(7
o.nl!!!
0,7183
0.7479
0,m4
0.8069
0.8363
0,8658
0.895 1
0.9245
0.9538
0.9831
1,0123
0.4009
0.4307
0._
0,4905
0.5203
0.5502
0.5800
0,6098
06396
0,7585
0.7MI
0.8178
0,8474
0.8170
09066
0.9362
09657
0.9953
1 0248
1.0543
1.0837
I 1132
I 1426
1 1721
1.2015
1.2309
1 2602
12896
1.3190
1.3483
1.3716
1.4069
1.4362
14655
1.4948
1,5240
1.5533
1.5825
1.6117
1.6410
1.6702
I.o·m
1.0707
I Il999
1 1290
1 15tU
1 l!m
1.21(>2
1.2452
1.2742
1.3031
1,3321
1.3610
13899
1.4187
1.4476
1.4764
1.5052
1.5340
1.5627
1.5915
1.6m
1.6489
0.2929
0.3226
0,3525
0.3824
0,4 122
0.4421
0.4720
0.5018
0.5316
0.5613
0.5910
0.6207
0.8854
02820
0.3116
03414
0.3713
0,4011
0,4310
04609
0,4907
0.5204
0.5502
0.5798
1.3~~4
1.31123
1.4[01
1.4379
1.4656
1.4933
1.5209
1.54/15
1.5761
1.6036
C'Olltleoy of'iI'E (39131.
•
0.809~
0.8.363
0.867 1
0,8958
0.9245
0.9530
0.98 15
10099
1.0383
1.0665
UJ947
1 1229
1 1509
1 1789
12069
1.2347
1,2625
1.2903
1.3180
1.3456
1.3732
1.4007
1.4282
0."""
0.0637
0.0851
0.1087
0.[340
0.1606
0.1881
0.2164
0.2453
0.2745
0 ....
011629
0.0840
0,1073
0,1322
0.1585
0.11159
0,2140
0.2427
02718
0.3013
0.3309
0,3607
0.3905
0,4204
0.4503
0,41\01
0.5099
0.5396
0,5692
1.45~6
1.44~2
1.43~7
1.4829
1.5 102
1.5375
1.5547
1.5919
14721
1.4989
1,5257
1,5524
1,5791
14622
1.4!1R6
1.51SO
1.5412
1.5675
~
~
•
2.2
2.'
O.!XKXl
0,0015
00000
0.0015
00069
0.0069
00158
0.0281
00435
0.0618
0,0157
00278
0,0431
0,0611
0.0815
0.1040
0.1282
0.1538
O. [805
0.2081
0.2363
0.2652
0,2944
0,3239
0.3536
0.3834
04133
0.4432
0.4730
0.5028
0.5325
0.5621
0.5916
0.1029
01268
0.1522
O. [787
0.2061
0.2343
0.2630
02922
0.3217
0.3514
0.3812
0.4110
04409
0.4708
0.5005
0.5J03
0.5599
0,5893
0,3198
0.3495
0.3793
0.4092
0.4390
0.4689
0,4987
0.5284
0.5580
0 ,5875
0.~S60
II f.2lfl
O('IIH
II f.IOX
0.(,(54
"
f)'W N
/l1>-llli'
1If>.j·t 'i
001<25
0.1054
0.1299
o 1558
0.1827
0.2106
0,2390
0,2680
02973
0.3262
0.3560
0.3858
0.4157
0.4456
0.4754
0.5052
05349
05645
O.W40
0.611\8
0.7\08
0,7397
0.7684
0.7969
0.8254
0.8537
0,8818
o 909f!
0.9317
0.96~4
0.99:\0
1.02Jl4
\.0·n8
1.0749
I 1020
1 1289
I 15~1I
I 11125
12fl1X1
1 2,155
1.2619
1,28111
1.3142
1.)403
1.3662
1.392U
141711
14414
146'10
1 ~9~4
I 511,111
I 54'iO
2.6
2.8
3.0
0.0000
0.0000
00000
0.0015
00015
O.OOIS
00068
00068
0.0068
00156
00276
0.0426
00155
0.0274
0,0423
0,0599
0,01.'>4
0.0273
0.0420
0.""'"
0.0806
0,6793
n.7062
0.7370
0,7656
0.7941
0.8224
0.85U5
0,8765
0.6170
0.7059
0,7346
0,7632
0,7916
0.8198
0.8479
0.......
09036
0.9311
0.951\6
0.98511
1.0129
I.OW!!
LOM6
10933
I 1198
I 1461
I 1723
I 1984
12243
1,2501
1,27511
1 .'\\JI3
1,]267
1.3520
1.3772
1.402]
14272
1.4520
I 47611
L.5()J4
1.5259
0.9340
0%15
0.9&\9
1,0181
1,{)432
J.()701
IO%S
1 1235
1 I~no
1 1763
1.2{126
1.2287
1,2546
1,2805
1,31162
J.3318
1.3573
1.3827
1.4079
1.4331
1.4581
1.4831
1.5079
15327
'un~8
0-0198
01018
0.1256
O.ISOB
0,1772
0.2045
0.2326
0.2613
0.29(1.1
0."'"
0.1)792
0,1010
0.1246
0,1497
0.1760
0.2032
0.2313
0.2599
0,2890
0,)184
0.3481
0.3779
0.,""
0.4376
04675
0,4972
0.5270
05566
1l.67~1
11.67'.0
0.70~'1
0.1n2~
0,7326
0.7612
0,7898
0.8178
0.1\4511
011737
() 9()14
0.9289
0 .9563
0.73\\
0.7597
0.7AAO
0,8162
0.8442
O.fl721
0.11997
0,9272
09545
0.9!U7
I'{KlS7
0,98~5
1.0105
1,0374
10641
10907
I 1171
1 14.14
I 1(1)5
I 1955
122]4
1.2471
1 2727
129111
1.\n~5
1,0622
l.fm!l7
1 1151
1 1413
I 1674
1 193)
1.2191
1,2447
1.2702
1.29~
J.)23~
U2Q9
I 34117
I.H3R
L39117
142:\<\
1.44113
1.4729
1.4974
15218
1,3460
1,3710
1.3759
1.4206
1,4452
1,4698
1,4942
1,5165
page number wise bole to 157/326
336
Cas Production Engineering
Steady Stale Flow of Ga,'l Through Pipe$
(tt'%t continl/ed from page 309)
337
~ _ 4251663 - 0.641. T" - (580)/387 - 1.499
From Figure 3-2, Z., - 0.967
p,.
G - (0.17584 - 0.002628)
+ (1.08235 - 0.01474B) T"
- (0.SI075 - 0.00771B)
(7·53)
For 2O:s 8.:5100, 10.:5 Pp.s30, 1.1 sTp,s3,
Using Equation 7-46, p ... - 400 eO 234012 - 449.65 psia
E - (0.297336 - O.001594B) T'~ + (O.OO967SB - 1664290) T"
- (O.ool963B - 0.42964S)
F - (0.019112 - O.oool7lB)"fl,
- (0.001259B - 0.188162)
U,ing Equation 7-47. , - (0.0375)(0.7)(5.000)/[(0.967)(580)1 - 0.23402
A second trial is not needed.
(b) Sukkar-Cornell method:
+ (0.000941B - 0.107041) T"
P 'wh - 400/663 - 0.603. T,.. h
G - (0.001435B - 0.212139)"fl, + (0.000941B - 0.107041) T"
+ (O.OO6320B - 1003890)
(7-54)
This method is simple and quite accurate: Equations 7-53 and 7-54 give
errors of less than 2% in the parameter ranges associated with them. No
trial and error is involved, which simplifies the calculation procedure conSiderably. For these reasons, the Sukkar-Cornell method is widely used.
E%ampk 7·2. Determine the SBHP in a gas well, given the following:
Depth, z - 5,000 ft; gas gravity, 'YK - 0.70; wellhead temperature.
T ... II - BOoF; bottom-hole temperature, T ....... 160°F; wellhead pressure.
p...b - 400 psia.
Use (8) average temperature and Z-factor method, and (b) Sukkar-Cornell method.
-
(80 + 460)/387 - 1.395
From Table 7-2a, by interpolation
0.,,"
1
(Z/p,)dp, - 10392
0.'
Using Equation 7-51.
1'''"
I. . .· (Z/p,)dp, 0.2
Thus,
1. . . (Z/P,)dp, 0.'
T,~ ~ (160
(Z/p,)dp, _ (0.0IS75)!7)(5.ooo)
0.2
1.0392
+ 0.11315 - 1.15235
+ 460)/387 - 1.602
Solution
From Table 7-2a:
T" - (SO + 160)/2 - 120"F _ 58O"R
From Figure 3-1, ?pc - 663 psia, T pc
=
0.6
387° R
10.'(Z/p,)dp, -
1.049
07
(a) Average temperature and Z-factor method:
1 (Z/p,)dp, -
First trial:
By interpolation,
Using Equation 7-48, p.... - 400 + 0.25(400/100)(5,0001100) _ 450 psia
p,~ - 0.6
Thus. pO' - (400 + 450)/2 - 425
pm-
0.'
1.210
+ (1.15235 - 1.049)(0.7 -
0.6)/(1.210 - 1.049) - 0.6642
Thus. p,., _ (0.6642)(663) - 440.36 psia
•
338
COl
Steady Slale Flow oj Gas Through Pipes
Product/orl Engineering
339
I"""' 1,000 -TZp d p = -21 [(P, - Po)(1, + 10) + (p, - p,)(I, + I ,) + ."
Cullender-Smith Method
Cullender and Smith (1956) used a more rigorous approach, accounting
the dependence,of Z-factor on both temperature and pressure. Takin~
~or
mto account the umts used by Cullender and Smith, Equation j·42 is rear-
ranged as follows:
I""
(PITZ)'(TZ. p) dp
.... (pITZ)'I(I,OOO) + (6.7393 x lO")(4)(fl4)<&L1(I,OOOzd')
where In _ 1,OOO(TZ/p)II' Greater accuracy in SBHP calculation can be obtained using more steps, requiring the use of a computer. For manual calculations, a tv.'o-step procedure is generally used, where only the value of pressure at the midpoint. Pnu is considered:
p.,
1
- (1,000)(0.01875»"
1000 TZ dp = (p~ - p..h)(l~ + l. h) + (P" - p",.)(I .. + 1=) (7-60)
p"t,'
P
2
2
0',
P.'
(P/TZ)dp
1p., "2'.69"5"7C:x;-U1O""'("'f1"4)~q;,~'L~/'i!:m~
( ')-'+-(P=/TZ=)'"/l;-,000= -
Substituting for the integral from Equation 7-00 into Equation 7-56:
18.75
>.'
(7-55)
Equation 7-55 is generally expressed as:
I"",.. F' + (p/TZ)dp
(pITZ)'/l,OOO - 18.75 >"z
Equation 7-61 can be separated into two parts, one for each half of the flow
string. For the upper half:
(7-56)
and, for the lower half:
where
F' _ 2.6957 x 1O·(f/4)q1.L
,d'
p/(TZ)
F' + (P/TZ)'/l,OOO
•
(7-63)
(7-57)
The expression in the left integral in Equation 7-56 is represented by 1:
1_
(7-62)
(7-58)
As demonstrated by Cui lender and Smith (1956), an accuracy equivalent to
a four-step solution scheme can be obtained by using this two-step calcula.
tion scheme and then using Simpson's rule (also called parabolic interpolation) to obtain a more accurate value of bottom-hole pressure as follows :
p...;
P..-h II...... + 4ImI + 1,....] - 37.5 ..,.~
(7-64)
For the case of SBHP determination, I reduces to:
1 - 1,000 (TZ/p)
(7-59)
The left integral in Equation 7-56 can be evaluated by numerical integration techniques. This is tedious, and acceptable accuracy can generally be
obtained using trapezoidal or Simpson's rule·. For the static case, the inte..
gral in Equation 7-56 can be written as:
• For y - f(I), y, - f(1J:
Trapezoidal rule:
fIx) cb
n
&
(h/2}(yn + 2)', + 2n + ... + 2y. _I + yJ
Sim pson's rule (more accurate than the trapewidal rule): J~ f(l) cb ,. (h/3)(yo + 4)",
+ .2YI + 4YJ + .. + 2Yo_1 + 4yo_' + yJ, forevt"ll n.
The following solution procedure may be used:
L Calculate 1....11 (using the general relationship given by Equation 7-59)
at the known wellhead conditions of pressure and temperature.
2. Calculate Ptru from Equation 7·62, assuming Ims - I ....h •
3. Using the value of Pm.. and temperature T ..... (obtained as the arithmetic average of T ...... and T ....), calculate Ims using Equation 7-59 .
4. Recalculate Pms from Equation 7-62 .
5. If this recalculated value is not within 1 psi (or any other small pressure tolerance) of the p"" calculated earlier. repeat stem :l anrl 4 until
this condition is met .
340
Gas Production Engineering
Steady State Flow of Gas Through Pipes
6. Calculate Pw. from Equation 7-63, a.ssuming I....... Izns.
7. Using the value of p...... and the bottom-hole temperature T ... ., calcu_
late I.... using Equation 7-59.
8. Recalculate p..... from Equation 7-63.
9. If this recalculated value is not within 1 psi (or any other small pressure tolerance) of the p., calculated earlier. repeat steps 7 and 8 until
this condition is met.
10. Use Equation 7-64 (Simpson's rule) to obtain a more accurate valuE'
('Of the bottom-hole presstrn' P".,
Exampk 7-3. Repeat Example 7-2 using the Cullender-Smith method
p., _ 425.61
341
+ (37.5)(0.7)(2,500)/(1,306.61 + 1,306.61) - 450.72 psi.
p.... _ 450.721663 - 0.68, T ...., - 620/387 - 1.602, and
z.... = 0.95
Using Equation 7.59, I., - (I,OOO)(620)(0.95)/(4SO.72) - 1,306.798
Thus, p..., ,. 450.72 psia
Using Simpson's rule (Equation 7&1):
[(p., - 4(0) /3][1,255.5 + 4(1.306.61) + 1,306.798J - (37.5)(0.7)(5,000)
Solution
or, p.... ,. 450.55 psia
For the upper half:
Flowing Bottom-Hole Pressure (FBHP)
Equation 7-42 describes the relationship between the pressure measured
at the surface (or wellhead), P"h, and the pressure Pwf at a depth z for a
flowing well:
P'wh - 400/663 - 0.603, T'wh - 540/387 ~ 1.395
From Figure 3-2, Z., ,., 0.93
Using Equation 7·59,
I., - (1,000)(540)(0.93)/(400) -
1,255.5
Using Equation 7-62,
Thus, PIN - 426.14 psia
z... - 0.96
Using Equation 7·59, 1_ - (1,000)(580)(0.96)/(426. 14) - 1,306.61
Using Equation 7-62,
p~ - 400
I
•
For nowing wells, the temperature-depth relationship presented by Lesem
et aI. (1957) or by Ramey (1962) may be useful for greater accuracy. In most
cases, however, the log-mean (or even the arithmetic average) temperature
gives satisfactory results.
(p= - 4(0)(1,255.5 + 1,255.5) - (37.5)(0.7)(5,000)/2
p,_ - 426.14/663 - 0.643, T,_ ~ 580/387 - 1,499, and
_ 0.01875
I, 1 + (6.7393 x (ZT/p)dp
1O-<fLql.Z'T')/(zp'd')
Yi'-
Average Temperotun! and Z.Foctor Method
An average Z-factor (and temperature) is used, similar to the static case,
to simplify the left integral in Equation 7-42:
+ (37.5)(0.7)(2,500)/(1,306.61 + 1,255.5) - 425.61 psia
Thus, PI"IIlI - 425.61 psia, and lIDS - 1,306.61
For the lower half:
Assuming IWI - I .... - 1,306.61, and using Equation 7-63,
I....
p,.,
p dp
pi + 6.7393 x 10-~fL(~.,T.,,)!/(zdS)
_ 0.01875-,0"
Z.,T. v
(7·65)
342
Steady State Flow oj Gas Through
CO" Production Engillcering
The integral of a function
343
Pip~
Solution
pdp .!In (C'+p')
1C'+p'
2
U,ing Equation 7-9, N" • (20)(7,000)(0.6)/((0.017)(3)) - 1.647
X
10'
lid - 0.000613 .. 0.0002
Therefore, Equation 7-65 becomes:
In
c:
From Figure 7.1, f - 0.014
+ ~'" • 0.0375Oy,z
C- .,.. p;.h
From Figure 3-1,
Z., T.,
~ =
672 psia, Tp<';' 358°R
The log-mean temperature, To.. " (ISO - 95)lln (ISO/95)
_ 580.41°R, using Equation 7·27.
0',
=
120.4PF
T" ~ (580.41)/358 - 1.621
where s .. (O.0375'Ygz)I(Z.. T .,). as given by Equation 7-47.
First trial:
Solving for p.. /:
Assuming P...f " 2,400 psia, and using Equation 7-32,
par •
C'(e' - I) +
Po.· (213)((2,400' - 2,000')/(2,400' - 2,000')] ~ 2,206.06 ",ia
..p;.
p" ~ 2,206.06/672 -
Substituting (or C:
...
.....
......1 - '" .,..b
6.7393
3.283
•
X
From Figure 3·2, Zn - 0.828
10 'fL(q.,Z••T,,)'(e' - I)
+ ---''-----''-'--=~=="-'''-----'.L
zd'
U~ng
0',
Equation 7-47,, · (0.0375)(0.6)(3,500)/((0.828)(580.41)).0.16386
Using Equation 7-66:
P<r • ..p;. + 2.5272 X
1O-'y.z••T"fL(e' - I)q!,
>d'
(7-66)
This method, applicable for wells up to 8,000 (t deep, should not be used if
the change in kinetic energy is significant (young, 1967).
P<r -
+ (2.5272 x 1O -')(0.6)(0828)(:;~~(~~:)(5,ooo)(.,o,... - 1)(7,000)'
P...·f
Example 7·<#. A 3.500-fl deep well is producing a 0.6 gravity gas at 7
MMscfd through a 3-in. I.D, tubing. The flowing wellhead temperature
and pressure are 95°F and 2,000 psia, respectively. BHT .. 150°F, tubing
roughness, f .. 0.0006 in., and Pox .. 0.017 cp (assume constant). The well is
deviated, with tubing length equal to 5,000 ft. Estimate the flowing bot.
tom-hole pressure.
(2,000)'.,0 '''''
-
2,196.4 psia
Second trial:
A$uming P.i. 2,196 ",ia, p" • (2/3)((2,196' - 2,000')1
(2,196' - 2,000'))
.. 2,099.51 psia.
3«
Steady State Flow oj Ga;! Through Pipes
Gas Production Engineering
p,. - 2,099.511672 - 3.124
B
345
_ (6.6663 x 10-')(0.014)(5,000)(7,000)'(582.5)' _ 2.02 ~ 2.0
(3,500)(672)'(3)'
From Figure 3-2, Z..... 0.830
p..... _ 2,0001672 - 2.976 ~ 3.0
Us;ng Equation 7-47, s - (0.0375)(0.6)(3,500)1[(0.83O)(58O.41)J _ 0.16347
T,•., - (95
Using Equation 7-66:
+ 460)1358 - 1.55. T,"" - (150 + 460)1358 - 1.70
30
Interpolating from Tables 7-2a and 7-2b, the integral
pi.; - (2,000),'" "'"
+ (2.5272 x 10-')(0.6)(0.830)(580.41)(0.014)(5,000)('" '0'" - 1)(7,000)'
(0.16347)(3)'
p....f .. 2,196.0 psia, which is quite close to the earlier result of 2,196.4 psia.
Thus, P... r - 2,196.0 psia.
Sukkar-Comell Method
This method uses an average temperature, but accounts for the pressuredependence of the Z-factor. Equation 7-49 stated earlier in the section on
SBHP
~
I""
P,.t
used,
1 1-1.6886
02
Using Equation 7-49,
1....1 - I'
0.2
0.2
I - (0.01875)(0.6)(3,500)1582.5
JP"""I
- 1.7562
0.2
Interpolation using Tables 7-2a and 7-2b yields Pr", - 3.208
p.., - (3.208)(672) - 2,155.8 ps;a.
CuUender-Smith Method
(ZIp")dp,, 0.01875-y,z
1 + BZ:Z/~r ..
T."
For a given rate (corrected to 14.65 psia and 520°F), B is calculated using
Equation 7.so:
•
The Cullender and Smith (1956) method uses Equation 7-56 as stated earlier in the section on static bottom-hole pressure:
_ 18.75 z
I'"' F2 + (PITZ)dp
(P/TZ)!/l,OOO
"rr
Pwto
B .. 6.6663 x
1O-4n.q~;n,·
zd'p1.
Thhles 7-2b through 7-2m, or Equations 7-53 and 7-54, are used in evaluat-
ing the value of the integral. The Sukkar-Comell method is preferred because in addition to being simple, consistent, and accurate, it does not require any trial and error.
with the expression in the left integral represented by I:
I_
pl(1'Z)
F' + (PITZ)'Il,ooo
As for the static case, a two-step procedure is generally used, where only the
value of pressure at the midpoint. pm! is considered:
Example 7-5. Repeat Example 7-4 using the Sukkar-Cornell method.
Solution
Using Equation 7.so:
(7-67)
3<6
CIlI Production Engineering
Steady State Flow of Gas Through Pipe!
347
Equation 7·fJ7 can be separated into two parts, one for each half of the flow
string:
(pm( - Pwh) (I...r + I. h) - 37.5 yrJ2 for the upper half
(p... r - PmlHI",r
+ Imf) .. 37.5 'YrJ2 for the lower half
(7-68)
(7-00)
And finally. Simpson's rule is used to obtain a more accurate value of bot
tom-hole pressure p..,r:
(7-70)
Calculation of F involves the use of the Moody friction factor f, which can
be found using the friction factor chart (Figure 7-1). The calculation can .
however, be simplified using Nikuradse's friction factor equation for full~
turbulent flow, based upon an absolute roughness of 600 ~in.·, to givt'
(ERCB, 1975),
F
.. F.<tc..
1.0797d X 1O - 4q.., f or d < 4217
.
.
m.
2612
(7-71 1
and
Although gas wells are generally produced through tubing, some wells
may be produced through the casing·tubing annulus. For this latter case,
the tubing flow equations developed earlier must be modified to reflect the
proper flow conduit diameter. The equivalent diameter relationship of
Equation 7-6 cannot be used because the diameter exponent is 5 in the flow
equations derived.
From Equation 7-11, the pressure loss due to friction is given by:
(7-721
Frequently, the kinetic energy term, neglected in the equations developed
earlier, is also included. The Cullender-Smith equation (Equation 7.56) be.
comes:
dp _ 1,000 z
(7-731
where 1.111 x 1O - 4q!,J(d"p) is the kinetic energy term.
The following must be borne in mind when using the Cullender-Smilh
method (young, 1967):
l. Smaller integration intervals obviously result in greater accuracy in
the trapezoidal integration of Equation 7-56 (or Equation 7-73). An
integration interval of 1,000 ft (or less) is recommended.
• 1 ,IIin. (micro-Inch) .. 10. 1 in
Gas Flow Through an Annulus
"I'< - fLpv'I(2g"d)
1 0337 X 1O - 4q,..
F ... F_n
for d > 4.277 in.
•.,..,__ .. .
d2 5o!l2
+ 1.111 x lO-·ql.J(d·p)
I'"... (lJO.01875-yJ(pITZ)
1" + (pITZ)'ll,ooo
2. Although Simpson's rule can be used to get a better approximation, it
cannot correct for inaccuracies introduced upon using large trapezoidal integration intervals.
3. Change in kinetic energy can be ignored if the well is greater than
4,000 ft deep, or the wellhead flowing pressure is above 100 psia. For
accuracy in determining the pressure traverse, the kinetic energy term,
however, should be included, especially if the flawing wellhead pressure is below 500 psia.
4. For the case of gas Injection, a discontinuity can develop when Equation 7-56 (or Equation 7-73) is numerically integrated. When this happens, the pressure change for that interval should be set equal to zero.
Also, Simpson's rule cannot be used when a discontinuity occurs.
The velocity v - K1q.Jd1 , where KI is a constant. Thus, the friction loss
term in the energy balance can be written as:
For the case of annular flow, where the outside diameter of the tubing is ~o
and the inside diameter or the casing is~, velocity is related to diameter as
follows:
Thus, the friction term becomes:
a
KifLpq!,
I'< - 2g,,(d1. -
d1o)'(do - d,.)
d,.)
•
348
eo, Production Engineering
Steady Stote FlolL oj Cas Through PipC8
Thus, for the case of annular flow, d5 in the vertical flow equations must be
repl,.,..j by,
(di. - d/.)'(do - <1,,) - (do - <I,,)'(do
+ <1,,)'
INLET
-....---'-0.;.
SECTION
I
(7-74)
z
34.
---.
OUTLET
Limitations in Vertical flow Calculations
7-5. Gas now over a hilly terrain.
.
pressure are rairl\" ae-
~urate for most engineering calculation purposes. Some serious uncertai~tie.-;
In bottom-hole pressure calculations, however, inevitably erist because of:
1. Departure of the actual temperature-depth relationship from that assumed in the method of calculation.
2. Variations in gas gravity with depth, assumed constant in the calculation methods. For condensate systems, the change in com{XISition \\ith
depth is even more significant.
3. Inaccuracies in determination of the Z-factor from the available correlabOns. For pseudoreduced pressu~ greater than 15, no correlation
charts are even available. Equation-of-state methods can be used.laboratory measurements are strongly recommended for greater reliability and accuracy.
4. Imprecise friction factor.
5. Presence of unknown amounts of liquids in the well bore. lWo-phase
flow relationships are necessary if liquid amount is significant.
6. Inaccuracies in flow rate, specific gravity, and pra<>ure measurements.
Gas Flow Over Hilly Terrain
Transmission lines often deviate conSiderably from the horizontal depending upo~ ~e ter:rain o\"er which they are laid. In some cases, gas ~'ells
may also exhibit sectiOns of different slope, such as the directionally drilled
~ells from off~hore platforms. This section on flow over hilly terrain essentially deals With the situation where gas is flOWing through pipes that are
non-uniform in thei~ slope, such as a hypothetical situation shown in Figure
7-5. A~y flow terram can be reduced to the form shown in Figure 7-5 by
approXImating the actual flow profile with small pipe sections of uniform
slope. The three approaches applicable to such a flow are described in the
follOwing sections.
Static Correction
To account for the difference in elevation between the inlet and outlet,
.:\oz, the simplest approach is to modify the outlet pressure for the pressure
exerted by a static gas column of height equal to .:\oz. As described earlier in
the section on static bottom-hole pressure. different techniques are available
for evaluating the pra<>ure exerted by a static gas column. Since the static
correction method is itself an approximation, the average temperature and
Z-factor method is quite satisfactory to use. Let PI be the inlet pressure, and
po the outlet pressure. Then, the outlet pressure po must be corrected as follows (Equation 7-46):
p~ - e"'2 po
•
where s is given by Equation 7-47:
Note that .:\oz is positive if the outlet is higher than the inlet (uphill flow),
and negative if the inlet is higher than the outlet (downhill flow). Thus, s is
positive for uphill flow, negative for downhill flow.
The flowline shown in Figure 7-5 is equivalent to a horizontal line with
an upstream pressure equal to Ph and a downstream pra<>ure equal to e"'~o'
This correction can be incorporated into any horizontal flow correlation to
give the flow through such a flowline. For example, the Weymouth equation for this situation can be written as:
q., - 31.5027
[T.][(P1- e'»l)d'·'f'
1>..
'Y;.z..~ T nL
(/-75)
Similar expressions can be written for the Panhandle A and B equations, and
the Clinedinst equation. This approach, though imprecise, frequently gives
an adequate approximation.
350
Caa Production Engilleering
StC'od!J Stall' Flow of Gos Through Pipes
351
Flow Correction
. A mo.re rigorous ~rrection for the flow profile accounts for inclined flow
~n t~e dIfferent sections of the pipe. Equation 7-66 gives the relationship fOr
mcllned flow, assuming aa average temperature and Z.factor:
Rearranging this equation, and replacing the pressures with the inlet and
outlet pressures P, and Po:
<& _
(pI - e'",}"J'
2.5272 x 10 -5')'~Z.\T.JL(e' - 1)
+~
I{e'u-l)I
'"
~[)'
s. '*
0
(7·78)
where s, represents the section i of the pipe.
Note thaI: if S. "" 0 for any pipe section (this will happen if the section is horizontal. z ,., 0). the equivalent length term for that section is replaced by the
actual length of the ~·dion.
Similar expressions can be written for the Panhandle A. Panhandle S,
Clinedinst. and other equation.~, This average temperature and Z-factor approach is not exact, and is generally used where flow is almost isothermal
and the pipe is essentially horizontal, \\-'ith relatively small and few sections
that are not horizontal.
Thus,
'k - [
e'p~}"J'
(T ,1520)
][ (p1 (2.5272 x 1O·')"(p,JI4.73} >,Z.,T"fL(e' - I}
General Method
j'
0',
q. - 5.634814
[TP..,.][Me'p'}d'j'
'YItZ., T.,£L.,
The ~nstant 5.634814 is slightly different from the constant 5.6353821 in
Equation 7-29 due to round-off errors. Thus:
'k -
5.63538 [TPo.:.][(1''YgZ.,T.,fI.."
1- e'pO}d'j'
(7.76)
where 4 is given by:
1.,. _ (0' - I) L
s
(7·77)
If more precise calculations are necessary, the most rigorous method is to
use a horizontal flow relationship such as the Clinedinst equation (Equation
7-39) for the horizontal section of the pipe, coupled with an inclined flow
relationship such as the Cull ender-Smith equation (Equation 7-56) for the
non-horizontal portion of the flow. This results in quite complex relationships that require a computer for solution. Chapter 11 provides some insight
into the modeling of gas flow in pipelines and networks. Usually, the computer program that is written for this purpose also has an economic analysis
package built into it, to enable design optimization for a complete gas flow
system.
Example 7-6. A section of a gas transmission system consists of three stations, A, S, and C. The 7-in. pipeline from A to B is 2 miles, and from S to C
is 5 miles long. Stations A, B. and C are at elevations above sea-level of
4,000 ft, 7,000 ft, and 2,000 ft, respectively. The inlet pressure at station A is
3,000 psia, and the outlet pressure from the pipeline at station C is maintained at 2,200 psia. Assuming )'It .. 0.6, T.v .. 85°F, and f .. 0.025, find
the gas flow rate through the system, and the pressure at station B.
Solution
Equation 7-77 gives the expression for the effective length for a single section
o~ ~ f1o~line. For the general case of non-uniform slope where the profile is
d~\']ded mto a number of sections n of nearly uniform slope (as shown in
FIgure 7-5), the effective length is calculated as follows:
From Figure 3-1, Ppc _ 672 psia, T pc _ 358°R
•
352
Gas Production Engineering
Steady State Flow oj Gas Through Pipa
First trial :
353
For section AB:
Assume PH .. 2,500 psia
Using Equation 7·77:
For section AB :
Us;ng Equat;on 7·32. p" - (213)[(3,000' - 2,500') /(3,000' _ 2,500')1
,. 2,757.58 psia
_ (~"''''' - 1)(2 x 5,280) _ ll,436.365 ft
0.15737
Using Equation 7·76:
p,. - 2,757.58,672 - 4. 104
From Figure 3-2,
L.
Z.y .. 0.787
111,919.16 - (5.63538)(520/ 14.73)
(3,000' - ~ ""'1'1)(7')
1"
[ (0.6)(0.787)(545)(0.025)( ll,436.365) J
Us;ng EquaHon 7·47, s, - (0.0375)(0.6)(7,000 - 4,000) /[(0.787)(545)1
- 0.15737
•
0',
For section BC:
P., - (2/3)[(2,500' - 2.200')/(2,500' - 2,200')1 - 2,353.19 ps;.
(3,()()()2 - eO· I.57 37 Pi)O ..5,. 1,177.093
Pp. - 2,353.191672 .. 3.502, and, Zn. " 0.780
PH - 2,550.6 psia
s, - (0.0375)(0.6)(2,000 - 7,000) /[(0.780)(545)1' - 0.26464
Second trial:
For the complete line ABC:
Assume PH .. 2,550.6 psia
P•• - (213)[(3,000' - 2,200') /(3,000' - 2,200')1 - 2,620.51
Ppr" 2,620.51/672 .. 3.90, and, Z.~
ps;.
"" 0.782
s - (0.0375)(0.6)(2,000 - 4,000) /[(0.782)(545)1 _ - 0.10559
•
For section AB:
p __ (213)[(3,000' - 2,550.6') /(3,000' - 2,550.6')1 - 2,781.36 ps;.
p,. _ 2,781.361672 - 4.139, and, Z" - 0.798
s, - (0.0375)(0.6)(7,000 - 4,000) /[(0.798)(545)1 - 0.15520
Using Equation 7.78:
For section Be:
1)(2 x 5,280) + eO·15i37(e-O.~ - 1)(5 x 5,280)
0.15737
- 0.26464
L.. .. (eD 1.5737 -
p" _ 2,379.62/672 - 3.541, and, Z_ - 0.778
- 38,585.154 ft
S, -
Using Equation 7.76:
q" _ (5.63538)(520/14.73) [
p __ (213)[(2,550.6' - 2,200')/(2,550.6' - 2,200')1 - 2,379.62 ps;a
(3,000' - e"''''''2,2OO')(7')
1"
(0.6)(0.782)(545)(0.025)(38,585.154) J
- 111,919.16 Mscfd - 111.92 MMscfd
(0.0375)(0.6)(2,000 - 7,000)/[(0.778)(545)1 -
- 0.26532
Using Equation 7·78:
(el.ls.'520 _ 1)(2 x 5,280) + eD 1s.520(e-O.26.\32 - 1)(5 x 5,280)
L. -
0.15520
- 38,504.546 ft
0.26532
Steady State Flow of Gil" Through Pipes
354
(or bottom-hole) chokes are frequently used to reduce the wellhead flowing
pressure, and prevent freeze-offs (hydrate formation) in the surface flow
lines and controls.
The velocity of a fluid flowing through a restriction (orifice, nozzle. or
choke) is expressed as follows:
Using Equation 7-76:
_ (5.63538)(520/14.73) [
'I.<
355
1"
(3,000' - e-' ''''''2,200')(7')
(0.6)(0.782)(545)(0.025)(38,504.546) J
- 112,036.24 Mrid - 112.04 MMrid
(7-79)
For section AB :
where
Using Equation 7-77:
d1
L. _ (e' "". - 1)(2 x 5,280) _ 11 423 443 It
0.15520
,.
r"
(3,000' - e' ""'",)(7')
(0.6)(0.798)(545)(0.025)(11,423.443) J
p _
v -
-
1,185.8601
change in flow diameter
diameter at the throat of the restriction device, ft
pipe diameter, ft
gravitationaJ acceleration, fUsec2
pressures at the upstream and downstream ends, respectively, of the flow restriction, Ibflft Z
fluid density, lbm/ftl
Equation 7-79 is generally written as:
0',
[3,000' - e' "'"'",f'
-
d2, g_
Pit P2 -
Using Equation 7-76:
112,036.24 _ (5.63538)(520/14.73)[
K _ a constant representing the entrance/exit loss due to the
C. [2g(p,
(7-60)
- p,)l pf'
where the coefficient of discharge, Cd, is given by:
PB '"' 2,549.9 psia = 2,550 psia
•
(7-81)
Thus, the gas flow rate, q.. - 112.04 MMscfd, and the pressure at station B,
PR ""' 2,550 psia.
Application of Equation 7-80 to the case of single-phase gas flow resu1ts in
the well known de Saint Venant equation, assuming that the gas is perfect
and that the flow is frictionless and adiabatic (see for example, Binder,
Gas FJow Through Restrictions
In several instances in a gas production system, the gas must pass through
relatively short restrictions. Chokes. consisting of a metal plate with a small
hole to allow flow. are the most common restriction devices used to effect a
pressure drop or reduce the rate of flow. They are capable of causing very
la~ge pressure drops: a gas can enter a choke at 5,000 psia and exit at 2,000
psla or less. Chokes have, therefore, found several applications as control
devices in the all and gas industry. Some of the purposes for which surface
(and subsurface) chokes may be used. are to maintain a precise wellhead
flow rate, provide sand control by maintaining sufficient back pressure on
the producing formation, protect surface equipment andior prevent water
coning by controlling the flow rate, and reservoir management. Subsurface
1958),
Vi-Cd [
where
{p )'>-11')1"J
k (
~\~k-l
l-~
2
(7-82)
k _ ratio of the specific heats for the gas, cp/c..
subscripts 1,2 '"" upstream and downstream side of the choke, respectively
Substituting for gas density,
PI -
(28.97pI'YJ'(RT I),
(1'2)"-"')J'
( -Vi-Cd [ RT,i!< -k- 1
l4.485-y1 k - 1
PI
(7-83)
35.
Cos Production Engineering
Steady State Flow oj Gos Through Pipes
The gas velocity Vi is related to the volumetric gas flow rate at standard conditions, q." as before:
Equation 7-86 is the general equation for flow through chokes. In common
units, it can be written as:
<J,c -
where ~ is the cross-sectional area of flow through the choke. Substitutin~
for"'" - (""4)~. and assuming perfect gas (~ - 1):
q. - v,(rd1h14)
(::)(~)
For an adiabatic expansion/compression process for a perfect gas, pVk
- constant. Therefore,
p,V! - p,Vl
357
[(v.)" (v.)"' ""])'"
1 ~l
k
974.61Cd PIrla. ('fITI
PI
-
PI
(7-87)
where <be'" gas flow rate, Mscfd (measured at 14 .73 psia and 520 0 R)
dm = choke diameter, in.
PI = pressure at the upstream side of the choke, psia
P2 - pressure at the downstream side of the choke, psia
TI _ inlet (or upstream) temperature, oR
The flow through chokes (and flow restrictions in general) may be of two
types: subcritical and critical.
Subcritical Flow
implying that
(7-85)
Substituting for T2 from Equation 7-85, and for
Equation 7-84:
VI
from Equation 7-83, into
Flow is called subcritical when the velocity of the gas through the restriction is below the speed of sound in the gas. In the subcritical flow regime,
Equations 7-86 and 7-87 apply, and the flow rate depends upon both the
upstream as well as the downstream pressure. Subsurface chokes are usually
designed to allow subcritical flow.
Critical Flow
0',
0',
0',
q.,
_ [ r(Rg,J''T. ]
(1
k
(4)( 14 .485)''1>.. C dp,d1h >,T, k _ 1
[tv.)'
\p. " - (v.)'" ""])'"
p,
(7-86)
Flow is called critical when the velocity of the gas through the restriction
is equal to the speed of sound (about 1,100 fusee for air) in the gas. The
maximum speed at which a pressure effect or disturbance can propagate
through a gas cannot exceed the velocity of sound in the gas. Thus, once the
speed of sound is attained, further increase in the pressure differential will
not increase the pressure at the throat of the choke. Therefore, the flow rate
cannot exceed the c ritical flow rate achieved when the ratio of the downstream pressure P2 to the upstream pressure PI reaches a critical value, however much this ratio is decreased . Unlike subcritical flow, the flow rate in
critical flow depends only upon the upstream pressure, because the pressure
disturbances traveling at the speed of sound imply that a pressure disturbance at the downstream end will have no effect on the upstream pressure
andlor flow rate. Surface chokes are usually designed to provide critical
flow.
The choke flow relationships represented by Equations 7-86 and 7-87 are
valid only in the subcritical flow regime, up to critical flow when the maximum flow velocity (equal to the speed of sound) is attained. If the pressure
•
358
Steady State Flow oj
CD, Production Engineering
ratio at which critical flow occurs is represented by (PZ/pl)~' then from elementary calculus (differentiate Equation 7-87 with respect to 1>2, and set the
resultant expression equal to zero) it can be shown that:
(7-881
F10w is subcritical for <Pi/PI)
> (PZ/pl)c,
and critical for <P2IPI) ::S (P~:lPI)<
U the operating pressure ratio is less than the critical pressure ratio, the pressure ratio in Equation 7-86 or Equation 7-87 must be replaced by the critical
pressure ratio, because the maximum flow rate through the choke is that
which corresp:lOds to critical flow. The critical pressure ratio {pz/pt)c is O.4g
for monoatomic gases, 0.53 for diatomic gases, and slightly higher for more
complex gases.
Note that the analysis here assumes a perfect gas, with an adiabatic gas
exponent k. No corrections have been made for deviation of gas from ideal
behavior. It has been found that these relationships give very good results in
field application, and a more complex analysis is generally quite unnece<isary_
The value of k is also, fortunately, relatively insensitive to temperature
variations as well as to the gas molecular weight for gaseous hydrocarbons.
Therefore, k is usually assumed to be constant. k :r; 1.293 for a 0.63 gravity
gas. Generally, the value of k used is in the range of 1.25 to 1.31, implying
from the relationship represented by Equation 7-88, that the flow is critical
when the pressure ratio is in the range 0.5549 (for k - 1.25) to 0.5439 (for
k - 1.31). As a rule of thumb, flow is assumed critical when the pressure
ratio is less than or equal to 0.55, which implies a k equal to 1.275 approximately. Substituting Cl>2/p.)" - 0.55, and k ... 1.275 in Equation 7-87, we
can get the well known choke design equation for critical flow:
GO.f
Through Pipes
359
Solution
Using Equation 7-88:
(J>i/pl)c ... (212.275)127.5'0.275 ... 0.55
(a) PIl/pl ... 600/750 ... 0.80, which is greater than (pz/p\)"
Using Equation 7-87,
q., _ (974.61)(0.88)(750)(28164)'
1
)(1.275) (0.8" '" _ 0.8"'" "')
[( (0.65)(560) 0.275
r'j
- 2,471.03 Mscfd
Using Equation 7-87,
•
q., - (974.61)(0.86)(750)(28164)'
1
)(1.275) (0.55>1 '" _ 0.55"" , "')
[((0.65)(560) 0.275
r'j
- 2,955.32 Mscfd
(7-89)
where q.. - flow rate through the choke, Mscfd
dm - choke size, in.
p. - upstream pressure, psia
T. _ upstream temperature, DR
1', - gas gravity (air ... 1)
Cd - coefficient of discharge, generally assumed to be 0.86
Examplf! 7-7. Find the flow rate, referred to standard conditions of 14.73
psia and 520 oR, of a 0.65 gravity gas through a 28f64-in.-diameter choke for
a downstream pressure Pt equal to: (a) 600 psia, and (b) 300 psia. The upstream pressure PI ... 750 psia, temperature Tl .. lOO°F. and k ... 1.275.
The same result can alternatively be obtained using Equation 7-89:
(456.71) (0 .88) (750) (28, 64 )'
q., -
[(0.65)(560)],,'
- 2,955.33 Mscfd
Temperature Profile in Flowing Cas Systems
It is quite clear from the flow relationships presented so far that flow calculations require the value of the flowing temperature in order to determine
300
Gas Production Engineering
the effective g~ properties and pressure drop. To avoid complexity, most
flow computations assume that the flowing temperature profile is linear.
This assumption is not too far from reality, and generally gives quite good
results. In some cases, however, more precise temperature and flow calculations may be required, such as in cases where phase changes occur during
flow of the gas through the pipe.
Pressure and temperature are mutually dependent variables in flowpressure loss depends to some extent on temperature (or heat loss), and the
te~perature (~r heat loss) depends upon pressure that governs the changes in
flUId enthalples, overall heat transfer coefficient, and other parameters.
Thus, generating a very precise temperature profile requires an enormous
amount of complex, trial-and-error type of calculations for which even the
amount of data available in most cases is insufficient. Thus, an approximate
temperature profile, independent of pra<lure, is satisfactory for most engineering applications.
•
F10wing Temperature in (Horizontal) Pipelines
For a given inflow temperature, TJ. and surrounding soil temperature,
T ... the temperatu~ of gas flowing in a pipeline depends upon heat exchange
With the surroundmgs, given by the overall heat transfer coefficient· the
(pressure dependent) Joule-Thomson effect- due to pra<lure changes c;used
by friction, and velocity and elevation changes; phase changes (condensation, vaporization) in the gas due to pressure and temperature changes; and
energy loss (due to friction) during flow that is converted into heat.
Considering these factors, Papay (1970) has derived the following equation, assuming steady-state flow of gas, for the temperature T Lx at a distance 1.. from the pipeline inlet:
TJ..r'" [T. + C 4/C 2
-
(C 1C s)/(C2(C 2 + C a))]CfzIC3
(C 1 + C 2 LJ C 2!Ca
_ C4 + Cs1.. + CS(C 1 + CaL.)
C 2 (C2 + Ca)
C2
PI-P2
C, - --L-
[ZVICpU'dL
V2 - VI
+--L
VI
+ (1 -
1+ ZV2-L ZVIQ
ZVI)CpVI'dV
T
+ ghlL -hd..
m- .
(7-9 1)
where
mole fraction of vapor (gas) in the gas-liquid fiowstream
p ". pressure, Ibf/ft 2
L = pipeline length, ft
v = fluid velocity, ftlsec
Cp = fluid specific heat at constant pressure, Btu/Ibm-oF
I'd - Joule-Thomson coefficient, ft2-oFllbf
m = mass flow rate, Ibm/sec
Q = phase-transition heat, Btullbm
k - thermal conductivity, Btu/ft-sec-oF
g _ gravitational acceleration, equal to 32.17 ft/sec2
h = elevation difference between the inlet and outlet, ft
d., = outside pipe diameter, ft
T, = temperature of the soil or surroundings, OF
Zv '"
Subscripts 1 and 2 indicate the inlet and outlet ends of the pipe, respectively
(except in the numbering of the constants C), and subscripts L and V represent liquid and vapor (gas), respectively.
In deriving Equation 7-90, Papay (1970) assumed that pressure, flow
rate, and phase-transitions are linear functions of distance from the inlet
end of the pipeline. This equation, therefore, is very accurate for short line
segments. For the case where phase changes can be neglected (single-phase
flow), Equation 7-90 can be simplified to:
(7-90)
_(v' - v.)[(v _v, - v.) (I _ e- 'L.) + (v, - v.)L,]
where
KLCpv
C1
,.. ZVICpL
C2
Ca
,..
+ (1 -
I
KL
L
(7-92)
ZVI)CpV
kim
", (ZV2 -
361
Steady State Flow oj Gas Through Pipes
k
ZVI)(CpL - Cpv)/L
• The ~ble adiab~ticsimultaneow; pres:sure and temperature reduction process that accomparues the expanswn of a flowing gas by pressure reduction is called Joule-Thomson or
throttling effect.
where K - - -
(7-93)
mc,v
In Equation 7-92, the first two terms represent the heat exchange with the
surroundings, the third term represents the Joule-Thomson effect, the fourth
term accounts for the elevation changes, and the fifth term accounts for the
•
362
Gal Production Engineering
Slead!l State Flow of Gal Through Pipet
363
change in velocity head. The last two terms are small and may be neglected
for most practical purposes. If the pressure drop is small, then the temperature drop due to expansion is also small, and the third term may also be neglected. Neglecting these terms. Equation 7-92 simplifies to the following
familiar form:
3. A 4,()()()'ft gas well requires a wellhead pressure of at least 100 psia to
enable flow of the 0.85 gravity gas from the wellhead through the surface facilities. The bottom-hole temperature is 200°F and the surface
temperature is 82°F. The casing is 4.5 in. ID.
(7.!J.l)
a. What is the minimum bottom-hole pressure to enable gas flow?
b. What is the bottom-hole pressure for a gas flow rate of IO MMscfd?
c. Repeat part (b) assuming that the gas flows through the casing-tubing annulus, the tubing being 2,1 in. 00.
Flowing Temperatures in Wells
The case of subsurface vertical flow is a special case of the general equation (Equation 7-90) where the temperature of the surrounding; varies with
distance along the flow length due to the geothermal gradient, C T (OF'ft),
of the earth.
A simplified equation presented by Ramey (1962). similar to Equation
7-94, is widely used:
(7·95)
where
1... - distance from the bottom-hole or point of fluid entry, ft
T l.I - temperature at location L., OF
TI - temperature at point of fluid entry (at L _ 0). OF
C T - geothermal gradient. °Fm
K :w k,'mc;.\', as gi\'en by Equation 9-93
Equation 7-95 assumes that the temperature of the fluid and surroundings is equal at the point of entry, and that the heat loss is independent of
time. The parameter K is quite difficult to estimate. An analysis based upon
measured temperature profiles in actual gas wells is recommended, similar
to an empirical equation developed by Shiu and Beggs (1980) for flowin~ oil
wells.
Q....oons and Problenu
1. A 12-in. 10, SO-mile gas pipeline is to deliver 100 MMscfd of gas at 250
psia. The average flOWing temperature of the 0.75 gravity gas is 90' F.
and lId - 0.()()()5 for the pipe. To what pressure must the gas be comp~ at the inlet end to achieve this? Use at least hvo equations and
compare the results.
2. What is the maximum throughput through the pipeline in Problem I?
Assume c - 0.05, E - 1.0, Y - 0040, and S _ 35,000 psi.
4. List some limitations of the flow equations described in this chapter
for (a) horizontal £low and (b) vertical £low.
5. A gas production system consists of three sections:
Subsurface section I: inclined , length = 5,500 ft. true vertical
depth - 4()()() ft
inlet temperature - lsooF, outlet temperature" 85°F
Surface section II: horizontal, length"" 1.5 miles
Surface section Ill : 2 miles long, inclined 30° from the horizontal.
The temperature in the surface sections can be assumed to be 85°F,
'Y, - 0.65, and f - 0.002. For a pressure of 4000 psia at the inlet of
section 1, find:
(a) Cas flow rate through the system.
(b) Pressure at the outlet of section 111.
References
ANSI, 1976. Code Jor Pressure Piping, Petroleum Refinery Piping, ANSI
B31.3, Am. Soc. of Mech. Engrs., United Engineering Center, New York,
NY.
Beggs, H. D., 1984. Gas Production Operations. OCCl Publications, Oil &
Cas Consultants International, Inc., Thlsa, Oklahoma, 287 pp.
Binder, R. C., 1958. Advanced Fluid Mechanics, Vol. 1. Prentice-Ha~l, Inc.,
New Jersey, 296 pp.
Chemical Engineers' Handbook, 1984. Edited by R. H. Perry and D. W.
Creen, McCraw-Hili Book Company, New York, 6th ed.
Cullender, M. H. and Smith, R. v., 1956. "Practical Solution of Cas-F1ow
Equations for Wells and Pipelines with Large Temperature Cradients,"
7Tan.f., AIME, 207, 281-287.
•
364
Cas Production Engineering
ERCS, 1975. Theory and Practice of the Testing of Cos Wells, 3rd ed. Energy Resources Conservation Board, Calgary, Alberta, Canada. .
Ikoku, C. U., 1984. Natural Gas Production Engineering. John Wiley &
Sons, Inc., New York, 517 pp.
Katz, O. L.. Cornell, D., Kobayashi, R., Poettmann, F. H., Var)" J. A.,
Elenbaas, J. R., and Weinaug, C. F., 1959. Handbook of Natural Gas
Engineering. McCraw-HUI Book Co., Inc., New York, 802 pp.
Lesem, L. B., Greytock, F., Marotta, F., and McKetta, J. J.. Jr., 1957. "A
Method of Calculating the Distribution of Temperature in F10wing Cas
Wells," 'Irons., AlME. 210,169-176.
Messer, P. H .. Raghavan, R., and Ramey, H. J., Jr., 1974. "Calculation of
Bottom-Hole Pressures for Deep, Hot, Sour Cas Wells," J. Pet. Tech.,
26(1, Jan.), 85-92.
Moody, L. F., 1944. "Friction Factors for Pipe F1ow," Trans. Am. Soc.
Meck Eng., 66(Nov.), 671-684.
Nisle, R. G. and Poettmann, F. H., 1955. "Calculation of the F10w and Storage of Natural Gas in Pipe," Petrol. Engr., 27(1):014: 27(2):C36:
27(3),037.
Papa)", J., 1970. "Steady Temperature Distributions in Producing Wells and
Pipelines," Koola; e8 Foldgaz, 11. Cited reference in: Production alld
1rallsport of Oil and Gas, by A. P. Szilas, 1975. Developments in Petroleum Science, 3, Elsevier Scientific Publishing Co., Amsterdam, p. 563.
Ramey, H. J., Jr., 1962. "Wellbore Heat Transmission,·' J. Pet. Tech., 14(4,
Apr.),427-435.
Shiu, K. C. and Sew, H. D., 1980. "Predicting Temperatures in Flowing
Oil Wells," 7rans., ASME; J. Energy Resour. Tech., 102(1, March), 2-11.
Sukkar, Y. K. and Cornell, D., 1955. "Direct Calculation of Bottom-Hole
Pressures in Natural Cas Wells," 'Irons., A/ME, 204, 43-48.
Swamee, P. K. and Jain, A. K" 1976. "Explicit Equations for Pipe-F1o,",
Problems," J. Hydraulics Div. ASCE, 102(HY5, May), 657-664.
Szilas, A. P., 1975. Production and Transport of Oil and Cas (Developments
in Petroleum Science, 3), Elsevier Scientific Pub!. Co., Amsterdam, 630
pp.
Young, K. L., 1967. "Effect of Assumptions Used to Calculate Bottom-Hole
Pressure in Gas Wells. J. Pet. Tech., 19(4, Apr.), 547-550.
8
Multiphase Gas-Liquid Flow
-------
Introduction
As stated earlier. rarely do gas wells produce "dry" gas. Some liquid (oil
and water) is almost always associated with it. For small amounts of liquid
production, the flow may be considered single phase and the relationships
for gas presented in Chapter 7 can be used with minor modifications to }ield
close estimates. When a large amount of liquid is associated with the gas,
however, true multi phase gas-liquid flow prevails and such simplifications
are no longer valid.
Although the existence of multiphase flow, defined as the simultaneous
flow of free gases and liquids. has been known for a long time, its complex
behavior has not vet been fully understood. The gas and liquid may exist as
a homogeneous ~ixture. or as independent phases in other complex flow
patterns such as slug, mist, emulsion, or bubble flow. The pressure drop for
multiphase flow conditions is usually greater than for single-phase flow
and, in some cases, the flow may be quite unsteady.
Early attempts to use modified single-phase flow relationships for
multiphase flow resulted in highly overdesigned or underdesigned flowlines.
An overdesigned line is not only expensive, but for two-phase flow conditions, it may result in unstable operations, with liquid slugging and pressure
fluctuations. Generally, liquid and gas are transported through different
flowlines at the surface, and such ca.lculations may not always be necessary.
Multiphase flow correlations are more important for wells with a significant
liquid production, or for prediction of conditions for liquid loading of gas
wells that are currently producing "dry" gas. This chapter outlines methods
for handling multiphase flow in the context of gas engineering. For a detailed treatment of multi phase flow per se, readers may refer to the literature, notably Brown and Beggs (1977), and Dew and Brill (1973).
365
•
366
Gal Production Engineering
(;aI_Oi! R.tial ..... lor Normal Tempe,.lura
Approximate Method for Tw~Phase Systems
Eumple
For Pseudo Rtdu~ed Tanp of 1.195, Pseudo
Reduud P'tlWfe o. 2.00 and G"-O.I Ral'o of
RedUCed P'tlwr. 01 2 00 end G"-Oil Ratio of
~ 000 SCF ISl8 Z F"::lor ',om 0 .... Ph_ Z
F~lor Coo,e!lIi~ tI O.SolS, Coo'Kled bel OW 10 0.732
$tpal'I'on o. Iha M'.N'I for. Wt..ch the
Z FKlor '1 Des""o (G_-Oil Ral'OS lor
Low Temp. Sep. M.y be Gliitly Olllllfnl.)
F10w streams with a CLR (gas-liquid ratio) greater than 10,000 scf/stb
may be assumed to be single-phase gas, This is commonly the case for retrograde and wet gas reservoirs, where the oil and gas produced at the surface
actually exist as gas within the reservoir. The small Liquid content of the gas
can be accounted for by modifying the properties that are affected by the
presence of liquid. These include molecular weight, gas gravity. and gas
compressibility factor (Z-factor) .
Molecular weight of the flow stream consisting of gas as well as liquid can
be calculated from the mixture composition, similar to calculations shown
in Chapter 3 for a "dry" gas mixture. The gas specific gravity (air,. 1 basis)
for the total flow stream, )''''' can be obtained by dividing the molecular
weight of the flow stream by the molecular weight of air, resulting in the
following expression (Craft and Hawkins. 1959):
10
!
!
~
0.9
~l"
•
Aecu,..::y
o.w PO'"" Oev"uon of Flom.
I~;~I
.S,
-,L~, .. ,!o
"
•
C-
""
~~
--
--
-
f--
.......
141.5
(8-3)
The gas compressibility factor (Z-factor) obtained from Figure 3--2 (Chap-ter 3) using critical pressure and temperature estimates for the total f10\\
stream (using ")'w), can be corrected for the existence of two phases using Figure B-1. If this two-phase Z-factor is essentially the same as the single-phase
Z-factor, the mixtu re exists as a single gaseous phase.
Using these modified properties, calculations can be carried out with the
relationships presented for gas in Chapter 7.
i
!
Ii
,
~
•
"'" L--':'
OB
~
,.~
Liquid specific gravity, frequently specified in terms of °APf, can be converted to specific gravity 'Yo (water - 1 basis) as follows:
API + 131.5
0.9
.~
--'
(8-2)
0
:::::::
~~ ~
~ ~~,s ,
o
'<
i ' .......
If not known, M., can be estimated using Equation 8-2:
K'"
O::ltn~::r flhase" P'I!SMI (... II Of
I
.,
where ~ - gas-oil ratio, sef/stb
1'. - specific gravity of the gas (air - 1)
')'0 - oil gravity (water - 1) at standard conditions
M., - molecuJar weight of the stock-tank oil
.5""
ISO " F 10
,
2SO"F. If Uncorftcltd."d eo ..
F"::lo'l O,Ue, by no MOle Thin T.n". 0 1M lollY
At
o
')'0 -
367
Multipha3e Cat-Liquid Flow
- + 2"
r-: 1'-~
1\1\ ~ r---- r---,
1\ ,'. "' .,"
'~~iT'
1\
~
J
0.1
!
~
0.6
•"
1
N
05
Figure 8-1. Gas deviation factor correction for two-phase natural gas systems.
(After Elfrink et aI. , 1949: redrafted by Ikoku, 1984; courtesy of SPE.)
Multiphase fl ow
For flow conditions that cannot be approximated as single-phase gas, it is
necessary to use more complex procedures. Multiphase flow has been stU?ied in detail by numerous investigators and several correlations are available. These correlations account for the flow geometry (vertical, inclined,
•
368
Gal Production Engineering
Mu/tiphose Gas-Liquid Flow
369
horizontal), flo" pattern (slug, mist, bubble. plug, etc.), fluid properties
(formation volume factor for oil and water, gas in solution in oU as well as
water, surface tension, density and viscosity of the multiphase mixture), and
other parameters related to flow (Reynolds number, friction factor, holdup.
etc.). They are. however. quite complex. requiring the use of computers.
Appendix B at the back of the book gives computer programs for two such
methods.
For our purposes. it is satisfactory to consider a fairly good and practically
expedient technique that uses pressure traverse curves. Pressure travcl"S(
curves are plots of pressure versus flow distance for a pipe of a gh-en diameter for selected oil and gas properties at various gas/liquid ratios and flo\\.
rates. Some of the most commonly used pressure traverse curves, prepared
usin~ the I.:orrelations of Hagedorn and Brown (1965), are shown In Figure
8-2(a-v). Such cun'es can easily be generated for any other set of fluid properties. pipe diameters. or flow rates using the available correlations for
multi phase flow.
Pressure traverse curves are simple to understand and use. fast, and fairly
accurate. Since no single correlation is best over all ranges, it is better to
construct a pressure traverse curve using the best applicable method for the
range that we are interested in. To generate better traverse curves, a combination of several correlations and/or experimental data can be useful.
Pressure Traverse Curves for Horizontal Gas-Liquid Flow
•
The hOrizontal flow pressure traverse curves shown in Figures 8-2a-f
were prepared using Eaton et al.'s (1967) correlation and give satisfactory
results except for low rates and low C, L ratios. Although these curves were
prepared for water, they can be used for oil, provided the free-gas/oil ratio is
used for the C. L parameter, as follows:
1. Select the applicable curve for the given flowline size, flow rate, and
gas/liquid ratio.
2. On the pressure axis, locate the known pressure, go vertically down to
the applicable gas/liquid ratio curve, and read off the length on the
length axis.
3. Correct this length for the pipeline length by: adding the pipeline
length to the length determined in Step 2. if the known pressure is the
outlet pressure; or subtracti ng the pipeline length from the length in
Step 2, if the known pressure is the inlet pressure.
4. The unknown pressure is the pressure corresponding to the corrected
length determined in Step 3.
Example 8-1 illustrates this procedure.
(tnt continued on page 380)
•
•
•
370
Cas Prodllctioll Eligineering
371
,
Ii
ii
,
~ II
r aJ
d.
.",•
N
~
~ ~ jJ
••
~
,
~
i~ go:;
!j; ~ , - 0_"1
-
,~
•i
0
,!
ill
r
III
III
III
•
-,•
_ ..' ...... o'n"
•
Ii
Ii
-
i• I'If
!••
I
I
•
I
" !;!I
.p>
J
~
~
u:'"
I~ ~i~ •,
.. ,--I
i
,;
I-
,
N
.- ~
00, •,
!
I !
,'}
!
"I
III
II,
•
~
_ _ ..... lII<tl
372
ell.t
•
373
Multiphase Gas-Liquid Flow
ProductiOIl Engineering
~~.p'"
,
"
'"
s'1
.\
1·~--~-4---+-•
,Lf---+------+--Vh4L-x<
.i--+---Y
.l!
, !'
ill
•r---,---,----r---~--,_--_,--~~'~·7·~T'~__,·• ,.
,!
'"
.\
I
I • r--+---1I---+----;r::0¥--/t7L-~
•
~?-+----1
1'r--+--+---Yh"¥--71-7"'z
. ~n.=tn.=to
_ _ ...... 00<1'1
•
GtU Production Engineering
Multiphase Gas-Liquid Flow
375
,
II
f·I---l-+-+-Dt4Lj.L----bL~~~
•
1,1---+--+-.,.1hL--I,L---i,,4
•
•
•
•
•I.,~--~--l___+~~~~~~~
i,I---+--+--AL,L.,/L-,.f,.
•
-_............
•
.
- _ ..... 00Q'1
•
376
Gas Production Erlgineering
Multiphose Cos-Liquid Flow
•
.-to., ,
~V 1/
~ ~ V l(V
,-t: ~ V V V V
,
•I •
;
·
•
•
t0V
;f:
,
:af// v:
V
I~ ~
,... h
~
-
~
•
VV:~,
....
VV~2
./
'
,.
•
",;
•
•
377
'1
,
•
0-
::t
,••
~
f·•
i:1"
,
F"'"
. - . .
.... _
.. 1U00tJ'
.li
.
. .
'I'
III
,
•
,
•
•
. . .
.... -
..... DIU'!
,.It['
•
,
ill
378
CO$ Production Engi'leering
379
Mulripha~e Gas-Liquid FIQU;
•••
•
.!
"
.'i,>---l---I-----A+-,.<+--++-----.L--~~
I
.1{
' I'
.~Etr.
-_ .. ntD..
III
"'."..,
•
"
.!
l· ~~--~--+-~~~~~~~/~~
•
I, ~__+___-J,:H¥---,l'_+J~-I-----+-___1
•
N
.;,
•
.
_ _ ..... twol1
•
CDs Production Engineering
380
(text continued from page 368)
Examph- 8·'. A \\'cU is producing 1,500 stb/d of oil with aGIO -; 800 sci'
stb at a flowing wellhead pressure of 700 psig. Determine the separator pres---
Multiphase Cas·Liquid Flow
381
Therefore. P.. h is equal to the pressure corresponding to a depth
_ 9,000 - 8,000 - 1,000 ft.
sure for a 2.5-in. ID, 9,000-ft line.
Thus, P"h - 100 psig.
Solution
Handling Directional Wells
Assume that at a pressure of 700 psig there is no gas in solution. Hence
free-gas/oil ratio is 800 scf/stb. Using Figure 8-ld and the procedure described earlier.
For directional wells with df"viations from the vertical less than 15-20°.
the true vertical depth can be used to ascertain the pressure trawrse. This
approximation, howe\'er. is im'alid for deviations exceeding 20 0 , becall5C a
directional well has a greater length than a yertical well for the same depth.
resulting in a greater frictional head ios.... Also. holdup. defined lU the volume fraction of the flow conduit occupied by liquid. differs and rna,· be
greater for inclined than for vertical £low.
.
For pressure tra,-er.,e curves. an approximate ansv.·er can be obtained using the vertical and horizontal flow curves as follows:
Psev
=
400 psig.
Pressure Traverse Curves for Vertical Cas-Li(luid Flow
•
The vertical pressure traverse curves, shown in Figures 8-2g-v, are used in
a manner similar to the curves for horizontal flow:
1. Select the applicable curve for the given tubing size. flow rate, and
gas/liquid ratio.
2. On the pres..~ure axis. locate the known pressure, go vertically down to
the applicable gas/liquid ratio curve. and read off the depth on the
depth axis.
3. Correct this depth by: adding the well depth to the depth determined
in Step 2, if the known pressure was the surface pressure: or subtracting the well depth from the depth in Step 2, if the known pressure was
the bottom-hole pressure.
4. The unknown pressure is the pressure corresponding to the corrected
depth determined in Step 3.
Erampl~ 8·2. For a bottom-hole flowing pressure of 2,000 psig, a well is
producing 1,000 stb/d of oil with aGIO - 300 sef/stb. Given that the tubing
size is 2.5 in. and the well is 8,000 ft deep, find the flowing wellhead pressure P.. h.
Solution
P",f
=
Example 8-3. In a directionally-drilled well, the true vertical depth is
~ual to 5,000 ft. and the length of the 2-in. tubing is equal to 7.500 ft.
<?Iven p..h - 100 psig, q., 1.000 stb/d (50% water), elL _ 800 scf/stb,
fmd the flowing bottom· hole pressure P,,'f.
Solutioll
Using Figure 8-20 for vertical flow:
A
I. Determine the pressure loss using only the true vertical depth and the
applicable vertical flow correlation .
2. Assume a value for the inlet or outlet pressure, whichever is unknown,
and calculate the average of the inlet and outlet pressures.
3. Determine the frictional pressure drop due to the extra length of the
tubing (i.e., total tubing length minus true "ertical depth of tubing)
using the applicable horizontal flow correlation, and the average pressure estimated in step (2).
4. Calculate the total pressure loss for the d(!\.iated well. This is equal to
the sum of the m'O pressure losses obtained in steps (1) and (3), From
this new total pressure loss, find the new estimate of the inlet or outlet
pressure, whichever is unknown.
5. Repeat steps 2 through 4 till the unknown pressure (inlet or outlet)
from steps (2) and (4) agree within a specified tolerance.
2.000 psig corresponds to 9.000 ft approximatel}'.
Using Figure 8-2m for vertical flow,
P=f - 1,100 psig for a vertical depth of 5,000 f1.
•
MIJltiphasl' Gas-Uqllid Flow
382
A trial and error procedure is required to determine p...f. As a first guess,
assume P.. f - 1,150 psig.
Then, the a\'erage pressure, P••
psig.
=
(p..-h + p"l)i2 .. (100 + 1,150)/2"" 625
On locatin~ P.v ( - 625 psig) on the horizontal flow correlation in Figur<.'
8-2c (100% water chart is a reasonable approximation). and using the addi
tional length of 2,500 ft ( = 7.500 - 5,000), the downstream pra;;urt: i.~
found to be 525 psig.
(8-4)
where HF ,., ele\·ation component of the total static pTe"Sure drop, fraction.
and V'I[ is given by:
\.
=
'11;
where
31lg., q,(ZT) ..
(520)p.,d2
\-'1[
=
(lg =
Therefore. the pressure Ios..<; due to friction in the extra 2,000 ft of pipe,
dp! 625 - 525 - 100 psig.
Thus, P.. f
-
P;f + .6.p! -- 1.100 + 100
Second trial: Assume
pw/ -
=
T •• =
P., .,
Z~, -d ...
1,200 psig.
1,200 psig.
P•• -- (100 + 1.200)12 - 650 psig. From the horizontal flow correlation,
downstream pressure - 550 psig. Thus, .6.PI .. 650 - 550 s 100 psig, and
P"I -- 1,100 + 100 - 1.200 psig.
Thus, p...{ - 1.200 psig.
Flow Over Inclined or Hilly Terrain
Inclined f10\\ implies flow through pipes that deviate from the horizon·
tal, such as flow over hills. Flanigan (1958) pre;entoo. the only a\'ailable
method that can be applied to field problems without the use of complex
computer programs. By conducting several field tests, Flanigan concluded
that most of the pressure drop occurred in the uphill section of the line, and
identified two main components of the p~re drop for multiphase flow in
an inclined system: pressure drop due to friction, which is the predominant
component in hOrizontal lines, and pressure drop due to the liquid head,
which is the predominant component in vertical and inclined flows. The
sum of these two components determines the total pTe"Sure drop.
The uphill sections are treated as equivalent vertical columns containing
an equivalent amount of liquid. Because in multiphase flow the pipe is
never completely filled with only liquid, Flanigan introouceci the term Hf' to
repre;ent the fraction of the total static pTe"Sure drop that exists as the elevation component. Hf" correlates with the superficial gas velocity, v'S, as follows (F1anigan, 1958):
383
(8-5)
superficial gas \'(·locity. ft,sec
gas flow rate. M\1scfd
avcrage flowing temperature, R
average £lowing pressure, psia
average gas compressibility factor (at P." T., )
inside diameter of flow conduit, in.
Bakcr (1960) showed that for v>~ > SO, the applicable relationship is:
0.00967
Hf'''''
o~
L O,5
">, ,
(8-6)
where L '" length of the flowline, ft.
Using H F , the pTe"Sure drop through the pipe is calculated as follows:
.6.p= -~p";,H,,,,:;:-E:.:H
144
(8-7)
where PI ,. liquid density. Ibm ftl
Example 8·4. A 4·in. 10, 2.000 ft long flowline passes over 5 hills having
the following vertical heights: 130 ft. 40 ft, 210 ft. 80 ft, and 185 ft. Gh'en
ql = 2.000 stbld (95% water). G,L .. 1,000 scffstb, I'll = 0.7 (air" I),
),,,, = 1.02. ),,, - 40" API, average pres.'iure P., - 300 psig, and average temperature T •• _ 120"F, find the pressure loss due to the hills.
Solution
For 'YK ... 0.7, at P., - 300 pslg, and T~. - 120"F. the average gas compra<;·
ibility factor Z.. from Figure 3-2 - 0.96.
•
384
Gas Production ElIgilweriug
Mu{tiphnse Gas-Liquid Flow
Using Equation 8·5,
Example 8·5. (After Kumar et aI., 1986). A well is producing through a
2.S-in. 10 tubing, 5,000 ft deep, at a rate go = 1.000 stb/d with a
CIO = 600 seE/stb. This well produces a large amount of sand when the oil
prcx:iuction rate is above 1,000 stbfd; therefore. it is required to install a
v ~ (31,194)(2,000 x 1,000 x 10-')(0.9£)(580) _ 13.9173 fU"",
>,
(520)(300)(16)
choke ("choke the well back',). Because hydrate problems have made it impossible to install a surface choke, a bottom-hole choke must be designed. It
i<; proposed that the choke be installed at a depth of 4,000 ft, i.e., 1.000 ft
above the bottom of the tubing. For a 1,000 stb/d oil rate, the oottom-hole
Using Equation 8-4,
1
!:H ,. 130
+ 40 + 210 + 80 + 185
, .. ~ (141.5)/(131.5
Therefo,e, "
+ 40)
385
~
~ (0.95)(1.02)
=
qui red,
(b) the flowing
pressure, assuming that the flow
through the choke is critical (Pu "" 2Pd)'
645 ft.
Solution
0.8251
+ (0.05)(0.8251)
~ 1.01
Using Figure 8-2p, the pressure at 1,000 ft above the bottom of tubing is
equal to 1.175 psig.
Using Equation 8-7,
Thus, Pu = 1,175 psig, implying that Pd = 1,175/2 = 588 psig.
~p"", ~
(1.01
x 62.4)(0.1781)(645)/144
~
50.28 p'i.
(a) Using Equation 8-9,
Flow Through Chokes
The generalized equation for critical multiphase flow through a choke is
written as;
d1.g9". (10)(1,000)(600)°·5.16 = 279.8
1175
Thus, d _ (279.8)11
(8-8)
where
ql = liquid flow rate, stb/d
pu = upstream pressure, psia
d = inside diameter of the choke, 64ths of an inch
R -.: producing gas-liquid ratio, scf/sth
a, b, c = empirical constants
89 =
19.71164 in., or 20164 inch.
(b) Using Figure 8-2p for Pd ,. 588 psig, the wellhead flowing pressure,
P ...h "" 100 psig.
Liquid Loading in Gas Wells
Various investigator:s have proposed different values for a, h, and c. Most
commonly, however, Cilbert's (1954) correlation is used, where a = 1.89,
b = 10.0, and c - 0.546:
(8-9)
The liquid loading of a gas well refer:s to the accumulation of liquids in
the wellbore of a flowing gas well. a common operating problem in gas pro-duction operations. Liquid loading imposes an additional back pressure on
the producing formation, restricting gas flow. In high-pressure gas wells,
liquid loading will result in slugging flow and reduced well deliverability:
fluctuations in gas flow rate and casing pressure will be observed, caused by
the buildup of casing pressure until it becomes sufficient to blow the liquid
to the surface. In low-pressure gas ,veils, the flow rate drops drastically and
•
3S6
MultiphaSl! Cas-Liquid Flau:
Cas Production Engineering
casing pressure starts to build up, but because enough casing pressure cannot be achieved, liquid loading may completely -kill" the well.
Liquid loading occurs in gas wells that have liquid proouction (however
small the amount may be). but do not provide enough energy for the continuous removal of these liquids. As stated earlier. Iiqu.id loading can be recognized by fluctuations in gas flow rate and casing pressure for high-pressure
wells, or by flow stoppage and casing pressure buildup for low-pressure
wells. Pressure surveys and flow computations are very helpful in determin·.h
nfl; '"
Preventing Liqu.id Loading: Minimum Flow Rate for Continuous Liqu.id
Removal
I
Turner et at. (1969) conceptuali7.oo two physical models for the removal
of liquid droplets from gas wells: liquid film movement along the pipe
walls, and entrairunent of liquid droplets in the gas stream. According to the
wall film model, the well is unJoaded by providing a gas flow rate su£ficient
to cause the movement of liquids up along the walls of the casing andlor
tubing pipe. The droplet model assumes that liquid is removed as entrained
droplets in the flowing gas stream. In a real system, both these models probably exist, with a continuous exchange of liquid between the gas stream and
the wall film. From an analysis of both these models, Turner et al. (1969)
found the droplet mooel to be superior because, among other reasons, it
agrees with observed data. The liquid film model does not represent the controlling liquid transport mechanism; the liquid film moving down along the
pipe walls eventually breaks into droplets that are re-entrained in the gas
stream, and the droplet model is applicable. The more complex wall film
mooel can, therefore, be ignored here.
According to the droplet model. the minimum gas flow rate to unJoad a
gas well is one that enables the largest liquid droplets that can exist in the
gas stream to move upwards. As discussed in Chapter 4 (Equation 4-17), the
terminal velocity V t (fusee) of a particle of diameter ~ (ft) and density Pp
(lbmfft3) falling under gravitational acceleration g in a gas of density PI
(lbm/ft3) is given by:
p~r'
(8-10)
assuming Newtonian (turbulent) flow. Thus. a particle of diame~er dp will
be removed by the gas stream if the velocity of the gas stream V,IS equal .to
the terminal velocity v. of the particle. Equation 8-10 can therefore be wnlten as:
.
There are tv.'o sources of liquids in a gas well: water and hydrocarbon
condensate from condensation of the hydrocarbon gas. and water from the
producing reservoir. If the gas velocity is not high enough to transport these
liquids to the surface, they accumulate at the bottom of the well The back
pressure on the formation due to the hydrostatic head of this liqu.id column
further reduces the flo", rate and the velocity of the produced gas. This process continues until the well dies, or produces onJy intermittently.
There are essentially two approaches in solving this problem: prevent liquid accumulation, or remove the liquid as it is produced. A brief description
follows of some available methods.
I
. - [4gd,(PP 3CdPtt:
"t
387
\' = .... _
,
4gdp(pp 3CdP,
pJ
.5
Substituting Cd '" 0.44 for Newtonian flow, and replacing the particle density Pp by the liquid density Ph we get:
v, ~ [4
g
d,(PI -
1.32p~
p~l"
(B-ll)
Thus, the larger the drop, greater is the gas flow velocity required to remove
it. The diameter of the drop, however, cannot be determined directly.
'furner et al. (1969) used correlations for the Weber number to determine
the maximum drop diameter that can exist under given flow conditions. The
Weber number, Nw~, is a dimensionless number expressing the ratio of the
velocity forces that try to disintegrate the drop, and the surface tension
forces that tend to keep it together:
N
w
_
C
vjp,/g, = v2sP.dp
aldp
(8-12)
ag.;,
The maximum drop diameter, d",... can now be specified using the fact that
the drop will disintegrate if the Weber number exceeds a critical value of 20
to 30:
(8-13)
Substituting for dmu from Equation 8-13 into Equation 8-11, the required
minimum gas velocity is given by:
- PJr'
v. - [(4)(30)ogg.,(PI
L32pjYi
o..._~
Substituting for g and g.,. and solving for v.:
•
.
CQ.f Productiorl E'I~i1lCf"rlllg
\" _ 17.514
Multiphou Cos-Liquid Flow
,.
- P~"
P, -
0"( PI
1980). Some of the methods that have been successfuJly used in field operations are briefly reviewed here.
As a safety ~eas~re, Turner et a!. (1969) use a 20% (approximately) safet\'
factor, resultmg m the folloWing equation for minimwn gas flo\, \-elocity;
'II. -
20A -
p~1 2
produced through the tubing-casing annulus. It is desirable to have the tub(8- 14)
For field applications, the folloWing equations are recommended by Thrner
et al. (1969) for use when the liquid is either water or condensate:
(
V \
v ....,.. -
5.62 (67 - O.OO3lp)l.
(O.OO3lp), ,
4.02 (45 - 0.OO3Ip)' ,
( V'
V""ndellSoo'. ""
(0.OO3Ip)"
(8-15)
(8- 16)
Equations 8- 15 and 8-16 were derh'ed assuming the folloWing:
1. A 0.6 gr~vity gas at a temperature of 120°F, to enable expressing the
gas denslt)' as a function of pressure.
2. For water, (J "" 60 dynes/em, PI ,., 67 Ibm/ft'.
3. For condensate, a,.. 20 dynes/cm, PI ,., 45 Ibm/ft'.
'~~en ~th water ~nd condensate are present, the water equation, which
a hIgher required gas \'elocity VI' should be used.
The gas '-elocit)· VI in ft/sec can be converted to field units of MMscfd as
gJ\'CS
follows:
_ 3.06Apv,
'"
ZT
w here Cia ..
A ..
p T Z -
Beam PUn/lnng Units
In this method. liquids are produced through the tubing, whereas gas is
00_'~'(~p~,~-~P~!L.
,,,
£
389
(8-17)
required minimum gas flow rate, MMscfd
cross-sectional area of the gas flow conduit ft2
flOWing pressure, psia
'
flOwing temperature, OR
gas compressibility factor at the flowing pressure and tempera_
ture
Liquid Unloading: Removal of Liquid as it Accumulates
Nu~erous methods have been proposed for the liquid unloading or dewatermg, of gas wells (Hutlas and Granberrv
1972·,L'b
d ' Henry,
;,
I son an
ing set as close to the bottom perforation as possible, and preferably below it
(Hutla!\ and Granberry. 1972). so as to provide a liquid cushion to prevent
gas interference problems in the downhole pump. If a liquid divcrter is provided in the subsu rface tubing string to allow only liqUids to enter the tubing, no liquid cushion is required and gas interference problems are
minimized .
One advantage of pumping units over other t}1)CS of liquid removal techniques is that they do not depend on gas velocity for lift-the energy for
Hquid lift is provided by the pump itself. Beam pumping units are quite inexpensive and economical for shallow wells, but become very expensive for
deeper and more highly pressured wells (Hutlas and Granberry, 1972).
Their applicability is best for low gas rates. with a liquid production of
greater than about IO bbliday. Beam pumping units cannot be adjusted to
handle very low rates and problems may. therefore, arise if they are used for
low liquid-rate wells.
Plunger Lift
This method has proved to be very successful in unloading liquids from
gas wells (Libson and Henry, 1980). It uses a steel plunger. equipped with a
valve, in the tubing string (see Figure 8-3). The plunger acts as an interface
between the gas stored in the annulus and the liquid accumulated above the
plunger in the tubing, virtually eliminating gas slippage and liquid fallback.
Both gas and liquid are allowed to flow into the tubing through a valve..
type opening at the tubing bottom. When the plunger is at the bottom of the
tubing, this valve is shut off , and all production goes into the casing. The
casing pressure builds up, until it is sufficient to transport the plunger and
allliqujd and gas abo"e it in the tubing to the surface. A motor valve. operated either by a clock or by well fl ow rate monitoring, may be used on the
flowline to control the cyclic rate of the plunger (Libson and Henry, 1980).
If a clock is used, the optimum time cycle has to be determined by trial-anderror.
Following plunger arrival at the surface, a bumper opens the valve in the
plunger, and the well is allowed to flow for a period of time. This time period may be preset by a clock, or surface flow controllers may be used to
aUo w the well to flow until the gas velocity drops to some critical value.
Flow controllers are more desirable. because they permit the well to flo\\
•
390
Gas Productioll Engi'leeririg
Mllltiphase Cas-Liquid Flow
1oI0TOA VAlVE
'~'~O~':.'f'~j~~~~~~~~l~1
CASING PRESSURE
-1._-"1
Small Tubing String
GAUGE CASINQ SHut-I'"
TlM£ CLOCK
CASING - TUBING ANNULUS
391
GAS PROOUCED EACH
CYCLE UP TU81/o10
This technique operates on the principle of increasing the gas velocity, to
enable liquid carryover to the surface, by providing a reduced flow area.
Small tubing strings of I-in. diameter are quite common for such an application. This method applies best to low volume wells in which friction loss is
not severe, and has proven quite useful in several field applications (Hutlas
and Granberry, 1972: Libson and Henry, 1980).
Surfactallt Injection
....
..
. . 1__ o!-4_-tWIlTEA PROOUCED EACH
0"5 E ... TEAS ""''''UlUS
FRO'" PAY DURING SHUT-IN
AS AFTEAflOW TO
HIGH PRESSURE GAS FOR
NEltT CYCLE
LEGEND
-
LIQUID
..
C",SIHC-TUBING ANNULUS
o
STORACE O"'S
PRODUCEO TU81"10 CAS
.....
••
CYCLE UP TUBING
LIft
CASING
-:..
::--!;-, .,"'" II
Injection of surfactants and foaming agents into the tubing-casing annulus has produced successful results in several wells (Libson and Henry,
1980). Figure 8-4 shows a schematic diagram of a surfactant injection system. Surfactant (or soap) is injected using a chemical pump and a time
clock. Water is continuously unloaded in a foamed slug state through reduction in surface tension. This method has proved less successful for unloading
condensate (oil), perhaps because the surface tension reduction dynamics
were not suitable in the cases tested.
peR~S
SPRING
.. . .".UO U'A~'""'O"_ _
J L~
~
, .... -
.
•
STOP
. . . " . TO ".~ I U U "
Figure 8-3 . Plunger lift operations. (After Ubson and Henry, 1980; courtesy of
SPE.)
for an optimum time period before shut-in. Wells having sufficient deliverability to maintain rates above this critical rate for short periods are ideal
candidates for flow controllers.
em Lift
The gas lift system also uses a liquid flow diverter in the tubing string.
with liquid production through the tubing and gas production through the
annulus. This system, however, uses a gas-lift valve (usually one, sometimes
more than one if liquid production is quite high) mounted on the tubing at a
calculated depth, and actuated (opened or closed) by anyone of the several
available techniques. Liquid accumulates in the tubing, until the gas-lift
valve opens to lift the liquid slug to the surface.
C .... 0 . . . . . ~ •• IIUA'U
II lI,nON 10AO . . . . . yO'
• OA, ... ",CTlD
''''''CTOo • .., ...
Figure 8-4. Gas well soap injection system. (After Ubson and Henry. 1980;
courtesy of SPE.)
Questions and ProWems
1. What is multiphase flow? For what purpose are multi phase flow computations useful in the context of gas production operations and how
important are they?
392
~
GaJ Production Engineering
2. Describe the development of flow correlations for muJtiphase flow.
3. A well is producing 800 bblJd oiJ with a gas-oil ratio of 1.500 seC/stb
through a 2-in. tubing, with a safety valve installed at a depth of 2,500
ft from the surface. The total well depth is 5,000 ft. The pressures recorded at the surface and bottom-hole are 150 psig and 1,000 psig, respectively. Is the valve partially closed? If so, what is the pressure drop
across the valve?
Multiphase Gas-Liquid Flow
References
8eg&';. H. O. and Brill, J. P., 1973. "'A Study of Two-Phase Flow in Inclined
Pipes," }. Pet. Tech., 25(5, May), 607~617.
Brown, K. E. and BeW. H. D., 1977. The Techrwlogy of Artificial Lift
Methods, Vol. 1. PennWell Publ. Co., Tulsa. Oklahoma, 487pp.
____________~j-fA~O;.~75~~~~g~a~S~~ff~IO~"~.;:ng~at~O~.~25~~1~~~I.cr~d~ili:,~O~Ugh~~a~2~.5~-,~.n~.f;ID~t~Ub:.:-________~~~B~.~c!.~a~n~d~~~~M~.~~1~95:9~.~~
pressure of 200 psig is desired for this.
ft gas well.
bottom-hole pressure is 1.100 psig. Use the approximate method for
two-phase systems to answer the following:
I . C an t he gas f 1ow under these conditions? If yes, do not anS\\ler any
of the parts below.
2. What methods are available to make this well flow?
3 . H ow much gas injection is required per day to keep this well flowing?
4. What is the pipe diameter that will keep this well flowing?
5. Repeat problem 4 using multi phase flow charts.
6. Use N-O methods to design the required flowline to transport a twophase gas-oil mixture from a wellhead o\'er hills with the follo\\in~
conditions:
Gas flow rate _ 3.5 MMscfd
Gas-oil ratio = 11.000 sefistb
Length of pipeline "" 4 miles
Total elevation of hills ,. 1,500 ft
A\·erage fl owing temperature _ 95° F
Gas gravity (air .. I) = 0.68
Oil gravity (water _ I) _ 0.85
Upstream pressure must not exceed 1,200 psig. and the downstream
pressure must not be less than 250 psig.
7. Solve problem 6 assuming a horizontal pipeline (no hills).
8. Design a surface choke. assuming critical flow through it, for a ~as
well with the following operating conditions:
Cas flow rate'" 1.2 MMscfd
Gas-oil ratio _ 11,000 sef/stb
Wellhead pressure _ 1,200 psig
Use two methods, and compare the results.
9. List the advantages and disad ....antages of the known methods of unloading gas wells. What data would you need to consider before deciding on using any of these techniques for a specific well?
393
J~~~~~~~~llc
________
437pp.
Eaton,
A., Andrews, D. E., Knowles. C. E., Silberberg, I. H., and
Brown, K. E., 1967. "The Prediction of Flow Patterns, Liquid Holdup
and Pressure Losses Occurring During Continuous Two-Phase F10w in
Horizontal Pipelines," Trans., AIME, 240. 815-828.
Elfrink, E. B., Sandberg, C. R., and Pollard, T. A., 1949. "A New Compressibility Correlation for Natural Gases and its Application to Estimates
of Gas-in-Place," 7rans., AIME, 186, 219-223.
Flanigan, 0., 1958. "Effect of Uphill Flow on Pressure Drop in Design of
lWo-Phase Gathering Systems," O. & Gas f., 56(Mar_ 10), 132- 141.
Gilbert, W. E., 1954. "F1owing and Gas-Lift Well Performance," Drilling
and Production Practice, API, 126-157.
Hagedorn, A. R. and Brown, K. E., 1965. "Experimental Study of Pressure
Gradients Occurring During Continuous Two-Phase F10w in Small-Diameter Vertical Conduits," J. Pet. Tech., 17(4, Apr.), 475-484.
Halliburton Energy Institute, 1976. Thbing Size Selection. Halliburton Services, Duncan, Oklahoma, 57pp.
Hutlas, E. J. and Granberry, W. R., 1972. "A Practical Approach to Removing Cas Well Liquids," J. Pet. Tech., 24(8, Aug.), 916-922.
Ikoku, C. U., 1984. Natural Gas Production Engineering. John Wiley &
Sons, Inc., New York, 517pp.
Kumar, S., Guppy, K. H., and Chilingar, G. V., 1986. "Design of F10wing
Well Systems," In: Slirface Operatiom in Petroleum Production, Vol. 1,
Elsevier Scientific Publ. Co., Amsterdam, 279-326.
Libson, T. N. and Henry, J. R., 1980. "Case Histories: Identification of and
Remedial Action for Liquid Loading in Gas Wells-Intermediate Shelf
Gas Play," J. Pet. Tech., 32(4, Apr.), 685-693.
Thrner, R. G., Hubbard, M. G., and Dukler, A. E., 1969. "Analysis and
Prediction of Minimum F10w Rate for the Continuous Removal of Liq·
uids From Gas Wells," J. Pet. Tech., 21(11, Nov.), 1475-1482.
•
Gao! Compres.Jion
395
volume in the enclosure, or by carrying the gas without volume change to
the discharge and compressing the gas by backflow from the discharge system. Positive-displacement compressors are of two types-reciprocating positive-displacement compressors, and rotary positive-displacement compres-
9
son.
Gas Compression
Continuous flow compressors acce.lerate a continually £lo'wing gas stream
and subsequently com-'ert the velocity head into pressure. The two types of
continuous flow compressors are dynamic and ejector. Dynamic compres-
Introduction
element, and
convert the \'elocity head into pressure, partly in
the rotating element
partly in stationary blades or diffusers. Ejectors
increase the gas velocity by entraining it in a high-velocity jet of the same or
another gas, and convert this kinetic energy into pressure in a long venturitype flow chamber.
Figure 9-1 shows a breakdown of principal compressor types, and Table
9-1 describes their approximate parameters. Among these. the ones currently used in the gas industry arc discussed in the following sections.
Gas production operations often require compressors to raise the pressure
of ("pressurize") the gas. One of the most important applications of compressors is for providing enough pre'iSure to a gas for transport through
transmission and distribution systems. Another transport-related application of compressors is for reducing the gas volume for shipment by tankers or
for storage. In reservoir engineering operations, compressors are important
in lowering the wellhead pressure below atmospheric in order to produce
the well at a higher rate, for reinjection of gas for pressure maintenance or
cycling, and for injection of gas into subsurface strata for underground storage. In gas processing operations, compressors arc required for circulation of
gas through the process or system, and for raising gas pressure to the required level for a chemical processing reaction.
This chapter presents the common types of compressors being used for
these purposes in the natural gas industry. Basic elements in the design of
these compressors are also discussed. Much of the material has been drawn
from an Ingersoll-Rand Company (1982) publication entitled. Compressed
Air and Cas Data, an excellent reference for readers who rna}' be interested
in further details about gas compression operations.
CO"PR[SSORS
•
IIEC"
--
"
Types of Compressors
Sl.IO'N"-YAN(
The two major types of compressors are positive displacement or intermittent flow, and continuous jlotL'. Positive-displacement units are those in
which successive volumes of gas are confined within some type of enclosure
(compression chamber) and elevated to a higher pressure, T his pressure elevation or compression can be achieved in two ways-by reducing the gas
394
5TII ... , ....1-.08(
lI01... O-"'5TON
C(NT
.. H,eAl- LOI(
" 'UO- ,,"ow
A."L - hoOW
Figure 9·1. PrinCipal compressor types. (From Compressed Air and Gss Data,
1982; courtesy of Ingersoll-Rand Co.)
300
Go.!' Compre&8ion
Gas Production Engineering
Approximate
ComprHSOr TYIM
Paramete~
Reciprocating
Vane-type Rotary
Helical·lobe Rotary
Centrifugal D)'JIamle
Asilli-flow D)-namk
•
~rom C:omp~
A
Table 9-1
tor Common Compressor Types·
Appro)!. Mulmum
Pr...ure, pallil
1(1(),OOO
400
""
5.:500
:500
397
Approa:. Maximum
Power, BHP
> 12,000
""
6.000
> 3.5,000
> 100,000
Air and GIl. DIl, .. , 1982, rourtes\- of inltf',wU·Rand Co
'~
l~
""'- ,;!,,------'--
~S~[
'~~
Reciprocating Positive-Displacement Compressors
Reciprocating compressors consist of a ringed piston that mO\'e5 inside a
cylinder. They may be of two types: single-acting, in which the piston com·
presses on only onc side; and double-ading, in which two single-acting pistons operate in parallel inside one cylinder, thereby compressing on ooth
sides. Besides the piston and cylinder, a suction valve and a discharge valve
are provided. The suction valve opens when the pressure in the cylinder falls
below the intake pressure. The discharge valve opens when the pressure in
the cylinder equals or exceeds the discharge pressure.
Figure 9-2 shows the various steps in a reciprocating compressor cycle. In
Figure 9-2A, the cylinder is full of the gas that is to be compressed, and is at
the beginning of the compression cycle. In Figure 9-2B, the compression
stroke has been completed. The discharge valve opens and the delivery
stroke begins; the gas is delivered at a constant pressure as shown in Figure
9-2C. Next, the expansion stroke occurs, as shown in Figure 9-20. Both
valves remain closed. The small amount of gas trapped is expanded, leading
to a reduction in pressure inside the cylinder. In the next step (Figure 9-2E),
the inlet valve opens and the intake cycle begins, filling the cylinder with
gas again.
Reciprocating compressors are the older type, with more moving parts
and hence a lower mechanical efficiency and higher maintenance costs.
The}' are still very widely used, and are available for all pressure and capacity ranges. Typically, they have a volumetric rate up to 30,000 cfm (cubic
feet per minute) and a discharge pressure up to 10,000 psig.
o
B
. '~~ 0=-
EXPANSION
E
c
Rotary Positive-Displacement Compressors
In this type, the positive action of rotating elements is used for compression and displacement. Rotary compressors usually offer low pressure differentials. but can handle large quantities of low-pressure gas at compara-
DISCHARGE
Figure 9-2. The variouS steps in a reciprocating compressor cycle. (From Compressed Air and Gas Data, 1982: courtesy of Ingersoll-Rand Co.)
•
39B
399
Gas Compression
Gas ProdllctiOfI Engineering
tively low horsepower. They are easy to install, operate and maintain, and
are used primarily in distribution systems where the pressure differential between suction and discharge is quite small. The four types of rotary compressors, indicated in Figure 9-1, are described as follows.
(\~
I
Sliding- Vane Compres:!lOrs
The sliding-vane oompr~or consists of axial vanes that slide
in a
identical in operation to the reciprocating compressor, except that it
no
valves. The inlet and discharge conditions are determined by the location of
the vanes that move over the inlet and discharge ports. The compression cycle begins when the leading vane of each pocket uncovers the intake port, as
~hown in Figure 9-~. As the rotor turns, the pocket volume decreases and gas
IS compressed, until the discharge port is uncovered by the leading vane of
each pocket. Because this discharge point is prefixed in the design, the rotary
sliding-vane compressor always compresses gas to the design pressure, regard.l~ of the pressure in the receiver into which it is discharging.
Shdmg-vane compressors can typically handle 3,000 cfm of gas, with a
maximum discharge pressure of 50 psig per compression stage. They are primarily used as air compressors, boosters, and vacuum pumps.
ROTOR WlTl'1 NDN-I>IETAlliC
SLIDING VANES.
GAS IS GRADUAllY COI>IPR[SSEO
AS POCKETS GET SI>IAllER
DlSCHARGf
AS ROTOR TURN~, GAS IS TRAPIN POCkETS FORMED 8Y VANES
Figure 9-4. The operating cycle of a rotary two-impeller straight-lobe compressor. (From Compressed Ai, and Gas Data, 1982; courtesy ollngersoll·Rand Co.)
Two-Impeller Stmight·/A.lhe Compressors
Also known as rotary blower, the rotary two-impeller straight-lobe compressor consists of two identical rotors (or impellers) mounted symmetrically
in a casing (Figure 9-4). The rotors usually have a cross section similar to the
numeral eight. The two rotors intermesh, and rotate in opp05ite directions.
One of the rotors is driven directly, while the other is driven and kept in
phase by means of phasing/timing gears. The rotors do not directly compress
the gas or reduce its volume and there is no internal compression; they
merely transmit the gas from the inlet to the discharge. Compression occurs
by backflow into the casing from the discharge line at the time the discharge
port is uncovered. It is a simple device. with no contact between the rotors
or between rotors and casing. The operation is shown in Figure 9-4, with
the light shading indicating gas at inlet pressure, and the dark shading indicating gas at discharge pressure.
Rotary blowers can typically handle gas at 15,000 cfm, with a maximum
discharge pressure of 20 psig or less per compression stage.
Liquid·Piston Compressors
COMPRESSED GAS IS PUSHED OUT
Tl'1ROUGH DISCHARGE PORT
Figure 9·3. The steps involved in compression lor a rotary sliding-vane comt~.)sor. (From Compressed Air and Gas Data, 1982; courtesy of Ingersoll-Rand
Liquid-piston compressors use water or another liquid as the piston to
compress and displace the gas. They are not used much in the natural gas
industry.
•
'00
Gas Production Engineering
IlelicaJ-LoJH or SpiraI·Lobe
Cas Compression
COlnptTSlJOra
Helical-lobe compressors use two helical-type intermeshing rotors, giving
a d~harge pressure typically up to ISO psig per compression stage for gas
f10wmg at 3.000 elm. They are primarily used for vacuum and specialty applications at moderate pressum;:, but have not found significant application
in the natural gas industry.
Dynamic Compressors
•
.01
impeller. The velocity thus generated is converted into pressure partly in the
impeller itself, and partly in stationary diffusers following the impeller.
Centrifugal compressors have low maintenance costs because they have
fewer moving parts-only the shaft and impeller rotate. Delivery is continuous, without cyclic variations. The discharge pressure from a single stage is
about 100 psig, but the flow capacity is very high, up to about 100,000 cfm.
They adapt easily to multistage operations, enabling greater compression.
Multistage centrifugal compressor units with two or more impellers in series,
each with its own radial diffuser. are often built as a single unit. as shown in
Figure 9-6.
Dynamic compressors operate by transferring energy from a rotating set
of blades to the gas. The rotor effects this energy transfer by changing the
pressure and momentum of the gas. The Olomentum also is subsequently
converted into pressure by reducing the gas velocity in stationary blades or
diffusers. The three types of dynamic compressors are as follows .
VOLUTE
/OIFFUSER
hVOI..UTE'I
OIHUSE~
VOLUTE
f-__-:____L-__:'O:'L':":T,;O'
I
STR[Afroj
LINE
SPACER
II
_~-IMP[LL[R---:f--fl-_
_
RADIAL _ _\---"~
DIFFUSER
•
/ ' - '" ,
:::::::::::::::::::
VOLUl£
OLLECTOR
Figure 9-6. Cross-sectional view 01 a typical multistage uncooled centrifugal
compressor. (From Compressed Air and Gas Data, 1982; courtesy of ingersollRand Co.)
ARROWS SHOW DIRECTION OF AIR FLOW
Figure 9-5. A typical overhung-impeller single-stage centrifugal compressor.
(From Compressed Afr and Gas Data. 1982; courtesy of Ingersoll-Rand Co.)
Ce1ltrifogal ComprTlflOrl
In centrifugal compressors, gas flow is radial, and the energy transfer is
e~fected predominantly by changing the centrifugal forces acting on the gas.
F~gure 9-5 shows a single-stage centrifugal compressor. The impeller has radIal or backward leaning vanes usually between two shrouds. The mechanical action of the rapidly rotating impeUer vanes force the gas through the
Axial-Flow
Com~rll
In axial-flow compressors, gas flow is parallel to the compressor shaft (axial), because unlike centrifugal compressors, there is no vortex action. Energy is transferred by means of a number of stages of blades. Each stage consists of two rows of blades-one row (mounted on the rotor) rotating, and
the next row (mounted on the casing or stator) stationary. Both the rotor and
stator contribute almost equally to the pr~ure rise generated by the axialflow compressor. It is a high-speed. large-capacity machine with characteristics quite different from the centrifugal type of compressor. A multistage
axial-flow dynamic compressor is shown in Figure 9-7.
402
Gu, Production EFlgint'erillf(
Gas Comprurion
403
Ejectors generally give a relatively small compression ratio. But they have
no moving parts. so that maintenance and wear is minimum. Although they
can handle liquid carryover without physical damage, they should not be
exposed to a steady flow of liquid.
Figure 9·7. Cross-sectional view of a typical axial·flow dynamic compressor
(From Compressed Air and Gas Data, 1982; courtesy of Ingersoll·Rand Co.)
'"
.\tixed-FfoU' CompreSllOrs
These have gas flow that is in between axial and centrifugal, and combine some characteristics of both the centrifugal and axial types. Because of
the long length required for each stage, mixed-flow compressors are generally not used as multistage units.
---- SHAM
Figure 9--8. Pressure and velocity variations within a steam Jet ejector handhng
air. (From Compressed Air and Gas Data, 1982; courtesy of Ingersoll-Rand Co.)
•
Ejectors
Compressor Selection
An ejector consists of a relatively high-pressure motive steam or gas nozzle
discharging a high-velocity jet across a suction chamber into a venturishaped diffuser (Figure 9-8). The gas to be compressed is entrained by the jet
in the suction chamber, resulting in a high velocity mixture at the pressure of
the steam or gas emanating from the nozzle. The diffuser provides the compression by converting the velocity of the mixture into pressure. The drop in
velocity and rise in pressure along the diffuser length is shown in Figure 9-8.
Temperature changes are similar to pressure changes, and follow the pressure curve quitecloseJy. The gas is separated from steam in condensers (coolers) that also seT\'e to reduce the gas temperature.
Ejectors are generally used to compress from pressures below atmospheric
(vacuum) to near atmospheric discharge pressures, such as for pumping
waste gases and vapors out of a system. A similar design, known as a thermal compressor, is used for compressing gas from atmospheric to above atmospheric pressures. Thermal compfeW)fS are used where available energy
in gas or ~team, instead of being wasted, may be used for compression.
Several factors must be considered in selecting a compressor for a particular application. A multistage compression system may use different compressor types for its stages in order to optimize performance or enable more desirable operating features. Some major considerations in selecting
compressors are described in this section. The discussion is limited to the two
principal types of compressors used most commonly for handling natural
gas: reciprocaU'lg, and centrifugal dynamic compressors. In some cases, the
analysis can be quite complex and these general guidelines may not be suffi.
cient. It is best in such cases to discuss the particular situation with the compressor manufacturers themsel\'es.
em Characteristica
Cas characteristics such as the ratio of specific heats, compressibility, or
moisture content, do not affect the choice of compressor type. Cas composi-
CD.J Compression
404
tion. however, significantly affects centrifugal compressors-many more
stages are required if the inlet gas density is low. Positive-displacement compressors are not much affected by the gas molecular weight, specific gravity.
or inlet density.
Flow
405
CO.J Production Engineering
(high flow rate -> centrifugal (but for low variation),
low flow rate-> reciprocating (even for high variation))
Rat~
For higher
f10y,
cracking of the lubricating oils. None of the compressors has any signifiadvantage in this respect; intercoolers are required to be used between
can es to overcome high_temperature problems. Were
h
lb"
st
u ncahng-Ol'1
a~ng and contamination problems are particularly severe, special par~~y_lubricated or nonlubricated reciprocating compressors may be more
suitable than the centrifugal compressors.
'" t
(centrigugal considered better if source is turbine, and reciprocating
better if the source is an electric motor)
rales, centrifugal machines may be used for the lower
atively lower flow rates, the reciprocating compressor can be used for all the
stages.
F1ow-rate variation is another factor. Reciprocating compressors can handle enormous flow-rate variations with little loss in efficiency. Centrifugal
compressors, howe\'er, do not perform efficiently below 50-90% of their
rated capacity. In general, reciprocating compressors are more flexible in
handling various t)'I>es and sizes of gas f10wstreams than centrifugal compressors.
Cumprnriol1 Ratioll Ulltl Operatil1g Prnt¥Urn
(low ratio= centrifugal, high ratio= reciprocating)
Low compression ratios with moderate capacities favor centrifugal com-
pressors. High compression ratios and higher pressures favor reciprocating
compressors. Because too many other factors are involved, defining a precise
borderline between these two types is difficult.
Variations in inlet and discharge pressures are important to consider also.
In reciprocating compressors, if the inlet (suction) pressure is lowered while
maintaining the same discharge pressure, the overall horsepower is lowered,
the differential pressure of all but the last stage is lowered, and the pressure
differential and temperature rise of the last stage are increased. If the suction pressure to the first stage is increased, horsepower of the complete system increases, pressure differential across all but the last stage is increased,
while the pressure differential and temperature rise in the last stage are low-
ered.
In centrifugal compresson, if the suction pressure is raised, the discharge
pressure ~iJl increase, frequently beyond the design point, and horsepower
will also increase. I£ the suction pressure is lowered, the centrifugal compressor will not compress to the desired discharge pressure.
Opemtil1g TffllpnTJtUtn (centrigugal less affected by temparature)
Centrifugal compressors are less affected by high or low temperature extremes than reciprocating compressors in which temperature limitations are
imposed by the lubricants. However, the maximum discharge temperature
must generall), be kept within some limit to avoid operating problems such
The power source to
or nvmg e compressor a. I uences
choice. Generally, the driver is selected based upon available power
source(s), the heat balance or utilization, waste gas use, and other factors.
Centrifugal compressors are always preferred if the driver must ~ a turbine; reciprocating type are preferred if the driver must be an electriC ~otor.
This is so because motor-driven reciprocating compressors can be dlTec~ly
driven by the motor, whereas motor-driven centrifugal compressors requue
gears for increasing the speed. The opposite is true for turbines.
Foundation and Floor Spau (less foundation need for centrifugal and more for
reciprocating)
The centrifugal compressor is usually favorable from the point of vie\\ of
floor space and foundation requirements. Reciprocating compressors .g~ner­
ally produce some unbalanced forces during their ope.rati?n, ~ulTlng a
foundation that will support their dead weight plus mamtam alignment of
the compressor and driver by absorbing the unbalanced forces that may be
present.
Contil1uity of o,Jer(ltimi
The value of lost production usually exceeds the actual cost of repairs, and
continuity of operation or availability becomes an important ~actor. ~y­
namic compressors can operate uninterrupted for a longer perIod of bme
and their malfunctioning (stoppage) is more predictable than reciprocating
compressors. However, the average yearly availability of both compressor
types is very high and quite similar.
Capital C03'~
It is difficult to compare the cost of centrifugal compressors versus rec.iprocating compressors. For the same \'olume, pressure, and other compressIOn
factors, gas specific gravity influences the cost of the centrifugal compressor
but not the reciprocating compressor. Often, the cost of the driver is used. as
a cost criterion. As stated earlier, if the power source is conducive to turbme
operations, then the centrifugal compressor will be cheaper.
•
Ga.r Production Enginemng
Operating
CQIIU
Ca$ Comprarion
(reciprocating better than centrifugal in terns of operating cost)
The operating cost, consisting mainly of the cost of power, throughout the
service life of a compr~r far exceeds the capital costs and is therefore a
more important consideration. The reciprocating compressor is inherentl}
more efficient than the centrifugal compressor, except at very low compression ratios. Very large volumes, low compression ratios, and low discharge
pressures favor the centrifugal compressor from an operating cost viewpoint.
Maintenance
'07
(9-2)
where k is the isentropic exponent, which is equal to the ratio of the specific
heat at constant pressure (Cp) and the specific heat at constant volume (c.)
for the gas (as discussed in Chapter 7 also):
(9-3)
where cp and c. are in Btu/lbmole.
COfIU
It is generally accepted that for the same gas that is clean, non-corrosive,
and under the same terminal pressure conditions, maintenance is less on the
centrifugal compressor than the reciprocating compressor. For more difficult
compression problems, maintenance requirements for both compressor types
increase, and become more nearly equal, though the centrifugal compressor
will frequently require a little less maintenance.
In thermodynamic terms, Cp for ideal gases is given by:
C, -
(ah)
aT, - Iff)
And c. for ideal gases is given by:
c" _
(au)
_(ah)
_R
aT,
aT
p
Compression Processes
Gas compression processes can be thermodrnamically characterized into
three types: isothermal compression, isentropic or adiabatic re\·ersible compression, and polytropic compression.
- c, - R - I(T)
implying that for ideal gases,
c, -
c, - R -
C, - 1.986
•
(9-4)
Isothermal Compression
Isothermal compression occurs when the temperature is kept constant
during the compression process. The pressure-volume behavior of the gas is
given by:
(9-1)
where
Ph pz - gas pressures at states 1 and 2, respectively
- gas volumes at states 1 and 2, respectively
C - constant
V I, V 2
where h - specific molal enthalpy, Btu/lbmole
u '" specific molal internal energy, Btu llbmole
T '* temperature, OR
R ... gas constant. equal to 1.986 BtuiJbmole
Thus, c p and c.. are functions of temperature only for ideal gases. For real
gases, however, Cp and c. are functions of both pressure and temperature:
c" c" - l(p, T)
and Cp - c.. is given by Equation 3-5i (Figure 3-(7):
Isentropic Compression
C, -
The compression process is adiabatic reversible or isentropic (constant entropy) if the gas behaves as an ideal gas, no heat is added to or removed
from the gas during compression, and the process is frictionless. The pres·
sure-volume behavior of a gas under isentropic compression or expansion is
given by:
2
c. _ - T (.p/aT),
(ap/aVh
The more complex the molecular structure, the higher the Cp is for the gas.
Using Equation 9-4, c.. can be eliminated, and k can be expressed for ideal
gases as:
...
Cas Production Engincmng
k -~-
c.
c,. -
c,.
I. 986
Ga! Compre:Rion
(9-5)
and
_k__
k- 1
,
1.986
,,"
~
~
•
,,
~
~
I
Polytropic Compression
For "real" gases under actual conditions (with friction and heat transfer),
the compression process is polytropic, where the poi)tropic exponent n applies instead of the adiabatic exponent k:
(9-7)
Characteristics of Compression Processes
Isothermal compression is difficult to achieve, because it is not possible
commercially to remove the heat of compression as rapidly as it is generated. Adiabatic compression is also not possible in practice because it is difficult to prevent heat exchange during the compression-expansion C)'CIes.
Most positive-displacement comp~rs, however, approach adiabatic behavior, and are designed using the adiabatic compression/expansion process.
Other compressors are designed using the polytropic cycle, which includes
the effect of non-ideal gas under non-ideal conditions. and makes no assumptions regarding the compression Procf'S'i. The adiabatic process is reversible, while the other two types are irreversible.
Figure 9-9 shows the theoretical zero-clearance work (or horsepower)
necessary to compress a gas between any two pressure limits for various
compression processes. For a given process, the area under its pressure-volume curve indicates its theoretical work requirements. The isothermal compression process gives the minimum theoretical compression work requirements (area ADEF). whereas the adiabatic compression process gives the
m~um theoretical compression work requirements (area ABEF). A polytropiC compression process for reciprocating compressors with water*cooled
cylinders generally exhibits theoretical compression work requirements that
are in between the upper and lower limits of the adiabatic and isothermal
compression processes, respectively (area ACEF). On the other hand, a poly_
tropic ~mpression process for uncooled dynamic compressors typically has
theoretical compression work requirements that exceed even the adiabatic
process (area AC'EF).
,,
M:-POLYTfIM'IC
AI·AOI .... ATIC
AC-POLTTAOPIC
.-~ ~~.I~
'\ \:~
" ' AO-lSOTH(AM'L
~
(9-6)
--
c .--c
\~ .~,
i,
W
~
0
... '"
H
FI gure 9·9. Theoretical pres·
S ure-volume
relationships for
,arious gas compressIon
pro·
TKEOA(TlCU
I
,NO Cl(l,AAMC[
,:"'>,
~~
,,
,
G
'09
cesses (From Compressed Air
8 nd Gas
A
Data, 1982; courtesy of
g.e.r:sol.l:Baod Co )
,-,
VOLUME
•
1
The horsepower requirements for an adiabatic or polytropic compression
process can be reduced by making the process approach isothermal compres·
sion, such as by using multiple stages with intercoolers between the stages.
This, in fact , is one important purpose of intercoolers between multistage
compressors. Reciprocating compressors most common1y cool the gas to its
original intake temperature between the compressions stages that are frequently built as a single unit driven from a single crankshaft. Dynamic compressors, however, have several stages in the same casing, normally without
any intercooling. To improve compression efficiency of dynamic units, their
internal diffusers or diaphragms are sometimes water·cooled, and the gas is
intercooled in external heat-exchangers after every few stages of compression.
Exponents for the Isentropic and Polytropic Processes
The exponent k can be determined using Equation 9·3 if Cp and Co. are
known, or from Equation 9·5 if Cp is known for the gas. As discussed in
Chapter 3, the low p~ure c~ can be determined using Equation 3·59 (by
Hankinson et al.) if the gas gravity, but not the composition, is known; or by
Kay's mixing rule if the gas composition is known. This low pressure cp can
be corrected for p~ure using Figure 3·19 and the gas pseudoreduced pres·
Sure and temperature.
For natural gases in the gravity range O.55<y.< 1, k at a temperature of
150°F can be determined using the following empirical relationship (Ikoku,
1984),
(k) 1!'iO'~': 2.738 - log Yl
2.328
(9-81
•
410
Ga.~
GO! Compres.rlon
Productwn Enl':ineering
Although the exponent n actually changes during compression, an effective or average value. determined experimentally for a given gas and compressor type. is generally used. The value of n may be lower or higher than
k: n is usually less than k for positive-displacement and internally-cooled dynamic compressors, whereas the opposite is true for uncooled dynamic unit~
due to internal gas friction.
411
The value of n is experimentally determined using the ideal gas law
(Pv ... nRT) along with the polytropic compression/expansion relationship
given by Equation 9-7, resulting in:
T! "" /P2)(n-ll,n _ T(n II'n
~I
Tl
(9-9)
where Ph p~ =
TJ. T2 =
r _
n ...
pressures at states 1 and 2, respectively
temperatures at states 1 and 2, respectively
pressure ratio. equal to P2iPI
polrtropic exponent
In compression terminology, PI and P2 are the compressor inlet and discharge pressures, respectively, and r is called the compression ratio. Equation 9-9 relates the intake pressure and temperature and the discharge pressure and temperature for a compre.w>r using the pol}tropic compression
cycle, or the isentropic compression cycle if n is replaced by k:
•
(9- 10)
,
Figure 9-10 may be used for solving Equation 9-9 or 9-10.
Another way of estimating n is by using correlations for polytropic efficiency, as shown in Figure 9-11. The pol~1ropic efficiency. 'lp. relates nand k
as follows:
(k - l ), k
1)/n
(9- 11)
"lip - (n
IHLET VOLUME - ]oil/MIN
so
u•
100
tOO
_00 toO
•~• ,."
•
<
"
•
n
~
""',' .•' ' .,...
,'~
"
,.,-," ...
..
::':~'::::-':'
.,,~.,
-:-::.;:.:::::....
.... 4 _ .......
Figure 9·10. Theoretical discharge temperatures for single·stage compression
Read r to k to T, to T2 . (From Engineering Data Book. 1981 . courtesy of GPSA.)
:000
V
u
u
1000
~
- -
~
"
~• "
•
,
'.
Figure 9-11. Approximate
polytropic compression efficiency of a dynamic compressor versus inlet capacity. (From Compressed Air
and Gas Dara, 1982: cour·
tesy ollngersoU-Rand Co.)
./
-
: I
I; I
V-
,,
•
, ,
Z
1
,
INLET YO\..UfIj[ -
,,
•
.
0
IIZO
100)010000
THOUSOlNOS ~ cr ...
•
GQ3 Productiorl Engineering
Cas Compres.rion
NO.te that '1p relates the quantities (k - 1)/k and (n - 1)/ n, which are reqUired more often than k or n.
Exampk 9.1. A gas is being compressed from 100 psia and 150°F to 2,500
psia. Determine its compression parameters (k, Z, 'YJ at the suction end.
The gas has the following composition (expressed as mole fraction):
C, - 0.9216, C, - 0.0488, C, - 0.0185,
i - C~ - 0.0039, n - C4 .. 0.0055, i - C~ _ 0.0017
C,
C,
C,
i-C 4
n-C 4
i-Cs
y,
M,
0.9216
0.0488
0.0185
0.0039
0.0055
0.0017
16.043
30.070
44.097
58.124
58.124
72.151
'"
667.8
707.8
616.3
529.1
550.7
490.4
To
c"
343.1
549.8
665.7
734.7
765.4
828.8
8.95
13.78
19.52
25.77
25.81
31.66
M .. Ey,M; .. 17.737lbm/lbmole
Therefore, 1'1 - MI28.97 .. 17.737/28.97
=
0.612
))pc, - I:YiPci" 667.313 psia, and TI'" -- I:ylT d
_
363.831 oR
Therefore, PP, = p/Pp.." 100/667.313 _ O.ISO
and T p,
-
From the perspective of compressor users such as gas engineers, compres·
sor design involves only the determination of compressor capacity and
power requirements for a given application, in order to select the t}1Je and
size of compressor required.
Multistaging
Solution
Camp.
Compressor Design Fundamentals
TlTpr " (460 + 150) /363.831 "" 1.677
There are practical limits to the permissible amount of compression for a
single compression stage. The limitations vary with the type of compressor,
and include the follOWing:
1.
2.
3.
4.
Discharge temperature-all types.
Compression efficiency (energy requirements)-all t}1JeS.
Mechanical stress (rod loading) problems- all types.
Pressure rise or differential-dynamic units, and most lX>Sitive-displacement units.
5. Compression ratio-dynamic units.
6. Effect of clearance-reciprocating units.
Whenever any limitation is im'olved, it becomes necessary to use multiple
compression stages (in series). Furthermore, muJtistaging may be required
from a purely optimization standpoint. For example, with increasing compression ratio r, compression efficiency decreases and mechanical stress and
temperature problems become more severe. Therefore, if a greater compression ratio is desired, multiple compression stages must be used. Intercoolers
are generally used between the stages to increase compression efficiency as
well as to lower the gas temperature that may become undesirably high (as
given by Equation 9-9 or 9-10), especially for high compression ratios.
From Figure 3-2, the gas Z factor at suction == 1.0
Compressor Design Methods
C; - I:Y4 .. 9.578 Btu/lbmole-°R
From Figure 3-19, for Pl"" O.ISO, and T p, " 1.677, ACp" 0.15 Btul
lbmole-°R.
Therefore, Cp .. c;: + ACp - 9.578 + 0.15
.. 9.728 Btullbmole-°R
- 0.548 Btu/lbm·oR
Fwm Equation 9-5, k - c,J(c, - 1.986) - 9.728/(9.728 _ 1.9B6)
- 1.2565
The design of each compression stage is best considered separately because
of pressure losses and temperature changes in the intercoolers and piping between the stages, condensation (if any) of water vapor from the gas, and the
consequent volume changes of the gas.
The three methods used for compressor design calculations are: (1) anal}tic expressions derived from basic thermodynamic relationships; (2) enthalpy versus entropy charts, commonly known as Mollier diagrams, for
ideal isentropic compression processes; and (3) empirical "quickie" charts.
frequently provided by compressor manufacturers for quick estimates. The
method to use depends upon the accuracy desired and the amount of data
available. In many cases, very great accuracy is not required: compressors
•
are rarely chosen to satisfy a given requirement very precisely. Overdesign is
quite common in order to provide an operating safety factor and to ensure
that expensive compression equipment is not required to be enhanced or replaced for relatively small capacity increases in the flOWing system. All three
methods. therefore, Bnd application in determining the compressor to use.
(9-14)
From the ideal gas law, for a unit mass of gas:
ZIRT I
Th~
AC'OOrding to the general energy equation (Equation ;·2 in Chapter j.
the theoretical work required to compress a unit mass of gas from pressure PI
at state 1 to ~ at state 2 is given by:
Jp, Vdp + .lvz!2g.. + (glg.J.6z + I"
I':l
(9-12)
where w - \",'ork done by the compressor on the gas, ft.lbf/lbm
V .. volume of a unit mass of gas, ft1llbm
p .. pressure, Ibf/ft 2
v - gas flow velOCity, (t/sec
z .. elevation above a datum plane, ft
I" '" lost work due to friction and irreversibilitie.s, ft-lbfllbm
g .. gravitational acceleration (= 32.17 ft /sec2)
g.. - conversion constant re1ating mass and weight ( _ 32.17Ibm-ft
Ibf-sec')
Neglecting frictional losses, and the changes in kinetic and potential energies, the energy baJance of Equation 9·12 can be written as:
w -
J
p,
(9-13)
where C is a constant, Upon integration, Equation 9-13 becomes:
~
k- 1
CI
k(~k
intake pressure, psia
intake volume, ft1
molecular weight of the gas, Ibm.'lbmole
gas compressibility factor at intake conditions
gas constant (
10.732 psia-ft1llbmole- O R)
gas intake temperature. OR
gas specific gravity (air - 1 basis)
Substituting for R and neglecting ZI which is unity for intake conditions at
or near atmospheric, we obtain:
(10.732)T,
PlY' -
(9-15)
(28.97h~
Substituting for PIV I from Equation 9-15 into Equation 9-14:
k (53.345)T, ((k
r
k-l
)'11:
w-~_
Ii k _
1)
•
(9-16)
r - (P2,'PI) is the compression ratio
w _ compression work. ft-Ibf.lbm
We usually need. to compute the compression power per MM.scfd of gas
flow, rather than the work \v required per pound-mass of gas, Now,
Substituting for V from Equation 9·2, we get:
w _
where PI '"
V,,..
M ""
Z ~ ""
TI ""
)'~ ""
where
JPtp, Vdp
w - Cl k 1'1 p lkdp
ZIRT,
PI V, '" ~ .. (28.9i h K
Analytic ",pproach
w -
415
Gas Compressioll
Cas PrUc/llcti(m Engilleerillg
414
I).k _ p\k-I)'k]
k
.. k -1 PI(C/pl)Ik[(Pt/PI)lk-llk - IJ
Converting pressure p from units of Ibf/fi2 to lbf/in.!, and substituting for Ci
PI from Equation 9-2, we get:
1 ft+lbf _ 1 ft-Ibf/min
Ibm
Ibm/ min
The gas flow rate in Ibm/min can be converted to MMscfd as follows:
z..,RT"" sef/min _ 1O.732T", :.t..'T
__ ~I OlIO
.
1 Ibm/min ____
p."M
28.97)'iCP..,
_ (1440)(10.732)T. MM"'lday
(28.97)(IO'h,p..
Using this and the fact that 1 hp - 33,000 ft.lb£/ min:
416
Cas Compression
1 ft·lbf _ (28.97)(IO'h,p.(II33.000) hp
Ibm
(1440)(10.732)T. MMocflday
_ (O.0568056h,v..
Toe
The compressor discharge temperature C;1n be calculated using Equation
9-9 for polytropic compression or Equation 9-10 for isentropic compression.
The heat removed in the intercoolers or aftercooler can be calculated using
the average specific heat at constant pressure, (Cpl." as fol1ows:
hp
Mr-.lscfd
Equation 9-16 can now be written in terms of the ideal horsepower per
"H - n,(c,).. "T
(9-21)
MM.scfd. IHpiMM.scFd (hp MMscfd), required for compressing the gas
through a compression ratio r as follows:
where
IHP
M~""fd
_ 3.0303 p.,T I _k_
TIC
(r1k-llk _
1)
k- 1
(9-17)
.o.H ., heat remo ....ed, Btu
n>l. - numher of mole«: of gas being cooled
(Cp)., - constant pressure molal specific heat of the gas at cooler
pressure and average cooler temperature, Btu/lbmole-°f
.o.T '" difference in gas temperature between the inlet and outlet
of the cooler, of
where PI<' (psia) and T sc (OR) aTC the standard conditions of pressure and
temperature, respectively, at which the standard cubic feet is defined. Thus,
Mollia Cha,.ts
the ideal (or theoretical) horsepower required for compre;sing Ck MMscfd
gas measured at pressure PO(' psia and temperature To< oR is given by:
Mol1ier charts for a gas are plots of enthalpy versus entropy as a function
of pressure and temperature. Mollier charts for natural gases with specific
gravities in the range of 0.6 to 1.0 are shown in Figures 9-12 through 9-17.
IHP _ 3.0303 q,..p..T! _k_
To<
(TI1- If k _
1)
k- 1
(text continued on page 419)
(9.18)
•
where k is the specific heat ratio at suction conditions.
This analysis assumed an ideal gas. Where deviation from ideal·gas behavior is significant, Equation 9-18 is empirically modified in several different ways. One such modification is:
(9-19)
where Zl, ~ - gas compressibility factors at the suction and discharge, respectively
Tl - inlet temperature, oR
i,
Ii
"i ,..
>
Temperature can be eliminated in Equation 9-19 if the gas flow rate is measured at suction temperature Tl (OR):
IHP _ 3.0303 Q.IP.(ZI + z,) _k_ (rHI" _ I)
2Z 1
k- 1
<
•
(9-20)
where q.l is the gas flow rate in MMscfd measured at any arbitrary pressure
p. psia and suction temperature Tl oR. A similar analytic expression can be
deri\'ed for the polytropic compression process also.
Figure 9· 12. Enthalpy-entropy diagram for O.60..gravity natural gas. (Alter
Brown, 1945; courtesy of SPE of AiM E.)
41'
cOJ
Compression
419
'."
!,
,
i
•
i,
•<
!
;,
•
f
'."
,;
i, ,
•
•>
•
Figure 9-13. Enthalpy-entropy diagram for O.70-gravity natural gas. (After
Brown. 1945; courtesy of SPE 01 AIM E.)
,
EntrOO>Y. BIY I*'
"
1>OU"Id-_
.
8
10
12
1* <Io9rM
Figure 9-15. Enthalpy-entropy diagram for a.90-gravity natural gas_ (After
Brown, 1945; courtesy of SPE of AIME.)
(text continued from page 417)
!, '."
'."
II
;l
f
•
[tt,. . .".
8tu
."'0'".
poor _ " " - _ _ ......
Figure 9-14. Enthalpy-entropy diagram for O.SO-gravity natural gas. (After
Brown, 1945; courtesy of SPE of AIM E.)
This method is a fairly good technique for solving comp~ion problems for
compressors that exhibit isentropic (ideal) compression, such as the reciprocating compressors, provided a Mollier chart is available for the gas being
compressed.
On a Mollier chart, an isothermal compression PI"()CeSS can be traced by
following the constant temperature lines, whereas an isentropic compression
process can be traced simply as a verticalJine parallel to the ordinate. Inter·
cooling, a constant·pressure (isobaric) process, is represented by following
the constant pressure lines. Thus, an ideal compression process can be represented on a Mollier diagram, and the state of the gas (pressure, temperature,
enthalpy, entropy) at the beginning or end of a compression process can be
determined directly. Figures 9-18 and 9-19 show such a procedure for a sin·
g1e-stage and two-stage reciprocating compressor, respectively. In Figure
9-18, inlet gas is compressed isentropically from the inlet conditions repre·
sented by point 1 to the outlet conditions represented by point 2. Point 1 is
determined by the given pressure and temperature conditions at the suction
end. whereas point 2 is known from the desired compression ratio (or dis·
charge pressure). Figure 9-19 shows a two-stage compression process with an
intercooler between the two stages and an aftercooler. The dotted line 1-2
•
420
Gaj ProdllC'tion J.:lIgineering
COJ
indicates isentropic compression in the first stage. The gas is then cooled in
the intercooler at constant pressure, as shown by line 2-3. Line 3-4 shows the
second isentropic compression stage, and line 4·5 shows the isobaric cooling
in the aftercooler.
Neglecting heat transfer from the gas to the compression equipment and
surroundings. lost work due to friction. and kinetic energy changes, the energy balance can be expressed as:
,
•! ,..
...
,
,I
•
i
(9-22)
where
,
••
421
Cornpre3rion
w - work done by the compressor on the gas, Btu
.6.H - change in enthalpy of the gas, Btu
n, - number of moles of gas being compressed, lbmoles
hI> h2 "" enthalpies of the gas at the compressor inlet and discharge,
respectively, Btu/lbmole
•
A lot of useful information regarding the compression process can be in-
-.
E~""",,_ 8,~
_
ferred from MolHer diagrams_ Referring to the Mollier diagram of Figure
" ,
-.0><1-"""" po.dtW..
9-19 for example, the net change in enthalpy (h z - h i) is known, and the
work done in the first stage of compression can be computed using Equation
Figure 9-16. Enthalpy-entropy diagram lor 1.O-gravity natural gas. (After Brown,
1945; courtesy of SPE 01 AIM E.)
9-22. Similarly, the work done in the second compression stage can be calculated using the enthalpy change (h.. - hJ). Intercooling requirements (heat
removed in the intercooler) are given by the difference in enthalpy beN'een
I
f,
I
I
•I
~
c
I'z
•
-11 -'4 -12 -10 -I
-I _ ,
-2
("''''''Y. "" -
0
2
111-- _
,
I
•
10
12
14
1
""""
•
Figure 9-17. Enthalpy-entropy diagram for O.70-gravity natural gas containing
10% nrtrogen. (After Brown, 1945; courtesy of SPE of AIM E.)
ENTROPY
Figure 9-18. Mollier diagram of a single-stage compression process.
•
422
Gas Production Engineering
Gas Compression
'23
hi - enthalpy of gas at intake, Btu/lbmole
hz ,., enthalpy of gas at discharge, Btu/lbmole
This power requirement in Btu/day can be converted to horsepower, IHP in
hp, as follows:
STAGE-I
o
1 hp
778.2 ft-lbffmin ng(hz - hlH Btu/day
IHP ,. 33,000 ft-Ibf/ min
Btu/m in
1440 min/day
(i)
1.6376 x 10 - ~ n,:(h z - hi )
t
(9-24)
where IHP - ideal compression horsepower required. hp.
G) ® <V KNOCKOUT ORUMSnO REMO .... E CONOENSEO LIQUID"
® @ COMPRESSORS .FIRST AND SECOND STAGB.
®
®
INTERSTAG[ COOLER/INTtRCOOLER
AI'"TERCOOL [R
-
PRESSURE, PSIA
Empirical "Quickie" Charts
This method uses actual compressor manufacturers' charts that relate
compression horsepower requirements to the applicable compression process
variables. This method has its advantages- it is simple and easy to use. and
it directly gives the actual requirements that include efficiency and other
factors for the actual real compressor. However, because only the most important compression variables are considered and the charts are quite spe_
cific for some assumed gas and compressor type, this method may not be
very accurate or more generally applicable to all cases. Usually, it gives
slightly higher results than the other two more exact methods. Further details regarding this approximate empirical method of compressor design are
discussed in succeeding sections on the design of reciprocating and centrifugal compressors.
Estimating the Actual (Brake) Horsepower From Ideal Horsepower
[NTROPY, Bhll'lbmol ·F _ _
Figure 9-19 . Molher diagram of a two-stage compression process.
points 2 and 3. Similarly, the heat required to be removed in the aftercooler
is equal to the difference in enthalpy between points 4 and 5.
The ideal compression power (or rate of work) required is given by:
The actual horsepower supplied by the compressor engine or driver is
known as brake horsepower (BHP). The BHP required by a compressor is
always greater than the ideal or theoretical horsepower IHP. The energy
Iosseo; are represented by two t)1>e5 of efficiencies: compression efficiency, "lie.
and mechanical efficiency of the compressor, "11m'
Compression efficiency is the ratio of the theoretical work requirement for
a given process (IHP) to the actual work required within the compressor cylinder or shaft to compress and deliver the gas (CUP):
(9-23)
where P - compression power required. BtuJday
ng - number of moles of gas being compressed
t - time for compression, days
oc.
(9-25)
•
Cal Compression
The compression efficiency fie includes effects due to thermodynamic deviations from the theoretical compression process (such as gas turbulence and
heating of the incoming gas), and fluid friction and leakage 1U'iSeS. For reciprocating compressors, it may also include a factor known as volumetric efficiency, to be discussed later. Compression efficiency does not include mechanicallU'iSeS. Besides some factors related to the compressor itseU that may
affect the compression process, compression efficiency is significantly affected by the operating conditions, such as suction pressure, compression ratio, and compressor ~~ and loading. The degree to which these factors
affect compression efficiency, however, is different for different compressor
types.
Mechanical efficiency, defined as the ratio of the compression power required within the compression chamber to the actual horsepower supplied
to it, includes frictional JU'iSeS in compressor packings and bearings, piston
ringo;, and other moving parts:
BHP
=
GHP + mechanical losses "" GHP
'm
(9-26)
The mechanical efficiency. flm' is related to the compressor type, its design
details, and the mechanical condition of the unit; the operating parameten;
of the compression process do not affect it significantly.
The BHP can be directly computed from IHP using an overall efficiency
factor, fI:
BHP~ IHP
(9-27)
•
425
compression to overcome the several limitations. such as compression ratio
achievable, inherent in single-stage compression. In designing reciprocating
compressors, the compression ratio r is rarely allowed to exceed a value of
4.0, and a r ::S 6 is considered the practical limit.
Theoretically, the total power required is a minimum when perfect intercooling is provided, there is no pressure loss between the stages, and the
compression ratio in each stage is the same. Thus, the optimum compression
ratio for each stage is given by:
(9-28)
where rop< r, ..
n,. ..
Pd ..
P...
optimum compression ratio per stage
total compression ratio desired
total number of stages
final discharge pressure, psia
suction pressure at the very first stage, psia
If intercoolers are provided between the stages, reduce the theoretical intake
prac;ure of each stage by about 3% to allow for interstage pressure drop.
This is equivalent to dividing the theoretical r from Equation 9-28 by
(O.97)'·~.
In practice. although Equation 9-28 results in minimum power, the net
work or energy required varies oo1y by a fraction of a percent for relatively
large variations in the compression ratios for individual stages. This is an
important fact, often used for flexibility in design for economic and technical reasons.
where the overall efficiency, fI, is equal to the product of the compression
and mechanical ef£iciencies:
Exam,m 9-2. For the problem given in Example9-1, what is the compression ratio and how many reciprocating compressor stages are required if: (a)
intercooUng is not provided, and (b) intercooling is provided.
In most modern compressors, 'Ie is in the range of 83% to 93% and '1m
ranges from 88% to95% (Ikoku, 1984). Thus, the overall compression efficiency 'I ( - 'le'l",) ranges from 73 % to 88 % for most modern compressors.
Solution
(a) Without intercooling.
Designing Reciprocating Compressors
Number of Stages
The first parameter in designing a compression system is to determine the
number of stages. As discussed earUer, it becomes necessary to use multistage
From Equation 9.28, rop! - (Pd/p,V"'''' (2.500/100)]· ... ., 25!· ...
For
For
n. ... 1, r .. 25, which is too high and hence unacceptable.
n. .. 2. r .. 5, which is less than 6, hence acceptable.
Thus, 2 compression stages are required, giving an r ... 5.
•
426
CD", Compression
GaJ Prod'lclioll Engineering
(b) With intercooling.
Allowing for Intcrstage pressure drop,
427
'.----!
Copt
=
(25:'0.97)1 ... _ 25.773
L
...
Repeating the procedure, for n. ,., 2. r - 5.077, which is less than 6. hence
acceptable.
Thus. 2 compression stages are required, gi~;ng an r - 5.077 ,
•
Horsepower Requirements
!--<'CfU.l
PISTON
The ideal horsepower IHP for reciprocating compressors can be obtained
using either the analytical method (Equation 9-19 or 9-20) , or Mollier charts
along with Equation 9-24. For the anal}tical method, intercooling requireme"l~ can be calculated using Equation 9-21. provided the specific heat for
the gas being compressed is known. In the Mollier chart method, intercooliog requirements can be determined directly from the enthalpy change indi o
cated on the enthalpy-entropy diagram.
The IHP can be converted to brake horse{XIwer requirements using Equation 9-27 if the overall efficiency "If is known. For reciprocating compressors,
volumetric (or clearance) efficiency is an important component of compression efficiencY"If< and, consequently. the overall efficiency "If.
Volumetric Effu:irtlCy
The ....olumetric or clearance efficiency. "If, . of a reciprocating compressor
is defined as the ratio of the \'Olume of gas actually delivered, corrected to
suction pressure and temperature, to the piston displacement. It represents
the efficiency of the compressor cylinder in compressing the gas. and accounts for gas leakage, heating of gas as it enters the compression chamber.
throttJing efrect on \·ah·es, re-expansion of trapped gas, etc.
The theoretical volumetric efficiency, "If" is a function of the compression
ratio and clearance, as follows:
_ __ _ YOlUIU
Figure 9-20, Pressure-volume diagram for the compression cycle of an actual
reciprocating compressor showing the effect of clearance.
(9-30)
where V I and V3 are the volumes on the pressure-volume diagram shown in
Figure 9-20. Volume V3 , representing the ....olume at the cylinder end not
swept by the piston, is called clearance volume. Clearance, usually varying
from 0.04 to 0.16, limits compressor throughput, and also results in horsepower being wasted in ~imply compressing and re-expanding the trapped
g",
The actual volumetric efficiency includes factors for other effects such as
incomplete filling of the cylinder, leakage. and friction (A), and lubrication
(Lu),
"lfv-l-A-Lu-Cl
where
"If, - 1 - (rlk - l )CI
where
(9-29)
r .. compression ratio
k .. isentropic exponent for the compression process
CI .. clearance, fraction
Clearance is defined as the ratio of clearance ....olume to the piston displacement (see Figure 9-20):
c.p.an
OtSPl .. t[~("T
(z~2," - 1 )
(9-31)
A _ factor for incomplete filling of the cylinder, leakage, friction, etc.; it is usually between 0.03 and 0.06
Lu _ compressor lubrication factor, generally 0.05 for non-lubricated compressors and zero otherwise
Z" ~ _ gas compressibility factors at the suction and discharge, respectively
From Equations 9-29 and 9-31, it is obvious that the volumetric efficiency 1).
increases with decreasing compression ratio, r, increasing isentropic expO-
,
428
Gat Production Engineering
G<u Compression
nent, k (for r > 1), and decreasing clearance. CI. These parameters can be
varied to alter the volumetric efficiency and, consequently, the flow capacity of a reciprocating compressor. Sometimes clearance is added to reduce
the capacity for fixed operating pressure conditions, or to prevent overloading the driver under variable operating pressure conditions by reducing the
capacity as compression ratio changes.
Figure 9-21 shows the effect of clearance on the volumetric efficiency of
reciprocating compressors. The effect of compression ratio (all other factors
429
RATIO-4
CLEARANCE
60
,l'~
y.
..." "",-<'
K '" I'~~
,'.'....,
r~l":-
141.
.~~
\~~
"-
~
o
114
PERCENT PISTON DISPLACEMENT
64 6'1. V
16." 'IE
o
881""'[
114 100
121 107
eo
60
40
20
o
Figure 9·22. Effect of different co.mpression ratios on the vol~metric efficiency
01 a reciprocating compressor cylinder. (From Compressed Air and Gas Data,
1982; courtesy of Ingersoll-Rand Co.)
PERCENT PISTON DISPLACEMENT
Figure 9-21 . Effect of clearance on the volumetric efficiency at constant compression ratio for reciprocating compressors. (From Compressed Air and Gas
Data, 1982; courtesy of Ingersoll-Rand Co.)
being the same) on volumetric efficiency is sho","T1 in Figure 9-22. Figure
9·23 shows the effect of the specific heat ratio or isentropic exponent, k, on
the volumetric efficiency, for a fixed compression ratio and clearance.
This discussion may lead one to believe that the clearance CI should be
kept as low as ~ible in order to maximize the volumetric efficiency. How·
ever, lower clearance may reduce the compression efficiency 11< which de·
pemis primarily upon the valve area, just like volumetric efficiency depends
primarily upon clearance. To obtain lower clearances, it is necessary to limit
the valve area (size and number of valves). Thus, the designer must find the
optimum clearance and valve area, depending upon the application desired
for the particular compressor design.
Direct Determination of Brake Horsepower
Brake horsepower (BHP) requirements for reciprocating compressors can
be estimated direct.ly from "quickie" charts. These charts plot the brake
horsepower required per million cubic feet of gas per day (BHPIMMcfd),
60
·N:
'~12~2<
~K.ll ",~
w
u
~ 40 r ~
'"
"'"w t--~~
'":t 20
..
", ,,, k.140
~
1-:-'
,,
~
I
o
1l~
•
100
80
~
~
"
~,
62,\V[
n.,\
V[
14''\V[
60
PERCENT PISTON
40
20
OISPLACEMENT
o
Figure 9-23. Effect of specific heat ratio k on the volumetric effICiency for a
given reciprocating compressor cylinder. (From Compressed Air and Gas Data,
1982; courtesy of Ingersoll·Rand Co.)
referred to some defined suction pressure and actual intake temperature,
versus the compression ratio r for different values or the isentropic exponent
k. Figures 9-24. 9.25, and 9·26 show such charts by the Ingersoll. Rand
Company (1982), based upon the analytic solution (Equation 9-20) cor(tn' continued on page 433)
430
Cas Compression
Gas Production Englfleering
IY I"
1/ I"
r/ I"
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to- V
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431
~ ~ V / /'
V '/ L
6 4~
66
6
, , ,, , , , , , , , ; , , , , ,
'
z;/ '/ V
60
58
IL: /'
V
COMPRESSION R.6.TlQ
56293 031
32333435363738394041424344 4 5
COt.4PRESSIQN
Figure 9-24. Compression power requirements for reciprocating compressors_
(From Compressed Ai, and Gas Data. 1982; courtesy of Ingersoll-Rand Co.)
RATIO
Figure 9·25. Compression power requirements lor reciprocating compressors.
(From Compressed Air and Gas Data, 1982; courtesy of Ingersoll-Rand Co.)
•
.32
Gal Compre.ulon
GOI Prodl4ction Eng/neerlng
"
"
6
V'
4
V
Vi
'"0
"
,/
4
,
/
./
6
,
/
110
/
108
7
/
~
rooo
,• .8
,/
N
u
,~
i
'4
88
/ ' 60
1. Suction pressure of 14.4 psia and actual intake temperature is assumed. The correction factor for intake pressure is generally included
in the calculation of BHP (as in Equation 9-32 or 9-33), or obtained
from Figure 9-27.
./
/
./
,\
,'0
./
./
7
./
/"
./
V
./
100TAlIl ,IIt:S_£-jOS,.
"
~
r"'<
,,
,
,~
o
1.4
IS
If
17
,I
,~
20
:1.1
n
•
--
, r-...
t.)
z• "
al'IOI'II{SSIOJ<
"
~UIO
-,, -
-
" "
'0 "
.. . .
~
~
Figure 9-27. Suction pressure correctIon factors for compression power requirements for reciprocating compressors. (From Compressed Ai, and Gas Data,
1982; courtesy of Ingersoll-Rand Co.)
~
>
•
CURVE C
2. Gas specific gravity of 1.0 is assumed. Correction factors for gas gravities other than 1.0 are shown in Figure 9-28 .
3. Cas compressibility factor of 1.0 is assumed. Corrections for gas compressibility are frequently included in the calculation of BHP (see
Equation 9-33).
4. A mechanical efficiency of 95% and a compression efficiency of
83.5% is assumed. BHP value:; should be corrected if this is not the
case.
5. The gas volume to be handled in each stage should be corrected to the
actual intake temperature and moisture content at intake to that stage.
6. Allow interstage pressure drop if intercoolers are used. As discussed before, reduce the theoretical intake pressure of each stage by about 3%,
./
./
01184950 51
.. ,
" "
..'" "
./
4 ~ 4 647
,
",
1\
8' . /
4
\
'\.
5
"
tUI'lV( 0
1\ 1;-'
4
./
86
",• ,
,
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./
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" ,
,
"
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./
./
,.
/ ' '0
/'
./
./
V
,/
./
84
./
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./
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./
./
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./
./
V
./
./
,/
./
./
, / ./
/
/
/
./
./
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/ ' 50
,45
./
/
,
7 7 40
/
./ /
/
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./ ./
./
'0
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./ ./
./
.6
V
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/ V /
./ , / ./
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'V
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0
o
rected for overall efficiency. These figures are applicable for designing each
compression stage individually and require the following considerations:
/
6
~
(ten continued from page 429)
70
/
8
'33
525354555657585960
RAllO
COMP~ESSION
Figure 9-26. ComPn:tsslon power requirements for recIprocating comressors.
(From Compressed Air and Gas Data, 1982; courtesy of Ingersoll-Rand Co.)
±
..
Gos Compression
,
"
.." \
,
I",
'",--
I'"
,~
t~
~
IZ
" ,"'0-
,
>
.....
I(
~ci
II
:;: ...
""
I~
:
100
••••
Q
-
~
'0
"
~tOM
O·
09
~
•
where Zl and ~ are the gas compressibility factors at the suction and discharge of the compressor. respectiyely. ;o..'ote that this procedure should be
applied for one compression stage at a time.
0-
~
Compressor Speed and Stroke Length
---y~
. " ';?: ~
" ~
,.
..
~
CURVE [
, "- I'---- ~
C-
0>
~
SPECIfiC GRAIIHf
""'-
0'
-
Note that Equation 9-32 includes the correction factor for intake pressure
and if Figure 9-2i is used for correcting the BHP for intake pressure, the
factor p..-' 14.4 should be omitted. The BHP from Equation 9-32 is corrected
for gas compressibility as follows:
(9-33)
,
~ ~
~~
The stroke length and/or compressor speed arc selected based upon the
following relationship for the flow capacity of reciprocating compressors:
(9-34)
,/
"
"
"
" "
,o
l
,
II
13
COMPRESSIO .. RAT,O
Figure 9·28. Gas specific gravity correction factors for compression power reqUirements lor reciprocating compressors. (From Compressed Air and Gas Dat8,
1982; courtesy of Ingersoll-Rand Co.)
which is equivalent to dividing the theoretical r from Equation 9-28 b\"
(0.97)1 _.
where q", = capacity of the reciprocating compressor. ftl/unit time
d = piston diameter, ft
L - stroke length. ft
S - compressor ~. strokes.'unit time
'I, - volumetric efficiency
For double-acting reciprocating compressors. the mlume occupied by the
piston rod should also be accounted for_ Thus. besides increasing volumetric
efficiency, the actual capacity of a reciprocating compressor can be in·
creased by increasing compressor speed and stroke length.
•
For a given gas flow rate of Clot MMscfd at standard conditions of pressure p,.
(psia) and temperature T ... (OR), the required BHP can be computed as follows:
(9-32)
where
435
BHP .. brake horsepower required, hp
ct,.; .. gas flow rate measured at pressure Po< (psia) and
temperature T", (OR), MMscfd
Tl .. gas temperature at the compressor suction (Inlet), OR
(BHPiMMcfd)fil .. BHP/MMcfd from Figures 9-24 through 9-26
E:tamplf! 9·3. A reciprocating: compression system is to be designed to com·
press 5 MMcfd of the gas in Example 9-1, with intercoolers and an aftercooler that cool the gas to 150°F. Find:
(a) Brake horsepower using the analytical method.
(b) Brake horsepower using ~tol1ier diagram method.
(c) Estimate the cooling requirements from the results of part (b).
(d) From the results of part (b). determine whether the first stage can be
handled by a compressor with a speed 1,200 rpm, piston diameter - 12 in., and stroke length - 3 ft.
Assume 'I ,. 0.80, A - 0.05, Lu ,. O. and CI - O.OS. Neglect any gas comPressibility factor effects .
•
436
Gas Productioll Enginemng
Gas Compres;rion
437
Similarly, forthesecond~i.age, niP - (1.6376 x 10- 5)(76,376.46)(5,300725)11 - 5,722.1 hp.
Solution
From Examples 9-1 and 9-2:
Thus. BHP for first stage - 3,039.310.80 - 3,799.1 hp.
1', - 0.612, k - 1.2565, r - 5.077,
n. - 2 stages.
and BHP for second stage - 5,722.1/0.80.., 7,152.6 hp.
(a) Anal)1ical method.
(c) Cooling requirements.
Using Equation 9·1ti. for each ot the m'o stages:
IHP
Cooling load for the intercooler (between stages 1 and 2)
- (76,376.46)(3,310 - 725) - 1.97 x 10' Btulda,..
(3.0303)(5)(100)(150)(1.2565) (5077"""" "'" _ 1) _ 2 9191 h
(0.2565)(150)·
,
.
P
And cooling load for the aftercooler (after stage 2)
- (76,376.46)[5,300 - ( - 200)]- 4.20 x 10' Btulday.
Therefore. BHP for first stage - 2.919.110.80". 3,648.9 hp.
and BlIP for ~nd stage - 3,648.9 hr.
(d) Compressor speed for the first stage.
(b) Mollier diagram method.
Using Equation 9-31, with Zj - Z2 - 1.
For a..,.~ - 0.612. the enthalpy-entropy diagram of Figure 9-12 is approximately applicable. Use of this diagram results in:
". - 1 - 0.05 - 0 - (0.08)(5.077' , "" - I ) _ 0.7385
Using Equation 9-34, the flow capacity of the given compressor is
Point
Process
1
Entering gas
2
After isentropic compression
3
4
After isobaric cooling
5
After isentropic compression
After isobaric cooling
Enthalpy, h
(Btu
p (psia), T(°F)
100 psia, 150°F
500 psia, 368°F
500 psia, 150"F
2,500 psia, 490"F
2,500 psia. 150"F
Ibmole)
q", -
«14)(1~(3)(1,200)(0.7385) - 2,088.06 cr'min - 3.0 MMcfd
Thus, the given compressor cannot handle 5 MMcfd gas.
B80
3,310
725
5.300
-200
Example 9-4. Assuming interoooling. repeat Example 9-3 using empirical
charts.
Solution
Using the gas law, the number of moles of gas is given by
From Example 9-3, "Y~ - 0.612, r - 5.077, k -. 1.2565, PI ""' 100 psia,
" - 0.80.
". - pVIZRT - (100)(5 x 10')1(1)(10.732)(610) - 76,376.46 Ibmolesl
d ay
From Figure 9-26, for the first stage, BHP/MMcfd
From Equation 9-24,
From Figure 9-28, the gas gravlty correction - 1.0
For the first stage, IHP - {1.6376 x 1O-5)(76,376.46){3,31O _ 880)1
1 - 3,039.3 hp.
Applying the appropriate correction factors, the BHP required for 5 MMcfd
gas measured at suction conditions of 100 pSia and 150°F is given by:
=0
98.2 hp.
•
Go~ Produdiorl EfI~ineering
44'
Gas CompressiOIl
Example 9-S. Find the horsepower required by a centrifugal (st raight.
through flo\\,. no intercooling) compressor for compressing 10 M~tcfd gal> at
suction conditions of ISO psia and BOoF to 500 psia. Assume ")'q .. 0.60,
k ... 1 296. and Z" Zz
:=
1.0.
BHP - (1.01)(9.181.3) + 30
447
9.303 hp.
Example 9-6. For the data given in Example 9-5. design a centrifugal
compressor using the empirical chart method.
Solutioll
SoIutioll
r .. 500 150 .. 3.333, \1,.. (28.97hll = (28.97)(0.60) '" 17.382 Ibm lb.
molt'
Flow capacity'" 10 M\tcfd ... (10 x 1(1)/(24 x 60) ... 6,944.4 dm
From Figure 9-11, for q ... 6.944.4 cfm, Ill' = 0.725
1. Horsepower.
From Example 9-5. r ... 3.333. M "" 17.382Ibmllbmole, k = 1. 296, and intake volume ... 6.944.4 cfrn al 150 psia and 80°F.
From Figure 9-32, for Cjl ... 6.944.4 cfm and r ,. 3.333, the basic
BHP ~ 900 hp.
From Equation 9·11.
n - 1 • _k_-_1 _
0.296
~ 0.315
n
k"
(1.296)(0.725)
From Figure 9-31, for r - 3.333 and k - 1.296, K""JT ,.. 0.967.
From Equation 9-43,
From Equation 9-36,
h _ (1.545)(460 + SO) (3.333"'" _ 1) _ 70,292.1 ft-lbflbm
,
(17.382)(0.3 15)
BHP _ (900)(150)(0.967)(28.97)
- 15,005.2 hp
(14.5)(17.382)
2. Number of stages.
~
Cas density at suct ion conditions is equaJ to
From Figure 9-30, basic head .. -ti,OOO ft-Ibf Ibm.
•
PI
PIM _
Z,RT,
(150)(17.382) _ 0.45 Ibm ft'
(1)(10.732)(540)
From Equation 9-42.
Therefore, the mass now rate, m is equal to
m_
qlPI
h _ (47 .000)(0.967)(28.97) .75.748.33 ft-lbf'lbm.
(17.382)
,
_ 10 x lQ"lftl/day 0.45 Ibm = 3 125 Ibm/min
1,440 min/day
ftJ
'
From Equation 9-41, the number of stages is equal to:
From Equation 9-38,
1\ ""' 75,748.33/9,500 _ 7.97 :::. 8 stages
GHP. (3. 125)(70.292. 1) .9 181. 3 h
(33.000)(0.725)
•
p
Using Equation 9-38, with the assumption that HPL m
HPLt. - I % of CHP,
3. Compressor speed.
_
30 hp, and
From Figure 9-29, for an intake volume of 6,944.4 drn. the compressor
speed S - 8,800 rpm .
•
438
Gall ProdUCtiOll Engineering
Co¥ ComprC8Sioll
where
BHP _ 'kPY (BHP/MMcfd). (0.95)(0.835)
14.4
11
f..
43.
hp - polytropic head. ft-lbfllbm
R "" gas constant, psia-ftl/lbrnole-°R
M '"' molecular weight of the gas, Ibmllbmole
144 - factor to convert from psia to Ibf/ft2
_ (5)(100)(98.2)(0.95)(0.835)
(14.4)(0.80)
- 2,704.8 hp
Thus, the ideal compra<>ion horsepower, IHP, for a gas mass flow rate of m
Ibm/min is given by:
The parameters for the second stage are the same. Therefore. second sta,a:l"
brake horsepower reqUired is also equal to 2.704.8 hp.
where
Designing Centrifugal Compressors
Analytical Method
Calculations for centrifugal compres.'iOrs are vcry similar to those for reciprocating compressors. An analytic expression for the ideal horsepower,
IHP, can be derived. similar to Equation 9-19 for reciprocating compressor\,
by replacing the i.~ntropic exponent k by the polytropic exponent n:
(r" "" _ I)
IHP _ 3.0303'kPYT,(Z, + z,) _n_
2ZJToc
n-i
(9-37)
IHP "" ideal compression horsepower required, hp
m ... mass flow rate of the gas, Ibmfmin
33,000 - factor to convert power requirement from ft-lbf/min to hp
The gas horsepo\\"er, CHP, is given by:
GHP-
mhp
33,000 '1p
(9·38)
where 'lp is the poJ}1ropic compression efficiency (fraction).
(9·35)
•
Mollier Charts
where, as before:
IHP - theoretical horsepower required for compression, hp
q,., - gas flow rate, MMscfd, measured at pressure p",. psia and temperature T . OR
ZJ. Zt - gas compressibility factors at the compressor suction and discharge, respectively
TL - gas inlet (suction) temperature. OR
n - pol)1ropic exponent
r - compression ratio
For centrifugal compressors, the theoretical work required for compression
is represented by the polytropic head hp, similar to the theoretical work requirement w for reciprocating compressors (see Equation 9-16):
hp _ (144)RTL(Zj + Z2) _n_ (rn - II
2Z j M
_ 1545TL(ZL
+ Z,)
2Z j M
n _
1)
Mollier charts, if available for the gas, can also be used for determining
the compression parameters. The procedure outlined earlier for reciprocating compressors is used. with the assumption of isentropic compression. The
polytropic head hp is then calculated as:
(9-39)
where hp - pol}1rOpic head. ft·lbflbm
6h - enthalpy change for isentropic compression determined from
the Mollier diagram. Btullbmole
'lp - polytropic efficiency
11k - isentropic efficiency
M - gas molecular wei~ht, lbmllbmole
n - 1
_n_ (rn-I)
n- 1
n _
I)
(9-36)
The factor 778.2 ft-lbf/Btu in Equation 9-39 gives the desired units conn'.'rsion. Subsequently, the gas horsepower CHP can be determined using Equation 9-38.
440
COl Production Engineering
Gas Compression
441
Estimating the Actual Horsepower
The BHP for centrifugal compressors is generally estimated br adding the
mechanical and hydraulic losses to the GHP:
BHP - GHP + HPL", + HPL,.
(9-40)
where HPL"" HPLt. - mechanical and hydraulic horsepower losses, repectively, hp
Mechanical horsepower losses, consisting of losses in the COmpressor seals
and bearings. are generally in the range of 7 to 50 hp, depending on the
speed and casing size of the unit. Hydraulic horsepower losses, consisting of
ctl5ing and piston leakage losses, vary between 0.3% to 2.5% of the gas
horsepower CHp, depending primarily on the size of the unit. With increasing Si7.e, mechanical losses increase, whereas hydraulic losses decrease.
Number of Stages
The polytropic head. hp • is an indication of the number of stages required
for centrifugal compression. The number of stages required, ,\, is given by:
..
h
n, - --"'--
9.500
(9·41 )
where 9.500 ft·lbf%m is a common limit assigned to each centrifugal compression stage.
Equation 9-41 assumes that all impellers are running at optimum design
speeds, and that each deve10ps a polytropic head of 9,500 rt-lhfilbm. Although the latter is true for most industrial units, machines with greater
polytropic head per stage can and have been designed.
~
Figure 9-29. Straight-through flow centrifugal compressor speed. (From Com·
pressed Air and Gas Data, 1982; courtesy of Ingersoll.Rand Co.)
Compressor speed can be estimated using Figure 9-29 as a function of the
intake volume. Cenerallv. the compressor speed is obtained from Figure
9-29 by reading directly ~t the center of the shaded area that indicates the
range usually involved.
Compressor Speed
Empirical Charts
Centrifugal compressor performance is highly dependent upon speed.
The capacity varies directly as the speed, S, the head deve10ped varies as the
square of the speed, and the required horsepower varies as the cube of the
,peed,
Centrifugal compre5S0r parameters can also be obtained from Figures
9-30 through 9-34. Figure 9-30 shows the polytropic head, h p , ver.sus thc
compression ratio r for various intake temperatures T 1. The corrections required in the computation of the actual polytropic head for a givcn case are
as follows:
1. For a polytropic exponent n other than 1.396, use Fi~~ 9-31 for. determining the "k" value correction factor, K.,..,. (Surpnslngiy, the !tter-
•
448
Gta Compreuion
Gos Production Eligillt'f."ring
ciprocating compressor, because of the speed and compactness .of the rotary
that provides relatively little time or surface area for gas coohng.
Designing Rotary Compressors
Rotary positive-displacement compressors follow the same basic theory as
reciprocating positive-displacement compressors and are designed using the
.
same theoretical relationships. There are, however. some differences and
empirical corrections introduced by the speciHe design.
\\ell-designed rotary sliding-vane compressors do not ha\'e the clearance
typical of reciprocating compressors. There are, howe\'er, leaka~e or slip
losses between adjacent cells across the vanes at their edges and ends - -some
amount of the gas escapes past to the suction side. These Ios.c;es are difficult
to theorize, and are generally estimated from actual tests.
The capacity of rotary two-impeller compressors also is subject to leakage
or slip losses rather than losses related to clearance. The losses are minimized
by operating at or near the built-in. fixed compression ratio for which the
unit is designed to give optimum performance. Low-clearance scaling is the
usual method for controlling slip losses. Factors that increase slip losses are
high pressure differential or rise across the compressor, and low gas density.
Slip is usually independent of speed, but for more complex designs. it may
be speed-dependent.
Slip is generally reported as capacity lost, dm (cubic feet per minute) at
suction conditions. It may also be accounted for as the additional rpm (rotations per minute) required to deliver a given amount of gas:
(9-46)
where
S, .. total rpm
qd - desired capacity, cfm
Questions and Problems
1. What are the desirable traits for a compressor?
2. List the applications of the various compressor types, giving appropriate reac:oos for the5(>.
3. Using basic thermodynamic principles, show that:
(a) cp - c.. - R
(b) Cp .. 5RJ2, and
4.
5.
6.
7.
. .
monoatomlc Ideal gases
For a reciprocating compressor, is volumetric efficiency the same as
compression efficiency? Why? Also, why is polytropic efficiency primarily a function of the intake volume?
Discuss the basis and applicability of Equation 9-39 for determining
the polytropic head of a centrifugal compressor from Mollier charts.
Express the relationship of Figure 9-11 as a correlation equation.
Calculate the isentropic exponent at 100°F and 500 psia for a gas with
the following composition (in weight %): C l - 89.1, C 2 - 6.05,
C 3 - l.1l, n.C~ = 0.35, i-C~ ., 0.18, H 2S - 1.55, and CO 2 - 1.66.
Determine the polytropic exponent from: (1) thermodynamic charts
(Chapter 3), and (2) polytropic efficiency, given an intake volume of
10,000 dm.
You have been assigned to a gas field where you notice an old compressor that can be repaired and used in the future. Searching through the
company records you find that the ratio of the inlet temperature (OR)
to outlet temperature rR) was 0.769 when the flow rate was 3,000
Mscfd. The inJet pressure was 1,000 psia and the horsepower was 200
c.. .. 3R/2 for
hp.
V d .. displacement, efr (cubic feet per revolution)
S, .. slip, rpm
The total rpm determined from Equation 9 -46 is used in horsepower or capacity calculations, as follows:
BHP - 0.005 VdS,(dp)
449
(9-47)
where ~p is the pressure differential (or rise), and 0.005 is a constant.
Capacity control is provided by var};ng the speed, or by installing multiple units. The discharge temperature of a rotar}' compressor can theoretically be calculated using the relationship for reciprocating compressors
(Equation 9-10). In practice, the discharge temperature of a rotary compressor is substantially higher than that for an equivalent water-cooled re-
(a) What is the compression ratio (assume k - 1.28 and )', - 0.6), and
the outlet pressure?
(b) Assume that the compressor is used as the first stage in a two-stage
compression system. The outlet gas from the first stage is cooled to its
initial temperature. If the gas in the second stage is compressed to
7,000 psia, what is the outlet temperature? Use Mollier charts.
(c) Determine the theoretical horsepower for the second stage in part
(b) using Mollier charts.
S. A compressor is to be instaUed for handling gas supply into a transmission line. The compression requirements are as follows:
Cas flow rate" 17.5 MMcfd at intake conditions of 450 psia and
goOF, discharge pressure _ 6,000 psia, and gas gravity 1', - 0.83. Intercooling to lOO°F or any reasonably low temperature is desired.
•
"2
Gas ProdU{'tioll Engineering
Cas CompressiOlI
ature consistently refers to this n" value correction factor as the "k"
value correction factor.)
2. Appropriate adjustment for a gas molecular weight other than 28.97
(air). As shown by Equation 9--36, the polytropic head is inversely proportional to gas molecular weight M.
3. Correction for gas compressibility factors other than unity. as included
in Equation 9-36.
..•f-k,.y,'" /
h
,
~o.,
u
•
, "-
~09
~
u
::! 09
,
"-
"-
~
~ 0 .•
- "-- .,..,
k
• 08
~y;
••
••
- .-
•
.-
~
0.'
~
?
7.~ /v.;:
,-:,~~
: ~T"!:':"":"OT-:::
:~:.::~
.
•
-
1
,
,
•
CO~PII(SSION
---- " ---, , ,
-
•
"ATIO (Pz p'l
Figure 9-31. k-value correction factors for the brake horsepower requirements
for straight-through flow centrifugal compressors (From Compressed Air and
Gas Data, 1982; courtesy of Ingersoll·Rand Co.)
Knowing the polytropic head, hI" the number of stages required for centrifugal compression. Il,., can be calculated as before using Equation 9-41.
Compressor speed can be obtained from Figure 9·29 as before.
Figure 9-32 shows the brake horsepower BHP '-ersus the intake gas volume measured at 14.5 psia pressure and actual intake temperature. In addition to correction factors applicable to head hI" determination of actual
BliP requires a correction for intake pressure other than 14.5 psia. Thus, the
actual BHP is determined from the basic brake horsepower, (BlIP),;", given
in Figure 9-32 as follows:
BHP _ (BHP)",(p,)(K o .,)(28.97)(Z, + Z,)
2(l4.5)Z,M
I
,
CQtolP"E5SION
-
~ 'i
!/
•••
o. ,
,
,
,,
,
7
.~
.. ,
j
0.'
:.
'-0
, ----
t'-
, •
~
flOM
"
,
uO.9
(9-42)
v U
1396
'00
•o
h _ (h pli,,(K,.,,)(28.97)(Z, + Z,)
I'
2ZIM
.J.
/.,/
;: 0.9
Thus. the applicable actual head hp is determined from the basic head (h ,h
given in Figure 9·30 as follows:
I
I
,.0
443
R4no
("alp, I
Figure 9·30. Basic head for straight-through flow centrifugal compressors
(From CompreSSed Air and Gas Dara, 1982; courtesy of Ingersoll·Rand Co.)
(9-43)
Basic brake horsepower requirements for intercooled centrifugal compressors are shown in Figure 9-33. Appropriate correction factors need to be applied for the polytropic exponent. intake pressure and temperature, intercooling temperature, gas gravity. and gas compressibility factor.
..
444
Gas Production Euglucrnllg
Gas Compression
§/ II
'"j
I
•
•o•
--
••
/
VII II.
7(1, r;
"
Ifill
I.
••
Flgu~e
9-32. Basic brake horsepower requirements for straight-through flow
0,ngersolJ-Rand
entnfugaJ compressors. (From Compressed Air and Gas Data 1982' courtesy 0'
Co.)
,
,
V-
$I
I,P'
J.
I.,~ /
/
;
1/
V
/ / /
~
~
~
I;
/
./
./
I-l'
I;
I;
~
V-
------ I'
./
------
-
l.--
I;
~ ~ '"
I:
,
./
/
'j
•
•
,••
•"~•
V
445
'"
I
rs / ~
~
Figure 9-34. Temperature rise multiplier for determining the discharge temperature for straight·through flow centrifugal compressors. (From Compressed Air
and Gas Data, 1982; courtesy of Ingerson·Rand Co.)
The discharge temperature of the compressed gas from a straight-through
flow centrifugal compressor can be obtained, using Figure 9-34, as follows:
(9-44)
where Tit T2 - intake and discharge temperatures, respectively, OR
T nn - temperature rise multiplier from Figure 9-34
The discharge volume, V 2 , of the compressed gas can now be calculated:
(9-45)
1IIT.u:1 ¥OUI' U -_
TIt(IIJ$A_ 01< aM
Figure 9-33. Basic brake horsepower requirements for interCooled centrilu
I
c~mpr~~rs for air at 14.1 psla and 95°F intake, with perfect Intercoollng (int~~­
~:u~~e~~ eOI t~~~;~I~~A~~~ ~~)F).
(From Compressed Air and Gas D8t8, 1982;
where Ph V" T J
intake pressure, volume, and temperature of the gas.
respectively
1>2, V\!, T2 - discharge pressure, volume, and temperature of the
gas, respecth·cly
-
•
450
Gos Prod,u·tion Engineering
Cive the design specifications (number of stages, compression ratio,
CHp, BHP, speed, intercooling requirements, etc.), using at least two
methods, for a reciprocating compressor. and a centrifugal compressor.
Compare the requirements and select the one, giving reasons, that is
most suitable for this application.
10
References
Gas Flow Measurement
Brown. C. C., 1945. "A Series of Enthalpy-Entropy Charts for Natural
Gases," Trans., AIME. 160,65-76.
GPSA. 1981. Engineering Data Book, 9th ed. (5th revision). Gas Processors
Suppliers Association, Tui5a, Oklahoma.
U:oku, C. U., 1984. Natural Gas Production Engineering. John Wiley &
Sons, New York. 5Jipp.
Ingersoll-Rand Company, 1982. Compressed Air and Gas Data. IngersollRand Co., Woodcliff Lake, NJ.
Introduction
Gas flow measurement constitutes one of the more important auxiliary
operations related to gas production and transport. It is required to enable
the determination of the amount of gas being produced or sold, and also as a
basic parameter for almost all of the design procedures. The produced gas
stream is in a continuous state of flow from the instant it leaves the reservoir
until it is consumed at the delivery end. Therefore. e:tcept for underground
storage or other storages such as LNG (liquified natural gas) storage facilities, gas measurements must be done on a flowing stream of gas. Accuracy
in measurement is obviously of prime importance: an error of only 1 % for a
typical pipeline delivering 300 MMscfd (109.5 Bscf'year) can result in an er·
ror of approximately 1.1 Bscf year of gas which. at a typical gas price of
S3.00/Mscf, would amount to a loss of $3.3 million to the buyer or seller.
Cas is most commonly measured in terms of volume because of the simplicity of such a procedure. However, to make this volumetric measurement
more meaningful, base or standard pressure and temperature conditions are
defined that yield measurements in standard cubic feet. This volumetric
rate can be converted to mass flow rate by multiplying with the gas density
at the standard pressure and temperature conditions. Since the gas density
at the specified standard conditions is a constant for the particular gas under
consideration, measurements in standard cubic feet are synonymous to mass
flow rate measurement. However, the number of standard cubic feet measured depends upon the standard pressure and temperature conditions chosen. Table 10·1 shows some such measurement bases. The most common basis is the ACA and API recommended pressure of 14.73 psia and temperature
of 60°F.
451
•
452
Gas Flow
GO! Production Engineering
Table 10-1
Common Ga. Pressure and Temperature Bases for Measurement
Base pressure
psi.
Ba. . temperlltur.
Thus. Oklahoma, Kansas. Arkansas,
and AlbertI! (C.n.da)
California
14.65
14.7
AGA. API
14.73
00
00
00
State
t: .5. 8",,,,, ... "f Shu..:i.uu.,
and Feckul Price Commbuon
l.oul>iana
14 735
15_025
of
453
measured rate of 100 MMscfd, it is between 99 and 101 MMscfd . An accuracy of ± 1 % of reading, however, implies that the measured flow rate is
within 9.9 to 10.1 MMscfd (or a measured rate of 10 MMscfd, 49.5 to 50.5
for a measured rate of 50 MMscfd, 99 to 101 MMscfd for a measured rate of
100 MMscfd , etc. Thus, the percent o( reading results in a better overall perfonnance because the error is proportional to the magnitude of the rate. Positive displacement meters and turbine meters usually have a percent of reading accuracy, whereas orifice meters and rotameters have a percent of full
scale accuracy in their <;pecifications.
00
Rongeability
'"
A flowmeter's rangeability is the ratio of the maximum flow rate to the
minimum flow rate at the specified accuracy.
Measurement Fundamentals
"'ow is one of the most difficult variables to measure (Campbell, 1984),
because it cannot be measured directly like pressure and temperature. It
must be inferred by indirect means, such as the pressure differential over a
specified distance, speed of rotation of a rotating element, displacement rate
in a measurement chamber, etc. For this and other reasons, many flow measure~en~ techn iques and devices have been developed for a wide range of
apphcatlons. This discussion is limited to those devices that have found use
in the oil and gas industry, primarily for natural gas measurement.
Attributes of Flow Devices
A flowmeter or measurement device is characterized using the following
parameters.
Accuracy
This Is a measure of a flowmeter's ability to indicate the actual fl ow rate
within a specified now-ratc range. It is defined as the ratio of the diHerence
between the actual and measured rates to the actual rate.
Accuracy _ Abs [Actual rate - Measured rate] x 100 %
Actual rate
MeOl1l.ltemlmt
(10-1)
where Abs(x) represents the absolute value of the argument x. Accuracy is
reported in either of two ways: percent of full scale, or percent of reading.
For example, for a loo-MMscfd flowmeter, a ± 1 % of full scale accuracy
means that the measured flow rate is within ± 1 MMscfd of the actual flow
rate, regardless of the value of the flow rate. Thus, for a measured flow rate
of 10 MMscfd , the actua1 flow rate is between 9 and 11 MMscfd, and for a
'l'
Maximum rate that can be measured
Rangea b I Ity - ;:;::::;:==.:c;=-T'::...:=..;:::..::===;c
Minimum rate that can be measured
(10-2)
Rangeability is usually reported as a ratio x: 1. For example, a meter with
maximum and minimum rates of 50 MMscfd and 10 MMscfd, respectively,
for a specified accuracy of ± 1%, has a rangeability of 5: 1. This rangeability can be increased to 10: 1 by decreasing the minimum rate by a mere 5
MMscfd to 5 MMscfd resulting in a 5- to 5O-MMscfd meter, or by increasing
the maximum rate by 50 MMscfd to 100 MMscfd resulting in a 10- to 100MMscfd meter. Thus, it is important to know the flow rate range over
which a quoted rangeability applies.
Repeatability
Also known as reproducibility or precision, repeatability is the ability of a
meter to reproduce the same measured readinw; for identical flow conditions over a period of time. It is computed as the maximum diHerence between measured readings, sometimes expressed as a percent of full scale.
Notc that repeatability does not imply accu racy; a flowmeter may have very
good repeatability, but a lower overall accuracy.
Linearity
This is a measure of the deviation of the calibration curve of a meter from
a straight line. It can be specified over a given flow-rate range, or at a given
flow rate. A linear calibration curve is desirable because it leads to a constant metering accuracy, with no portion of the sca1e being relatively more
~r less sensitive than the other. Note that a flowmeter could have a good
linearity, but poor accuracy if its calibration curve is offset (shifted).
•
454
Cas Production Engineering
Gas Flow Measurement
455
Selection of Measurement Devices
The selection of a measurement device depends upon:
1.
2.
3.
4.
Accuracy and reliability of the device.
Range of flow rate-maximum and minimum.
Range of flow temperature and pressure.
Fluid to be measured-gas or liquid, their constituents and specific
gravity.
5. Maintenance requirements.
6. Expected life of the device, and its initial and operating costs.
7. Other considerations, such as simplicity. availability of power or other
inputs required by the device, its susceptibility to theft or vandalism,
etc.
Methods of Measurement
Figure 10-1. ~ ve~turi meter. (After Corcoran and Honeywell, 1975; courtesy of
Chemical Engineering.)
\/fmturi Meter
This type of meter, shown in Figure 10-1 , consists of a short pipe section
tapering into a throat, coupled with a relatively longer diverging pipe section for pressure recovery. It is similar to an orifice meter, with the advantage of low pressure loss, and is a preferred choice where less pressure drop is
available. Venturi meters have a rangeability of 3.5:1, with an accuracy of
± 1 % (Corcoran and Hone)'\\!ell , 1975).
A brief introduction to the different fluid measurement methods, well described in the American Society of Mechanical Engineers' report on this subject (ASME, 1971), and by Corcoran and Honeywell (1975), is presented
here.
-
Differential Pressure Method
In this method, the flow rate is computed using the pressure difference
over a flow interval or restriction and other data. There are basically two
types of differential pressure devices: one in which the pressure difference is
measured across a flow restriction, such as the orifice meter, venturi meter,
etc., and the second type where the difference in pressure is measured upon
impact, such as the pitot tube. The dynamics of the relationships involved
have been studied in great detail for these types of meters, and very precise
and accurate results can be obtained from them. Some of the commonly
used differential pressure devices are described.
Orifice Meter
This is by far the most commonly used device for metering natural gas. It
consists of a flat metal plate with a circuJar hole, centered in a pair of
flanges in a straight pipe section. The pressure differential is mea~ured
across this plate to yield the flow rate. This is a rugged, accurate, simple,
and economical device, and can handle a wide range of flow rates. Orifice
meters have a rangeability of about 3.5: I, with an accuracy on the order of
± 0.5% (Corcoran and Honeywell , 1975). Details of this important meter
type are discussed later in this chapter.
•
Figure 10-2. Flow nozzle. (After Corcoran and Honeywell, 1975; courtesy of
Chemical Engineering.)
Flow Nozzlel!
Flow nozzles have a rounded edge that aids the handling of solids in the
flow stream (see Figure 10-2), The analysis is similar to orifice meters. Flow
nozzles are used for high flow rate streams, because they permit, for the
same line size and pressure differential , a 60% greater rate of flow than an
orifice plate (Corcoran and Honeywell. 1975). Flow nozzle; have a rangeahility of 3.5:1, with an accuracy of ± 1.5-2% (Corcoran and Honeywell,
1975).
Pitot (]mpacl) l ... be
Figure 10-3 shows a pitot tube installed in a pipe section. The pitot tube
measures the difference between the static pressure at the wall of the flow
conduit and the flowing pressure at its impact tip where the kinetic energy
of the flOwing stream is converted into pressure. It gives the flow velocity
<5.
Gas Flow Measurement
Gas Production Engineering
GUIde wine for
po$'I'on and
dorKtion of
ImPKt 1<P~~
is maintained, and it is only necessary to determine the upstream pressure,
~
Figure 10-3. Pilot tube metering. (Aller
Corcoran and Honeywell, 1975; courtesy 01
$Iat" pressure,
Chemical Engineering .)
,
\~ ImpiICl
liP
only at a point (at the tip). To compute the mean flow velocity. the calibration must account for the velocity profile in the flow conduit. Another factor
that makes the cAlibration of a pitot tube difficult is the low pressure differential produced by it. The tip can be easily clogged by liquids or solids.
Because of the relatively poor accuracy of this device (most of the error is in
measuring the static pressure), it is not used very often, except on a temporary basis.
This device
.57
co~ists
gas gravity, and the £Jawing temperature (see Equation 7-83) in order to calculate the gas £Jow rate.
II is important to note that the critical-flow prover u.ses a rounded-edge
orifice, because sharp-edged orifices do not conform to critical flow theories
and do not give a good repeatability.
Displacement Meters
These meters measure the volumetric displacement of the f1wd at flowing
conditions. The number of such known volumes through the meter per unit
time, corrected to the base pressure and temperature. are counted to give
the flow rate, instantaneous andlor cumulative. through the meter. Displacement meters are also called positive-displacement meters because they
afford a positive volume at flowing conditions: the flow is divided into is0lated measured volumes, and the number of these volumes are counted in
some manner. This is in contrast with the other meter types, sometimes referred. to as rate meters, in which the fluid passes without being divided into
isolated quantities.
Figure 10-4 shows the two types of displacement meters commonly used:
rotary or impeller type, and slide-valve diaphragm type. The rotary type
Drove 10_.
•
of a nipple, equipped with a flange to facilitate the
attachment of different sharp-edged orifice plates at its end. The device discharges the gas to the atmosphere, and only the static prm;ure just upstream
of this plate needs to be measured. It has limited accuracy, but finds application where gas is at relatively low prm;ures and is being produced to the
atmosphere.
Critical· Flow Proven
Similar to the orifice well tester, a critical-flow prover consists of a special
nipple equipped to facilitate the attachment of orifice plates at its end, and
it discharges the gas to the atmosphere. The critical-flow pro\'er, however, is
based upon the principle of critical flow of gases through £Jow restrictions
(see critical £Jaw through chokes in Chapter 7), In this device, critical flow
Cvhnders
tfourl
(two)
Figure 10-4. Displacement meters: (a) rotary meter, (b) reciprocating·piston
meter. (After Corcoran and Honeywell, 1975; courtesy of ChemicaJ Engineering .)
45.
Go, Flow Measurement
Ga. Production Engineering
consists of a rotating element, whereas the diaphragm type has a piston-C)'Iinder arrangement. Both are quite similar in operation. They contain measuring elements (or chambers) of known volume, with valves that channel
the gas into and out of these measuring elements. and counters to count the
number of times the measuring element is filled per unit time.
Turbine MetelV"'"
The.se- mf"ter; art> sometimes classified as positi"e-di>plaLtment meters.
They consist of a turbine or propeller that turns at a speed proportional to
the velocity of the gas flowing past it. converting linear velocity to rotational speed (see Figure 10-5). The speed of the turbine is measured as pulses
that give the rate. These pulses are counted to give the instantaneous rate, or
accumulated to give the cumulative rate.
45.
Elbow (Centrifugal) Meter
This device. shown in Figure 10-6. is based upon the principle of centrifual force that is generated when the fluid changes its direction of flow along
g irCuiar path. The magnitude of this centrifugal force is governed by the
a.c diameter, the radius of the circu1ar bend in the pipe, the flow velocity,
~: other fl uid properties. An elbow meter creates relatively little pressure
loss or differential , and is therefore used primarily for control o~ other ~ur­
poses. It finds some application in large pipes where a substantial centnfugal force is generated. Elbow meters have a rangeability of 3: 1, with an accuracy of ± 1 % (Corcoran and Honeywell, 1975).
-
•
__
Pr"~~lJfe
IJIJS
•
Figure 10-6 . An elbow meter. (After Corcoran and Honeywell , 1975; courtesy of
Chemical Engineering.)
FIgure 10-5. A turbine meter. (After Corcoran and Honeywell, 1975; courtesy of
Chemical Engineering.)
Rotameter (Variable Area Meter)
The driving torque for the propeller is proportional to the fluid densit~
and the square of the fluid velocity. Turbine meters have therefore traditionally been used for measuring liquid flow rates rather than gas flow rate!>
Fluctuations in velocity, caused by pressure fluctuations, turbulence, or un·
steady-state flow conditions, will cause the turbine meter to give a higher
than actual value. To allow sustained accuracy and trouble-free operation.
filters are almoo always used ahead of the turbine meter. Thrbine meter~
typically have a rangeability up to 100: 1 for gases, with an accuracy of
±0.25% and a repeatability of ±0.05 % (Evans, 1973). Further details
about turbine meters can be obtained from November (1972) and Evans
(1973).
A rotameter is essentially a variable orifice meter. The fluid stream is
th rottled by a constriction, but instead of measuring the pressure differential across a fixed sized orifice. rotameters vary the size of the flow constriction to accommodate the flow rate, keeping the differential pressure constant. Rotameters consist of a float that is free to move up and down in a
vertical tube that has a gradual taper down to its base. The fluid entering at
the base of the tube causes the float to rise, until the annular area between
the float and the tube wall is sueh that the pressure drop across this constriction is just sufficient to support the float. The flow rate is directly read-off
from the graduations etched upon the glass tube (see Figure 10-7).
Rotameters have a rangeability of 10:1, with an accuracy of ± 1 % (CorCOran and Honeywell , 1975).
460
St~!f",q
Gal Production Engineering
1)0.
t
gMtlltd
0"9"
"I~
ours.dt !>ere
se,e",o" ••,
Gas I-'Jow MeaSllremelit
1984). The rate of vortex formation and shedding is directly proportional to
the volumetric now rate, and ino.·ersely proportional to the diameter of the
object. Thus, the flow rate can be inferred from vortex shedding measurements,
The formed vortice; can be detected in a number of ways. Four methods
are mainly used:
",.;:==~
_,.".--::::::::;p
S,,,tI,"9 boa
Sr~ff'''Q bOo ,,,.,... ---6",-,,~'
10
I~hltn
CO~OCI'Y
q,oduahons erched
.Iull,n..
Figure 10-7. A rotameter (From
Chemical Engineers' Handbook
1984; courtesy of McGraw-Hil',
Publishing Company.)
-Dead "q""oe pree.s,on - bore
00<05','COI.-90U lope,ed
mete""o; r.. ot
Soul/,nq boo 10 ....1.".0 hom
o.. !. dt ~., ....IIl on9'.
~
Inltl
These devices.are based upon the principle of vortex shedding, which occurs when a £lUld flows past a non-streamlined (blunt) object. The flow is
unable to follow the shape of the blunt object, also referred to as £low element, and separates from it. This separation of the flow leads to the forma?on of eddies or turbulent vortices on the surfaces along the sides of the obJect that grow in size as they move downstream, and are eventually shed or
detached from ~e obj~ (see Figur~ lO~8a and b). Shedding takes place
alternately at either side of the object (Chemical Engineers' Handbook ,
!..... -ryWoo-~
112
~~~
~@
\0
1. Thermistors that detect the change in temperature caused by the
changing flow of the fluid as a vortex passes.
2. A magnetic pickup coil to count the oscillations imposed on a spht!re or
disk by the vortice; as they alternate on the two sides of the object (a
transverse passage is provided in the flow element to allow movement
of the sphere or disk).
3. Counting the motion or the induced mechanical stresses on a vane that
extends behind the blunt body and moves from side to side with the
passing of the alternating vortice;.
4. Ultrasonic transmitters and receivers that detect the vortices using a
sonic beam.
Vortex-shedding flowmeters have a rangeability of about 15: 1 or greater,
an accuracy of ±O.Z5 to 1 % of reading, and a repeatability of ± I % of
reading (DeVries, 1982). The flow regime, however, must remain turbulent
over the entire range of flow rate. Additional details on these meters can be
obtained from Powers (1975) and DeVries (1982).
Vortex-Shedding F10wmetcrs
-=@i
461
~
@-o::::::
~
w
'#
I
2 I
,
t
I
I
~
-..... -,.. ...
2
,
w
Figure 10-8, (8) Idealized Karman vortex trail behind a circular cylinder; (b)
vortex flow pattern. (After Powers, 1975: courtesy of on & Gas Joumal.)
Ultrasonic Meters
Although several ultrasonic measurement principles are known, only two
types are commercially used (Munk, 1982): the Doppler, and the contra-
propagating (or transmitted energy) methods. Of these two, only the contrapropagating method is applicable to natural gas measurement. The Doppler method, using the reflections of ultrasonic energy off particles, is not
applicable to natural gas, which is generally free from particulates.
The contrapropagating ultrasonic flowmeter computes the flow velocity
by measuring the time difference between two ultrasonic waves traveling
over the same path, but with one with the flow and the other against the
flow. For this purpose, two transducers are used, as shown in Figure 10-9,
that alternately transmit and receive ultrasonic pulses, This flowmeter can
measure flow in either direction and indicate the direction of flow. It has a
rangeability of 50: 1 and an accuracy better than ± 2% (Monk, 1982).
There are some difficulties with ultrasonic meters caused by the effect of
solids, gas bubbles, etc. However, because these meters can be mounted out·
side the pipe, they do not disturb the flow, cause no pressure loss, are portable, and offer applicability to large pipes.
•
462
Cas "'lou: Measurement
Ga$ Production Engineering
Tn'n-.:luc:.r
up.lt"",
Row
r---- l - - l I
Ultrnonlc
path
o
-
o
463
o
--'----''k-!'-- I· - - - k -
o
BORE W/ 8 EVEL
Figure 10-9. Installation geometry of a contrapropagaling ultrasonic flowmeter.
(After Munk, 1982; courtesy of Oil & Gas Journal.)
Orifice Meters
Because orifice meters are simple, accurate. relatively inexpensive, rugged. and reliable, they are the most important and widely used of the
flowmeters for gases. Other devices such as turbine meters have also been
used because orifice meters have a limited rangeability (typically 3.5: 1), and
are difficult to adapt to automation.
An orifice meter consists of a thin plate, 0.115-0.398 in. thick depending
upon the pipe size and pressure, held perpendicular to the direction of flow
by a pair of Clanges. with a circular sharp square-edged orifice (hole) accurately machined to the required size in the center of the plate. Pressure taps
are provided on the upstream as well as downstream end in the fitting that
holds the orifice plate. A pressure measuring and recording device is connected to the pressure taps. The orifice fittings are designed to permit easy
changing and inspection of orifice plates.
The Orifice Metering System
Oriface Typn
In addition to the concentric (centered) orifice, there are two more types
of orifices as shown in Figure 10-10: eccentric (off-center), and segmental
(part of a circle).
The concentric type is the most common, because of its low cost, ease of
fabrication. and ease of calibration. It has a rangeability of 3.5:1, with an
accuracy of ± 0.5%. The sharp-edged plate, however, is subject to wear and
a consequent loss in accuracy.
ECCENTRIC
SEGMENTAL
Figure 10-10. Types of orifice arrangements.
The eccentric and segmental types are very useful for two-phase flow
streams and for flow streams with suspended solids. such as dirty gases or
slurries.' They have a rangeability of 3:1, but with an accuracy of ± 1.52%, they are less accurate than the concentric type. The segmental type ~as
the additional advantage that it does not retain solids on the upstream Side
of the plate. Centering the hole, howe"'er, is critical to its performance. and
it is recommended for use only on large pipe sizes (Corcoran and Honeywell, 1975).
Location of Preasure Taps
The magnitude of the measured pressure differential is obviously affected
by the location of the points across the orifice between which it is measured.
The four types of pressure tap locations (see Figure 10-11) that have been
used are as follows:
1. F1ange type: In this type. the pressure is measured 1 in. from the upstream face of the plate and 1 in. from the downstream face of the
orifice plate. This is the most common type of pressure tap.
2. Pipe taps: In this type, the pressure is measured 2.5 pipe [Os from the
upstream, and 8 pipe IDs from the downstream (where the pressure
recovery is maximum) face of the orifice plate. This type requires location tolerances 10 times higher than the flange type.
3. Vena contracta: The point at which the velocity is the highest, and
pressure is the lowest. is called the vena contracta. In the vena contracta type of pressure measurement. pressure is measured 1 pipe ID
upstream or the plate, and at the vena contracta downstream. It is
used where flow rates are fairly constant, because the location of the
•
464
'.
465
Gas Plott: Measurement
Gas Production Engineering
/1.-""", • •• ,.
lutely necessary, because they introduce additional pressure loss, clog easily,
and are subject to erosion.
'-Yo" I."
C-1"1,. I.,.
Si:.e and l.oca/ion of OrifICe
lIJJ.!!it!1
o' .., ......
For commercial measurement of gases, the ratio of the orifice to pipe diameter. /3, should be between 0.15 and 0.70 for meters using flange taps,
and between 0.20 and 0.67 for meters using pipe taps (CPSA. 1981). The
lhiclmc<>S of the orifice plate at the orifice edge ~h(l\lld not exceed ltv! of the
1-'
g
8
,~
6
'ti
""'". c--j
~~
~
1-'
g tc-<~~
, ""'"
~i
Figure 10-11. Pressure prolile through an orifice meter and the relative
locations of taps.
g
Straightening
\~JJJn
Straightening vanes consist of a symmetrical bundle of small diameter
tubing. welded together in a concentric pattern as shown in Figure 10-12.
Th~ vanes are placed in the upstream section of the orifice meter in order
to eliminate any flow irregularities, such as eddies, swirls, or cross currents
caused by the pipe fittings and valves preceding the orifice meter, that may
affect meter accuracy. The diameter of each of the tubes should be less than
li4 of the inside pipe diameter, and the length to diameter ratio for the tubes
must be greater than 10 (CPSA, 1981).
Installation of vanes reduces the length of straight pipe required upstream
of the orifice considerably. Vanes, however, shouJd not be used unless abso-
1-' l:n
""" ~:i 8
- ....,lP
H U I
l
8 C:C---jH,
<1<0250
. ....
c
,.,
'"
,..,, " "" ""
"u "".,
'"
.,"" "••
..
,
'"
"
,.,
..,
'"
'"
..
1'. _ _
0
.."..,,
",."
'"'"
0.."",,-
~r
~73
E
...,.,
"
'"
'"
'"
8-1 -1J1
l
V
1
""'"
-
"""
~-=~
• ,
Jf5,~
""'"
r8r1~~
a "
I 11m
"'~
((I
r """"
•
1','1
\[1
l'k.'.,1
-
vena contracta depends upon the orifice size, and the orifice size chosen depends upon the rate. This type of pressure tap provides greater
accuracy because it gives a greater p~ure drop.
4. Corner type: In this type. the pressure taps are located immediately
adjacent to the upstream and downstream faces of the orifice plate.
The use of this design is limited, for the most part, to some European
countries only.
I - 1l:J
""'"
t-'
!,
- -
1 +-°-1
Ul
_.
r'F~
~-
t'''IOd
,
,
.,
"" ...
,
..."
., .,
," ,'" ",
'" '""
'"
'" '" ,.,
... .... ..
0
H
•5
11.$
1$,0
...
lO.l
'05
K
..
'"
,,
17.'
,
.,
".'"'"'"
".,
'"'"." '"
'"
'"
OII01"1keIO _ _ oI_
Figure 10-12. Proper installation of an orifice meter-required meter run and
straightening vanes. (From Engineering Data BOOk, 1981; courtesy of GPSA.)
•
Gas Flow Measurement
GaI PrlHi!lction Engineering
pipe diameter and lIs of the orifice diameter. The orifice location should be
such as to have a stabilized flow to ensure proper metering. Figure 10-12
shows the minimum requirements of straight pipe section and/or \'anes recommended by GPSA (GPSA, 1981) for this purpose.
467
The common chart ranges for differential pressure are from 0 to: 10, 20, SO,
100, or 200 in. of water, whereas for static pressure, the common chart
ranges are from 0 to: 100. 250. 500, 1,000. or 2,500 psia.
Measurement Calculations
Preau" .\lwwritlg aml Recording
Cas is a hi~ly compressible fluid and its density varies considerably with
pre<ClIrE'. Recau<;(' prE'5SUIl' variations are quite substantia! through the flo"
path in an orifice meter, it is necessary to measure both the differential pressure as well as the flowing pressure. This is also illustrated b\' the orifiC('
flow equations derived a bit later (Equation 10-12 or 10-14). The f1owinlo'('
pressure is often referred to as static gas pressure in gas measurement terminology.
The orifice meter is generally equipped with a two-pen recorder for recording both the static as well as the differential pressure on a circular reo
cording chart. The chart itself has a pressure scale on it to enable reading the
measured pres.~ures that it records continuously. Static pressure is generally
measured with a bourdon tube type of device that actuates the pen on the
chart. Differential pressure is measured using either a mercury manometer,
or a bellows meter. The be110ws meter is preferable because it avoids the
problems of mercury contamination, and mercury loss and the consequent
change in calibration. It is important to choose pressure measuring device;
that can handle about twice the maximum anticipated pressures.
Two types of circular pressure recording charts are in common use-dired-reading charts, and square-root charts. The direct-reading chart has a
pressure scale with lines spaced equally apart, whereas the square-root chart
records the square root of the percent of the full-scale range of the meter.
Therefore, pressure from a square-root chart is determined as follows:
Actua 1 pressure -
meter range
. ,
(chart readmg)100
For example, for a square-root chart with a range of SO in. x 100 psi, a differential reading of 7 is equivalent to a differential pressure of
Differential pressure -
1~
(7)2 - 24.5 in. of water
and a static reading of 9 is equivalent to a static pressure of
Static pressure .. 100 (9)2 _ 81 psia
100
The relationship for orifice meters can be derived from the general energy
equation (see Equation 7-2). written between two points in the flowing
stream~point 1 bein1! some point upstream of the orifice plate, and point 2
representing the orifice throat:
~
1 2
g 2
·Vdp+-l vd\'+-1 dz-w,-I"
lI
(k I
&c I
(10-3)
where V "" specific volume of the fluid, ft3/lbm
v "" fluid velocity, ft/see
p = pressure, Ibflft2
z = elevation above a given datum plane, ft
WI '"' shaft work done by the fluid on the surroundings, ft-tbf/lbm
I" = work energy lost due to friction, ft-Ibf/lbm
g = gravitational acceleration, ft/sec2
g., = conversion factor relating mass and weight, Ibm-ft/lbf-sec2
For most meters, the elevation change between points 1 and 2 is zero, and no
work is done by the flOWing fluid stream. Therefore, Equation 10-3 can be
written as:
1V dp + -l
&
,
1 '
I
I
,dv + I. - 0
Il1<..'Orporating the friction loss term I" in the compression-expansion term to
avoid the complexity of referring to the friction factor. and multiplying both
sides by fluid density p (lbmlftJ), we get:
C2
I'
l 'dp+-l
&
p vdv-O
I
(10-4)
I
where C .. an empirical constant
A£suming a constant, average density P.v for simplicity, and integrating
Equation 10-4, we get:
C'(p, - PI) + P.. (v; - vj) - 0
2&
(10-5)
•
476
G(U Production Engint't'rlng
Gas Flott: Measu rement
Table 10-3 Continued
" b " Values for Reynolds Number Factor F. Determination_ Flange raps
.."
•
''''
5.189
S_~1
•
."" ""
Onl,ce
8.071
0816
1),01>70 I) 07}4
1),0578 00645
Q,0SQ2 O0S67
00852
01)7';]
OD66S
0.05117
00430
1),0442 O,OSOO
00520 OOS57
1125
003811
1),0]9(,
1315
0361 (),O)M 00)99 D04H OO<Ul 00464 0.0519 (1.(1566 1),0"71
0,0347 OIl}44 I) 0J61 I) 0375 0_0403 I) 00119 00501 005111 O.05lJ
'SOl
'W
,.'"
1),11'S
UD)
.'"
'''''
2125
0.0467
0.0507
00S4fl
00589
0.0626
0.0659
,'"
2.315
'SOl
..
2625
2.7SO
,''''
0.0l16
OOj)8
0,0)50
0,0370
0.0]95
00427
0046l
0,0501
0.0540
0.057')
00615
ODM7
0.0673
''''
3.)15
,.""
,.'"
,.'"
....'''''"
O()44.4 00462 004'316 0.0517 00602 0_Ob19 Q,Ob2J
0336
0_0318
O.()307
0.0305
00308
I)
00344
O_OlD
ij,03()(,
0,02911
0,0296
0.0367
0,01]7
0.0314
0.02'13
002&7
I)
(1474
OlW7<I
D_OOS 00439
00l'J9 01J.101
OOlM 00371
0014O 00341
0.0271
0.0274
00174
0027'9
0.02117
00300
0.0114
0.0112
O,OXW
O~
0,0271
0,0259
0.0251
00246
0,0244
0.0245
0.0)15
0.0295
0.0278
0,0264
0.0151
0,0245
00240
0.0238
00118
00197
0028D
0.02M
0.0254
0024~
00240
0.02)7
O.OS)}
0.0S64
0.05<)4
O,062()
0060
00479 0.03119 00353
0.0510 0,0416 0.0375
0.~1 0,0443 0,().4()()
00569 O.04n 00416
OOS97 0.0500 00452
0.0621 00527 0047')
00640 0,055) 00505
00578 OOS11
002~
0.0239
0.0242
0.0248
00255
00265
0.027.
0.0289
0,(l)()4
0.D'll7
O.OHO
00244
00251
OOM
0.0271
0028.l
00297
0.021\1
00281
0.02116
O.om
O,OlOll
0.0124
0.034)
00)66
0.0254
0.026J
0.0273
O~
O.OJOO
0.0)16
0,0034
....""
,.
,...
""'"
S.'"
DI.~I"',
95b1
"
"
10.020 10136 11.376 11.9lII 12090 lHIIII
o.wn
0.034b
0.0322
0.0302
0.0283
0.02f>J
0.02S4
0.0243
00)89
0,0J62
00B7
0,031$
0,0296
00218
0 026J
002S0
0.038.1
0.01'>6
OOllO
00308
002117
O.OM
0025J
o,om
0,0438
0.0410
O.OID
0.0)59
0.0)36
0.0]16
00291
0.0278
0,0458
0.0429
0(1402
0.0377
0.0354
00332
00312
00294
O.~
0~2
0.(4).1
0.0401
0,0382
0,0358
0,03}6
0,0111
002911
00514
0,0467
00461
00436
00413
0,0391
00370
0,0214
00226
O,Cr.!21
0,0219
0,0218
0,0218
0,0221
oons
oom
002:Ml
0,022)
00216
0,0214
0.0213
00211
0.0214
0,0241
O,02Jl
0,0224
0,0218
0,0214
0,0212
0.0111
00212
0.026-1
00251
0.0239
0.0229
0.0221
0.0214
0020tl
0,0204
0.02711
00lf,1
00250
0.0216
0.0226
0.0219
0.0212
0.0206
0.021\1
0.0lfit>
0.025)
00241
0.0230
0.0221
00211
0.0207
0.03SO 00J5ll 0.0365
OOlll 00319 00146
0.0114 0,0321 00328
oom 0,0305 00311
0,02112 0,02':10 00295
0.02&8 0,0275 00281
00155 0,0262 0.Olto7
ODJ43 0,0249 0.0254
0,02)11
0.0256
0.027':1
0,(1307
0.0222 0,0219 0,0200
0023<> O,erlJl 0,02()1
0 0254 0,02~9 0,02()7
00277 0,0270 (1,0217
001911
00195
001%
0(1202
0.0191'1
0.01<).1
0.019<1
(1.019')
00223
0.0206
00193
001..
002211
00210
001%
0,0185
0.0]];
0,(l3ro
0,0404
0,(1;138
001l)} o,am G,02l1 00212 0.020II
O,O}J2 o,om 0,02'9 oom 0.0221
0,0363 O.oJS4 0.0270 0.0243 0.0217
0039& 00Jl\& 0.02901 0.0163 0.0255
00178
0.017&
00176
00110
0,0178 00179
0,(1174 O.OIN
0,(1174 o.oln
001710 0.0173
0.0473
0.0505
0.053&
0.051>2
0000'
0046l
OOO}
00S2l
o OSSO
''''
2,]75
'SOl
..
2.75(1
,
2,175
3.125
'''''
3.375
'.SOl
....''''""
H25
• SOl
~7SO
S""
S""
S.SOl
S,7SO
'''''
15000 15,250
10000
"
o 06M
O.O?ll1 00705
0.0635 0.0652 00656 0.0f.9II
005IIII 11,0606 0.0610 0.0654
0,os..5 0,OS6J 00S6l 0,0612
o 0S04 0052) 0,0527 O,OS73
00461 000lllS 0.Ge90 O.05:Mio
0,0714 O,G'IB
0,06]1 00676
O.Q6jl 0.0615 0.0706 007lJ
(1.0'>92 00597 0,0670 00671 0.06&1
0,0S55 00560 0,06l6 0.Dt>W 0.0650
"
2125
,."""
0.05J9 000t97 00417
0.OS74 OOS35 Oos.:!4
0.0S69 0.055'1
S.soo
O.if,ce
DOno
0,0]66
0,040';
0.0446
"
11.9)4 11090 146&& 15,000 15250
00451 0.0455 0,0501 0,0511 0.0526 O.Q6O.I 0.0612 006111
00419 0,0414 00469 0,04118 0.0492 oosn 0,0581 0,05117
..
....'"
.',.."
0,0620 0.0579 o.O)n 0.0338
00618 0,0414 0,0)116
0,0457 00416
O.OSOO 00457
10.136 11376
0.04]]
0.0401
.""
..,'"
'.SOl
1,250
S."
1,625
l.7SO
0D4~7
IH1418
0,038.1
0.0)53
0.0327
00]00
00110
00314
00342
0.0]65
0.0391
00418
0.0+408
4.750
"'"
•.soo
00151
(10343
00322
0.0301
0.02M
0.0111
0.01J4
00354
0,03711
O.04Ob
00436
0G4611
0.0500
'.SOl
1,315
00718 1),0742
0.OS7& 0.0&60 DOb7b 0.06tI0
...
"
101Y./O
,
3.750
3.125
1.125
oam
I)
..
,
D_OIIl!O 0.0892
I) n7A~ (I (lOOIIJl
00701 0.0718
00f02S Q,Ob(4)
'"
'J.!ioM
1,175
2,625
O0J4S
00]54
OO}72
00398
00430
16n
1.750
1,115
I)
Table 10-3 Continued
" b" Values lor Revnolds Number Factor F, Determination-Flange Taps
o.i~l .. r,
0.1047
O.OI!'J.4
0076)
Q,1lf>53
0.0561
01)137
0.]75
I) 10$4
1),0907
I) 077<.1
•
477
'SOl
''''
'.SOl
o,osn
0.04111
00'51
GO4&]
G.osn
00540
0,0Sb0I
00)2() 0.0285 00277 001&6
0.0)0 o.om 00300 00195
GO)i6 00}15 0.0J25 00206
G.04G6 0.0)62 00351 00220
0G435 00390 00179 0.0235
0,(1463 0G418 0.0401 0.0252
0,G491 00441> 0.043-4 0.0271
0,0517 0G47J 0.041>1 00291
O,QSooIO 0,04911 0.0417
00S60 0,QS22 O.OSl1
0,0543 OOS14
0.OS5J
0.0551
O.osn
0.0496
0.(471)
0.0445
0.0422
00399
0,0371
00160
001l1li
0.01911
0.0210
0022'
00240
0,0257
00276
00558
0,0529
00502
004'&
0G452
O,G4la
0,0406
0,0385
0.0232
0.0213
0.0196
(1.01117
ODIn
0,0183
00191
00202
0.0216
G.02JO
0024(0
0.02601
00}12 0.0296 00211)
OOll-' 0,0017 O,OlOJ
0.0151 o,om 00)2'
0.01110 0,0361 0.01016
''''
'SOl
''''
000402
0G42S
0044'
0,(10169
O.OJIIJ
0.040£>
0.0427
0.0449
00l6e
00)90
0,00t12
0,00tl-'
100250
10.SOD
10750
11000
11.250
0.0489
00501
00526
0.Q5.41
0.(471)
0.04'iO
0.0S09
0052t1
0.0541
00455
0,(1475
00495
0,0513
00521
(table continued)
•
468
Cas Product/on Engilleerillg
Gos Flow Measurement
Equation 10-5 uses pressure p in Ibfl ft2. Converting to commonly used pressure units of psia (lbf/in.2) and rearranging, we get:
vi -
vi _ 2(144)g.,C'(P,
- p,)
The pressure differential, PI - »2, is generally expressed in terms of inches of
water. This conversion can be achieved, using the relation .6.p - pg(.6.h)/~,
as follows:
(10-6)
P.
469
(PI -
N
.
(62.43 Ibmi£t')(g fusec')(&h in. wate,)
psla ... (144 in.t/ftt){12 in./ft)(g. Ibm.ft/lbf-sed)
The mass flow rate, m (Ibm /sec). is given by:
m _ p..-A
(lO.j'
62.43 "h
(p, - p,) - (144)(12)
where A - cross-sectional area of flow, (t 2
This analysis assumes steady-state flow conditions, for which the mass flo\\rate is constant. Equation 10-6 can now be expressed. as:
m' [~_ ~l- 2(144)g.,C'(p, -
p~" A~
AT
0',
(10-11)
where .6.h - pressure differential in inches of water.
Using Equations 10·10 and 10-11. Equation 10-9 becomes:
p,)
P ••'
(28.97)(62.43)g,>sP" "h
f'
m - c.dl [ (1,152)(144)(12)(1 _ ff')Z.,.RT.,J
m'
Aj [I
(A,/A,)'] - 2(144)g.,p.C'(p, - p,)
(10-8)
Let d j and d 2 be the diameters of the pipe and the orifice, respectively. in
inches. Defining /3 - dz/d j • and solving Equation 10-8 for m:
m - CA [2(144)g.,P"(P' - p,)f'
,
(I Il')
(10-12)
Gas flow is generally reported in terms of the flow rate q.., in scf/hr at standard conditions, which is related to the mass flow rate m in Ibm/sec as fol·
lows (m ... qp):
m _
q,., (28.97 h,p.
(3,000)
z,.RT.
•
Using standard conditions of PM: - 14.73 psia, TIC ., 520 oR, and the fact
that ~ ... I, we obtain:
0',
(28.97)(14.73)
(10-9)
Using Equation 10·13 in Equation 10-12, substituting R '"' 10.73 psia-ft31
Ibmole_oR, and solving for cp." we obtain:
Using the gas law, the gas density P., can be expressed as:
(10-10)
where
"f, - gas gravity (air _ 1)
P... - average pressure, psia
T•• - average temperature, oR
Z., - average gas compressibility factor
R - gas COnstant
(10-13)
m - (3,000)(520)R >,q,.,
q,., -
~,
7,717.96 Cd!
J" ['h
up."
[(I-ll'h.Z.,T.,
(10-14)
Note that in Equation 10-14, cp., is in sef/hr, d 2 is in inches, .6.h is in inches of
water, p.~ is in psia, T.~ is in oR, and C. {3,
and Z... are dimensionless.
Equation 10-14 is commonly expressed as:
1',.
q,., -
K. ["h
p"J"
(10-15)
470
where the constant
K.. is given
Table 10-2
Flange Taps-Bule Orifice Factors-F b
by:
flowm, lemperJIU,e ,. 6O"f
lIue p,e'ss.lre .. 14.73 ps..
Spec:,foc ,rimly .. 1.0
line tempe,aTu,e .. 6O"f
~
In metering practice, the average pressure P., is replaced by a measurable
gauge pressure Pt. Factors are prm;ded to account for this Pf being measured
at the upstream Or downstream, or being measured as the mean of upstream
and downstream static pressures. and for the type of pipe tap. Equation
10-15 is then written in the following form:
q. - K [h.
Orifd
p,r'
(10-16)
,
2
in,
1,689
1,9:)9
2067
')00
a.2S0
12MS
12701
unl
lZ.71O
1I~~.
:u.~lq
1lI~'~
a~"
a.m
0.,500
a blS
o.m
1.000
50m
110090
50W
" wt
lI~.W
117.0'1
lW'J5
219."
1~W.
212 '7
SO S21
" )11
liS I~
lsa'7
no 22
~" ro
).15 1l
.n 50
SOl 16
l.llS
U.
,,,.,
1.625
and the constant K is expressed as a product of several different factors
follows (AGA, 1969):
il.\
Fb - basic orifice factor, sci/hr
F', - Reynold's number factor
Y - expansion factor
Fpb - pressure-base factor
FIb - temperature-base factor
Ftf - flowing temperature factor
F~ - specific gravity factor
am
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1147.7
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IS) III
M'.
»OM
It'.1ll
5.761
5(1,1:'1
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""
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"'. ,
,~
n,.
50197
066.J~
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10'111.4
.,. .," ..
5.1&2
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119.hl
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103&1
,
•
DumM ....,
20ns
6S1J.~
2,)1'5
.~
(text continued Oil page 4;5)
12.1R"
;:aJ&;'
7""
",.
.~
The factor Fb is simply the constant K., in Equation 10-15, Its va lue depends upon the type of pressure taps, and the pipe and orifice diameters, Fb
can be obtained from Tables 10-2 and 10-7 for flange taps and pipe taps,
respectively, For sizes that cannot be found in these tables, interpolation is
1l.70)
11)99
156 00
50 OIS
,~
U)75
These factors, determined through extensive tests and reported for use as the
industry standard by ACA, are given in Tables 10-2 through 10- 14 for two
pressure tap types-flange taps and pipe taps,
~
a,rJ
~'"
I1H2
3438
12
;:a,r"
,~
."
Fp. - supercompressibility factor
Fm - manometer factor (for mercury manometer)
Fl - gauge location factor
F. - orifice thermal e:tpansion factor
3152
U71111
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..."
O.il,ce
br_ me pb ghusaya to tb ho gaya,
tf g__nd me ghusate to pvmla ho jata
•
HI68
1271l
2.125
(IO-li)
0
SUet-Nomi-w and I'IIbliWcIlns;oe DLomet",- Inc: ....
,."
Pr - absolute static pressure of the flowing fluid, psia
"h..p, - ..
h...IPr -
.,....,~.
o.~
where h.,. '"' differential pressure at 60°F, inches of water
where
471
Gas Flow Meollurement
eaoS Production Engineering
~.
1m)
1727,S
1891'
~.I
IS1,]<I
"'''
lSl'"
11l.91
_v
4H.02
m.ll
6lun
no.n
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1027,1
11 .... 2
1272,]
1405.0
154S]
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1143.6
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7.981
B071
151.]1
1OOl'J
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lSJl>'J
11l.7a
lIJ006
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7Il'J,/7
IIOII.SO
2S1 ri1
111.74
JIJOO2
451.72
S]l.ri1
.17 SO
91J all
111lS.'
11.." 7
1270.3
1002.9
l';fl .S
161J'J,1
1&1].5
911.1>4
10256
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llt191
10021
1541.8
Ilia 0
1&12.J
lOOU
lIn 9
lJ499
r;1,
l250a
2011,6
2182.6
2005.2
2174.&
Z....-..
2)1,18
26'\049
~
=.0
2511.1
1Il'i1>4
IJOII.]<I
(tablc continI/cd)
•
Gas Produl't/(m Erlgiflcerirlg
Gilt Flow MellSllrement
Table 10-3 Continued
" b " values 10r Reynolds Number Factor F, Determination_Flange Taps
..
,, us
"
OttfOCI!
18814 19,QOC 19250 116.2(, 2].000 2.1250 2116.28 29.000 19250
0.0667 0 OWl
0.1,)6-('
O.{l6.I()
0 (16.49
0ClM4
11,75(1
12000
J ..
0.Ob14 00618 006.l!
0,0511$ 00592 0.05'r 0,0659
o OSI>J 0 OSM 0.0571 0 0bl6
n(,t<.U'l O~ 0!.'54'l !lotH
0,0511 O,Oill 0.051(, 0.0592
00490' 0 0499 O.~ 0 OS11
00471 0().\7)' 0048l 00551
3125
00451 0,049 0.0462 0.OS31 005111 0,0542 0,06.26 0.0631 00b}4
3250
3.315
3500
3625
3.750
3.875
4,000
00411
0().\14
0,0395
00378
00361
00345
00129
0,().I)7
0,0'118
OOW'I
0,0J82
0,0365
O,O,W'I
O,OIH
0.0511
0,051)4
00486
0,04b8
0,0451
O,M]S
0041'1
0,01>08
0,0590
0,05N
0,05$7
(1,05..11
0,(1525
0,0S09
0061J
00596
00579
00562
0,0546
0.0530
00S15
00';82
005-&6
00550
00534
00S18
00.101
o (l2i5
00252
(1.0232
0,113(14 0,0310 00]76 0,0].6.1 0,03M
0027';1 0.0111) 0.0348 00355 Q,03hO
(1,02)6 (I,Q2W (1.0122 00328 O,ODl
0,on5 o,om 0,0297 0(1304 O.OlOe
0.0479
0,0450
O,MB
(1,0)97
00435
0045-&
0,0429
00-103
004&8
O().l6()
00433
00407
00214
0(1199
001U
00176
00117 00210 0,0175 00281
0,02(}1 (I,02G4 (I,02S4 00260
00UI8 0,(1191 0,023& (10241
0 DIn 0,1n]9 0,0219 o,on~
00285 O,OJl} 00376
0,026-1 0.0.l4'1 0,03$5
0.();!45 00127 O,O)3J
00~2.8 0,0)06 0,0312
0.0382
0(1359
OOlli
00311,
"'"
2500
2,J7S
~
"'5
VSO
,""
.,'"
• 5W
4750
S...
S250
SSOU
5750
6000
6250
0O-H2
0,0423
O.IHOS
0,0387
0,0370
0,0154
0.0339
(10511
0.0493
0.0474
00457
O,O-HO
0.0423
(10-107
0,1l665 0(166')
0,0&42 0,111>46
O.tl(.,.";l 0,0/.;:4
o.om 0,(1601
0,0578 O.OW 0,0662
0,0557 0,0SI>2 0 0b44 00&4'1 0.Ob~2
00520
(1.0500
0.0431
0.G464
0.1).147
0,04]0
00414
00616
0.0~99
00167
(10161
0,0157
00155
001611
001f>l
00157
00155
(1.0170
00161
00157
001'>4
00204
00191
0.0179
0,011>9
O.OD
(1.0195
0018)
ODIn
0.0155
(10157
00160
0.01&6
001504
00155
00153
0.0163
001$3
0,015-4
0,0156
0,0160
0,0161
0,0154
0,01411
0,0144
0.0161 00165 DonI 0.0226
0,01'M> 00lS7 0020II (10112
0,0150 00151 0.0195 00199
0,01~5 O.01-1fo 0.01&-1 00187
00165
00172
001110
110190
00201
0.021]
0,on6
(1,02.-0
0.0142
00141
0,0141
0,014]
00146
0.0150
0,0155
0,0161
O,OI~l
001~1
10.00:>
0011>9
00177
001116
(10196
0,0213 0.010II
0,0126 0.0220
0,02~ 002304
0.02'if> 00249
001.-0
00140
00141
00143
0.0146
0.0150
0.0155
00140
0011'1
00140
0,0141
0,0144
0,0147
0.0152
00174
0 DIM
001';6
0014'1
0,0141
0,01111
0,1ll3)
OOllO
00177
0.D1W1
0,015'1
001$1
0.0145
Oong
0,on5
0,01)1
(10179
0,0170
00161
0.0153
0.0146
0.0141
00136
001)2
10250
10,SIIO
10,7S0
11000
0,0271
00215f1
O,OJOS
0,0)22
0,0255
0,0270
0028&
0.0J03
O.ln66
00176
0.0165
0.0194
0,01&2
0,0169
0.0176
0.01116
0,0153
0.0164
o,lnn
0,0181
00128
OlnU
0012S
O.01lS
00128
00126
O.OllS
00124
00126
0.1ll26
0,0125
00114
11.250
0.0340 OOJJ2 0,0320 0,020'; 0,0196 00190 00126 0,0125 Oln24
O.OlSa 0,0349 0,01)(1 00216 0.0207 0,0200 O,lnl& 0,0126 0.0125
6500
"'"
~ooo
...
......
....
nso
'500
77SO
"'"
8.?SO
.".
..""
11.500
Table 10·3 Continued
"b" values for Reynolds Number Factor F, Determination-Flange Taps
00172
001110
00190
00201
0,0264
002t10
0,0297
0.0114
00212 (10287 O,02'n 00296
001911 0,0169 00274 002"
0,Olt15 0,0252 00257 00260
0017~ OOll6 0,02.-0 O,OJ44
o.om
(1021;
001'(11
0(1190
0037f> 0.0367 0.0155 00lla 00118 00211 1I.0llD 0,ln26 0,0127
0.0394 003&5 0.0)73 0.0241 00230 00223 001).1 0,0111 0.0129
12500
!looo
0.0429 004'20 0040B 00267 00255 002411 00142 0.0133 0.01.16
0.04&3 00454 0 DoW2 0,0296 0,Olll2 001"4 00153 001411 0.0145
13500
14000
004')4 00435 00474 OOlU 0,0111 0,0101 00166 0.0160 0.0157
00520 00512 0,0502 OOJ'M> O,O:W, 0,03]1 001&! 0,0175 o.om
14.500
15,000
00186 0,0)70 0,0360 O.ln99 0,0192 0,0187
0,0415 00400 0,0191) 0,0118 0,0209 0,0204
1;,500
16,000
O,DoW) 00426 0,0418 0,0219 0,0210 0,on4
0,0470 0,04S5 0,044& 0,02bO 0,0250 0.02+1
16,500
17,000
00494 0,(1460 0,0471 0028J 0,0273 0.0266
0,050] 004'.1-4 00W7 0.0296 0,02811
17,500
18,000
Oro31 0.0319 0,0312
0.0355 0,0.143 O,OllS
18,SIIO
19.000
00119 0,0366 0,035-8
0,0402 0,OJ9O 0,01112
19.500
0.0424 0,0412 O,Q.K1oI
0.044& 0,(10134 0,0426
.....
"
"
21.000
00466 0,0455 0,(1448
0,0485 0,0475 00467
~.500
0,0492 0G4/1S
(text l'Onlinued }rom page 475)
Expansion Factor, l'
The expansion factor, Y, accounts for the change in gas density with the
pressure changes across the orifice. It is computed assuming a reversible adiabatic expansion of the gas through the orifice, and is a function of f3, the
ratio of the differential pressure to the absolute pressure, the type of taps,
and the specific heat ratio (Op/c,) for the gas (generally ignored). The expansion factor can be obtained from Tables 10-4, 10-5, and 10-6 for flange taps,
and Tables 10-9 and 10-10 for pipe taps, These tables indicate the pressure
tap from which the absolute static pressure PI is measured- YI for upstream, Y2 for downstream , and Ym fo r static pressure recorded as the mean
of the upstream and downstream static pressures. As with F" an average h",
Pf should be used .
(text continued 011 pagc 489)
•
472
Gas Flow Measurement
Table 10-2 Continued
Flange Taps-Basic Orifice Factora-Fb
Table 10-2 Continued
Flange Taps- Basic Orifice Factors -Fb
•
Onfice
o.,~e.,
.n
3.826
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.."
•
5.182
5.761
=,
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1.821>.'
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1.5230
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10,136
12090
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15,000
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10.b09
9.781.6
10,60
9,4lI04
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11.....
12.434
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18.141
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1',511
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11.711
16.519
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16,962
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19,565
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(table contilllll'dl
•
Ga., Production Engineering
474
Cas Flou' McaSlu'(-'I/INlt
Table 10-2 Continued
Flange Taps-Basic Orifice Factors-F b
(tnt contim4ed from page 4(0)
not recommended; the exact equations or charts given by ACA (ACA, 1969)
must be used.
JO
'8,114
19<XX1
19.250
22.626
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" b" Values for Reynolds Number Factor F, Determination-Flange Taps
'50)
'65
44,2')1
17.5(10
18,500
(text cOIltinll('d
In
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This factor accounts for the variation of the orifice discharge coefficient
with Reynold's number, Tables 10-3 and 10-8 .show the value of F, for flange
taps and pipe taps, respectively. The pressure extension, [h" Pff 5, should be
some sort of average pressure extension. These F, values have been calculated assuming average values of viscosity equal to 6.9 x 10 6 Ibm ft-sec.
temperature equal to 60°F, and gas gravity equal to 0.65, These tables do
not , therefore, have a general applicability to all sy!.tems. In any e\'ent, the
variation in F, in gas measurement l~ quite small. and is often neglected.
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Ga3 Flow Measurt'Jllnlt
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Yt Expansion Factors_Flange raps
Table 10-4 Continued
Y Expansion Factors-Flange Taps
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482
Gal Production Engineering
Gas Flaw Measurement
Table 10·5
Table 10·5 Continued
Y2 Expansion Factors-Flange Taps
Stetlc Pre.. ure Taken Irom Downstream TIps
Y2 Expansion Factors-Flange Taps
Static Pressure rakan from Downstr.am Taps
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'-,-,-,-,-,-,-,-,-,-,-,-,.,""' ,-,-,-,-,-,-,-,-,-,-,-,-,'-,-,-,-,-,-,-,-,-,-,-,-,•• ,-,-,-,-,-,-,-,-,-,-,-,-,...."••, ,--,,-,-,-,-,-,-,-,-,-,-,,-,-,-,-,-,-,-,-,-,-,-,-,,-,-,-,-,-,-,-,-,-,-,-,-,,-,-,-,-,-,-,-,-,-,-,-,-,..,. ,-,-,-,-,-,-,-,-,-,-,--,,-,-,-,-,-,-,-,-,-,-,-,-,"" '-,-,-,-,-,-,-,-,-,-,-,-,,.. ,-,-,-,-,-,-,-,-,-,-,-,-,..
10011
10011
IOOIl
l00U
1.0012
10011
10011
10012
10011
10011
,-,-~.,-,-,-,-,-,-,-,-,-,­
"
"
,.
"
'",.,"
""u
10071
1007\1
1_~
,-
1.0087
1 00II1
10081
l00v
l!011i
100801
UIOII2
UIOIIO
UlO78
10077
'.001S
loon
IOU,.
un07
1 010&
101001
111101
lOO'lf1
1.~
10095
1 QOIJl
10114
10111
101211
10US
1.01,.
10'121
1.01211
1,0114
1.01U
1.0120
10126
IOUl
1.(nl0
1.0117
10I0Il
1 (Ill.
1.0121
1.0127
l!MOf
unl!
10111
IOID
1010]
'(1101
10099
10109
10107
1.01001
1.00tS
1.0121
10TH
1.0119
10110
1.0116
,,- ,....
tim}
U,I1JO
HlO9Il
1.0102
1.01D!!
10114
UIOM
1.0105
10110
1.0102
1.0107
1.0141
101~
10116
101.M
1.0129
1.1t117
1.0125
10122
1.0n,
1.0116
1.0114
'Olll
,-,-,-,-~.,-,-,-,-,-,-,-,­
,-~·,-,-,-,-,_,_,_,_w»~.,_
,-,-,-,-,-,-~.,-,-,-,-,-,1.0182 LIlh!O 1.0m. 1.01n 1.0161 1.0164 LIl16, HilS/! 101504 101SO 10148 10141i
1.0182
'_~.'_'_~R'_'_~.'_'_,_,_,_
1.0196
1 OlD)
1.0196
l.o2OJ
UI'I'I
UIlIl1
1.0'89
1.11196
101115
1.0192
1.0180
1.0186
1.(nn 10171 1.0110 10166 10162
1.01&)
1.01110
1.01'"
1.00n
101~
I.OI~
1.01M
100S'
1016!
","".. ,-~.,-,-,-,-,-,-~.,-,-,-,~
,..
,"'"
l.o:zsa
""
,.".
,""
" "'"
,"'"
U
..
10210
umo
101011
1.020)
1.01"
10192
1.01"
1.0186
10182
1.0111
1.0173
1.011'1)
10166
10Zl4
1.Q1lO
lill)]
1.m3
'-'1210
1.1I2ll
1Il221
1.11221
HIlJj
10216
1022l
'OlQS
I~
1.0211
10218
1(1224
10211
10211
1_020".1
1.0lDI
1.0214
101...
102001
1.0210
10194
10200
1.1llO(,
1,0189
1.019S
1.0201
1,011'
10190
1,0196
1,0111
100Si
1,0193
1011't
101i1-<
1.01'10
102<44
1,0251
'0244
1.O:ZS1
1 ~l
102)6
1.02l1
1,0224
1 026.l
1,0251
1.0lfi
1.0220
1.D2lfi
Ullll
1.02)')
llmS
1,0216
llJ222
1OZ2'J
l,on5
10141
1,0212
1.llll'
1.0224
10210
1.02)6
1,0l07
1,1ll1l
1,021'
1.0225
1 WI
10202
1.0l07
1.021)
10219
1,0215
1.0199
1.0204
1,0210
1.0216
1,0222
10191>
10.'01
1 (P.Ol"
, rull
1,0218
1025f
I
~
, IDio4
1,021'
10255
1024)
Il--Roloo
...
••
,w
O,fo'I
070
D
.n
.n .n
,-,-,-,-,-,-,-,-,-,-,-,-,"" ,-,-,-,-,-,-,-,-,-,-,-,-,,-,-,-,-,-,-,-,-,-,-,-,-,••• ,-,-,-,-,-,-,-,-,-,-,-,-,,-,-,- ,-,-,-,-,-,-,-,-,-,,". ,-,-,-,-,-,-,-,-,-,-,-,-,,-,-,-,-,-,-,-,-,-,-,-,-,..",.. ,-,-,-,-,-,-,-,-,-,-,-,-,,-,-,--,,-,-,-,-,-,-,-,-," ,-,-,-,-,-,-,-,-,-,-,-,-,,." ,-,-,-,-,-,-,-,-,-,-,-,-,,-,-,-,-,-,-,-,-,-,-,-,-,. ,-,-,-,-,-,-,-,-,-,-,-,-,., ,-,-,-,-,-,-,-,-,-,-,-,-,"
'"
OJ
u
0.14
1,00151.OIIU
10015
UID14
10014
1.0014
1,0013
lOO1l
lOO1l
1.0012
1,011\1
101m
10011
!CO" 1.0041>
100015
U)(I.4
\ 00013
1.0041
101141
10CM0
HI013
1.00)1
1,011:16
lOOl4
loon
100511.0056
10055
l00S4
IODS3
10051
l11DSO
1004'1
HOI'
1,01146
I,OOU
loon
!lXlll
1~ 1.0IIIIl
10081
UlOIl6
\.0091
l007'J
1.110114
1.00&9
1 fX1T1
10082
11)(18]
11101'S
UlOIlO
101185
'.0073
1,11011
10083
10011
I.OOM
1001>1
HID!19 1,00M;
I.IXl'JoI 1.0093
1.0016
1-(10110
'0014
1,0018
'0011
1.0076
1001>5
UOt.9
101113
l00b2
10066
10070
10060
101J601
IOI)6IJ
10105 1.00Ql
1.0101
1.00'19
l00'J7
100'IS
1.0092
lOO9Il
10087
100&4
100111
lOO7tI
1007'S
10111 1.0109
1.0\16 1.0114
'0121 1011~
10121 10124
1.0012I.111l1l
1.0106
1.0112
1.0l11
'-0122
\.0121
1.0l04
1.0109
10114
'0\20
1.00lS
'-0102
10107
'0112
1.0111
10122
1,0100
1.0104
'-0109
10114
10'"
'0097
1.11102
1011.16
'.0111
1.0116
llXl'Jo1
1,00'19
1.0104
10108
111111
1.0II'J2
10096
1.11101
1,0l05
101'0
1.0IIII'J
l1lO'11
1011'Ja
1.0101
10106
11101!11i
10090
10094
loo.t
1.(10)
1.00113
100111
1.0091
1,01195
100'19
1,001'9
10081
ItlOll1
10091
lOO'K
1.01)11.0135
101431 .0140
Utl<la 1.0146
101504 10151
'.OIfoO'OIJ1
1.01])
10113
1014)
10148
10154
1(1)0
1.0115
10140
10145
1.0lj(!
10121
10112
1,0117
1.0142
1.0147
1,0124
1.0129
1.0134
1011'
10144
1,0121
1.0126
1.01l1
101:16
10140
1.0118
10122
1.0121
'0112
10111
10114
1.0119
1.0124
1.0121
1.011)
10111
10115
10120
1.0124
1,0129
1(11)1
10111
10116
10110
1.0124
1.0101
1.0101
10112
1.0116
111120
lOO9'J
10101
10107
10111
lOll'
101115
1,0110
1.01'"
1.0181
1.0lSi
1.016:2
1.0161
'0111
1.0111
lOll'
1 015~
1.01601
10110
\.OIl'S
101110
1.0156
10161
1,0166
1.0111
1.00n
1.0152
lOIS/!
1.0163
101611
1.(11)
1.0149
1.01504
1.0159
1.0164
101M
1.0145
1,01511
1.11155
101611
101M
10141
10146
1.0151
1,0156
101611
1.01l7
1-(''''2
11'147
1.00SI
1.0156
1(1))
101111
10142
1.0141
1,0151
10129
1.01)3
10131
10142
1.0146
1.0124
10121
1.00ll
1,01l1
1.0141
10120
1.0124
10111
100ll
1(1)6
10192
1111911
'.02001
1020t
10215
10189
1.019S
UI200
II1'2l)6
',0111
UlllIi
101't1
1.0196
1.020".1
\,0201
10182
1.0111
1.0192
1.01911
1.D201
10118
1.01&)
\.01.
\.OI'M
'0199
10114
1.1117'9
1.01&4
1.0189
1.0194
1,0110
1.1IlTS
1.0180
1.01M
'0190
101M
1.0110
10175
1.0180
10185
'0161
1.0165
1.0110
HII75
1.01110
1,0156
10160
101M
1.0170
1.0114
1,0151
1.01S5
10160
1,0164
'Olfo'l
1.0146
101j(!
1,01504
10159
1,0163
10100
10144
100<1a
1015)
10151
u
"
OJ
U
1.0103
1,(1109
,-,-,-,-,-,-,-,-,-,-,-,-,,." ,-,-,-,-,-,-,-,-,-,-,-,-,,.,.""
10142
483
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u
,.,a
u
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,..
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•
Cos l'roductioll Engineering
·84
...
"100
"
u2
Table 10-6
Y", Expansion Factors-Flange Taps
Table 10-6 Continued
Y... Expansion Factors-Flange Taps
Sqtlc Pr.ssure Muo of Upstre.m end Downstr•• m
Stetie Pr...ure Mee" of Upstream and Downstream
DWM
O~
G9'A6 099'>&
099'K O~
6,,")
09991 09990 0"",,
O,'J'lIIf 09'J8il 0..9988
11
12
U
'4
I ~
O'l'lelJ
09964
O'l'!i8l
O<m<!
o')'m
0997~
O'l'l71
0'1910
0.9!I6a
09'11>1:>
0,",'
69'191
o.9'1e6
0'1'181>
0911&1
09'1111
0.997'1
0'19"
099l!l1
09981
0'197'
09976
09975
0.9'/72
0'l'l7(l
09!l6a
09966
09"1601
0"'"
0'l9S9
0.9957
099'S;
il99"F
0.9'/95
ow;;
0.,,,,",,
0.'1992
O'lMil o.,9'iI'J
0,'" 11._
099'1'2
0.9'/&1
0.9'182
0.9980
0.9977
0,.;1&1
0..9'1111
Q.9'J78
G'l9'I7 O'»i~
0._ 09'1'11
ij,':I'/9l
O_'I'HI 11._ D,99'JI)
0._ O'I'IN 69'1117 0.991;1
0.9985 O.9'JM 0.,9\1&1 0911&1
O,1ffi7 D'l'I'i;
6,'I'/'l0l 0."""
0.998.2
0._
0,'1977
0.""'.
0..998.2
O.9'J7'j
0.,9976
6.'1'971
0..9970
0.99boI
,.
0,')968
09965
0,9961
0,9974
09910
0.9966
0.9!162
o,me
0997'
09969
0,9965
099101
0,99$6
09960
09955
0,'997.1
0.9'lfI8
099I\J
0,9956
0.9'JS.!
09956
0995)
0.99S0
09961
0995a
0.995-1
09951
09')017
0.9960
09956
0995\
09950
O~'>
0.9956
0.9954
0.9951
0.'1947
0.9943
0.9957
0.9953
0.9949
0.9946
0.990
099S6
09952
0'l9l8
09'1+1
0'194<1
0995S
0.9951
0.'l9I7
099U
09939
09953
0'1949
09945
0'1941
099)7
0,9951
0'l9l8
09'1+1
099]9
0.9915
09951
09946
09942
09933
099lJ
0.9949
09945
0,99010
09'J16
09931
0.'l9I8
D.'l9IJ
0,9919
099)1
0.9'J19
0.9'J046
0.9942
099)7
09932
0,'1927
0,'1945
0.'194<1
09'1)5
0.9'I1O
0,992.)
0.'1941
09933
D.9'JH
0.'1'128
0.99ll
09'141
0.'1'116
099Jl
O~
1.1
1.1
I.J
1.'
1.5
0.9!M4
0,99010
(99)7
099}<
0,")0
09942
099"
099.16
09912
0'l9l1
099.
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09910
0.99" 0.9936
0.99)1 D9911
0.9'l30 0,9'129
0.9927 0992S
0992] 0.'192'
09'1),
0991'
0.9917
09')1)
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09911
09929
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09921
09917
099)1
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0992)
09918
0.9914
09925
09920
0,9'116
0,9911
09907
0.9911
0.99011
0.9'IOf
0.9920
0.9915
0.9910
0,9'lO!I
0990T
0.9918
09911
0,9'iOII
09903
09912
0.9927
0.9921
09918
0.9914
09909
09'll2
0.9'118
0.992~
0.99'0
0.99l6
09911
0.9'129
0.9925
09929
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1.1
U
U
U
0991;
0991D
09'101
0.9900
0.'IIm
(992)
1.1
1.1
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0,9921
0.9918
0991,
1.4
0.9911
0.9907
0.99"
09916
0.9911
0.99011
0.990S
09917
09914
09910
0.9906
0990:.1:
09915
09911
09907
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09'100
(991)
09'10'1
09905
0.9901
091197
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09906
09902
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0.')11904
09'iOll
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0t1199
0.91I9S
0'"'
0.9905 09'102
0990T 0 _
0'lll!l6 O!IMl
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09890
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0.9817 O'llllll
0'lMl 0.'1B78
0'11U7 0.'lII71
0 .... 09ll'!6
0,'JIII9!i 09l9l
0'Jl91 0.9888
09817 0.91164
091164 0 _ '
0'J89]
0.9M9
09MS
0_'
0'J177
09190
0'J111116
0'lMl
09878
0987'
09817
09lll:.l
0.9178
091174
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0.'1190
0990T
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0.91194
0.W90
0.911117
09V'i
0'Jl15
0.'JI7V
0.'J11L6
0...,
0'J17S
0'lll71
0.'lIIf>7
0'Jl6l
O'JIII?'
0.'II7l
0.9167
0.'JIII6l
0.'J8SI
0.')871
0.'II16II
0.'JIII6l
0.'J8SI
0.'J1S4
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0,'JI59
0.'J1S4
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0.')116.1
O'lllbl)
0.'JIIISol
0";(1
D....,
0'lll16
0'Jlll
0986'1
0,'J1166
0,9873
0.'JI6'l
0.9Il66
09862
0"73
09870
0.91166
09ll6l:
09MI
0.9870
D.'*"
09l6l
O'JIIISII
0'J1S4
091166
09861
O'JIIISII
0.91S4
091150
091162
0'J8S1
0.'JISoI
O'MSO
0.9845
0.91I5a
0.'JISoI
0 ....9
O'J8oi,
0,_'
0.'lIS4 0 .....9
0 ....' 0 ..... 5
0 ....5 D.'il&tO
0'il&tO 0.91)5
0.'I1I.l6 O,'lIIJl
0.",,"
0.'il&tO
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O,'JI}(!
0.'lIl6
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0.'1M3
0,'lIIlO
0 ..76
0.'lII71
0,91!I69
0'11U7
14
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0.'1M3
0.9V'i
D.'J176
0.9IIn
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0.986'1
09866
O'llMil
0'l1lS9
1.'
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1.1
3,'
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0.'1&b9 0.'J166
0._ O.!iIl6l
0.'l8b2 O.'JIS'
0.'J1S9 O.'JIS§
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O.!iIl6l
0.'J111S8
O'J1S5
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O.'JIISII
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0 96M
09115001
O!l85O
0 .... 7
0 .... )
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09846
0.960
0.91»1
09llJ5
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0 ....1
0.91)0
O,~
O,'JIJO
0,91\011
0911]7
O,'JIll
0.91129
0.9112S
0.'11SJ6
0.'lIIJ1
0.9828
09824
0,"19
O.'JIll
09QJ
0.9123
0.91118
0."14
0.91121
0.':11116
091111
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0.9961
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09'JSS
0.9951
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69971
O.'l'ji'fl
0.996& 69%7 69%6
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0.9%2
0.9960
0'1\157
09961
O,'J'JS/I
O,995S
0.'1'162
0.9960
099Sa
09956
09'J5ot
09960
0'l'Y.>1
0995S
0,9951
09950
09'JS7
0.9955
09951
0.9950
0.'l9I7
0.9'J5ot
09'JSl
099<19
0._
0,99011
0.9952
0,'J95(I
099017
0.'1'M4
O.'l9Il
D.9'JS1
0._
0.99oIS
09942
(99)')
0.99<19
0.99<11
099)9
0.99.16
0.'I'Jo'6
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0.99010
09917
099.14
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09951 099019
0.9948
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0.99012 0.99.
D..,.., O,99)S
0")7 09912
0"ll5 0'19)0
09938
0.99.16
099J]
09910
0.9927
0,99)6
09930
0,'1927
0'l9l4
D.99))
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0'l9l7
0'1924
0'l9l1
0.9930
0.9927
0'l9l4
0.9921
0.99'11
09927
09924
0,99lO
099'17
09914
09925
09912
0'1911
0""5
0.",1
0.9920
0.9916
(991)
09910
0.99)1
09930
D'I92B
0.9925
0992]
0.9927
09924
09922
09919
0.9924
0.99'22
0,9'119
09917
09'114
0,9922
0.9919
09916
0,9'111
0.9910
0.9911
0991S
09911
0,9910
09906
D.""S
0.9911
099011
0990S
0.9902
0,9911
0.9'107
0.9904
0,9901
0.'"'
0.99011
0.990S
0'l'lO2
0.9Ige
0.91I9S
09906
09901
0.91199
0W'16
0'J1192
U
1.7
2.1
U
l.G
0."'"
0.9886
0_1
0.9V'i
).1
l.2
U
27
Z.
n
)0
(9901)
0.,..,
0""
09').16
0'99)1
0,,",2 0"'"
0.....0 0'19.
099" 0.99.16
099.16 099}<
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0.9')4~
0990lS
0"")
099.16
(99)1
09911
09'129
09927
0,991~
)~
099»
0'99)0
0'1'128
0.9'126
Ow.z4
099)2
09930
o.w.z.
09926
09924
09910
099211
0.9926
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486
CO$ Production Engineering
Gal Flow Measurement
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Fb Basic Orifice Factors-Pipe Taps
Table 10-7
Fb Basic Orilice Factors-Pipe Taps
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•
488
Gas Production Engineering
Table 1C).7 Continued
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Fb Basic Orltice Factors-Pipe Taps
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Gas Flow M easu rement
4 .~'
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6.1021
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6.NII S
PretllrUre·8aM! Factor, Fpb
This factor corrects fo r cases where the base (standard) pressure, Ph in
psia, at which flow is to be measured is other than 14.73 psia:
10.116
11,016
11.006
11.11JO
12,6711
11,119
12,665
15'l'J
16.41'
15.'"
17 ....
17,421
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tun
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14.$G1
15,'57
16_'SO
17._
9
(text continued from page 479)
F
14.73
"" ---I'b
(10-18)
Fpb - 1 for a desired base pressure of 14.73 psia, because the flow relationship assumes a standard pressure of 14,73 psia .
16.l97
(text con tinued on pag€' 498)
•
490
C08 Producllon Engineering
Gal Flow Measuremen t
Table 10-8
" b " Yalue. for Reynolds Number Factor F, Determ ination-Pipe Tap,
Table 10-8 Continued
"b " values for Reynolds Number Factor F, Determination-Pipe Taps
Onfi<e
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D.07ll2 0.0614 0,0576 0.0521 00471 00452 0,0445 0.0441 00441
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0.0513 0.05l4 0.0575 0.0S92
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00609
0.0555
0.0506
0.0462
8071
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00351 00336 0011) OO)IS 0032'J
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00)38 0036J 00192 00281 0027]
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(table contimll,d,
•
492
Gas ProductioFi Engineering
Gas Flow Measurement
Table 10-8 Continued
" b" Values tor Reynolds Number Factor F, Determination _ Pipe Taps
...
....,....,,,..""
,'"'"
,....
""
'.564
10020 10136 11.l71:o 119311 12.090
DQlV 00244 0_0239 0,0194 0.011'
O.Ol81 0 0'26J 00251 00207 D.ono
O.OJ01 0,0282 0_0276 0.0221 0_0l0'2
OIlJ26 oo.m 0_0295 D.WI 00215
0.0197 0,0155 0_0154 G.OlSJ
0 0'l10 0.0151 00154 0.OlS3
0.0320 D.om O.02M 0.0195 0.01&1 om!'!
D.OU4 00]10
Q,OJ(M
0.0349 0,0344 0,0246 00235 0.0221
0.0259 0.0244 0.02.-0
'"
(021) 00262 002S1
00286 00216 00267
• >SO
0.0299 002113 00280
'500
9.1SO
0.0311 D.OJOO 0.0292
00022 00]12 00»1
00132 (0)2) 00]1$
10000
...
IO.2S0
0,0)41 DOl]] OOlU
0.0341 D.OllS
" " . 19.000 19250 22.1>Ui 23.000 23.250 28.623 29000 29.250
,.uo
2.125
0(66) 00667 0.0&12
0.06J5 0.06J9 0,0644
00609 0061) 006111
2.m
00S8) 00511$ 0.0591 0.06SII 0.066S 0,0669
'.500
...
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1.125
'.250
,...,
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3.175
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5.150
0,0206 0.0198 0 (tI91
1l.0J.47 D.om 0.011& 00219 01l209 0,020'2
0.03311 00332 0,0232 0.0222 0.02'.
'.500
2.625
0,0151 0.01504
0036) 0,0:)59 00J04 0.0279 Q,02n 0.01&4 001n 001n
•.uo
..
0.0162
0.0186 O.t)1S6 0_01.56 0,0156
0.0151 0,0)46 0.O'28e 0.02f.2 O.1l:2S6 0.0174 00169 0.01604
,.'"
,
15000 15.250
0.0178 0.0160 0.0161
O.ossa
0.05304
0.0510
0.1M8II
00466
0.0562
0.0539
0.0515
00492
0,0470
00S6ll 0.0635
O.~ 0.0613
00520 0.0591
01M'll!! 0,0570
00476 0.0549
0.04045
0.0425
0.0406
O.OJ&]
0.0J69
0.0152
0.0JJ6
0.OJ2O
0.04049 00455 0.0529 0.0536
00429 0.0435 0.0509 0.OS16
0.0410 0,0416 0.049(1 0.00t97
o.o:m 0.0)!!7 0.0471 0.0479
o.ren 0.0379 0.0454 0.0461
0.0356 0.0)62 0.0436 0.0444
0,0J040 0,0)46 0,0419 0.0427
0032. O.OlJO 0040l 0.0411
006042 0.0646
0.06l0 0.0624
0.05'11!! 0.060J
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00SS6 0.0561 0.0649 O.or.s. 006S7
0.0S41
00521
0.D502
0.04&4
0.0466
0,04049
0.04Jl
0.0416
0.06J0
0.0613
0.059S
0.0571
011561
00S45
0.0528
0.051)
Table 10-8 Continued
" b " values for Reynolds Number Factor Fr Determination-Pipe Taps
O"fKe
O.crua 0,03J6 o.om 0.0Z70 O.020t6 0,01)9 0.0167 0,0162 00159
...
....
"
lH,ae
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,...,
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•
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"
0.06J6
0.0616
0,0601
0,05&4
00S61
00639
0.0622
0,0604
OIlSIll'
0.0571
oasso 0.05S04
0.05304 005111
0.05111 0,0522
0.0'291 0.0295 0,0)01 o.ren O.OlllO O,OlllS 0.G4$l 0,04&& 00492
0.02fa5 0.Cll69 00274 0.1lJ.t1 O.OJSI 0.0JS6 O.04Sl 0.04S9 0046J
0,0242 0, 0246 0 02S0 O.OJ16 0.0124 0.0328 0,0425 00411 00435
0.0Z21 O.ons 0,0229 00292 0Cl299 0.0l0l 0.0)99 0,0405 00409
0.020) O.CI206 0.0210 0.0l69 0.0276 0.02fIQ 0.0314 O.OleO 00l&t
493
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m.
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0,0175 001n 00180 00210 0.02J6 0,0240 o.om 0.Q3}./. O.OlJ3
0,01&4 00165 001611 00212 002111 00222 00307 0,031] 0.0117
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0,0'.'
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001SO 0.01&4 001119 0.01'12 0,1I2M
0014S o.oln 00176 0,0179 0.0251
00141 001102 00166 0,01611 0.0236
00193
0,0274
0,0257
0.0241
0.01';17
002711
0.02f,0
0.0244
00140
0.0140
0,0142
00146
00140
0.0140
0,0141
0,01....
001)9
0,0139
0,0140
0.0142
0.0226
00212
0.0199
0,0187
0.0229
0.0215
0.0202
O.ot90
0.01S1 0,0148 00146 001)) 0,01}./. oom O.ot7) 001n
0.0156 0.D1~ 00151 00132 0,0132 OOllO 001&4 00167
0.0163 0,0160 0.ot57 00111 0.0130 o,ono 0.0155 00158
0.0171 0,01611 00163 O.Onl 00130 0,0130 0.01411 00151
0.0179
0.0169
0.0161
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0015)
0.0146
00140
0.0136
0,0156
0,01411
00142
0013&
001S11
OOISO
0,0144
0,013&
0.0221
0.0207
0.0195
0.01113
0.0180
0.0189
0.0191
0.0209
0,0176
00185
001901
0.0204
0.0171
0.0180
0.01119
0.0191
0,0133
0,0136
001)9
00143
0.01l1
O,O1ll
0.0136
0.0140
0,0130
0,0132
001304
O.011S
0,0142
0.0136
0.0132
0.0128
0.0144
0.013&
0.01))
0.0129
0.0146
0.0140
0.01304
0.0130
"...,
0.0219
00230
0.0241
0.0252
00214
0.022S
0,0236
0.0247
O.Q2OI
0.0219
0.0229
0.0240
0,0148
0.01S04
0.0160
0.0161
0.01....
0.0150
0.0155
0.0162
0.0142
0.0147
0.0152
0,0151
0.0125
O.ot23
0.0122
0.0121
0.0126
0.0114
0.0122
0.0121
0.0117
0.011.
0.0122
0.0121.
".250
"...,
12.000
0.026) 0.0261 0.02S1 00175 0.0169
0.021l 0.Q2611 0.0262 0.01&1 0.017'6
0.02&4 oava 0.0V2 0.0191 0.01&4
0.0293 0.02811 0.02S2 0.0200 0.0192
0.0165
0.0112
0.01110
0.0190
0.0122
0.0122
0.011.
0,0126
0.0121
0.0121
0.0123
0.011.
0.0121
0.0122
0.0122
0.0123
12.500
1).000
0.0312 0.0307 0.0l01 00211 0.11210 00204 0.0112 0.0110 0.0128
0.0127 0.03ll 0.0318 0.0236 01X22l 0,0222 0.0140 0.O1l7 00135
1).500
14.000
0.0250' 0,02"6 0,0240 00150 0.01"6 0.014)
0.0V2 0,1l2f>4 002Sl 0.0161 0.0156 0.0153
14.500
15.000
0.02S9 0.0280 0.0275 0.0173 0.0161 0.0165
0.0»1 0.02'J6 0.0291 0.0166 0.01 81 0.0117
15.500
16000
0.Ol10 00311 0,010& 0.0200 0.0194 00190
OOl21 O,OllB 0.0215 0.0211'1 0.02G4
16,500
0,0230 0.0223 00219
00244 0,02J8 00231
'.250
'.500
..""
10.000
10.250
10.750
11.000
" .".,
17,000
..
..
..
17.500
"
"
"500
"
18.500
0.0259 0.0252 00248
0.0266 00261
o 02n
00286 00279 0.0275
0.02'II!I
002'J2
o112M
0,0)09 0.0)0} 00299
0.03111 00313 0,0310
•
'9'
GU$ Prod'4ctioTi Engineering
Gas Flow MeaslIreml'llt
Table 10-9·
Table 10-9 Continued
VI Expansion Factors-Pipe Taps
YI Expansion Factors-Pipe Taps
Static Pressure Taken from Upslre.m
.
..
"
..
r.pI
Static Pressure Taken from Upstream Taps
d
d
J--1lo1lO
o
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051
060
10000100001000010000100001000010000100001000II100001000010000
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0.9971
0.99';6
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0,9452
0.9436
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09716
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09611
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•
496
Ga.s Production Engineering
CO.f Flou: M easuremCJl t
Table 10-10
Y2 Expansion Factors-Pipe Taps
Static: Prenure, Taken from Downstream
..,
Ito,..
0..
Static Pra..ure. Taken from Downstream Taps
~
_
,
, __ Rob<>
o
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-;~---;~---;;----;;---;;;---;;;--';;';--'C:---:CO--c,~-0'
0.1
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0.45
0,50
052
0.504
0.56
a sa
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0,9'JI'lQ
0.99lI'J
0 ....
0.9991
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09972
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0.9962
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0,9952
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0.99').1
0.9'184
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1.0084
10057
1.0l90
1.0022
1.0014
10112
1.Q296
1.112)7
10H9
1.1II!Jl
1,0Q2S
1.0026
10)10
IOXM
1.0243
1.1)153
1.0095
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'1D\6
UI070
1.01.~
1,~
.....
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10000
10000
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,
10000
1 0000
..
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Table 10-10 Continued
Y2 Expansion Factors-Pipe Taps
~p.
h.
1.0021
0.9916
0,")2
O'l'lSJ
0.'""
09'J61
D9!IS'J
om)
09'Wi
09'MO
0 'l9Jl
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09!llO
09914
099011
099S"
09')f;
09')1()
099}!
O.992S
091190
.-
0.'115-1
0'M41
0 'J&I1
U._
0.'IIIIl
0.'J171
0')17)
0,'"
0._
0,'IeIiO
0'.I8J7
0'18)1
0.91121>
0'!ll\2O
099011
0'1874
0.'IIl56
O'l8SS
0'l8SO
O.'1&t6
0'J&l1
0,'J1)6
0'7'111
09n.
09199
0.911'16
0'J126
0'J122
0'l1li17
0,<)111
O.<JIOoI
D,9!lJJ
D99l!
0'l8S1
0.'.1801&
0.'M41
O.
0,'111)5
0.91109
0.99601
0'Jl71
0"'7
0._
0.'II!IbO
0.'JIS1
0~1
O"l~
09906
0,'J9O(
0.9'lO1
0,979)
0.9788
09"f111
0 .i61
0·9994
0.9994
D."'"
0.996)
099Jl
0.9!I2'J
D'.It'iN
0.9II9l
0'JllSol
0.'111)2
0.'JI08
0.'783
0"n8
09756
097;0
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0.9961
o.me
091190
O.'J111118
0.'J128
09G24
0,9(10)
0.9995
0.9995
0'.18$0
0,'M4;
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0'11116
09l'94
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0,9761
0,97f>l
097)8
0.'JI4O
0.99£.2
0.'.1926
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0.9'l'2O
0 9909
0.9898
0.<)667
09'l11
O. '11199
098&7
0.9875
0.'lIIIM
091176
0.9II6J
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0.91178
0.'IIlI\3
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0.911'"
09&.15
0.'1A22
0,9BS9
0.9644
0'/8S1
0.96]9
0.9827
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0.9&19
0'll!.l3
0.'I81~
09i')16
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0'lllO
0,9Bll
0,'J812
0.9804
o 9711J
09792
0,98l1
0'.1811
0'JllOl
0.'l801
0.9;"91
0,97lIl
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0.977\1
0.9757
0.9769
0.9:""57
0,9711
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0.9'l17
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0'lll64
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0.9996
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0.9917
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0.9750
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0.9503
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•
.!IS
Cas Production
En~ineeri"ll:
COf Flow Measurement
(text continued from page 489)
TI'III~atlf""BOM Faclor. F Ih
This factor corrects for cases where the base (standard) temperature. T
in R, at which flow is to be measured is other than 520' R:
(10-19,
As expected, F!b - 1 for a desired base temperature of 520oR.
The flowing temperature factor corrects for cases where the flowing temperature. Tr (OR), is not 520 o R, using the fact that the gas flow ratc varies
inve~ly as the square root of the absolute flow temperature:
Ftf
-
[
T,Jr'
520
(10-20)
The basic orifice factor, Fh , is determined assuming a gas gravity of 1.0.
So, a correction for gas gra\;ty is required. as follows:
1
F• - 05
(10-21 )
>.
SU'~lIIprnsibi/ity Factor,
F~
Because of the tremendous variations in gas compressibility factors with
gas composition, pressure, and temperature, it is advisable to determine Fp'
experimentally or through proven empirical techniques. AGA (AGA. 1969)
provides two approximate empirical methods for determining the supercompressibility of natural gas mixtures: the specific gravity method. and the
heating value method.
The specific gravity method uses the specific gra\;ty, and the carbon dim:ide (CO!) and nitrogen (N 2) contents of the gas to calculate the pressure and
temperature adjustment indices. fpt! and fl~. respecth·ely. as follows:
r~
-
ft~
- "Y8 - 0.472yc - 0.793h;
'YI - 13.84)'(;
+ 5.420)'~
(10-22)
where Zb, Z - gas compressibility factors at the base (generally assumed to
be equal to 1.0) and operating conditions, respectively.
(10-23)
where 'Yg - specific gravity of the gas (air" 1)
yc - mole fraction of CO 2 in the gas
ys - mole fraction of N2 in the gas
The;e Cpi and fIg values are used to determine the pressure and temperature correction factors from Tables 10-11 a and lO-llb, that are added to the
actual flowing pressure and temperature of the gas, respectively. Th~ corrected pressure and temperature values are used in Table 1O-11e to estimate
the supercompressihilit}' factor, Fp,'
The heating value method uses the specific gra\;ty ("Yg). total heating
value (I-It in Btu/sef). and the CO 2 content of the gas to calculate the pressure and temperature adjustment indices. fpl> and fth' respectively, as follows:
fpl> - 'YI - O.OOO5688HI + 3.691)yc;
fth - "Y, - O.OO1814H t
This factor corrects for the deviation of an actual gas from ideal-gas behavior. It is calculated as follows:
'99
+ 2.641yc
(10-24)
These fph and flk values are used to determine the pressure and temperature
correction factors from Tables to-llc and 10-lId. that are added to the actual flOWing pressure and temperature of the gas, respectivel}'. These corrected pressure and temperature values are used in Table lO-lle to estimate
the supercompressibility factor, Fp,'
This method gives reasonable results for a gas with a gravity within 0.75.
and non-hydrocarbon content of less than 12 mole% N2 andJor 5 mole%
CO2 .
•
500
Ga" Prodllction Engineering
,_
Table 10-11b
Supercompresslbility Temperature Adjustments, LiT
(fhsea on Specific Gl'llvity Method)
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This factor is requ ired only where a mercury manometer is used for measuring the differential pressure. It compensates for the different heads of gas
above the two mercury columns of the manometer. It is generally negligible •
and is totally ignored for pressures below SOO psia . Table 10· 12 gives this
correction factor as a function of gas gravity, flowing pressure, and ambient
temperature.
(text continued on page 51 i)
•
502
Gas Flow MeaslJ remt!1lt
Gas Production Engineering
Table 10·11d
SupercompreulblUty Temperature Adjustments,
•J
!,
,
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•
504
Cas Production !ngineering
Go.~
Table 10-11e·
F"" Supercompresslbillty Factors
Table 1()..11e Continued
F.,. Supefcompfessiblllty Factors
(811" O.W- O.6 Specific Grnity Hydroc.lfbon Gu)
(811.. 0.t.-0.6 Specific Gravity Hydrocarbon Gas)
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1.01.ta
1.0178
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1.0297
1.0241
1.0274
l.ons
1.0139
1.01&11
1.01911
1,0228
1-01)04
1.0218
1.0151
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1.0145
1.0175
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1.11265
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1.0140
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1.0401
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1.0128
1.0360
1.0192
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1,0317
1.0347
1.0377
1.D425
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10522
1.00499
1.004711
I.OS)1
1.Q5U
1.0551
j ,05/19
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1.0494
1.0529
1,0441
1.1M74
1.0507
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10221
1.(/461
I.OS75
1.0&42
1.0n]
1.0nl
10816
1.0614
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1.0m
11106
11002
11051
1-1159
1-1100
1-120
1.114'J
11200
1.1252
1.1)79
1.1.)9
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1.1562
1.1626
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1.1537
1.1647
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1-0129
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1.0183
1.0210
1.0237
1.011'J
1.1261
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1.0706
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1,0787
1.0&75
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1.0910
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10053
10051
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1-1004
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1.1692
1.1159
1-1t1904
1.19(,7
1.2041
1.2116
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10955
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1.1045
1.0910
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1.01102
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1.01$'
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10469
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11047
1.1199
11138
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1.1181
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11162
1,1'96
1.1413
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1.1242
1.1~32
1.1155
1.1399
1.1283
1.1324
1.1365
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1.1407
1.14.49
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1.1607
1.1769
1.1835
1.1901
11968
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1.1568
1.1622
1-1676
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1.1577
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11083
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10918
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1.2537
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1.2221
1.228&
1.2351
1.2'111
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1-3505
1-3561
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1.3655
1.1;-68
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1.1913
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1.17'9&
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12612
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1.2726
1.21113
1-21139
1.2t1904
1 .2529
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12642
1.2]52
1.2]'19
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1.2732
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1.202J
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1.215<1
1.2197
1.21010
1.228J
1.2326
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1.1534
1.1577
11620
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13264
1.3932
1.3926
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1.3897
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1.].497
13289
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1.3708
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1.3716
1.21130
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12466
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1.25508
1.2763
12979
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1.31l0
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1.27112
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1.21!1Oo4
,.,977
1.2812
(table continrll'd)
•
506
GO$ Production E'lg/neering
Gas FlolC Mt'asurcmetlt
Table 10·11 e Continued
F"" Supercompresslbility Factors
Table 10-11 e Continued
F"" Supercompressibilily Factors
(Sue Oat.-0.6 Specific Gravity Hydrocarbon Gas)
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1.3151
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1.1150
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1.28.JI
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1,2838
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1.2893
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1.3147
1.3119
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1.271!O
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1 2816
1.2787
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1.2741
12717
1.2693
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1 ,21136
1,1971
1.1955
1 ,19-17
1.1937
1.2828
1.2823
12811
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1.2'126
1.1915
1,21101
1,17'93
1,278<1
1.3010
1.2891
1.2n4
1.28711
1.27601
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1,21150
1.2943
1 .2907
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1245-4
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1.2401
1.2421
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12149
1.2124
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1.211~
l.an
1-219$
1.2114
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l.n46
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1.2252
1.2227
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1.2178
1,2153
1,2157
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1.2111
12633
12584
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125-4)
125B
1-2463
l,lSSS
1,2526
124'11
1.2476
1.2~54
1.2~13
U424
,.ms
".;
1.2).\11
1,2)09
1.2469
\2441
'''''
1 ,2356
12328
1,2101
1.2271
l.m?
12261
122.3<1
1.2221
12195
"
"
"
"'"
"'"
12400
T~mJH' ..ture.
IS
124M
114.\11
1 2~1_
I.Ul5
1.2322
1,2199
1,2Jn
\ 2155
123)4
11]11
12315
12290
1 221:>&
\,2246
12224
1.2202
"'"
1 2214
1.2251
1.2228
Il:!"l~
12175
1.2255
112J.o1
I
nil
11191
121n
12152
1.211!1O
UBI
121S8
12135
1.2110
12112
12091
12069
.
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, ""
12027
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JI)
" " "
so
"
10000 10000 1.0000 I 0000 10000 10000 10000 10000 I 0000 10000 10000 1,0000
~1~1~1~1.~1~1~1~1~1~1~1~11~
1,2788
urn
1.2755
1.m7
1.271'1
'""00
1.26112
'.2702
..""
1.2674
1.2659
U641
1.1627
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1.2611
12624
~
1 ~1~1~1.~1~1.~1,~1~1~1~1~1~)
~1~1~1~I~l~ldll~l~l~l~I~I~
lOll 1.0"121
120 un."
I~ 1.0110
160 1.0195
I~ 1.0ll0
1.0"117
1.0"141
1.01f>.l
1,018&
Hl:!l}
10"11)
1.01111
1.0158
1.01&2
I.mm.
10"10'1 10"105 I.O"IOl
101JI 1.(1'121 1.0122
1.01~l 1,0"148 \.0142
\.017to 1111" 1.0"161
101. 1.0191 I ('I"
1.009II
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1.01S11
101711
1.~
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1.0111
100U
1.0"111
100'11
1,0"110
1.0128
10147
1.0116
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1.0101>
1.0124
1.0141
1.0160
1.0015
1.0101
1.012(1
1.00le
1.000n
I DOlI)
'0100
1.0116
10Ill
l.OnO
_'_'_,_,_,_,_,_
,_'_~.,_
,~1,~I~I~IOllOI.OlI)I,mm.I~I~I~I.O"I~I01nl~
:MIl 1.D29I 1.0211 U1271 1.(126;7 1.1IZS1 1.02'" 1.0019 10l.l1 1.022) \.0l15 1.0201 lmol
160 I.OJ14 1.0JIl 1.0102 I O2'JI I Ol8Cl I ,00J'll I m60 I 02S0 I .0142 I on4 1.0:!26 I.O!I'I
280 1.0)SI \.0))9 1.0ll' I.OJIS 1.0XIl I eml 1.0l11 1.01n 102f>1 1.0252.I.IIl'" 1.0ZJlo
lOO I.oJ" 1.0lIIS 1.0352 1,0})'1 I.om I.OJI4 1,010) 1.02'J\ 1.(1211 1.Clln 1.0162 loaJ
~1~1~1~1~1.~1~1~1~21~1~1~1~
1()4)4 1()417 10401 10lIIb l.ru11 101~ 1.0)4.4 IOll2 10llO 10JOe IOHII 1.02"
lIiO 1,006l 1.1M44 HNV I ()411 10195 1.0_ I.~ 1.0)5) 1.0J000 10J2I I.OJI' IJlJQS
).4Q
1.2W4
1.2535
12524
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1.2_
1.2470
12451
125'J7
1.2507
1.2484
1.2505
1.2693
126f>J
, ,
o
1.2493
1 24~)
1.2)}6
urn
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12596
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1.2521
1.2557
12531
1.26-1)
12614
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1,255'1
-.
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1.2670
1,21\.41
1,2612
1.275-4
12m
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1.2n6
1.2sn
1.2575
1.2553
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1.2820
12804
1.2663
1,2661
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Of
12105
12644
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l.m?
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Tempe'~!llre.
p,
1.2i'S1
1.27(1
12748
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'25'"
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1.2"..1
1.3052
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'''''
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1.)199
1.)170
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1.2&46
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1.3lOS
1,]Z911
1.3289
1.2505
1.2484
507
1.24)J
1.241'
1.241>2
,m<
1.2441
1.2420
1,2175
12356
lID 1.CM9l
1.()471
1.()45J 1.()4JE. 1.()4M 1.001(l0I 1.1IJII8 1.0114 1.0llo1 1.0147 1.01)4 1.0J22
400 I.OS" 1.!N'iIII I.()o179 1.(1461 11M44 l()o1l' 1,()o110 10m 1000l 10JMi I.01SJ 100.>0
420 I.~ 1~ 1,O!nt 1001II> 1.~ 1 ()4SO 1 ()01)) 1b11~ 1.040l 1.0)86 IJl}lI I.on.
~1~1~I~I~II~I .()4nl~I~I~I~l~l~
~1~1~11~1~1~1~I()o1~I~I~II~I~l~
..., I~ 10!I09 1.0S8S 1.0Shl los..a 1.05" 1.04'iIII 1.()o1" I _ I 1.\MoW 1.()o1V 1.110111
(table continued)
•
508
Cus Flow Measuremelll
GOJ Production Engineering
Table 10-11e Continued
Fp" Supercompresslbillty Factors
(Ban Oete-0.6 Specific Grnlty Hydr~rbon Gal)
Table 10-11e Continued
FJI'I' Supercompresslbility Factors
(B... 0.ta-0.6 Specific Gravity Hydroe.lrbon Gas)
,.,
'M
'"
"'
,
o
-
1.0667
lOi'JJ'
10127
1.11159
1.06)9
1061.1
1~
I.on.
LIl1\lO "'1]\;
" "
2S
1 CBS)
wo
1~
,-,
HlilII 1117'1]
780
1.11l~
11159
120 11ln
1.121'0
11)1»
MIl I1UO Illll
'li'O 1.14-18 I.un
. , 1.14S 1 1-407
lot.ll 100;-. I,OSC'
,~
1
, "" "'"
11~
1.11~
1.1175
11205
1.llJoI
1 1265
1.1C1'l1
1111.
1.1146
1.1175
1.1:!OJ
ant
,~,
,=
,'0'"
,~
, OIo6J 1 0Ii)6 1 01>11
10120 106t1
1.0~.2 1071l I. (W,&4 I ot.S/t I (It, 10
1,0766 107j.t 1071)01 lObI'S 1O(,..a
.ons
1 (IrioO 1 00>;
1.0788 1.07S6 1
111771 1 0745 1.0714 1 Ob3~
u"no
'-'1&70 1000l 107911 10765 1.0711 1.0704
1-10010
1,0991
11~
1.I\II~
Ill'Jo4
1.1114
11)51
l.ll1J
I,."
1.12JO
1,1251
11285
I,U11
1.1340
1.1170
1,11%
LIID
1.1249
11m
11011
"M
11-40
"..,
".
1.1:>117
117"'4
1.1711
II."
1.1N
11612
""'7
11I0Il1
Iln61.1751
11524 1''''''
1.1555 1 1471
11567 1.1SOI
I ' ' ' . llBI
11651 IlsS9
I.I:IM
"m
1.1114
un.
1.111>]
1,1111
1.1211
11'J1ll
1.lG16
1.104&
11071
11.7
111197
1.1926
11954
1.17)(1
1.17511
1.171l6
""4
1.1640
111>]7
\.li!J1;)
I1W1'l
1.1714
1.I7ft
,~
110102
1.10$(
11107
1.1111
l.lIn
, ,,'"
1.15SO
1.1514
I.IS'iI'J
lllr.22
I'''':;
11#>9
1.14<r.!
1.151.
1,15)6
1.IUl
1,07S~
10&" 1.01111 10m
10906
1.0921
10'150
1097'
1 0992
11*01 UIII)o
1.0811 1 _
1090II1._
1.0928 1.01187
1 OMI 1 0906
1.1011
1 HIlS
1.1057
1.1073
1.1099
,,,.
...
, ""
,~
,""
" i l l 11175 1.1120
1 1141
llUS 1,lm
I.HIl 1.1120 1.116-3
I un ,,~ \12<') 111114
1.14C!Z 1,1111 11265 1.1105
1100 1 , _ 11114 11611 1.1st1 1.1505 1.1427 I U'!04
11."
IISU 1.145.) Inn
IllS] 1.1145
11551 1.1417
1. '''''
11m ,,~ ,,~ 1.1502
l.lO'II \ Itl. 11105 IIJ'QJ II." 1.1S2f> 1.1....
11~1
L~7
10'17V
1.1092 11041 1.C19M
1.1119 1.10f.S 11\1161.1145 1 11190 1 10)9
11)65
1.1.l97
11421
1.1#>1
11491
1lD1S
1,1109
1.21"'4
l-l1711
L1210
1,0752 1,0721
1.0171 1.0740
1.0$(1
1.1475
1.1509
115-4-1
I1S7I
1100
1J20
lJo1O
IlIoO
Ileo
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,., so."
11520
1.1ssa
1.15'J5
1."ll
1,_
"
, 0104' 1.0611 I.IMJ
106'It
1.0II1~
1000
11120
10010
lor.o
1011l
11M
1.1421
1.1451
1.1411
1.05-11 1.\1'>l1 1 g-,:;:
1 Irn)oI 1 0I01S
11000 109S4 I.CI'l11
1.1206
11217
1.12M
1.llO1
1 U3o'
, 0501 1.D'&j 1 ().Ihi
1.OSlJ 1.0S0l I.IJ.I.8J
l.ons
, _ 1011Jl
1,116') 1.1112 1 IOS7 I.IID
111M 1.1m 1 1141 1 10117 1 10)7
MO 1.1.lO1 112)6 11175 1.1117 ,,~
!OO I,UI7
'-!O I.un
1.0464 1.00WIi 1.0-129
1_04&C 1.1)1(6 1()l.4"
,-
",.,
1,1m
SS
1.0:710 1 1lIIIO 1 06.U
1,103/1 10Wl
1.0'i00 '0IIb0
1.11170 11019 1O'J71 1 0917 1.01IIII5
1110)
111)5
SO
1 056J 1 CJSoIO lOS"
1 0SIl \.05\" 105)3
lOIIOl 1,0578 lOSs..
1"", 1 01198 lOIS] 1 (11(1', 1.07&'
no 1,1020 1 or3 1 0'n8 , OMS 10847 10810
7-40 1.1Q5.4 l.l00s 1 09S& 1.091. 1 OV) 1.08J5
eoo
4S
1O!.].f 10100'J
1.ow.
1t.O 1.1011'l1
",,,
40
,....
NO U""
610 1,0951
700
lS
1,1)61) I.os. 1.05f6 l0S4J 1.0521
1.1M&!
1010)9 1 (61) !usee 10565 l0S4J '~n 10501
10661 10!.010 I.06U 1.0SIII lOSM LOSt) l05ll
,0&95 l0E066 1.0bJ'/ 10611 10S87
10!j,01.1
luJ24 u",Ojj 1 . _ ,.o.,.v 1 ..... 11 1.~; 10>e.;
60tI 101W 10:'17 Lanl 111721
WI)
JO
109Y
1091le
1.100II
\1028
\.1043
,,-
1.0l"95
101111
1.(1112
1.0150
1.ca.a
1.092:5 Ul8IJS
1.(I'jo45 10'l04
1,0'J(,< 1.0922
1~ 1.0!M0
I,HIOI UI~7
11069 1.1020
110)$
11109
11121
111411
1.0976
UJ9IJ3
1 1011
1.1C121
I.ItM6-
11111 I 1m 111101 1.11U
I nOlI 1.124S I " . I Illi
I Illi 11266 1.1X16 I I I "
lun
1 IllS 11167
l.ll74 1.I.107 112" '''114
1-101>3
1.1181
11)95
11411
l.l.l7
1.1451
1.14"
1,11.7
1.111.l
1.11l1li
1,119'5
1.1211
,,,,,
11111
1.1)017
1.1)66
1.llIIIi
11400
11261
IIlSI
l .l2'iI'J
I.U"
l.lll4
509
11202
1.1l1'
1.1217
1,12Sl
1.IVU
o
,,.,
"'"
"" ,,,'"
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JO
" "
,~,
1]tIl
1720
11.j()
17t!O
1780
1.2606
1,2620
1.l'3)
1.1645
1..2(0S6
1.24S7
1.2411
1.2411S
1.2497
12509
18iXJ
lllO
18«1
1160
I..,
I.l46S
1.2674
1.l6lIO
1.26115
1.2690
1.2519
1.2S19
1.25)11
1:!SoI5
1,:lSS1
..
TemperlOlure. Of
I.U.7 12112
1.1900
12421 , 1271 1 211t
1.1921
1 2"'47 122'l18 I 2160
1.20S4
1,1'J040
12)10 1.1111
l.n04
1.201l
1.1'l1h1)
11492
16110 1.1S14 12)65
lUO 1.2D!i 1.llM
16«1 1.1U5 1.1_
IW) US11 1M3
ll1M1 1,1St1 1.1""1
,",.
..
, ",.
1.11147
1.1861
1.2091 1.1'Il10 1187.
1.210& 1.19\1) 1.1&117
1.2111 1,2ODS 111199
11751
1.1764
1 1m
1.1787
11799
"m
114M ,,~
11450 1,1]71 l.nU
1 '''''' I Il'l] 11327
114110 1.1407 1.1).40
1149'5 1.14;"0 U)S2
1.204~
11590 11510
1116-'1
1.178f> , 1692
I 152'
1.1:>117 ,,~ 1.1517
1."'OS
1.1911 1.1'" 1.11ll 111.l1 115SO
1,19)1 11m ,,~ 11647 1.1~
12Oi.O
1,1~)
1.~llm
1.1171
,,~
"
,""
1,21'"
1.11"
1.2115
I.ll11
1.2)015
I llS7
l.ll1O
UIQ
1.21'Ja
U2U
1.2227
l.ill9
1.2181
1.239:1
1.2401
12410
12417
1.2251 l-lIJD 1,2017 11~10
1221>2 1.2141 1.2(I,!8 11921
1.2m 1.2151 l,lOla II~JD
1.2Ul 1.2160 l2Of1 I.19ft
1.22119 Ul'" I 2OS6 1.1948
"'"
so
l.lb7. 11591 11510
1.17'15 11697 1.16011 1 1526
11504)
1.1.'5 1.1116
111)01 1.17]1 1.1642 IIS5~
1.1151 1.1752 11660 1.15]}
1.207'1 1.1'167
, "'"
1.105
1,144/1
1.1461
11411
l1eas
1.1)66
11171
1.1!tO
,,~
1.14U
IUi61 1.1S]} 1.14% 11414
111>74 1.1517 1.1S011 11415
1.1686 1 1600 1.151' , .1"'4S
1.1610 1.152'1 1.1455
1,1701 1.1621 1.1SJ9 U ....
,,,,,
11510 1.1718 1.11>]1
1.1121 IlnS 1.1640
'-'alii 1.11)8 11649
11&19 11747 1.1r.5e
1.18411 11755 1.16f>7
1,154~ 1.1473
1.lsse '-'411:1
1,1SfJ6 1.1490
1.1575 U49I
1,15&) I.1SOf>
I~ 1.l!694 I.lSS6 U'24 1.~ 1.2117 1.:!(I6,I 11956 1.1856 11M 1.167} 1.1591 1.1514
1'J20 1.M7 1.256112429 I.no1 U1114 1.:zon 11964 1.1864 1.1170 1I!IIl u s . 1.1521
-,-,-~.,-~.,-,.~,.-,-,-,-,­
".., 1.2700 1.25W> 1-l'lI 1.2114 UI97 l.lOIS 11'71 1.1177 1.1714 1,16')6 1.IM2 U»I
1_ I.VOO 1.lS68 1.2"'41 1.211' 1.22CIl '-2092 l.l'l11S IleIIo1 1.11\10 1.1701 \,1617 1.IJoIO
-,-=-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,.....
~1~1~1.~I~l=I~I.~ll~II~I.lml,'wl.~
lO'II 1.2695 1."B6'I 12446 1,l:\26 I,UIl 1.2104 1.199$ 1.11191 1.111OS 1.1716 1.1632 1.15'!04
-,-,-,-,-~"'-,-,-,-,=,-,-
,-
11909 1.1"6 11724 1,1643 1.1566
1.21~8 1.:/217 \.2110
1.1646 1.156'1
1,2327 1.2217 1.2111
l-11ll 1.1.... ' 11512
I .ml 12H1 1.2325 1.2117 1,2212 1.2010
\,1651 1.1574
l.2S4S 1201 1.2122 1.2116 1.2112 I lOll
l .lSlI 124%8 Ill19 I,nl~ 1.2111 1."lO11 1.191' l.lll4 117)(, 1.1M) lIS,,"
21011 1.2iIIO 12S61
,,~
I 1114
linD
1400 1.2244 '-1101 1.1'*1 1.1166 I.In.J 1.16f>7 1.1sn 1.1_ II42l llill 1.1111 I.1U(o
14211 I.Wfo 1.1117 I.JOIa 11m 1,17Il6 1.11iII'J 1.1598 11516 11"'41 IIJM 1.llOl 1.11.'
~1~1~~I.~I.lml.~lln21.~I.I~I.l~lll111il,~II~
1460 1.1))1, 12191 l.lOU 1.1"2 I.llll 1.17]2 1,I(oJ'l 1.15S4 II." 11402 1.lllJ 1.lVU
~1~1~1~11~1~1,1~11~llml.lffil.14111.~I.I~
,
",,,
1 2"")
l.lWO 1.25JI
I~I
l.nlJ
1.l6l1 l.lSl4
11610 I 250S
1,26OD 1.2<'~
1.2411
1.l417
1.2410
1.1402
1 D94
DIIO 1.25&11 12eas
2120 1.2576 1.2475
2J4O 1 2S6l 1.1465
2160 1."il4'I 124'!04
1.2535 12441
:ueo
,,~
, ""
1.191' 1 HIlS \.1m 1,1654 11517
1 19" I. IllS
1.1655 11m
1
1.1125 1.17311 1,If1U 1.1S7"I
l.lne 1.1~ 1157"J
1
1191J 1.151' 1.17111 1.1"' 1,1~
I 211S 12112 1.1110
12111 ,~ 111011
I ZlO7 123l1o 1.210&
I Jl03
1.l3Dl
Ill% 1.2197 12100
,.16
'''5
..=
"."
, ""
Illllli Inll'! 11191
1.19')1
12371 1:z:!82 1.2186
1.2)69 l:U15 1.11110
".
1.1'il'J1 l.l9OJ
1.2l6O 12267 1.I17l
1.2150 1 moll I 21i!J1; 1 ;"076 1,1'117 1.11199
nne
"'"
llell 11117 1.1r.!6
1.11l1 1,17)1, 1.1655
1,1"9 '-17)4 1.11154
1,1"6 unl 1.1651
1.18U 1.17)(1 1.1650
usn
1,IS7'I
1.1571
1.1S"
I.lS74
-,-,-,-,-,-,-,-,-,-,-,-,-
2400 1.lS21
1.2410 IllM 1.22'" 1.21511 120;>0 11"-1 11f19S 11810 un7 1.164/1 usn
-,-~"'-,-,-,-,-,-,-,-,-,2460 1.247S 1llt1 1.2lIIl l.n:ll 1.11'" IlOO't l1'AS 11., ""'" 1.111' 1.I(oJ'l 1.1s.5
-,-,=,-,-,-,-,-,-,-,~,-,.-
(table continued)
•
518
Gas Production ElIglneering
Ga a Flow MeaaureT/lclit
519
Table 10-13
F1-Gauge location Factors (Gravitation Correction Factor. tor
L fl OW rate: flow rate uniformity, maximum and minimum flow rates
Manometer Factor Adjustment)
(hied on Elev.tion and Latitude, Appl ~ ble Unadjusted Factors in Prec::edlnSl
Ta ble)
2. pressure: expected static and differential pressures, and their range;
permissible pressure variations.
.....
....
,..,'" ,,....
'''''
,,.., '''''' ,.'''''
'''''
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,.".,
' '''' '''''
,.""
,,.",.
,2,1XXl'
...
,
""
"
(EquoolOrl
O.'IiiI7
• .000'
0.99117
0.9987
,.".,
~
6,000'
8.000'
10.000'
,- ... ,,,"" ,0.9'JIII7
0.9991
0.9993
""
""
,.".,
0.9983
,''''''
""
,
,
....
'''''
,.-
0.9991
0_9983
099$5
0.9967
'''''
0.9991
0.9997
1.0002
, 0000
1.0001
....
1.0002
...
"n
"
1.11007
1.(11)10
...
T,0011
1.0011
10010
U lOID
10010
OS
10011
1,0012
1.00l)
90 (Pole)
HIO!)
.....•
1.0007
10010
1.()O11
10012
\.0012
H 1OOi'
,"'"
"«""'" "" ........ bo.of _
-
\\...... I, ........... konlt- _ _ .. lJaon, lei
- " " "....... ..,.... ' ...... _ d .... .....,.~ ............., .....
,,--
09995
1./XXll
1.0007
.....
"''-0 "
from Or;jk-, Mtlmn,l!
"1 ,\-at"...1 Qu,
1969:
courtft)
Emmpfe 10-1 . An orifice meter with a 2-in . orifice, equip~ with pi.pe
taps using upstream static p ressure connections in a.6-in. n?mmal (6.065- ~n .
. ternal diameter) pipeline, shows an average differential head .. 6O-m .
~ater and an average upstream static pressure .. 90 psia. The flowing temperature is 50°F, and the gas gravity is 0.65. Using a base p ressure of 14.9
psia and base temperature of sooF, calculate the gas flow rate indicated by
the meter.
Solution
t.(XXll
...
~
- 216.065 - 0.3298 .
Ave<age (h. p,)" - [(60)(90)r' - 73.485.
..10<1 ........ ..... _
foe ...
Average h...Ip, ..., 60/90 .. 0 .6667 .
of AC.<\.
From Table 10-7, Fb - 870.93.
OriflC~ Thtrmal Ef/",nnon Factor; F"
This factor accounts for the expansion or contraction of the orifice hole
with fl OWing tem perature, calculated as follows:
Fro m Table 10-8 , b _ 0 .02 i3. Th ere fo re. F,
- 1.00037.
From Table 10-9, by suitable inter polation, YI
F... 1
+ [0 .0000185 (T f
F... I
+ [0.0000159 (Tf - 528)] for monel
-
•
" b e < _ .. ,,~ ....... _".,.
-..100;._'...... .-.___ ,_ . . . _ , 0.'"_
- - . , . ..,.. ......... " _ , _. ...t>,o<' '''~ .. '~ __ .r..:.,....... -...' ' _ _
~
'Stem can only be achieved if all these factors are carefully c:ons1der.oo In
;hoosing the size and type of orifice, and the pressure measunng devlces.
0.9983
'''''
'''''
'''''
,.""
0.9995
,09993
'''''' ,."" ' ''''
0.9997
,
, "'" 1.0003
,
"'"
'''''
UIOOJ
I.oem
,
'''''' ' ''''' ,
'
''''''
UWS
'''''' '''''' '''''' ",
'''''' ,
''''''
'''''' '''''' ,1.0007
'''''' ,
O. 999J
SO
55
OJ
6S
_Ii . . . . .
. of the orifice affects the range of flow rates that can be measured,
an~ :::pressure differential that will be obtained . A well designed ~eteri~g
50.
"!Jtudf
.
Th
G.iull" ~! 'on ~ ~~ I~d-fl!'et
""o
expectoo .
-
=
1 + 0 .0273 '73 .485
0 .9914 .
528)] for stainless steel
From Equation 10-18, ror Ph" 14.9 psia. Fpb - 14 .73/14.9 - 0.9886.
(10·25)
From Equation 10-19, for Tb - 5Oo r~ FIb - {460 + 50) /520 "" 0.9808.
where T, .. gas flowing temperature at the orifice, " R
From Equation 10-20, for T/ _ 50°F. Flf .. (5201510)°-5 - 1.0098.
Orifice Meter Selection
Several factors need to be considered in chOOSing an orifice metering system:
From Equation 10-21 , ror 1'. .. 0.65, F~ - I /(O.65)o.~ '" 1.2403.
From Figure 3-1 , fo r 1'K - 0.65, Proc - 670 psia, and Tp<"'" 375°R.
510
Gas ProductioTl En1>(lnccrjll~
Gas Flou' Mcasurl'mCllt
Table 10·11e Continued
Fpv Supercompressibility Facior.
Table 10-11e Continued
Fp¥ Supercompresslbllity Factors
(Bu. 0.t.-O.6 Specillc Gravity Hydrocarbon Gas)
(811.. 0818-0.6 Specific Gravity HydrOCllrbon Gas)
p,
PS'I
2SOO
2520
~
2'iW
~
-~---C~--~---';C--co,c'·~m~..~'."'"~'~.~.~"~:o---,,-__-c___________
0
5
TO
IS
20
Z5
JO
lS
'Il
.($
so
114'1
11161
1.2~27 1.2lo'~
1.2411 1.2115
12m 12120
123711 12104
12282
1.2269
1 US6
11242
1 ma
1.2199
121113
12'76
111M
UUl
1.2115 1201] 1.1'JSl
1.21010 120lS 11'1+1
12016 119)6
, _ 12001 11928
11075 1.1'1'17 1.1919
1....,.,
1.11169
1186)
11456
1.1&1'
11642
117$11.1708
1.1711.1 l1ro]
1.1176 1.1698
11170 116'1)
1171•• 11667
1,1611
116Ui
!1WI
1.1617
1 Ifill
1.1SSII
1.1555
1.1551
l1So16
1 ''''~
-'-'-,-,-,-,-,-,-,-,-,-~.
1 no 1 un 1 22«1 1 211" 1.!0S2 '-1m !.I'JOT !.111lS 1.1 ~.9 1 1~ 1.1601 UUl
21040 1l12S lln6 1211'S , 211l 12040 1.1'1W; "192 11e1' 1.1742 1.1668 TWA 1.1527
Z660 1.2lOI l.ll40 Ilno 12100 1.1021 11";5 1.llISl 1.180lIl 117J.4 1.1"'" 1.1S'30 urn
~1~1~1~"1_'~51~11ml1~11rn'~ll~11ru
:vm
,.=
1710 1,22SJ
511
12206 121), 12Ol':! 12001 I."n 1.1A2 111ft 11117 11646 IlSn 1.1510
1,218'1 12124 l20Sa II~ 1.1'1n 1.1~1 1.1~ 117O'l 1-1r.J11 1.1SM ll50l
-'-,-,-,-,-,-,-,_,_,_,_u.
-'-,-,_,_,_u_,_,~,_,_,_,_
~1,~I~~I~I~I~II~l'~II~lll~llrnl.~llm
~ln~1~MI~t~llml~II_I,'~I,ml~llrnl,lm
-,-,-,-,_,_,_u~,_,_,_,_,_
.,
p,
no
'00
40D 1032. 10)17 1(1)05
I.~
1028S 1027S
10~S
10lS6
I(I,~
m
10m 1.0230 102B 1,0215
.,-,-,-,-,-,-,-,-,-,-,-,-,~1~IOl"lrull~l~l~I~I~I~I~I~102~I~
~1.~I~10l~1.~10l111~1~1~lmnl~I~1~1.02~
~1~1~ll0~1~1~1~10l181~1~1~1~1~1~
~1~1)1~1~1~1~1~1~1~1~1~1~1~1~
~1~~I~UI~I~I~I~I~IOlUlmll~I~I~I~
S40 IOW7
I~)I
III$IS 10400 lOla!; 1.ID71 I.onll 1(\)40 10UO lOll, 1.0)1(1 IOJOD I.am
5I.G 10465 I GU8 I ~12 I ~16 lOOOD 10J8S 10J?"2 1(1159 10).46 100M 10Jl2 10Jl1 10lOD
5110 1.~ lOOt>'1 100147 I 0U! 10015 10199 10l8S I (l3n I Irn8 I (\)40 100ll lonl 10010
~1~1~II~I~I~I~141~1~1~11rn81,~I~lml
~1~171~1~~I~I~I,~1~110ml~I~I~I~I~
"..0 1.05M I (151' 1.~9S 1.(J.I~6 10460 10442 102-16 1.{)IIO 10J'lOL 101111 1.0Jl>l! 1.I1lSS 1.0)41
&60 I(15S2 IOSlO 1(1511 I ~92 10474 10456 10439 I ~21 1.040I!I I 0191 1.01~ J.(/ltJ6 1.01>1
~1~1~1~71~1~1~1~1~ll)Irol~I,~I~I~
~1.~I~I~I~l~I~I~I~ll)Illl~~I~l~l~
ml~I~I~I~I~171~1~1~1~1~1_121~1.~
-~.,-,-,-,-,-,-,-,-,-,-,lI60 1.1120 1,2\166 12(110 • 1951 118'11 1.1&l:! 1.1770 111'01 116012 115" 1.1sn 1.145]
~1,~I~I~I~I~II~IOI~I04~I~I~I_I~I,~
2M)
~1.~I~I~I~I~I~IOSI91~1~1~1~1~3010414
-'-'-,-,_,_,_u_,_,_,_,_,_
131/1(1 I~ 1.19111 1.19)7 1187& 1.1811 1.17V 11f>9{, llfoJl 1.1S6111~ 1,1,,",5
-'-,-,_,_,_u~,_,_,_,_,_,_
~1~1~1~1~1~1~llnlll~II~I~I,lmllm
-'-'-,-,-,-,-,-,-,-,-,-,~
~1~1.~11~11~1.~I,IWI.~I~llmll~IIQI~
~1,~IIWll~I~II~I.1mll~I,~II~ll~11~llm
~1~I~OI~I~I~I_I~I.~I~I~I~I~l~l~
DI~I~I~I~I~I~I05lll~)I~l~I~I~I~
~1.~I~I~I~JI~l~I~I~l~I~I~·I~I.~
~1~11~ll~I~I~I~I~I~I05111~1~1~1~
1.Q5.4~ 10';29 10500 I (14M 1.{)I71
1.07.5 UIl14 106810 10!.S8 1001 1.0607 1.0S1I4 I.oo;t,.l 1.OS4O 1.0519 lOSOO 1.0Ia1
160 I,ons I DII97 lOb70 Ulb4J 1.(11)17 1.(lYIl 1.05"
_
1.0453
I~
~1~1~1~1~1~1~1~1~1~1~1~IOI,~I~
"
PI'I
60
•
ml~I,~I07I&I.~I~I~I~101~'~1Q5.411~1.~I~
1.07111 100;75 1.0&41 1.000J I OWl 1.(K15 lOSS) 1.05Jl 1.0511 1.~<J2
'HO l.m1 107&) 1.01))
'00
_1~1~1~1071~1~1,~I~IObIOl.~I~I.Q5.4II~II~
'"
_1,OOII~I~I~I.~I~I.~I~I_I.OO~I.~I.~l~W
II ItI(Q) l,tI(Q) I tI(Q) 10000 10000 10000 10000 10000 1000 1000 1.0000 1000
M 1,001& I.oon 1(1(/1. 1001. 10014 1.001) I.oell] 1.0012 1.0012 10012 1.0011 1.0011
1,0000
1.0010
~I~I~II~I~I~I~I~I~I~I~I~I~I~
601~1~1~1~)1~1~1~1~1~1~1~1~1,~
.. I roM 1.110&2 1.0061 l00sa l00S6 1.00S00 1.00Sl 1.0051 IIJ(I09 I ~7 10lM6 1.00004 I.~}
~1~1~1~1~1~1~1~IOOMI~I~I~I~I~
1201~1~1~1~1~1~1~1~1~1~1~1~1~
1«1 um 10109 10105 10102 IOJ9!I 10095 lOO'l2 10081 looes 1.001) I,com 10071 I.om.
160 l.G1n 111125 10121 10111 1011l 1.G101 1.0105 ll1nn 1.1X1'II 10095 lOO'l2 1.008'11.0017
110 I,OI'S 101010 IOU' 111131 1.0121> 1.lI1n 1,11118 1,0114 1.0111 1.0107 UnO) 1.0100 l.!1D'J$
200 1.111112 1,1I1S6 10151 t.O'''' 1111«1 1.01» 1.0111 111121 llI1n Hnl. 1.11115 111111 101011
120 l.11171I,OIn 1111'" 10160 111150' 1.014' 10145 111140 lOU6 1.11131 1111~ 10112 1.1111'
l~ 1.0191 1.II1M 10181 UIll'S 10168 Hl1fo.l 1.0158 10lSJ 1.0148 1,01')
1fIIl 1.0211 I 0104 1.01~1 1111'10 101lll llI1n 1,0171 1.0165 10160 10155
1 (lUll 1.013) 10129
111150 1.01+4 1,01»
~1'~I~I~11I~I.II1Ul~III1MI~I01nl(l~I~II11HI015O
I (lIn
10115
1.0196
10lIV
1.021'
1111"
1(1171
1.018'1
10200
UIlI1
1.0162
I.01n
1.0113
1.G1'H
HI20.
1000
1(JlI)
II)j(\
1060
I'*'
10!U7
1,01165
101182
10900
1"".
101111
1.01121
10&'1
10lI60
IQI7}
1.1:."
1100 10911
IUO 109SO ID!IOII
11~ 109i4 1.09:1.
1160 1.0'lIl1 1"'19
1\110 11000 I09SS
1200
1120
1240
Il60
1.101'
I lOll
1.1043
1.10ft4
lzaJ 1107'1
10m 1.074t1 1.0717 1-(1687 10660 1.(1634 1.060II lOS&!; 1.\I!i6:l
1.01'!l4 10761 1.0730
10lI09 10775 lW,,",
10000S II17'lO lO:-sa
101J9 1.0lI04 10:71
I.05l9
107111 10ft1) I~ 1.(11)19 1,QS9S 1.05n 1.0549
I.on. 10b6S I (l6S1!1 HII>JI 1./I60I0 1.0582 1.055'
IIrl7 101>97 1(1670 1.~1 1.(1617 HI5<J2 1.OS6'J
1./f,"40 IOn19 10bII1 lOI>S4 I.OI>ZI 1,!IIIIll 1.0571
IOIJS,I 10111' I.071S UI75] 1072l 101192 10M6 1,0fUI
1~ 1.01.49
loeas 1.0&C3 10111. 10:"7') I074t1 107" I.CI681 1.0ftS9
lOI!I99 10M.l 108.!6 107'11 10J"Sa 10m IIMI II\W.I
I"''' l.oe1} lOIIl9 1.0lI04 10m 1.07)1 1(1)W IIIb7'J
lOVO lOilJ.4 10Il00 1.07(,6 10J"l.4 10000J
1"'10 1"'201 1.0lII!'I 1011S1
10000S 10942 1.0'102 llJ!1!.o1
U(\()I 1.0951 1.0916 1.01176
lIon 10971 1.0929 1011e'l
UOlQ 1(I9M 10942 1.0901
101116
1.0&28
1.1l&fD
1.08>.2
1-(1116)
1.078<1
101'!l4
LOIIOS
1081b
I 0&27
I·OlSO 1071'
1.0no 10m
1.0nl 1.07»
107'1 I (174&
1.0~1 1,07St
1 (1612
1.0ftll
1,0ftll
1.(I64}
ll1bSl
1.11b89 1.(11)61
1.!IoI'J9 1.0ft11
1.07'Il'J 1.(11'&1
I (ln9 1.0690
1.0728 1.0b9II
1.(\51'
1,0529
1.(5)11
1.0541
I(\S~
1.0S8I 10566
I,CMII 1.0574
1.0!0a1 1.05IJ
1,0b16 1.0592
10000S 10601
1.1IbJA
1,0ft4]
I.ObS2
1.1Ib61
10b7tl
lObIO
1,0b1'
1.()6.l6
1(6)5
1~)
1100 11094 11(1+1 I (l99'!I I09SS I,I)'JU 1.0IIl"S 1.08)1 l\*ll I.(\;'M 1.IJ711 1.0107 1.(1671 1.0651
H2O 11110 1105' l1(1ll 10961 10'125 101l8I0 10149 10112 I.Onl 107'" 1,0716 1.0681. 100'
(table continued)
•
512
Gas ProdurtiQII EngiflCenllg
Table to-1le Continued
Table 10-11e Continued
Fpv Supercompressibility Factors
Fpy Supercompresslbillty Factors
(Base 08t8-0.6 Specific Gravity Hydrocarbon Gas)
,.
(Base Oata-O.6 Specific Gravity Hydrocarbon Gas)
,.
T~mpe'OIU'~"f
,-
"
"" '"
l],4O I IllS 1.1073 11025 1.0'JII0 1,1l'IJ71011911011S~ 10lUll.0738
10755 l\ll'lS 1.0695 1.0661
lll,o 1114() 1 10117 1 Ion 1 09113 1.0'}<9
1,01170 1.(11))
1 07M 1.071J 1.11703 1,01.]5
1l8J 1.11;.0 11100 11052 l1tm
1-(1920 H)Ml 1.!.84]
10773 1.0741 1.0111 1C632
,...,
1~
111~
1.11"
1.1~
11017 I.!l'll] 1.0911
1.01!5] 101116
,""
l'l\I 1.11&1 'l1l8 11073 1.11l.J1) 10985 10941
,=
lC11!61
1.0791
14010 1.1197 l n4 1 1.11l'lO 1.1()42 1.0'Jn 1.0951 1 0912 1 tel] 1.I111l4 ,~
141:(1 11210 1.11~ 11103 '.1053 l.100b 1.0'l6.l 1.11'121 1.01182 1.0&'1 1.01I.III
1~ llUS 1.1167 l111S 110M 1.101& 1,!l'l71 1.0931 HilI'll 1.0S52 '-01116
,~
1,0759
1.0767
1.0775
1.07113
,-,-
100,Q
I.OT.!7
lOllS 10705
I 074Z '-0712
1,07SO 1.1))"19
'00
"
""
m
1,09J'8
1.0978
1.0978
1.0977
10931
1.0'l37
10937
10936
10935
ll40 1. I50J 1.14]] 1.1J71 l.lll1 1.1258 ,,~ 1,1156 1.1110 1.10r0) 1.1020 1.0977 1.1)'l3} 1.0&J6
lJfoII 1.1502 1.1432 1.1]70 I,1l1l 1.1258 1,1205 1.1156 1.1110 1.10f.) 1.1020 1.0'178 1.0936 1.0S'l7
2l1JO l.lS01 1.14]1 1,1369 1.1]11 1.1257 1.1205 1,1156 1.1110 1,106] 1.1020 1.0978 1.0937 1.01197
2400
14!O
1440
2460
2480
1 1499
1.1497
1.1495
1.14'3
1,1491
1 142'1
I.HUT
\.1426
1 1424
1.1422
I.llfoa 1.1l1l 1.1156
1.1361 1.lll0 1.1256
11.l66 1.1.lO'! 1125S
l.l1M 1.1)011 1,1254
11161 1-1306 1.1253
1.1105 1.1156 1.1110
l1lOS 1.1156 1.1110
,,~
1.115S 1.110'1
11M3 \,11\.4 1111l1!
1.1201 I.11S) 1.1107
\,106]
110(0)
1,10(0)
110hl
1.101>1
1,1020
1.1020
1.1020
11019
1.101&
"'"
1<;00 UlJa
1 1251
1.12bl
1.1176
1.12M
1.11;:-' 1,1126 1,H)~ 1.1027 1.1)'.18) 1.O'JoII 1,0900 1.01161 1.0IIlS 10:>91 1,07'SII
'.11'1' 1.11.l11 1.10117 1,10.le 1.0911]
1,0'!09 1.()II70 I.OIIJJ 10m 1.0766
,,~
1.1ISO ,,~ 1.1(lo19 1,1001
U)'l18 1,011:>9 I.~l '-0lI07 I.om
'.1215 111M 1.110/1 1.1OS9 1 1012
'-11'127 1.(18117 '.01150 U1815 1.07110
11227 1.11n 1,1119 1.101\8 1.1022 1.0'17& 10915 '-0II'J6 '-0II5II 1.(11123 1,07l1li
10727
1.0734
1.0741
1.0743
1,0755
1SI)J
1600 llXl!
11112
1.1JU
1.11.14
1.1345
1.1233 1.1183
1.1l'~ 1 119]
11260 1 1101
1.1"'0 1,1213
1,1281 11223
1.11:1'.1 1.10711 1.1011 '.0':157 1.0'J044 1.0'J0.I 1,08(,t, l.D5lO 1.07'.15
1 11)<) 1 10S11 11041 1 099S
1.0912 I.OVl 1,l1li37 ,~
'-1149
11049 1,1004
'-0910 1.0IIII1
111'>3
1.10$& 11012
1,0927
1,01115
1.07b]
1-0763
1.0775
10781
1.12l'J
1.1D6
11232
1.1219
1.lill
1.118'1
1.11116
1 1181
1.11110
1,1177
1.1141
1.113'.1
1,1136
1.11l3
1.1130
1.1US
1.1.l66
1,117ft
1.13M
1.1)<)1
1,12')0
11300
l13O'J
1.1]18
" 1J26
11212 '-"]t; 11n4
1,1241 1.1IM '-lIll
1.12SO 1,119J 111.l'J
1,12sa 1.1Z<l1 1.1147
1.1266 1.1209 1.11\.4
,-
1.1l45
1.11-41
lU17
Ll331
1.11:rl
1700
1720
1740
17(,0
1710
,-...
MOO 1.1470 1.1401
2620 1.1466 1.1400
1.1461 1,1l'16
1.1456 11]91
2680 1.1450 1.1387
2700
1720
2740
27100
1710
1 1)25 1.1]70 1.1221
1.1l111 1.1~ 1.1217
11115 1,1261 1.1113
1.1110 1.12>7 1.1:/011
1.1lOS 1,1251 1,1204
1.1173
1.1170
1,1166
1.1162
1,1157
1,1120 1.107ti 1.103J 1,11'l'J2
11100 1.14Ol
1,1410
1.1418
11426
1.14n
1.1ll4
'-1l41
1,1l49
1.1l57
I.U7l 1,1216 1.1161 1.1111
1,1281 1.1221 1.1163 1,1118
1.12M 1.12)(1 1.11lS 11114
1.129'1 1.1ll7 1.1181 uno
1.1JO:.! 1,124] 1,1181 1.1H7
1,011:21
1.006
1,(18]1
1.(1836
1,(11140
,-
Z1IOO 1.1414 1.1154 1.12'l'1 1.1247
1.1408 1.1l49 1.1l94 1.1241
1.1401 1.1l43 1.11M 1.1llT
1 . 1~ 1.1l36 1.12al 1.1 ll1
1.13117 I.U30 1,1176 1,1225
,.-
2'JOO 1.1l7"'l 1.1124 1.1170 1,1219 1,l1n \,1128 110115 1-1042 1.1DOl 1.0%4 1.092>
1.0!J(,0I
1 0567
,.
, """
,-
,-
,,~
1900 1.1440 I,UlT 1.1.lO'!
1m 1.144' 1.1]18 1.1315
1...a 1.14$01 1-1:1114 Ulll
1.1460
1,IJlfi
1,1465 1.1»4 1,1]31
,""
,
l1Z49 1,1193
1.11'.1'1
1,1261 11204
1.1266 1,12O'!
11271 1.1214
l.ass
1.1074
1.108l
1.10119
1,109J'
1 .1104
1.141'
1.1422
'-1425
1.1427
1,14:r1
l200 1,ISOl 1,14)1
2220 1.15(101 1 14)1
2240 1.-;505 1.143J
1260 1,1505 1.14l4
:!l80 11505 1,14l4
1.1l55
1.1358
1,1361
1,1l63
I.Ix,s
1,1294
1.1291
1,1100
1.1)02
1,1304
I.Ull
1,\24(1
1.120
1,1145
1.12.....
1. 1)06
I.llfoa 1,1108
1,1l6'1 1,lltO
1,1J7~ 1.1l11
1,1]71 1.1l12
~,!2S0
'-1)61
... ,'''''''
"""
1,1028 I 09&1 L0'J0I1 1.(190] 1.()II65 '-08l8 1.07"'lJ
1.1036 '-il'l'Il
10'110 ullin 1.01135 ,-om
,,~
1.0917 101178 I,OM!
1.1051
10923
1.(1847 1.111111
1,1053 1,1(111 1.0970 1.0919 1.0I1'J0 101151 1.01116
,-
,"
1.1(l1.i.4
1.1071
1,1077
1,1l1li3
1.10II'J
1.1142
111.....
'-11n
1,1158
1,10'J01
1.1()'l'J
1.1104
11109
1.11~ 1,1114
1.1470 1,1)'.1'1 1.ln.. 1,1176 1.1219 1.1163
11415 I.IOOl 1.IJ.<O ,,~ I I1ll l11n
11410
1.1144 112114 1.1227 1,11]t;
1,14&1
1.1l49 1.128& 1,12Jl 1.11110
1.14118 1.1416 1,1l5J 1.1291 1.1:04 1,11114
2100 1.1491
~120 1.1494
2140 1,1497
21100 1,14')9
1180 1,1501
1.1119
1.1Ill
11127
11131
11114
1,1(119
1,0935 1.08'l6
1.1025
1.11941 I,09O:!
1.1031 1.0'lI!3 1.0'J0I7 1.11'lO7
1.1OJ7
I09S1 1.0911
1.1GO
1,11'lS7 1.0916
1.104l1
,,~
1.1OSJ 1,1009
,.'""
,"'"
1,1l858
1.0!I6l
1.0568
1,01173
1.0V7
,~
1.1073
1 IOn
1,10111
1.10115
1,10IIII
...
,
'"""
'"'"
,~,
1.1186 1,1117 1.111'l1 \,1045 1.1002 1.0000IJ 1.0911
1.1189 1.1140 1.10'J01 1.104a 1.1004 1.0961 1 091~
1.0IJ6J 1.0921
1,11901 1.1145 1.111'l11 1,10Sl 1,100II 1.0IJ6S 1.092J
\,I1'.1f. 1.1147 1,1100 I.l~ 1,1010 1.0IJ61 1.0925
1. 1149
1,1151
1,1152
11151
111S4
1.1102
1.1104
1,1105
1.1107
1,11011
1,D'lM
1.0lI70
I,OVl
1.0II7~
1.0117&
1.0!1110
101182
1.011&1
1,0etJ6
,-
10972 1,(9)0 1.1IIJ91
1.097J 1.0911 1.0II1l
1.0!I74 1,1)'lU 1.01193
2)00 1,1505 1,1434 1.1)71 1.1)12 I.Usa 1.1105 1,11SS 11101J 1.106l 1,1018
2320 1,1S04 1,14l4 1.1)71 I·UO 1,1258 1.1205 1.1156 1.1110 1,10h] \,101'
10911 1 . _
1.1)'l}.l 1111195
1.!)'Vl
""'"
1.1'\45
11440
1.14l4
1.1428
1.1421
1.1J3l
1.1 377
1,1l71
1.1)66
1.1360
1.1l71 1.1l16
1-1)601 1.1JO'J
1.1)55 1.1)02
1.1l47 1.1l94
I.U),) 1.128&
,.-
1.1027 1,0'!II4 1,0942 1 090:!
1 lOll 109118
10'i106
,,~
1,11'lO'J
1,10lll
10912
11<Ml I.D9'.I'I
1.1)915
1,11n 1.1141 1,101J6 1.1050 1.1006
1.11"
1.1lOO
1.1201
U20l
1.1204
I.lo1!111 1.1420 1.1)1;1 1.1](101 1,1251 1.1:/00 1.1152 1.1106 1.1or,(J 1.1017 1,0'17S 1.0934
ZSlO 1,1485 1.14" 1.1158 1.1)02 1.1l4~ 1.11" 1.1151 1.1105 1.1059 1.1016 1.0974 l.09ll
1.0973 1.0932
1.09T.! 1.0911
lS80 1.1474 1.14OIJ 1.1l49 1.1294 1.1141 1.1191 1,1145 1,1()'l'J 1.1053 \,1011 1.0970 1.0'130
l$4O 1.14&1 1,1414 1,1)56 1.1100 1,1247 1,1196 1.1149 1,11OJ 1.1057 \,1014
2560 1.1478 1.1411 l.llS2 1.12'17 1,1l44 1.1194 1.114' 1,1101 1.1055 1.101)
1.1)925
1.1058 1.1014 1.0'171 1.0919 10Ma 1.01152
1.106l 11019 U)9]t; 1 0914 101194 ,~
1.1068 1.111lJ 1,11'l8O 1.09l11 1.0B'lI1
I,III'i6 1,1(111
,,~
1.1(114
1.10S'.1 1, lOIS
1,11160 1.1016
1.10r01 1,1(117
1.1ID
1,1254
1.1256
1.1251
513
Gas Flow Measurement
1.1263
1.1256
1.124'1
1.1141
1.1235
1.1:1'lO
1.1287
l1la3
1.117"'1
1,1175
1.1213
1,1207
1.1201
1.1194
1.1181"
m
,=
o
1.0000
1.0000 1.0000
~ 1,0010 1.11010 1.0010 UXll0
,~
,~
40 1.0022
100 1.0032 10030 100.30
eo 1.0042 1.0040 1.00)') 1,00l9
100
120
140
1100
180
I.DOS1
1.00u
1.(1074
1.00II4
1.0094
1.0051
1.0061
1.0071
1.00II1
HO~1
1.0049
1 DOS~
1.0068
1.0078
I.DOIle
UK148
1.0057
1.(1066
1.001(,
I.DOIIS
1.1097
1.10'J01
1,1091
1.10&8
1.10115
1.091&
1.0917
1.0914
10911
1.0'.l0I1
,.-
1.0'i0l
1.1121
\.1117
1,1111
1.1105
1,109'J
1.1079
1.1074
1,1069
1.1063
1,10S8
1.1024
1.1020
1.1016
1,1012
1.100II
1.0'lIIJJ
1,0979
1.0'1r.;
1,0972
1.0'168
,-
,""
1,0000 1.0000 1.0000
,.'"'
,oon
'"
,=
10019 1.001& 10018
1.0018 1.0017
1.ClOlil
1.0047
1.1llS6
1,00f0S
1.0074
1.00I!J
1.0045
1.005-4
!.C1(6)
1.00n
1,00II1
, oov
1,1III9S
1,1lI!94
1.0S'l3
1.0II1l
1. 01191
1,lIII90
1.01179
1,1lI!76
1.01174
1,000n
1.0116'1
,-,- ,,- ,-
,L0'J0I3
,,.,.
,~
1.0'l36
I.09J3 1.()II9S 1.01157
1.09"2'/ 1.1lI!92 1.01154
LIlI!SI
1.11'l59 1.0921
I.OM7
l.t017
Ll012 1,()'l'J] 1,09SS 1,0917 1.0I!80 I.CJ1I4.4
1.1027
1.0'l1l ,~
1,00000S
1.1012
I.OVI 1,01135
1.1017 1.0918 1,00000I 1.11'JOoI 1.\lIl67 1.01131
,- ,- ,10000 1,0000
, "'"
1.11'129 1.01III'.I
1.1010
1.0927 1.0IIII7
11006 1,096S 1.091} 1.0IIII5
1,1004
1.092] 1,0IIII3
1.11'll1 1,0000l
1,1001
1.1127 LI08l 1.1039 1.~ ,~
1.11 23 1.107"'1 1.1036 1.099S I.11'lSS
111'l51
1.111 6 LIon 1.1030 1,1l'I89 1,0'J0I9
1.1112 1.1069 1.1027 1,0'lIIJ6
1.1199 1,1153 1,11011 1.1065
1.1194 1.1143 1,1104 1.10&1
1,l1M 1,1144 1,1()'l'J 1.1057
1.11~ 1.11)<) 1.10'J01 1.1051
1,1177 11114 1,10'i0 1.1047
1.11610
1,1160
1.1155
1,1149
1.1142
1.1OSl
1.1G411
I1G47
1.1G45
1,10012
1,01197
1,0i!97
1,01197
'"
'"
,=
,-
1.0000 \ .0000
1.CKJ07 10007
10016 1.0016 1,0016 10015 1.0014
1.0024 1,00"23 1.0023 UIOZZ 1.00:11
I.DOlI '-ClOlO 1.(1029
1.000II 1.000II
1.!J044 1,000Il 1.0040
I,DOS1 1.00s0 1.0048
1.(J060 l,oosa 1.0056
1001'>9 1,0067 1.0064
1,0078 1.0075 I.oon
,.-
1.00)<)
1.0047
I.DOSS
1.0063
1.0070
1.00l8
1.0045
1.(I05l
1.0061
1.006II
1.0037
1.!J044
U JOSI
U058
I .oor.s
1.00lS
1.0042
1,0049
I.IllS6
1.000J
200 1.(1104 1.0101 1.1)0'17 1.0094 1.(0,;/ 1,008'/ 1,1XlI6 1.00IIl 1.00l10 1.(1078 1.001S 1.00n 1.0070
220 1.0115 1.0111 1.0107 1.0104 10101 1,00'lIIJ 1.011'lS l.wn 1,00IIII 1.(10116 1.00IIl HOllO 1.(1077
(ta ble continued)
•
Ca, Flow Measurement
Gas Production Engilleering
514
Table 10·11e Continued
Fpv Supercompre.. lbllity Factors
(BaH Oals-0.6 Specific Gravity HydrOCllrbon Gas)
Table 10-11e Continued
F,.. Supercompresslbility Factors
(B... Oata-O.6 Specific Gl1Ivlty Hydrocarbon Gas)
....•
,~
,.
'00
"
14S
,....
lOCI 10125 IOIlI 10111 ,cn14 1.0110 1.0107 1.(11I1l I.01OJ 1.009!i 10JII0I lllO'1O 1,0011 1.00&1
M , all! , 0112 lOT:M 1.012l 10119 1.1t1l' 1.0'111 1.0'109 1.1)104 11)102 lD0911 l009S 111091
. , I en.. 10142 Ullll 1.0112 10118 Ions 1.0121 1.0'117 1.01\1 1.0109 I mos 1.0102 1009II
100 I01S1 10152
no 1011>1 10161
)00 I DIn 10111
,.,.. 101V 1.(1'1'
Ja) 10191 1019'
1111'" 10141
'0116 10m
1 DI(oS 1.111110
'.1)175 I.U'1>9
lOllS 1.0P'
IOU7
101016
1.015S
1.01601
1.!I171
101M
10142
I.01S1
unS9
1.016&
lono
I(.na
1 en66
1.01S<!
1.016.1
1.0125
10lll
U'1'I
1,,""'1
1.0151
1.0121
111119
un11
1.01+1
1.0'152
0100 1.132011 1.1.201
4:10 1.11118 1.0111
.wo 1.0'l2I 1,0210
.."., 10B8 lC1tl'l
410 \.0248 IOU')
10195
1.0204
1,021)
11n22
102J2
1.1t111l
1.01'1"1
1_0100
10219
10218
UTl77
l.fI1lSS
l_fIlU
10202
1.0211
1.0171
1.017'1
1.fIl81
1(n'lf>
1.02001
I.OlloS
l_fIl71
l.fIll1
10111'J
l,fIl'17
1.01110 HnSol
1.01~ 1.fIl&1
l.fIl1"5 l,fIl'"
1.0182 1.011$
1f1l'ilO 1(18)
unll9
1.111'"
1_0l07
1.021&
1.0225
50() '0259 10249 I02H 102)1
1 !Ill' 1011l 10109 10105
10U4 UII1' 1011. 10111
1.00ll '0127 1.0122 1011$
1.0U' 1.1)1)4 1.0129 1.0125
101'16 1.0141 11:n~ 101)1
'.0'"
1.0156
I OIU
1016.
1011&
1.01'1
101SO
1.0156
1(16)
1.0169
lana
10144
1.0151
10157
1016)
1,0227 I.ono 1.0212 10205 1.0197 1.01'iO 1018) 1017& 10170
~1~1~1~1~1_'~102101ml11~Im'1710~101~I01n
s..c
1021'9 1026a 10260 10252 10243 1,02.16 10m 10110 1,0212 1,0:104 10191 101'iO 1.0181
%0 10289 10.1111 10269 10:161 10252 10245 1.Ol.l6 10227 10219 10211 10l(U 1.01911 101"
500 10m 10288 1.0219 10170 10"lt11 10253 1,0244 10.HS 10216 1.0218102101.020210195
600 10)09 lime 10288 10219 UIl70 10"ltI1 1.0251 10242 I02JJ UIl25 10211 10'20II 1020"1
IolO 10)19 101011 10l'M 100M 1021$ 10l6'J 1025' 1,02S0 1,0:241 lOU2 102l} lOllS 10201
.., 101)') 10111 10)07 102911 1(Jl81 loon 1.0267 1.0257 10:243 10:219 10210 10212 10214
IJ60 1.0J0I0 10127 10l" 1 OXIS 11l2'1S lD:!l1S 1.021"5 1.D2M 1,02SS 1_02* I.OUl 10228 1.0220
WO 10lSO 10111 1_0125 10114 10»1 102'J} 1.I1l82 nnn UllIU 10151 10244 10lll 10226
1'00 10159 1_0301(, 10»4 10m 10)1l 1,0101 lCU'i1O 10V'1 10'l6.f 10m 10250 10241 102:11
no
10""'
740 10J"
1tIO 1.'111
1110 10)'l1li
I OlS5
I 0)65
1.0l14
10)14
10)l}
I om
10)61
IOJ71
1.0111
10)40
1.0].09
10354
1.0ll0
lOll.
1.0116
10)14
1.0l0'J
101"
1 fUl4
1.00ll
1.02'JI 1,0'lII7 I.~ 1,02(,6
UIJOS 1_1!l')oI 102&1 IW)
1.0l1l 1.0101 1,0190 1,0280
' .0l20 10lOll 10l'97 10lIl6
1.0251
UJ263
10269
UIlI1
1.0241
U1251
1 (125'
I(I2M
1.0211
1 cr.!O
10249
10255
100
S20
1000
860
_
10)<)1
I D'02
lQoIU
111'21
100)(1
10lllO
10J8I
10""
1.00105
1.0014
10)66
I.OP4
10loll2
10J91
10199
1,0)5) IID40
UIl60 10)17
10)61 1.0]55
I.om. 1.0l62
10)14 10]10
10117 lOllS 10l0) 10192
1_0))1 10m 10110 10m
10M2 lOll'! 10]11 1 '106
1-10., 1.0))6 l.fUl4 1.O)1l
1.0156 1_0)1) 10110 lOllS
I_D2II1
10'lII7
102')4
10lOCl
I_on
10271
10211
l0lill
10211
102')4
10260
1026&
900 IQoISS 100)<) I.QoI11 10001 10m 'OJ17 1-0363 10150 11Il)6 10124
10Jll
I_om 10281
la..ot
1110118
IQoIV
10011
l00W6
5 15
ulln
10211
'-OW
ml~I.~llI'nl~~I~I~I~I~I~I~Imll~l~
~1~I~I~I~I~I~I~I~I~I~I~I~I~
~1~1~1~1~II1'I~I~I~I~I~I~I~I~51~
, . 1 a.92 111'11 1.0056 II1'M 1.lI'n 1(M07 10J91 1_0J1t. lOl6J 10)48 101)1 10)21
IOlOll
~1~I~II.~1~1~I~ll~I~I~I~I~I~IM1J
1~1~1~1~1~\~I~I.~I~I~I,~I~I~I~~
1000 IOSII 1_00'111 1,0480 100101 '-0444 1.11'18 1.1I'1l 1.01911 1,0111 10)65 10lSO 10116 101H
1060 IOSl7 10S06 I .QoII1 I QoI6i 10052 '-QoIfi 1,00119 I~ 1.0ll] 1.0111 '-01S6 10}oll 10118
lceo IOS)5 I.OSI4 111'95 1,11'16 I_II'S~ 111'42 1.11'25 1.640'1 1,0393 1.0177 10., 10}ol6 10Jll
115
,.
m
'"
12;10 UJ6O\ losn 1.os54 HJSll I_OSll 10091 1007) UMSS lOO}l 111'20 lOOOJ IOJB(, 1.0170
1260 1.0Ii1O 1.0S8S 1.000l 10519 10511 111"11 III''' HM61 1044) 1001:5 HM07 1,0391 1.0)1"5
'lID 1.0Ii18 UIS92 1,0S6I 11lS46 '-0Sl4 1050f 1 QoI8S 1.Mb& I.~ 111'10 1_11'12 1.0l9S 1.0)1"9
~I~'~I~'~1~)(II~IO'~1~1~)IOOHlooI7'01991~
lJl1l I_OIill I_OIi01 1051J IOSS9 IOS)6 lOSIS 100911 1.11'17 I,II'S7 111'39 1.11'21
l)o1Q 1 .
I05W 10S6S 10S0I2 IOS21 HrsOl 104a2 1 QoI62 10444 1.(1426
...a
I."'''
IQoIOoI 1.0l8I0
\.IMOS 1.0)'10
1160 1.1"'47 l_OIilI 1.1IH1 I,osn 11154 10521 10S06 100II1 111'6] 1.11'49 1,11')1 1.11'12 10J94
lJliO 1.0654 1.IlfolI 1060.) 105111 1_05501 105)2 IOS11 111'92 lll'n 1 IM5) 100S 111'16 1.0)'l1li
1400
IHD
1440
J.46D
,48(J
1,06611."']5
I.IIWJ 1Il1041
1.0r.76 , ' 1.0&8.) 1.11655
1.06'10 I.GIoW
H1610
I."'''
1.1lf>21
1.0E.J9
1,1lf>l5
UI51S
I,OS91
105911
I OWl
10609
1.115410
10S66
1.OS11
IOS17
10S&l
105)1
10000l
1_0S43
lOS,..
1.0560
IOS16
IOS21
10521
IOS)2
1.0511l
1,11'91
1,0501
1.0S06
IOS10
1.05IS
111'17
10481
1.1M86
1,0090
1.0094
1.11'54
1.CM6.2
1.0066
1.11'70
1_1I'1~
1.11'39
1.044J
1.0447
1.11'51
1.0054
1.0020 I.QoIOl
11I'1~ 1(M!16
10018 1.0010
10411 111'14
1.04fi 1.0411
ISOII 1,1)697 1,~ 10641 10614 IOSSII 1.0S6S 10542 10Sl0 111'9") 111'18 1,11'54 1.11'19 10421
1S20 10704 1,0Ii75 10641 10620 lOS94 lOS70 10541 I,osn 10s0) I,1M32 1.CM6.2 10441 1042>
1S40 1,0711 l(lt,1!l 101i5J 1111>26 10600 IOS1S IOSS2 lOSlO 10507 1 JM.I!I> 10466 10«6 1.0428
156(1 107111.06a11,1J65,8 10631 I OliOS lOS1'9 IOSS6 I.Q5}o1 IOS11 1,00'ilO 10470 1.005(1 I.QoIll
15811 I .on~ !.ClUJ) 101i601 1001 10610 IOSIo! 10561 100Ja I_OSI6 111'94 111'7) 1,11'53 10015
16011
1620
1640
1660
11080
I .D1lO
1_07)1,
1,07.)
1,074a
1,075A
1.1IW1
1 0105
1.0711
10716
lOr.11
10670
1 (J675
1.(lt,I!1
1~
10691
17'1lD
lno
17-40
11¥oil
1110
1_0]$'
1_01f0S
I.D17O
1_07161-1&",
1.0126
107ll
1,07]7
1.0742
1,0741
106911UI.701
10701
1.0711
1.0716
lOIi4Z
10641
1.000U
l0Ii51
10142
10615
10620
1.01>25
1 DO)
1.06J.4
IOSII'J
lOS91
IOS'17
1.11602
1.0&06
10566
10570
IOS74
1.0S7e
1.0SS2
10541
1.05<17
1.0551
lOS5-4
lOS54
I OSlO
10Sl4
I.OSl'
1.D511
IOSJS
1.11''111
10S01
1.0s0s
lOSO'i
lOS12
1.II'S7 100)9
1.<M6D 1,0442
1.1Mf>ol 1.0445
1 (M67 1,0447
10070 111'50
loe41 106J9 1.0611 I.ose. lOSU I.OSl'J lOSI. 1.0494 104n 1.0053
10611 10643 1000lS 10S91 10S67 1000l lOS" 111''17 1_11'16 1,11'56
1_
I fI6l1 106<1 10620 1.0S95 10511 1.0s.6 'OS:U I05()D 1.11'79 I.oo~
UJ681 106Y 1 ~~ IOS'JII IOS74 1.0Sf'J I.OS25 1.I.SOJ I Q.I8l 1.11'6.2
I ~ 10656 106211 106(l2 I,OS17 I,OS§l I.OS18 UlSOS I.CMIM
1100 1.117116 1.0752 10120 100>90 I CIfM I ClUI III60S
1820 '-0791 1.11751 I.ons 11lii10i U)66) '-OIilS 1060II
lle1 1.117'16 1 0161 I.~ lOMe 10147 106J9 101i12
1_ 1'*X1 I .w.s 1.01)) 1_0702 1.0671 u)(oo 10615
1lIII0 U*,S I.Q7M 1.0111 107116 I (J675 1.0Ii47 \ 0618
105111
1OS4J
10S111.
1115M
I.OS'l
1_ I.,*" 1_017) 10741
1921) 1_011) 1.0117 10:14S
1940 1.0117 1.0711 1.0749
IOIlO 1.07&1 ID7Sl
1'lIIO I.OIl] 1.0717 1075A
105'J5 1.056'1 IOS+I
lOS'lll I.osn 10s.6
10f,0D IOS14 10S4I
10Ii0l 1057(, 10550
10605 1.0578 I.OSU
''*'
111'17
10481
1.04&1
1 I)4a8
10491
1.0i'09 106111
l071l 106&l
10116 llI6ti
10"9 106M
1.0121100>90
10IiS0
1065)
10656
I 0659
1.,*,1
lOIilI
101>25
'-DUa
I OIi)(l
lOIi)2
IOS56 IOS)1
1.lI50II
I_OS11
IOSU IOS)l t OSI~
1.0Sf04 I,OS)9 L0516
1.0s.7 1000l lOS"
'-OSS') 105M
lOSlI
lOSl)
,-OSl4
1_0S26
1.0S2a
10481
1.04'10
10492
1.1M'Y,;
1.0497
1_
1.046'J
1_11'71
1_11'71
111'75
1,11'99 1.lI'n
10S01 111'1"9
1.050) I.JM«I
I,OSQS l1M32
1.0S0Ii I.~
2000 10!21i 1.07'J0 l1m7 lon4 I (69) 10Ii60I lOIoJS 10601 I.OSIO IOS5-4 I_OSJO 10501 1,048S
2020 1.0Il0 I m ) 111760 10121 I l169li I0Iit>7 I 06lo11 10Ii0'J 105&1 10S56 '-OS12 10S0'i 1 0431
204D 101SJ) 1079{, 101U 10729 lOMe 1 OWl 10640 10611 105l0I I.OS54 IOS}ol IOS11 1,1)4a8
10lIO 10116 1.0719 1.01f0S \.1'7)2 1.0701 lOIi71 l0Ii42 '_061l 1.0586 1.0560 1,05.16 1.0512 1.0489
2OaO 1.0I]'J 1.0IICI1 1,07l07 101)4 1070) lOIi1) 10Ii44 1.0615 IOSSII 1.QS62 I .OS11 I_OS14 1.0490
10)11
10)13
10).48
1,0152
10351
-,-,-,-,-,-,-,-,-,-----,-,-,-,-,-,-,-,-,-,-,-,--"-,-
1200 10585 IOSW 1,OS4Q 10519 lOO'J'J 111'7'1 10461 10443 111'16 111'10 lim) 10171 1.0161
lDO IllS'll 105M 1_05<11 1.0526 1,0506 1 , _ 1.0I{01 1.0449 IlI'll I.II'IS 10l'JI 10111 10)65
(table continued)
1100
1120
1140
1160
1110
I,~
IOSU
10Sl1
105M
1.0571
HIUl
I OSlO
IOSle
10501(,
l.os",
11150l
IOSIO
IOSl1
I,OS25
I.OSll
1,0464
'-001
111"11
1.0s0s
l.osl2
'-~ I~
1.0015-4
111'78 1.Do46Q
I.II'&S 111'67
100I'1.I 1.003
lMn
1.11'11
111')7
1.0443
I .OOSO
1.0&56
1.11'15
111'20
1,11'26
10Ul
III'''
10199
I_(NII'
1.11'10
111'15
1_0421
1.f3&)
lOW
1.0)')01
10199
I QoIOoI
10]61 10)'1
I Ol~
101111 10l6J
10l1Z 10)61
IOlII 1,00n
1.0)n
2100 HilMI 1.0lI04 10170 107)1; 10705 101074 1,01045 1.0Ii11 1.OSM 1.0st.3 I.OSla I,OSI5 1.11'91
21100 1,011-47 10111 1.0nt0 10142 1,0111 101179 1.0IiS0 lOUl IOS92 1.0567 1.05-12 I,OSI8 1.(149]
2110 1.... 9 1_011) 10m 10140 10712 1060C1 IOMI ll16Z2 I.OS91 1.QS61 1.0543 I.OSI9 I_QoI<N
•
Gas Production £nlo:inl'ering
516
Go.! Flow Measurement
Table 10·11e Conti nued
F"" Supe rcompreS5lblllty Factors
(Bue Oata-O.6 Specific Gravity Hydrocarbon
"
JKl8
Table 10-12
F", Mercury Manometer Factors
~.)
lrmp.ututt. "f
m
IZ'i
'"
l200 I.DlS1 1011,. 1.11180 1.07<16 1.0711 11. .'
1.(111~ Uillel
12«1 1CJ1S.O 10111 lD712 1.117... If)715 1.0l0I3
Z260 10155 1011. 1.078) 1 CP# 1071& 1._
ualI 10!S6 101119 10714 1.11750 10711 lOMS
UN U18Sl , 01'6 1 0711 1.1)141
'"
1.06Sl
1 0Ml
IQr.s4
10f>S,1
I.OMS
'"
1062J 1.0S94
UIS9S
1.06025 tosw.
1.('6.15 1.«>'iIf>
1 ~ 1.11597
1.06l~
,.,
1051>9
1.0569
U1510
1.11510
1.11571
llOO 10!S6 1.01119 107&' 1.0750 lana 1.0685 10655 101>26 1.0597 1.osn
ll2C 10ftS7 1.0Il0 107M 10751 10n9 1,061\6 1.0655 101>26 1.0597 l.osn
10S0W
U15""
lQ5015
1 OSH
'0S46
UI5Z1l
UI52<,
1.11521
10S11
, 0'>21
SpecifIC
Gr,vity,
'"
10t9S
1.0t9S
100'15
11)1'M1
1 Df9lo
1.MotIi 1.11511 1()196
1,1)5016 1.05Z1 100196
2J,oIIJ 1.I.SS1 lOll! 1071S '.01S2 lon' 1.06&7 1010S10 1.0621 HI5!18 losn 1.054' lOSZ2 111491
1360 101S1 1 Dill 1 (1781, 10m '.0719 IOIJV UI(,56 10621 105'111 l.osn 10541 1.0522 1001"
2110 1 011I0Il 1 OIl! 1 07810 I 0112 I 071' 10681 1 06S6 '0bV ',05'J8 111572 ,os.1 1,052l HM91
l.osn
1.0Il2
lOUl
101m
10822
101m
10717
1(1787
10787
10786
10736
1.117'>2 l.ln' 101\17
lonl 10719 10l>Il7
I,07SJ 10119 10l>Il7
107~1 10718 10I;S7
1.0751 lone HIbII7
1.111011
I 0&57
10&51
10&57
HI651
106J11
I I.I6l8
I ~8
11.1617
10611
1.11599
105'J'1
105'1'1
105\111
105\111
l05n
l05n
10571
1.0571
1~
1 0S<I6
10S41\
10545
1 ClS45
1.«ill
10521
10521
10521
IOS20
1 Of"'"
1.00196
10'%
10'9S
10'95
2500 UIIS1 HII21
2520 10156 1 ClI20
zs.tO UII5S UII19
lWI 10&1 101111
Z50IIG 101151 1.01116
1.07BS
10,;'&1
1.078J
10782
UJ781
U1750
11174'
10748
U"47
10746
lor.M.
UIbII5
106&1
10l>Il]
10bS1
1 001
10.56
1005
1.0654
1065)
10b21
10b21
101.26
10t.25
1(1624
U15911
1.0S'iIII
1059]
IOS'll6
1059S
10511
IOS1l
IOS7'O
1056'J
HIS61
1 ClS45
I.OSM
10S41
10542
10S41
10510
II;I!;"
1.0518
1,0517
11;1!;16
I~
104'93
UI4'Jl
1(loI')2
10'91
1.0S«!
1.05)9
l05l7
10741 10:'09 1 tI!o1f 101>41 U16l1 lO5'JD 1.1lS62 I.OS)6
101l'J 101V7 1.0IJ6 1,01>45 10616 1.05IlI 10560 IOS)4
1.0515
1.0514
IOSll
IOS12
\,0511
1.()<I'lO
1.0489
1048&
104a1
1048S
1.00;0,
1.0501
1.0505
T.05O.1
1.0501
1 ()<I8l
lo.M
10"8
lOP'
2-100 1.0SS9
2~lD 108.'1'
2"-10 II1M9
HID 108>8
1.DB5&
2'"
2600 1.002 1.(11114 10m
_
1.0IIS(I 1.0111l 1.0178
2640 1 , _ 111111 ID77f>
2660 IIl146 1.oe:J') 1 fJJ74
26ID 1.11144 IIl101 1,11772
Z700 1,l1l-I2
2720 1Il140
1740 1,0838
2700 1005
1710 1.0&:1)
10711
t 0716
I."'"
I 071S
10714
1.0745 1071) 1.0l>Il1 UIIo51 I.CI!ol2 I.OS~ I,0S66
1./lJ44 10712 1.01ie0 I.CI!oSO Ulloll UIS'] 1.11S6S
1/lJ42 10710 1.0&1'9 10&48 1061' 1.0591 1.056]
1 MI5 10770 1.0717 urnl5
LCIIIOJ 101M 1.07)4 !Ol'O)
10000l 1076& HV)J 10701
1.07'99 101M 1,07l0 lC1699
111196 \.07fIJ \,07lI lor.w
1.067'5
1067)
10611
I OWl
1.06i1
1.0644
1.01>41
101>41
106)9
1.06JI
10615
106'4
10611
10610
10601
1.05&' 1.I1:5S9
l.oser. I.OS58
1.0534 10556
IQS12 1,05n
Hl5110 10SSl
1.05])
I.OS)2
I.OSlO
IOSU
1.0527
1.~
1.II1JO
lU827
1,0824
10f1U
1.11119
1._)
1.01'91
107lIl
10186
ID78l
1.015'9
107S1
1.0150l
10m
l,on. I~ 10660$ 1.DU5 l.06OIi 1.0571 Ulnl 1.0525 10ffl
!On4 106" 1.1JI,ti;l 106)J 1.060f 1.0515 10S49 1.0Sll 1 CM91
10521 1.04'.r.i
1071' 106811 !.0bS6 1.062'l 1.0600 I.OS1l 10S44 IOSI' T,()oI9]
1/lJ49 1.0716 10685 1.0653 1.0626 1.05911 1.056'J 10S42 I .OSI6 1()oI'rI
1.()<I"
10''1
1.0'10
1046&
1.1)0166
1.11116
!IIIU
I.,*"
IIl105
~ Ullin
lOOO 1,0197
10180
1.11171
1.G71l
lono
107f01
107f04
10746
10743
1.0140
1,01J1
1"'J4
tonI
111461
10461
1.()oIS&
1,()01)6
I()o1SoO
1,()oISI
1*10
2l2O
2140
2860
28110
290D
192D
lt4D
2960
_
\,0121 106'l0 lOIrS9 1.06)1 10602 1-051] I.CIS41
1."'1)
HITIO
I.CI7Ql'
1,1ll'O4
ICI7\l1
1.06'JI
1061l
10&1'9
1.(16;:1\
lor.n
1.06l'0
106/)1
10650
1.060II
Ulfo46
1.01>41
10640
1.0617
1.06l)
IGUO
1.0617
1.061.
10611
1,06IlI
I(IS95
losn
1.0SIJ
10$IIi
1.05el
105ID
105116
1,QS64
1.0561
1,0551
1055f>
1.055-1
1.05"
1,05l1
1.05l4
10511
105J"J
1,0527
, ........ """" •• _ _ " ' _....... ~ ........ _bolo~
517
1051l
10511
10509
10506
1(1504
10501
1._
1._
1.04l0I
1()0131
I,()oI7')
1()o176
"
,.ss
,.,
,.ro
'",."
.
,,."
."
,ro
,."
,,,
...
."
.ro
,
,.,
..,""
'''''
..,,,'" .""
,"'"
,"'"
,"'" "'"
099117
,"'"
,"'"
,"'"
,"'"
,."'"
,"'"
,"'"
,"'"
fIow.ng P,e-nu,e-. PS'S
"."
0,9976
..""
0.9'172
0,9961
,,.,
'''''
09952
09941
09917
.-.""."" .. ·
•. ..
.-· ·
··.0,997'9
0,9976
09987
""
""
""
0,997U
0,99')1
0,9'181
0,997'9
O.99n
0.997.
0,9971
,"'" .""
""
,."'"
"'"
099043
0.99)2
.""
09907
."" ,.""
'''''
""
0.9955
099017
09937
""
""
"'"
"',.
0.9917
0.9926
0.9915
0.9942
09933
.""
•.""
09912
0.9912
09923
0.9913
0.990}
0.989}
''''' .""
'''''
'''''
''''' ."" ."'"
0.9955
0.99013
0.9935
0.9941
0.9933
0.9915
,."
",.,
,"'"
,."" , "" ",..
•." ,"'"
'''''
""
,ro ,"'"
'"
,"'"
,." ,"'" ,.""
"'" •."" "'" .""
""
0,9967
...
Ambiml
09951
Trml"""~l u~
0.99)1
• 12O"f
0997.
0,9992
0.9'181
0.9979
O,99n
0,9975
09971
09967
0.9955
0.9959
0.99013
0.991&
.-.""
0.9941
0.9914
0.99}7
0.9918
,"'Ol~' F'ac:tors for intermediate ~.Iues of p"""",e. lemperltu",. and 'p<'f.'if~ ,''''il}' ohould ~ Interpola-
ted. This tllble Is for ..... with me-rc:ul) minometer type teOOrding ,",ug<!' Illal hi,... gu in rontad .. ilh the
lnanI.y SU"""Ie. The n:al g.. dnuit} iI equal to II ,z"...- z..._); Ihm for.1I practical purpore!. the ",.1
P-I m.ltive demit) .. Ipprmimlllel> equ.llo 1M PI specific gr"it). ~I'
From Orifice Mnmng oj .\'atu",1 CIlI, 1969; rou.tl'$)' of ACA
(text con tinued from page 50n
Gauge Location Factor, F,
The gauge location factor, F" gi\'en in Table 10-13, is used where orifice
meters are installed at locations other than sea-level elevation and 45° latitude. T his is also a very small ~rrection .
•
520
Ga! Flow Measurement
Cal Production Engineering
Thus, i>pr - 90/670 - 0.134. Tpt" - 510/375 - 1.36, and Z from Figure 3.2
is equal to 0.98.
Therefore, F", - 1/(0.98)°·,5 '"" LaID.
For 1', - 0.65, Pf - 90 - 14.7
from Table 10-12.
=
75.3 psig, and Tf
SO"
50°F, Fm - a.999F!
NeW.ectiOlZ FI and F.> and using Equation 9-17.
K - (870.93)( 1.00037)(0.9914)(0.9886)(0.9808)(1.0098)(1.2403)(1.010)
(0.9998) - 1,059.23
521
6. Differences or changes in prevailing operating conditions from those
used for calculation purposes.
7. Incorrect zero adjustment of the meter.
8. Non-uniform caHbration characteristic of the meter.
9. Corrosion or delXlSits in the meter internals, or contaminated mercury.
10. Emulsification of liquids with mercury.
11. Leakage around the orifice plate.
12. Formation of hvdrates in meter pipinJ{ or body.
13. Incorrect pen ~ovement on chart , such as incorrect arc for the pens,
or excessive friction beru:een pen and chart .
14. Chart malfunctions-incorrect range, incorrect rotation time.
15. Overdampening of the meter response.
Using Equation 9-16,
Common Measurement Problems
q - (1,059.23)(73.485) - 77,837 ft'/h,
Factors Affecting Orifice Meter Accuracy
According to the Petroleum Extension Service (1972), the following are
the sources of constant errors (errors that are constant over time for an installed meter):
1.
2.
3.
4.
5.
6.
Incorrect estimate of orifice size.
Convex or concave contouring of the orifice plate.
Thick or dull orifice edge.
Eccentricity of orifi ce with ~ to the pipe.
Incorrect estimate of pipe diameter.
Excessive recess between the end of pipe and the face of the oriritt
plate.
7 Excessive pipe roughness.
The Petroleum Extension Service (1972) also lists the following as tht
most common sources of variable errors:
1. F10w disturbances, caused by insufficient provisions for flow stabili·
zation, or by irregularities in the pipe, welding, etc.
2, Imprecise location of the pressure taps.
3. Pulsating flow,
4. BUildup of solids or sediment on the upstream face of the orifice
plate.
5. Liquid accumulation in the bottom of a hOrizontal pipe run , or in
pipe sags, or in meter body.
Some of the common measurement problems encountered in gas metering
are (Petroleum Extension Service, 1972): hydrate formation (freezin g);
pulsating flow; slugging; and sour gas.
Hydmre Formation
Hydrates may be formed at the orifice, or in the meter piping or internals,
whenever the gas temperature falls below the hydrate-forming temperature
for the gas. Such an instance should be recorded on the meter charts, and
the estimated static and differential pressure lines should be drawn in.
Hydrate formation can be prevented using any of the following (see
Chapter 5):
1.
2.
3.
4.
Cas dehydration .
Use of hydrate inhibitors.
Installation of heaters along the line or near the meter.
Other methods-elimination of pipe leaks. enlarging meter piping
and valves, and replacing needle valves with plug or gate valves (Petroleum Extension Service, 1972).
Pu.lsating Flow
Pulsating flow is flow comprising sudden changes in pressure and f10\\
rate of the flowing flUid . Common sources of such flow in gas measurement
are (Petroleum Extension Service, 1972):
•
522
1.
2.
3.
4.
Gas Production Engineering
Reciprocating systems-compressors, or engines.
Improperly sized, loose, or worn valves and reguJators.
1\vo-phase flow conditions.
Intermitters on wells and automatic drips.
Pulsating flow can be a source of considerable metering errors. There is
no known method to correct for such a flow. The Petroleum Extension Service (1972) outlines the following methods to reduce pulsating flow and/or
diminish its effect on orifice flow measurement:
1. Locate the meter along the flowline in a position where pulsations arE'
minimized.
2. Reduce the amplitude of the pulsations by placing a volume capacity.
flow restriction, or specially designed filter between the pulsation
source and the meter.
3. Operate at pressure differentials as high as possible, by using a smaller
diameter orifice, or by allowing flow only through a limited number
of tubes in a multiple tube installation. The same can also be achieved
by using smaller sized tubes, keeping the same orifice size and maintaining as high a pressure differential as possible.
Slugging
Slugging refers to the accumulation of liquids in the gas flowline. In lowpressure lines, the liquid accumulates at low spots in the line, restricting gas
flow until enough pressure is built up for the gas to blow through the liquid
In high-pressure lines, liquid is swept through to the orifice and beyond
Both these situations result in flow disturbances that cause erratic and inaccurate measurements. A common method of preventing slugging flow is the
installation of liquid accumulators in the flowline.
Gas Flow Measllremeni
523
Other Types of Measurements
Mass Flow Rate Measurement L - - -
In recent years, fluids are being handled near their critical region, where
the fl uid density changes very rapidly with small changes in the flowing
conditions. Consequently, several instruments and techniques have been developed to measure mass flow rate. There are essentially two types of mass
flowmeters: tnle mass jlowmeters that respond directly to mass flow rate,
and injerential mass jlowmeters that infer the mass flow rate from separate
volumetric flow rate and density measurements.
True MOM Flowmeien
Several types of true mass flowmeters have been developed, including the
following (Chemical Engineers' Handbook, 1984):
1. Axial-flow, transverse-momentum mass flowmeter.
2. Radial-flow, transverse-momentum mass flowmeter.
3. Gyroscopic transverse-momentum mass flowmeter.
4. Magnus-effect mass flowmeter.
5. Thermal mass flowmeter-commonly uses vibrating tubes and heat
transfer.
Of these, the axial-flow transverse-momentum mass flowmeter is the
most commonly used. Also known as an angular-momentum mass flowmeter, it uses axial flow through an impeller and a turbine in series. The impeller imparts angular momentum to the fluid, which in turn supplies a torque
to the turbine. The mass flow rate of the fluid through the meter is obtained
by measuring this torque which is proportional to the impeller's rotational
speed and the mass flow rate.
Inferen tial Masa Flowmeten
Sour
em
As discussed in Chapters 5 and 6, sour gas is detrimental to all flow equipment for two reasons: corrosion and accelerated hydrate formation. Sour
gas in a closed line causes little or no corrosion; it is the hydrogen sulfide in
the surrounding atmosphere that affects the measurement equipment (Petroleum Extension Service, 1972). Common preventive measures to ensure
proper gas metering include using hydrogen sulfide resistant components in
the meters, and sealing the meters against the atmosphere.
The several types of inferential mass flowmeters can be classified into
three major categories (Chemical Engineers' Handbook, 1984):
1. Head-type meters with density compensation. In this type of mass
flow measurement, a head meter, such as an orifice or venturi, is used
along with a densitometer. The signal from the head meter, proportional to pv 2 , is multiplied with the density p given by the densitometer. The square root of the product thus obtained is proportional to the
mass flow rate.
•
Gos Flow Measuremellt
Gas Productioll Engineering
524
2. Head-type meters with velocity compensation. This type of mass measurement Use!i a head meter and a velocity meter (pitot tube, or a turbine meter) . The signal from the head meter is divided by the velocity
signal from a velocity meter to obtain a signal proportional to the mass
525
For mass flow rate measurement in pounds per day, the following equation
by the Foxboro Company (1961 ) may be used:
(10-28)
flow rate.
3. Volume or velocity-type meters with density compensation. In this
method, the signal from a velocity meter (such as turbine meter or
sonic velocity meter) or a volume (displacement) meter (such as rotary
meter or reciprocating piston meter), is multiplied by the signal from a
densitometer to generate a signal proportional to the mass flow rate.
where ml..
hw
liquid flow rate, Ibm/day
differential pressure across the orifice, in. of water
S = a constant determined by the orifice and pipe diameters
d = inside diameter of the meter tube. in.
Fa " orifice thermal expansion factor ( = 1.0 for temperatures between 23 and gg0F)
F m '" manometer factor
Fe = viscosity factor. generally assumed to be unity
Fp = correction factor for liquid compressibility
')'1.. = specific gravity of the flowing liquid stream
Various types of densitometer.; are available for determining the density of
a flowing gas stream, based upon different principles, such as buoyant force
on a fluid-supported float , radiation attenuation , and piezoelectric crystals
that respond to pressure.
For the popular orifice-meter/densitometer combination for mass flow
rate measurement , AGA (AGA , 1969) gives the following equation:
=
=
Equation 10-28 is often used in the following simplified form:
(10-26)
where
m '"' mass flow rate of the gas, Ibm/hr
h" = differential pressure across the orifice, in. of water
Wg "" gas specific weight, Ibf/ftl , equal to (gas density) X (gIg.,)
Natural Gas Liquids Measurement Using Orifice Meters
Natural gas liquids are generally measured under static conditions using
conventional tank-gauging methods. For flowing liquid streams, orifice meters are used quite often. For volumetric flow rate measurement in gallons
per hour, the American Meter Company (1973) provides the following equation:
(10-27)
q h", Fb =
Fill FII =
F, '"
liquid flow rate, gal/hr
differential pressure across the orifice, in. of water
basic orifice factor
specific gravity factor (for temperature correction)
factor for seals (if required)
Reynolds number factor
1\vo-Phasc Systems
F10wmeter accuracy is generally quite poor for measuring two-phase
f1owstreams. No good method is currently known~most techniques give
only an approximate value. Murdock (1962) gives the following equation for
two-phase flow through orifice meters:
F b , Fro Y, Fm, F], and Fa are the orifice factors as described earlier.
where
(10-29)
(10-30)
where
mTP ,., mass flow rate of two-phase flow, Ibml hour
Kg, KI.. .. orifice flow coefficienl~ for gas and liquid, respectively
Yg _ expansion factor for the orifice
F. - orifice thermal expansion factor
d = orifice diameter, in .
Pg, PI.. = gas and liquid densities, respectively, Ibml ftl
(hw)TP - effective differential head for the two-phase flow, in. of
water
X - liquid weight fraction in the flowstream
and subscript 1 represents the value at the orifice inlet.
•
526
Gus ProductiOIl Ellgineerillg
For metering two-phase flow, the Petroleum Extension Service (1972) recommends the following precautions:
1 Keep pressure and temperature as high as possible at the meter.
2_ Use a free-water knockout upstream of the meter.
3. Use a vertical meter run that may impro,·e the differential pressure
and flo" ,·olume relationship in some, if not all, cases.
4. Determine a meter factor to correct the metering results. using test
data from (periodic) separator tests.
5. Connect manifold lead lines to bottom of bellows-type meter With sell
drainin~ pots installed above orifice fitting.
"
,~,
Questions and Problems
I. What would be the features of an "ideal" gas measurement device?
2. Why is gas measured in terms of volume? Compare the requirements
for volumetric versus mass flow rate measurement.
3. Discuss the problems in two-phase measurement. Address the issue of
flashing of liquids into vapor (a common occurrence for undersaturated steam and all except dead oils), and what strategies can be
adopted in such a situation.
4 Is a linear meter necessarily better?
5. List the advantages and applicability of the various flow measurement devices.
6. Compare the orifice t}l>es, including their effect on gas £low measurement.
7. Discuss, giving reasons, the important factors that affect orifice meter accuracy. What operating conditions need be assured to enable
accurate orifice metering of natural gas?
8. Given static and differential pressure recordings on an orifice meter
chart, show the calculations that are required for computing flow
volumes for the case of: (a) a linear orifice-meter chart, and (b) L-IO
square-root chart .
9. Calculate the gas production from a well with the following orificemeter information:
Readings from a square-root chart with a chart range of 50
in. x 100 psi: differential .. 7.1, static - 8.5 taken at downstream
flange-type tap.
. Pipe diameter .. 3 in ., orifice diameter .. 0.5 in., 1', .. 0.72, flowmg temperature .. 95°F.
Cas How Measuremellt
527
Neglect F"" Flo and Fl' Assume base conditions of 14.73 psia and
OO°F, and that the gas has (in mole%): CO 2 ,,, 1.2, N2 .. 0.58, and
H,S - 0.96.
10. It is suspected that the chart recording device is malfunctioning in a
field orifice measurement system. A test with a mass flow meter indicate; a gas rate of 18,000 Ibm ·hr. For the £oHowing conditions, determine if the orifice meter chart is in error:
Pipe diameter .. 8-in_ nominal (8.0il in. ID)
Orifice diameter - 3.0 in.
1'_ '" 0.63
F10wing temperature - 85' F
Static pressure reading,., 110 psia
Differential pressure reading = 175.5 in. water
Pipe taps downstream
If there is an error, find its dollar value, given that gas sells for $1.0
per Mscf (measured at 14.73 psia. 60°F).
Hcfercnces
American Meter Company, 1973. Orifice Meter Constants: Handbook E-2,
revised.
AGA, 1969. OriJice Metering oj Natural Cas. Cas Measurement Committee
Report No.3 (Revised), American Cas Association, New York.
ASME , 1971. Fluid Meters- Their Tlleory and Application, 6th edition.
Report of AS~·1E Research Committee on Fluid Meters, The American
Society of Mechanical Engineers, New York.
Campbell, J. M., 1984. Gas Conditioning and Processing, Vol. I. Campbell
Petroleum Serie;, Norman. Oklahoma, 326pp.
CliemiClJI Engineers' Handbook, 1984. R. H . Perry and D. W. Green (eds.).
McCraw-Hili Book Co., New 'ark, 6th ed.
Corcoran , \V. S. and Honeywell, }., 1975. "Practical Methods for Measuring F1ows," Cilem. Eng .. 82(14.}uly 7), 86-92.
DeVries, E. A., 1982. "Facts and Fallacies of Vortex F1owmeters," Hydr.
Proc., 61(8, Aug. ), 75-76.
Evans, H. }., 1973. "Thrbine Meters Cain in Gas Measurement," Oil & Gas
J., 71(34, Aug. 20), 67-69.
Foxboro Company, 1961. Principles amI Practices oj Flowmeter Engineering, 8th edition. Foxboro Company, Foxboro, Massachussets.
CPSA, 1981. Engineeritlg Data Book. 9th ed. (5th revision). Gas Processors
Suppliers Association, Tulsa, Oklahoma.
•
528
GO$ Production
Eflgifleerifl~
Munk. W. D .• 1982. "Ultrasonic Flowmeter Offers New Approach to
Large-Volume Gas Measurement," Oil & GQJ /.,80(36, Sept. 6), 111117.
Murdock. J. w., 1962. "Two-Phase Flow Measurement With Orifices,"
Trans .. A5ME: /. Basic Eng., 84(4, Dec.), 419-433.
November. M. H .. 1972. "How to Use High-Capacity Axial-Flow Turbine
\feters for Gas ~teasurement," Oil & Gas J., 70(14. Apr. 3), 69-77.
Petroleum Extension Service. 1972. Field Handling oj Natural Gas, 3rd edition. University of Texas Press, Austin, Texas, 143pp
Powe~. L.. 1975. "Vortex Shedding Provides Accurate Flow," Oil & Gas J.,
73(31, Aug. 4), 84-88.
11
Gas Gathering and uansport
Introduction
Natural gas produced from several wells in a given area is collected and
brought to field separation and processing facilities \1a a system of pipes
known as a gathering system. Processed or partially processed gas is then
sent to the trunk lines that transport the gas to consumers. Cas is often distributed via pipeline grids that introduce a lot of complexity into the flow
computations . This chapter briefly describes gathering systems and the
transport of gas through pipeline neh\·orks. building upon the concepts for
steady state flow through a single pipe described in Chapter 7. Some basic
elements of unsteady state gas flow. encountered quite often in pipeline
practice, are also introduced.
Gathering Systems
The surface flow gathering system consist.. of the section of pipe and fittings that serve to transmit the produced fluid from the wellhead to the field
treatment facilities (generally, the oil-water-gas separators). Production systems with extremely high capacity wells may provide individual separation,
metering, and possibly treatment. facilities to each of the wells. Because
these single well systems are seldom economical, it is quite common to design gathering and separation facilities that enable combined handling of
several wel1streams.
The two basic types of gathering systems are radial, and axial. In the ra.
dial system (Figure I1-Ia), flowlines emanating from several different wellheads converge to a central point where facilities are located . Flowlines are
Usually terminated at a header. which is essentially a pipe large enough to
529
•
530
""''
Gas PrOllut'tiOrt F.'lgille'ering
ff
Cas Go/hi'ring
- - ~(AO[~
1l0.l'~[
Figure l'-1b. An axial gathering
system.
Figure 11-1a. A radial gatherrng
system.
:a~~e todhe flo,:,,'
of all the flowlines. In the axial gathering system, .'ie\'eral
pr uce mto a common flowline (Figure 11-lb).
For larger ~eases. these two basic systems are modified a little. The wellcenter ,gathering s?'St~~ (Figure 11-2a) uses a radial gathering philoso h at
~~:I:~;~[e\-'el for IOdl,vldual wells, .a.~ well as at the global level for grO~:S of
.
. h e common-Ime or trunk-hne gathering system uses an axial gatherIO~ sc e;~ for the groups of wells that. in turn, use a radial gathering
sc e;ne. ( 19ure 11-2b). The trunk-line gathering system is more applicable
e
!~ ~:I~~v:~~ lf~~f~rpJ~;. andf tOl~a.ses where it is undesirable or impractical
Gild
Trallsport
531
It is obvious that \'ery complex metering facilities are required to measure
the production of individual wells Simultaneously. Generally, a test header is
used to route fluids from a single well through the metering system. This
well test header also pro\'ides the means to control the production from inru"idual wells and to conduct well tests on individual wells.
The choice between the gathering systems is usually economic. The cost
of the several smail sections of pipe used in the well-center system is compared to the cost of a single large pipe for the trunk-line system. Technical
feasibility may be another criterion. The gathering system may have to be
buried a few feet beneath the surface, favoring one system o\'er another in
terms of cost and ease of maintenance. The production characteristics of the
field are also important to con.~ider. These include current and estimated fu·
ture production distribution over the wells in the field, wellhead flowing
presmres, future development of the field, and the possibility of the development of underground storage operations.
Steady-State Flow in Simple Pipeline Systems
r...........,.,mg aClltJes at a central point.
Figure "-2a, Welt-center
gathering system.
Figure 11-2b. Trunk-tine
gathering system.
The term "simple" is used here to indicate the gas pipeline systems that
can be handled with minor modifications to the flow relationships presented
in Chapter 7. The one feature for simplicity is that gas flows in at one end,
and flows out at the other end; no flow occurs at any other point in the
piping system. Such a scheme is orten used for increasing the throughput of
a pipeline while maintaining the same pressure and pressure drop (such as
when new gas wells have been developed that must use the existing pipeline)
or for operating a pipeline at a lower pressure (pressure-deration) while
maintaining the same throughput. The latter may be required when the
pipeline has "aged" or corroded.
The three possible ways of handling these requirements are to replace a
portion of the pipeline with a larger one (pipelines in series). place one or
more pipelines in parallel along the complete length of the existing line
(pipelines in parallel), or place one or more pipelines in parallel only partially along the length of the existing line (series-parallel or looped lines). For
each of th~ systems, relationships will be derived here, based upon the basic equation by Weymouth (Equation 7-29) for steady-state flow of gas
through pipes , that reduce the set of pipelines to a single pipeline that is
equivalent to the set in terms of the pressure drop and flow capacity.
The We)'mouth equation (Equation 7-29) can be written as:
q - K, [d'/fLl',
Where KI is a constant, given by
(11-1)
•
532
GOt Pmduct/O'l Eng/Fleering
K, _ 5.635382
Cas Gathering and Transport
(T.)
[vl- Pij'
p. ,iTZ )"
(1l-2)
533
where the subscript t indicates the total for the system. The pressure drops
through the pipe leg;. however, are not equal. The total pressure drop is
equal to the sum of the pressure drops in each of the pipe I~. Thus,
Note that q denotes ~ throughout this chapter for simplicity. Equation 11.1
can be written as:
(1l-7)
and
L - Kd I(£q')
(1l-3)
(11-8)
Consider two pipelines A and B. of lengths L" and LB. and diameters d ... and
dB. respectheJy. \\e can e(luate these two lines A and B using Equation 11.3.
For example. the length 48.\ of a line of diameter d .. that will have the same
pressure drop as line B of length Ls and diameter dB (i.e .. the equivalent
length of line B in terms of the diameter of line A) is given by
From Equation 7·29 (or, Equations 11·1 and 11·2), we know that the pres·
sure drop.dp in a pipe section is proportional to the length L, all other fac·
tors being the same. Substituting in Equation 11·8,
(1l-9)
where
Altr>rnativeiy, the equivalent diameter d"BA of line B may be used:
Le - equivalent length of the total system
LA "" length of segment A
48A. L.c... = equivalent lengths of segments Band C, respectively
(1l-5)
where c4BA is the diameter of a pipe of length L.", and friction factor f... equivalent to the line B of length LB, diameter dB, and friction factor (8'
Series Pipelines
Consider three pipelines A (length L ... and diameter d ..). B (length La and
diameter dB). and C (length Lc and diameter de). connected in series as
shown in Figure 11·3. The inlet and outlet pressures for the system are PI
T herefore, the three lines A, B, and C in series are equivalent to a single line
of diameter d A and length 4 given by Equation 11·9.
Let <WeI be the old flow rate for the pipeline of length LA + LB + Lc and
diameter d A , and <lne-,r. be the new flow rate obtained by altering the sections
B and C of the pipeline to two pipe sections of length LB and diameter dB
and length Lc and diameter de. Using the fact that q is proportional to
(1IL)0.5, we get
<!new _
<loid
11(L,,)o.~
l/(LA + L8 + Lc)O 5
_
(L.~ +
L8 + 4:)O'~
L"
(Il-IO)
The fractional increase in flo\\ capacity. .6.<}, is gi\'en by:
;
c
•
A
Figure 11-3. Pipelines in series.
(II-Il)
and 1>2. respectively. For this system, the flow rates through each of the pipe
legs are equal:
Q.~ -
ClB - q(; - ql
(1l-6)
Parallel Pipelines
Consider pipelines A (length L. . , diameter d ...), B (length LB. diameter
dB), and C (length Le. diameter ~.) in parallel, as shown in Figure 11·-1.
•
534
Gus Prodllction Engineering
Gas Gatllering alld Transport
Assuming LA ,. La -
Le.
Equation 11·16 reduces to:
(11·17)
Figure 11·4. Parallel pipelines
c
535
The ratio of the new flow rate for lines in parallel to the old flow rate for the
single line A is given. as before for the .series pipeline. by
The inlet and outlet pressures for this system are PI and 1>2. respectively. Because the pipeline:, are in parallel ~ ith a ,-:ommon inlet ami outld, the pre..
sure drop through each of them is the same, but the flow rates are not. The
total flow rate, however, is the sum of the flow rates through each of the
pipe legs. Thus,
( 11.12)
1/(4)o.~
q.-....
..<loki
lI(L A)O.5
(L'4 )"
(11·18)
where 4 is obtained using Equation 11·16 or 1l·17, as the case may be. The
fractional increase in flow capacity, .:l.q, can then be calculated using the
following relationship used earlier for series pipelines:
(11·13)
and
(11.14)
A special case of two lines in parallel, also called a fully· looped line, with
both lines of equal length, Jeserves mention. Substituting for L" from Equa·
tion 11·17 into Equation 11.18 for such a system:
Let the length and diameter of the pipeline equivalent to the three lines A.
L~'
+ (dil~ dll,)' 'I
B, and C in parallel be L.. and d., respectively. Then, substituting for q in
Equation 11-14 from Equation 11-1:
q_.
(11·15)
•
(~" + (~:;~"
In Equation 11 -15, any value may be assumed for two of the three unknowns, d.. ft. and 4, and the third calculated. Equation 11-15 can also be
expressed as:
-
[(~" + (~fl(~)"
L~'I [ (IJI,)"
q".
•
( 11·19)
Looped Pipelines
~5
1
• (d!IJdll,L,)" + (d!IJdll,L,)" + (dtIJdl1cLc)"
Choosing
L.-
d. - d A • we obtain:
[(IJI,L,)"
1
'
]
+ (d!lJd\I,L,)" + (dIf.ld!lcLc)"
(11· 16)
A looped pipeline is one in which only a part of the line has a parallel
segment. The original pipeline is looped to some distance with another line
to increase the flow capacity. In the loop!..>d line shown in Figure ll·S. the
original line having two segments A and C of the same diameter is looped
with a segment B. A looped system may be considered to be a combination
of series and parallel sections. For the two lines A and B in parallel, Equation 11-15, 11-16. or 11·17 can be used. The resultant equivalent pipe for
the parallel segments A and B is then combined in series with the segment C.
536
Cas Gathering alld Transport
CO" Production Engineering
531
and Equation 11 -20 becomes:
,
~
.
Figure 11-5. Looped pipelines .
[::]' - (I - ,,) +" [[(1';1.)" +
•
Relatively simplified expressions are often found in the literature for the
case when the loop-line B has the same length as A. For this case. the equivalent length for the parallel section A-B, (4)AB. can be determined using
Equation 11·17:
(~iI,Jd\f,)U'I']
0'
Solving for
Xr:
(11-21)
,,- I - 11[(1,11,)" + (d!I,ld\fu)"1'
Then, the equivalent length for the total system,
l.." becomes:
Note that A indicates the original line. and B indicates the added line.
I.e - Lc + (4)"8
Extensions to Commonly Used Pipeline Equations
- Lc + [(1,If,)"
LI'
+ (d,l,Jdll,)"
]'
The old length (without the loop-pipe B) of the system was LA +
Le.
From
Equation 11·18, the ratio of the flow rates is
q,.,. _
q...
(L' L. Lc)"
+
The expressions for series, parallel, and looped pipelines described contain the friction factors for the individual legs. t>,fost non-iterative equations
for gas flow, such as the Weymouth, Panhandle-A. and Panhandle-B equations, assume a friction factor correlation that simplifies the flow calculations (see Chapter 7). The resulting expressions are given below for these
equations for series, parallel. and looped lines. The values of the exponents
a, b, c, and d are given in Table 11-1.
Equation 11 -4 for the equi\-alent length of a line becomes:
0'
L", - L,(d,/d,)'
[::], -L,: Lc
- LA':;" Lc +
k,':
Lc ][[(1,11,)" +
(~iI,Idll')"l']
where
I.
L.21
is the equivalent length of line 2 in terms of the diameter of line
(11·20)
Let xf be the fractional length of a line that must be looped in order to
achieve a desired flow rate. Then,
Table 11 -1
Coefficients for Serlea, Parallel , looped Une Equations
Equation
Weymouth
Panhaodle-A
Panhandie-B
LcI(L, + Lc) - I - "
(11-22)
•
1613 .. 5.333
•. 854
4.961
•
,.,0
0.5394
0.510
,
8.'3 - 2.007
2.618
2.530
d
2.0
,'"
,
538
Gas ProduNion Engineeri.rrg
Ga.t Gathering and TranS7'"rt
Equation 11-5 for the equivalent diameter of a line becomes:
(11-23)
where ~I is the equivaler!t diameter of line 2 in terms of the length of line 1
For lines in scries, the equivalent length is the sum of the indh-jdual equi\alent lengths of all the pipe sections (Equation 11-9). For lines in parallel.
the equivalent length can be calcwated as follows (compare with Equation
11 16)
539
Example 11·1. Gas of specific gravity 0.65 is being transported from station A to stations C and D. A single pipeline of diameter 8 in., length 3
miles, runs from station A to a pipeline junction at B. A &'in., 2..mile pipeline connects junction B to station C. while a 4-in .. 3-mile pipeJine connects
B to D. Given that the pressure at station A (PA) .. 400 psia, and that stations C and 0 are at the same pressure (Pc. Po) - 30 psia. determine the
capacity of the system. Assume that the flowing temperature is BOoF, and
use the Weymouth equation.
Solution
(11-241
where 411 is the equivalent length of pipe leg i. determined using Equation
11·22. If all the parallel pipe legs are of equal length, Equation 11·24 sim.
plifies to (compare with Equation 11-17):
L, _ d'L
I
[
di+dS+dS+ ... +d~ ]
"b
(11-25)
If all sections in the parallel lines afe of equal length. the ratio of the new to
the old flow rate is (compare with Equation 11-19):
::;-1 +[~
where
d..a.t dip
=
(11-26)
diameter of the original single line
diameter of the pipe installed in parallel with this line
For looped lines. the looping requirements, analogous to Equation 1l.21,
are (Campbell, 1984),
Because Pc "'" Po. we can consider sections BC and BD to be in parallel.
One caJculation strategy is to reduce the parallel lines BC and BD to a single
8 in. diameter line, and add the equivalent length thus determined to the
length of the section AB which is in series.
Using Equation 11-22, the equi .... alent length of the 4-in. line in terms of
an 8-in. diameter line is
l...4 ".
Similarly,
],,,
1
- [
- 5.689 miles
4
{11l20.9525)O~ + (1 9.2i62)U ~
Thus, the complete system is cqui\·alent to a single 8·in. diameter line of
length -..- 3 + 5.689 - 8.689 miles
For "1'1" 0.65. Ppt - 670 psia. and Tp<' - 373' R. Using Equation 7-32.
"
If the diameter of original and parallel lines is the same, Equation 11 -27
to:
x _ 1-
(qoldlq,~.)d
'-I
IIl1+ 1]'
(qold/q......-)d
1- 2 d
- [(400)' - (30)']- 268 ps;a
(400)' (30)'
So, PI"" " 0.4, and Tpr - 1.44, and therefore. Z., - 0.955.
Using the Weymouth Equation (Equation 7-34),
520 [
q.
1
L...6 - 2 (4/3)163 - 9.2762
Using Equation 11-24. the 4·in. and 8-in. lines in parallel an' thus equiva·
lent to a single 8-in. diameter line or length:
p
_~impli(jes
3 (8/4)16.'3 "" 120.9525
(l1-2Il)
~ 31,5027 IU3
f'
[(400)' - (30)'](8)'"
(0,65)(8,689 x 5,280)(540)(0,955) J
- 28,957.85 Mscfd - 28.96 MMscfd
•
540
COJ
Production Engineering
Gas Catheri'lg and Tra'isport
Example 11·2. A portion of a large gas.gathering system consists of a
6.067- in. to line 9.4 mile; long, handling 7.6 MMscfd of gas of average spe-
On solving this, we get:
cific gravity equal to 0.64. The pressure at the upstream end of this section is
375 psig, and the average delivery p~ure is 300 psig. The average temperature is 73°F. Due to new well completions, it is desired to increase the capacity of this line by 20% by looping with additional 6.067-in. ID pipe.
What length is required?
Ul:I)! + 17.847.084
x, =- 1 1
(111.2)2 _ 0.4074
A
For the unlooped section:
From Equation 7-32,
Soilltion
Note: Weymouth equation paramete~ are used throughout fo r the calculations.
Using the approximate relationship of Equation 11-28,
151.866.09 ... Equation
Xf -
p.,
(314.i~Lj
_ [{3/H.i3)3 .. 340.31 ia
(384.73)' - (3 14.731'
1"
pp.
= 0.51, and TpI - 1.48, and therefore, Za, - 0.945.
Using the Weymouth Equation (Equation 7-34),
9 120 - 3 1.5027 520 [
[(PJI' - (3 14 .73)'J(6.0671'"
,
14.73 (0.64)(533)( 1 ,,)(9.4 x 5.280)(0.9451
2'
Thus, the length of looping pipe required - (0.4074)(9.4) - 3.83 miles
The more accurate method involves using the basic relationships as fol ·
lows.
Desired flow rate q... - (1.2)(7.6) = 9.12 MMscfd - 9, 120 Mscfd
For 'Y, - 0.64. P.... ,., 671 psia, and T.... _ 360 0 R
For the looped section:
541
r'
On solving this, we get:
{P3)2
+ 71 ,768.06
Xf "
170,804. 15 ... Equation B
On solving Equations A and B simultaneously, the values obtained for the
two unknowns are:
Xr - 0.3512, and P.l ... 381.57 psia.
From Equation 11-25, the equivalent length of the looped section is:
j' "
Lt - (6.067)163(9.4x,) [ (6. 067)~ 3 +1 (6.067)" 3
P3 is quite close to the assumed value of 364.73 psia: Z factor will not
change substantially for such a pressure difference. A second trial is not necessary.
Therefore, the length of the loop required "" (0.35 12)(9.4) ,. 3.30 miles
- 2.350 XI miles ,. 12,408 Xf ft
Assuming the pressure P3 at the point 9.4 x/ miles from the inlet (where the
loop ends) to be equal to 350 psig ( ,. 364.73 psia), and using Equation 7-32.
,_ [(389.73)' - (384.73)'j_ 377.34 ".
P.
(389.73)' - (384.73)'
P
So. Ppr - 0.57, and T p, - 1,48, and therefore, Z., _ 0.940.
Using the Weymouth Equation (Equation 7-34),
9.120 _ 31.5027
~ [[(389.73)' -
(p,)'J(6.067)"'»,
14.73 (0.64)(533)(12,408,,)(0.94) J
Steady-State Flow in Pipeline Networks
Gas transmission systems often form a connected net, flow through which
is almost always transient (unsteady). Most design and operation control
problems, however, can be solved reasonably well assuming flow to be
steady-state . The basic model considers the transmission system to be a pipeline network with two basic elements: nodes and node connecting elements
(NeE's). Nodes are defined as the points where a pipe leg ends, or where
two or more NeE's join, or where there is an injection or offtake (deliver~)
of gas. The NeE's include pipe legs. compressor stations, valves, pres!Oure
and flow regulators, and underground gas storages.
•
Gas Prodlldi(m Engineering
542
Ga~
Before constructing a model of the pipe1ine network, it is necessary to describe the mathematical models for the individual NeE's. These models are
essentially pressure \;ersus rate (throughput) relationships, as described be·
low.
543
where P is the compression power and k.:!, ~, and ks are compreswr
constants (see Chapter 9),
4, Pressure regulators, Pressure regulators are similar to chokes, and may
be described by the flow relationships (or chokes, For subcritical flo".,
Equation 7-87 rna}' be used:
High-pressure pipe leg. The characteristic equation for a high pressure
pipe. according to Equation i-29, is as follows:
(11~291
Gathenlli/, and Troruport
q" kr.PI [(P2 I PI)l. - (P2'PI),,·1 'r~
where 14;., 974,61 C dPId.:1. [Ilh(T1)fS[J(I(1r - 1)]:15
(11-36)
(11-37)
For critical (sonic) flow, the flow relationship given by Equation 7-89
0'
is applicable:
(11~30)
(11-38)
(11-39)
(11~311
5. Underground gas reservojr~' and storages.
2. Low-pressllre pipe leg. For a low pre;sure pipe leg. with pressure close
to atmospheric, Z., = I, and
q ~ k,(p1 - plI"
(11-40)
where PI - average reservoir pressure
P2 '"' wellhead pressure
ks = productivity index of the reservoir
Thus. the flow relationship simplifies to
(11~32)
0'
•
\Vith these relationships for the components of a gas transmission system,
a model can be constructed for the system using the analogy of Kirchhoff's
laws for the flow of electricity in electrical networks to gas flow in pipeline
networks. According to Kirchhoff's first law. the algebraic sum of gas flows
entering and leaVing any node is zero:
(11-33)
!:F..I
where k2 _ 0.015744
PiCj"~!~.,fL
(11-34)
•
3. Compressors. Compressor characteristics vary depending upon the
type and the manufacturer. These are usually provided by the manufacturer, and can be approximated as follows:
Qj"
0
(11-41)
where m .. number of NeE's meeting at the node
q ... positive for flow into the node, negative for flow of gas out
from the node
By Kirchhoff's second law, the algebraic sum of the pressure drops (taken
with consistent signs) around the loop is zero. Thus, if n is the number of
NeE's in the loop, then for a high-pressure pipeline:
(11-35)
1:1., (pi - pO, - 0
(11-42)
544
Ca,~
Product/oil Ellgilleering
Gas Gathering and Transport
and for a low-pressure pipe system:
(11-43,
A pipeline distribution system may either be loopless. or contain one or man:
loops. The application of the relationships developed so far is described bt-10", for each of these system types.
I ,()Opl~
Sy~tems
A loopless pipe S)'5tem, defined as onc where the NeE's joined by nodts
form no closed loops. is shown in Figure ll-B. There are n pipe legs. and
n + 1 nodes. Cas enters through node I and leaves through nodes j, for
j - 2, 3, .. " n + 1
"!, , "!, , j------l
P,
"
'" ,
"""
CVIU_.o
NJM8ER
PR[ssufIE: ~
"'~.I
.,
The problem requires a trial and error type of solution if the maximum
throughput through the line at the oudet (node n + 1) is desired for a given
set of terminal pressures and flow rates into or out of the intermediate
nodes. Hain (1968) describes an efficient procedure for solving this problem:
1. Guesstimate the maximum throughput of pipe leg 1. q~ll. The superscript (1) indicates that this is a first approximation.
2. Calculate the throughputs for individual pipe legs, q;11 using Equation
11-41.
3. Using Equation 11-44, calculate the outlet pressure for the system.
( pn .. 1) .
4. [f (p~l~ 1)2 differs from the given outlet pressure p~ .. 1 by a value
greater than the prescribed tolerance, then correct the throughputs for
the individual pipe legs determined in Step 2 using:
'"
(11-46)
t ,-, ,! ,
,-,
,-,~--"'V"'I
'h-,
P".,
P,
545
'" I"~
where ~q" (p"+1
-Pii .. 1
"
2 E
(11-47)
k,q;i)
, .. 1
Figure 11-6. Loopless pipeline system.
5. Repeat Steps 3 and 4 until convergence within a specified tolerance is
I£ one of the terminal pressures, inlet pressure or outlet pressure, is gh-en
and the other is to be calculated for a given set of pipe leg parameters and
the flow rates into or out of the nodes, then the calculation procedure L\
quite straightforward. If the inlet pressure, PI. is known, the pressure at an~
node j can be computed using Equation 11-29 (for high-pressure pipe legs)
summed over the applicable pipe legs in the system:
p/-pj-
E
,- ,
k,qr
,
where j - n, n-1. ... ,2, 1
[(P~'~')'-pl .. ];2
[(pl)< - (pf)<]/q< +
(11-48)
1:
,-,k,q;"
where (P1)c, CP2}c - compressor intake and discharge pressures, respectively,
psia.
Similarly, If the outlet pressure, Pn+ I, is known. Equation 11-45 can be used:
E k,qr
'-I
In Step 4, the correction A.q becomes more complex for flow systems with
a greater variety of NCE·s. Hain (1968) gives the following correction for a
line containing a compressor station:
Aq(11 -441
where j - 2, 3, .... n, n + 1
Pf - P~+1 +
reached .
(1l-45,
Looped Systems
There are two types of looped pipe systems: single-loop (Figure 11-7a),
and multiple-loop (Figure 11 -7b). Cross (1936) gave the first solution for
low-P~ure looped systems, which was later extended to high-pressure systems (Hain, 1968).
•
546
Gas Production EIlginet"ring
Gas Gathering and Transport
547
Solving Equation 11+49 for aq, and assuming that I1q < < ql. we get:
"""-",
'jL-72-_---'~-«- -
'"
'h ---
,
\
-CY3
(11-50)
.
The gas throughputs for the next iteration. {L -', are computed as before
(Equation 11-46):
,"
I
'l;
A
This procedure is repeated until for an iteration k, a.q is less than or equal to
a specified tolerance. After this (successful) k·th iteration. the node pressures
can be calculated using the relationship (Equation 11.44) for a high-pressure
network:
•
---
j
,
E krl qi
pf- Pi ~
k
,
I q:kl
(11-51)
;. 1
for j
=
2, 3, . _., n, n
+1
B
where k, for pipe legs arc calculated using Equation 11-31 for high-pressure
lines. For a low-pressure network, k, for pipe legs are calculated using Equation 11·34. and the node pressures are computed using Equation 11-52:
Figure 11·7. Looped systems: (a) single loop, (b) multiple loop.
Consider first the single-loop system shown in Figure 11-7a. In a typical
problem, the flow rate ql and pressure PI for nooe I are known, and it is
required to find the flow rates and pressures at all the other nodes. For a
looped system, the direction e1ement for flow is important: We have taken
clockwise flow to be positive, and counter-clockwise £low to be negative in
OUf analysis here. The arrows on Figure 11-7a indicate the flow directions.
The problem requires a trial and error solution scheme. An initial \alut'
for the flow rate in pipe leg 1 is assumed. If this assumed value. qlll, differs
from the actual throughput by .6.q, then by the node law of Equation 11-42
or 11-43 for steady-state flow (Szilas, 1975):
,
1:I k;(q)" + 6q) I 'll" + 6q I -
,
0
where n .. number of pipe legs in the single-loop system.
(11-491
j- I
PJ" P, -
E
,-, ~I ct:
k
'
Iql'"
(II-52)
for j .. 2, 3, ... , n, n +
For a mUltiple-loop system, an individua16.q is computed for each loop, and
the flow corrections are done for the pipe legs loop by loop. A pipe leg which
is COmmon to two loops can be handled in two ways:
1. Correct the flow rate using the correction for the first loop, then cor.
reet it again using the correction for the second loop (Cross, 1936).
Thus, the flow rate is effectively corrected twice at every iteration for
any line common to two loops. Note that the flow rate through this
common line will be equal in both the loops.
2. Use the sum of the Aq 's for the two loops to which the pipe leg is com·
man as the effective flow correction for the pipe leg. This has been
5.'
Gas Production Engineering
GO! Gathering and Transport
suggested by Renouard and Pemelle (see Szilas, 1975). The /1q values
are computed by solving the n linear equations in the n throughputcorrection unknowns (~CL for i = 1, ''', n) obtained using Equation
11-46 for each of the n pipe legs in the network. These values are then
used for updating the pipe leg throughputs. The procedure is repeated
until convergence.
Method 1 by Cross (1936) is simple, but converges rather slowly to the
final solution and is generally uneconomic for large systems (Szilas, 1975).
\'1ethod 2, developed to overcome these problems. is approximate and applicable only to relatively non-complex networks for which it may be fairly ac-
549
imbalance at the node and will be equal to zero when the system is in balance. For example, consider nocle 2 that receives gas from underground storage (1,2) and pipe leg (10,2), and delivers gas to compressor intake (3,2),
and consumer supply attached directly to node 2. Equation II-53 for node 2
can now be written as:
(11-54)
With the substitution of the appropriate NCE equations (from Equations
11-29 through 11-40). Equation 11-54 becomes:
curate.
Stoner (1969. 1972) has presented an effective method for handling
looped networks with all kinds of NeE's. In this method, the equation of
continuity is used to express the flow at each node in the system. The solution to the system of equations is complex, but the method offers the ability
to compute any set of unknowns. It thus overcomes the limitation of the
Cross method that can only be used to generate throughput or pressure solutions. See Figure 11·8.
,
,I
,,
,
I
sign (PI - PJ)
+lforpl~pj
--lforpl<p,
8... ....
,
,
,,
where SI.j is the sign term that accounts for the flow direction:
s..j =
23 ~/
•I,
(11-55)
~
•
Figure 11·8. Illustration lor Sioner's method
For any node j, the continuity equation (Equation 11-41) expresses the
fact that the sum of the inflows and outflows at the node is zero:
(11-53)
where fL. is the flow from node i to nocle j. F10ws into the nocle are consid·
ered posith'e, flows out of the node are negative. F j thus represents the flo\\
(11-56)
Similar equations are written for all the other nodes in the system. Consider
a system of n nodes and m NeE's. Steady-state flow through this system of n
nodes is mathematically represented by a system of n non-linear equations.
There are a total of (2n + m) variables: for each nocle, there is one pressure
and one node flow rate variable, and for each NCE there is a constant k,
defining the flow resistance through it. Thus, we can use this mocleJ consist.
ing of n equations in (2n + m) variables to sol\'e ror any n variables, given
the value of the remaining (n + m) variables.
Each of the node continuity equations, such as Equation 11-55, can be
expressed as follows:
(11-57)
This non-linear system of equations can be solved using various iterative
t~hniques on a computer. Stoner (1969, 1972) used the most popular solution method: Newton-Raphson iteration. The values of the unknowns are
computed repeatedly. until the values rrom any two successive step5 converge (i.e., differ by a value less than or equal to a specified tolerance). The
values of any unknown at the (k + l)th iteration is computed as follow~:
•
Gaa Production Engineering
550
,
~k.1i
where
,
_ xlkl
t
I_I
,
+ ax("k+11
~ llXj -
ax,
Ga.f Gathering and Transport
(II-58)
- Fl , for j "'" 1,2, .... n
(II-59)
where the derivatives aFjiaxj are obtained by differentiating the node continuity equations. The method requires an initial estimate for each of the un·
knowns. xf. Generally. good initial guesses are required to achieve satisfac-
tory convergence. A standard mathematical technique for improving and
accelerating convergence is to introduce an acceleration factor. Ct'lt in the
correction equation (Equation 11-58), as done by Stoner (1969):
(11-60)
where QJ is computed using the llx, for the current and previous steps. Stoner
(1969) proposed the following scheme for obtaining ell:
Let AI - llX~k.ll/ax:kl. For the first two iterations, where divergence is
most likely to occur, an 0', '"' 0.5 is be5t to use in order to ensure convergence.
In subsecluent steps, the value of Il'j is determined as below for every other
step: for the steps in bern·een, Il'; - 1.0 is used:
For A, S - 1.
For - 1 < A, < O.
ForO<A,<l.
For A, 2: 1,
cr,
=
Il', ,.,
Il'j
~
Il'j ""
O.SIA,I
LO - 0.51 A, I
LO + 2.01A j l
3
(11-61)
Stoner obtained these specifications for aj by experimenting with the mathematical model on a computer. Naturally, these are empirical, system-dependent values, and the user may have to do some experimentation to obtain
similar or better schemes for the acceleration factor a, applicable to his or
her own system.
In designing and operating transmission systems, it may be useful to ascertain the effect of varying the several different parameters that influence
the system, such as pipeline diameters, operating p~ures, and so on, and
determine an optimum design and operating condition that maximizes thc
pipeline utility at the lowest cost and satisfies all the requirements. This is
known as sensitivity analysis. Sensitivity analysis requires generating a large
number of solutions using the computer mode1 for all the possible system
configurations, entailing very high computational and associated expenses.
Readers interested in this topic are referred to the work by Stoner (1972)
who has presented a further development of his steady-state model to enable
sensitivity analysis of production and transmission systems.
551
Unsteady-State Flow in Pipelines
F10w is said to be unsteady-state if it is, in addition to flow resistance and
the pf"(S';ure drop, a function of time. F10w through gas transmission systems
is usually transient (unsteady-state), primarily because of variations in demand. Unsteady-state flow occurs whenever the rate of withdrawal of gas
from a line differs from the rate of supply to it at the inflow end. 1f the fluid
flowing in the line were incomp~ible (most liquids are almost incompressible), then any imposed change in throughput would be transmitted instantaneously throughout the pipeline, and consequently, the flow would have
the same magnitude at any pipeline section, including the head and tail end.
For gas, a highly compressible fluid, it takes some length of time for the
pressure change at the outlet end to transmit through the line and make itself felt at the head end of the pipeline. The assumption of steady-state flow
for such a system, therefore, is valid only for infinitesimally small pipe sections in the flowline.
FWldamental Relationships
Unsteady-state flow of gas can be described using four fundamental
equations: the equation of state, equation of continuity, equation of motion,
and a re1ationship accounting for the deviation of the gas from ideal-gas behalior. For flow through long pipelines, it is generally assumed (Streeter
and Wylie, 1970) that the flow is substantially isothermal, steady-state friction is valid, the slope for a pipe section is uniform, and that the expansion
of pipe walls due to pressure changes is negligible.
The simplest equation of state is commonly used (see Chapter 3):
p
ZRT
-~--
p
M
(11-62)
where the gas compressibility factor Z, a measure of the deviation of the gas
from ideality and a function of pressure, temperature, and gas composition,
can be expressed in a variety of ways (see Chapter 3). Assuming isothermal
flow and a constant composition, this necessary relationship simplifies to:
(11-63)
Several relationships are available for representing this functional dependence of Z on pressure, as given in Chapter 3. In practice, howC\'er, an a\·erage (COnstant) value of Z is used, reducing the number of equations to three.
Equation 11-62 can now be simplified to (Streeter and Wylie, 1970):
•
5:>2
Gas Gathering and Transport
Cas Production Engineering
pip - ZRTIM - B'Ig.,
0'.
p ..
pg.,..·82
(11-64)
where 8 .. isothermic speed of sound
!k .. conversion factor relating mass and weight (32. 17 lbm-ft'lbf-
sec')
553
Note that each of the terms in Equation 11-63 has the units of Ibflftl. Also
note that instead of v2, v I v I is used in order to include the direction of flow
in the friction term .
[f A is the pipe cross-sectional area , then the flow velocity v is related to
the mass flow rate m as follows:
v = m /Ap
Substituting for p from Equation 11-64 and rearranging. we get
mB'
Apg.,
(11-66)
v---
The equation of continuity can be wTitten as:
Substituting Equations 11-64 and 11 -68, the equation of motion (Equation
(11-65)
where
In"
x ..
p ..
A ...
t -
11-67) becomes:
ap + E. [mB' a(mB'IApg.) + a(mB'IAPg.)]
ax 8 2 Apg"
ax
at
mass flow rate of the gas, Ibmlsec
distance along the flow path, ft
gas density, Ibmlftl
cross-sectional area of flow, ft 2
time, sec
+ pg sinO' + _ 1_ m l ml8~ Pik = 0
B'
2dg. (Apg.)' B'
Substituting for p from Equation 11-64, the equation of continuity (Equation 11 -65) can now be written as:
0',
ap + 1:
ax
am + a (ApgJB' ) _ 0
ax
at
~ [m82 am _ m2B2 ap +..!.. am _ ~ a p ]
8 2 Ag., Ap 2g.,
pg .
B'
ax
Aplg"
ax
p
at
p2
•
at
f m l m l B2 0
2dg. A'pg.
+~sma+--
0'
0<,
(11-661
ap
p
m~B2
ap
p m ap
p mB2
am
----- - --- - +
a, Ag., Ap'g. a, Ag. P' at Ag.,Ap'g. a,
The equation of motion can be expressed as:
ap +!!... [v av + a v] + pg SinO' + fv lvlp _ 0
ax ik ax at g.,
2dg.,
P 1 am
Ag., P at
(11 -67
where p" pressure, lbf/ft 2 ; conversion constant of 144 required in EqUlltion 11-67 if psia is used
g - gravitational acceleration, 32.17 ftlsec2
a - angle of pipe inclination from the horizontal
f .. pipe friction factor (Moody)
\- .. gas flow velocity, ft /sec
d '" internal diameter of the pipe, ft
pg.
+ ---+~SlOa+
2
8
fm I m I 82 - 0
2dA2~p
Substituting for ap/at from the continuity equation (Equation 11-66) and
rearranging, we get
[
1_
m~B2] ap + 2mB! am + _ 1_ am
a, A'p~ a, Ag. at
A'p'~
+pg.
fm l m l B!
82 sma + 2dA2
w-
0
(11-691
Ga$ Gatllerillg and Tran$port
Gas Production Engineering
554
In Equation 11.69, the second term in the coefficient of oplox. is negligible
compared to unity. Also, the om/ax term is negligible as compared to the
other terms. With these simplifications, the equation of motion for transient
gas flow reduces to:
(11.70)
Equations 11·66 and 11-70, describing the transient flow of gas in a pipeline. constitute a system of two non-linear partial differential equations
(NL-PDEs). Equation 11-70 is often used in the following form that results
on muJtiplying it throughout by p:
1 opl
p _
am +_sma+
pZg.
fm i m B~ '" 0
_+ _
2
ax
Ag,.
at
B~
2dA2~
(11·71)
Initial and Boundary Conditions
Initial conditions as well as boundary conditions for the system must be
specified in order to obtain the applicable solution to the differential equations just given. The initial conditions of the system are required for resoh-ing initial pressure, velocity, density, compressibility, and other properties as
a function of position (x) along the pipeline. Boundary conditions must be
specified to obtain a unique solution.
Initial conditions can be specified in two ways:
1. Determine the pressure and flow rates by actual measurement at \'arious points along the pipeline. The initial state of the system will be
given by the pressure and flow rate distribution obtained in this manner.
2. Assume £low to be steady-state at the beginning of the unsteady-state
flow analysis, i.e. , at time t - O. Use the steady-state £low relationships to calculate the initial pressure distribution (rate is a com1ant for
steady-state flow) in the pipeline.
The first method is difficult to use. Precise measurement at several points
is difficu1t and usually impossible in an installed pipe in the field. Even if
this could be done, the pressure and flow-rate pro£iles obtained may not be
at the same instant in time at all points along the pipeline, resu1ting in an
inconsistent specification of the initial state. Therefore, the steady-state initial condition is almost always used.
At least two time-variable boundary conditions must be specified to obtain a unique solution, chosen from among the four variables: input presSllre, input flow rate (or velocity), output pressure, and output flow rate (or
555
velocity). Depending upon the choice exercised for specifying the boundary
conditions, two cases are possible:
1. Both time-variable boundary conditions are specified at the same end
of the pipe, either input or output. In this case, the numerical solution
is obtained backwards in time and away from the known boundary.
Note that it is not possible to compute the flow parameters at the unknown end of the pipe from their gi\'en values at the other end at the
same instant in time. We must work backward in time, calculating the
pressures and flow rates at various points of the pipeline at time t - .:1t
on the basis of their known distribution at time t.
2. The more common approach, where one time-\'ariable boundary condition is specified at each end of the pipe. In this case, the numerical
computations are not made backwards in time. The two end-point
boundary conditions are used to determine the values of pressure and
flow rate (or flow velocity) along the length of the pipe. Thus, the
pressures and flow rates at \'arious points of the pipeline at time t + .:1t
are calculated on the basis of their known distribution at time t.
Numerical Solutions
The system of NL-POE's (Equations 11-66 and 11-70) previousJy given for
transient flow in a gas pipeline cannot be solved analytically. Any anal}1ic
solution must incorporate some simplification, or assume some specific set of
initial and boundary conditions. Generally, the anal}'tic solutions thus generated reduce computational expense, but are applicable only to the analysis
of a subproblem, or a simplified problem. Thus, the equations for transient
flow must be solved numerical I)'.
Four types of numerical methods for solving the system of NL-POE's for
transient gas flow have been reported in the literature: (a) explicit finite difference method; (b) implicit finite difference method; (c) method of characteristics; and (d) variational methods. All of these methods proceed in steps,
computing the required parameter values (pressure, flow rate) at various
points along the pipeline at the instant t + .:1t on the basis of the known distribution of these parameters along the pipeline at time t.
Explicit Finite Difference Method
The NL-POE's are transformed into algebraiC equations using finite difference methods such that the values of the unknown parameters (pressure.
flow rate) being soh·ed for at time t + at depend only upon their \falu~ at
the Preceding time step (at time t). Thus, the equations can be solved indi·
vidually. The method is faster because it requires lesser computation than
the implicit scheme, but is subject to instability and a restricted time step
•
556
Gas Production Engineering
Gas Gatheri"g and Transport
size. For these reasons, and also because of the inaccuracies in computations
that generally result from the use of this method. the explicit scheme is
rarely used, except in conjunction with the method of characteristics.
The partial differential equations can be discretized along the space (x)
and time (t) axes in three ways: backward difference scheme, central difference scheme. and forward difference scheme (see Figure 11·9). Let o.x be
the length of each pipe segment: solutions are computed successively at values of time increasing (or decreasing) in time steps of size at. Then. usin~
,+0
•••
t
t
P,
P;.~I
pP+PP.1
2
(11-.3)
2
The transient £10\\ equations can now be linearized using the relationships
of Equations 11-72 and 11 -73. The equation of continuity. Equation 11-66,
becomes:
-m'l
~n'l
H
,,'
p.
Figure 11·9. Nomenclature lor finite difference
methods.
_B' [mHI
"
Ag.,;1x
Solving for
I
+ p,d_ p '
I
,
_
0
~t
p~. I:
,
(11-74)
the explicit forward finite difference method, the partial differentials in
Equations 11·66 and 11-71 can be expanded for any grid point i at time
n + 1 as follows:
~_pr+l-p~
at
557
Since the values of all the parameters on the right side of Equation 11-74 are
known from the solution for the previous time step, pro I can be directly Dbtaine<i. The equation of motion can also be transformed in a similar manner
using Equations 11-72 and 11-73. as below.
at
am _ mp+l_ mr
at
.6.t
~_ mr~l-
ax
.6.x
mr
Solving for the unknown mp,l at the new time n + I, we get
(11.72)
where the subscript i indicates the grid along the x direction, and superscript
n indicates the parameter value at the previous time step.
Thus, pr is the pressure at section i at time step n, pr~ I is the pressure at
grid point i + 1 at time step n, pr· I is the pressure at grid point i at time step
n + 1 (at which solution is sought), and so on . .6.x and .6.t indicate the grid.
block and time-step size, respectively. The pressure p and mass now rate m
are discretized as follows:
mr· 1 - mr - [
1(~ti;1x) [(pr. 1)2 -
All<
pr+prd
fB2~t
-;-;-:-'~"-:;;--; (mr
4ciAll<M + pr.,)
+ mr. d I
(pl')2] -
2(P~~t
)B2 sino
+P.I
mr + mr.ll
I
(11-75)
Additional details may be obtained from the published work of Thppeck and
Kirsche (1962) and Distefano (1970) who have described and used the exPlicit method .
•
Cas Production Engineering
558
Ga,9 Gathering alld Transport
559
Implicit Fjrlit~ DiJf~~ Method
In the implicit method, the NL-PDE's are transformed into algebraic
equations using finite difference methods such that the values of the unknown parameters (pressure. flow rate) being solved for. at ti~e t + ~t d~­
pend upon their values at the current time t + ~t at n~lghbonng POints In
the pipeline. Thus. the equations must be solved. slmultaneo~sly. The
method is slower because it requires more computation at each time step,
but provides stability. The aJlowable time step size, restri~t~ only by the
accuracy desired. is always greater than that for the explicit scheme. Implicit difference procedures have been formulated by Guy (1967). Streeter
and Wylie (l9iO). and Wylie et al. (1971).
.
Streeter and Wylie (1970) used the central difference scheme for the Implicit expansion of the differentials as follows:
ap
at
pr *1
-~
n
n
Ut
ap'
-ax
am
-at
am
n.1
+PI.l -Pi -P,·l
ax- ""
(P~:11)2 + {pr.I)2 _ {pp+l)2 _ (pf')2
Ux
mr+ l + m~:/ - mr - mr.l
Ut
,.\
r
r"
m;+1 +m+l-m
2.lx
m~
m-
,
-mj
_I
n+
'
+m n+1
m,+,
j . , +m,
n)1 mjn~l +m;*1
n_l
+m jn.l
*1 +m,n +m,*1
+m r
+mr.ll-O
(11-78)
Equations 11-77 and 11-i8 must be sohed ~imultaneously. The parameter
values at time-step n (i.e_. at time t) are known from the initial conditions or
from the previous solution step. There are four unknowns in the two equations for each grid ceIl i: pr+ 1, pr:/. mpol. and mj'!/. For the complete
pipeline divided into m grid blocks. the total number of unknO\,>'OS is
2m + 2, including the two unknowns at the boundary_ The total number of
equations is also 2m + 2, including the two known boundary conditions.
Thus. we ha\-e a system of 2m + 2 non-linear algebraic equations to be
solved_
These equations can be solved in many different ways, all of which in,'olve iteration (trial and error). Streeter and Wylie (1970) have used Newton-Raphson iteration (described in the section on steady-state flow through
looped systems), perhaps the most commonly used method. Additional details for solving such equations can be round in any text on numerical analysis or reservoir simulation, such as Aziz and Settari (l9i9) .
Thylor (1962), Coacher (1969), and Streeter and Wylie (1970) have pro-
"
a+ I -mrl
-B'- (n.'
mi.1 +m,.l-m;
A~x
and
BdA-g;
(11-76)
Substituting the expressions of Equation 11-76 into the equation of continuity (Equation 11-66) and the equation of motion (Equation 11-71). we obtain:
At
Ill' ( l I * l
+--,-~mj
.Hethod of Chamcteristies
4
1 ( , .. + P'+l-t'l-P,+In·1
'"'"
II I
0
+-p,
1 (n*1 +PI+I
n+1 +p,II +P,.l
n)( m,n*l +m,.l
n*I_"_
II)
+---Pi
m, m,.1
2A!(c.lt
(l1.77)
posed and used the method of characteristics to solve the transient gas flow
problem for pipelines. In this method, paths (called characteristic lines) are
defined in the (x, t) plane, along which the system of NL-PDE's is transrormed into a system of ordinary differential equations (ODE's). These
ODE's can then be solved numerically, using either the eKplicit or the implicit finite difference method of solution_ The procedure used by Streeter
and Wylie (1970) is described in the rollowing section.
. Equations 11-66 (designated by F,) and 11·70 (designated by F2), describIng the transient flow of gas in a pipeline, have two independent variablcs. x
and t, and two dependent variables, p and m. These two equations are combined USing an unknown multiplier >., and rearranged as follows:
•
Gaa Produclforl ElIgi'leerlng
560
G(U
F .. )'F1 + F2
p
fmimtB2
pg
+--sina+
=0
1
8
2dA2~
1
111-79)
~
~
Figure 11-10.
t I--------¥'-------+--------'~----~_l Characteristic hnes
R
I
),
OI$TANCE,X - - - - - - - -
implying that
(II-SO)
B
By putting any of these two values of A, the quantities in the brackets in
Equation 11-79 become total differentials. The controlling equations for use
in the method of characteristics now become:
However, the ordinary differential Equations II-Sl and Il-S2 themselves
must be solved using some finite difference procedure. Either the explicit or
the implicit scheme may be used for this. Streeter and \VyJie (1970) have
shown solutions using both these schemes. For the explicit method, the C~
characteristic line (Equation II.Sl), on multiplying throughout by B dt, becomes:
B
Ag" (mr - mR) + (pp - PRJ +
1. The C + characteristic line corresponding to )., ... + (lIB), or
midt - B, given by
Ag. (mr - mK) + (Pr - PRJ +
(II-SI)
2. The C characteristic line corresponding to ).. .. - (1 B), or
m/dt - - B, given by
Ag., dt
_.!.. dp + pg sint:r + fmlmlB2 .. 0
B dt
B'
2dA'gip
[pg 82sino: + {mlm
B2]
2dA~~ Bdt
=
0
•
Since dx/dt ., B, we can replace B dt by dx to obtain:
B
1 dOl
I dp pg.
fmlmlB2 0
- +--+-sma+
Ap< dt
B dt
82
2dA 2W
_1_ dm
on an x-I diagram.
I
--).,B~-­
I
+Bo r
S
"
Equation 11·79 can be transformed into two ODE's using a)., gh'en by.
)..=
561
t+4t~------~------~~------+-------1
_ I [)'B,am + am] + ), [(II),) ap + ap]
Ag.
ax at
ax at
dx
dt
Gatheriug and Transport
[pgSino:
82
fmlmIB!]
+ 2dA2gip dx
= 0
Discretization along space (x) yields (see Streeter and Wylie. 1970):
8
roll
6.x
Ag.. (mp - mR) + (pp - PRJ + 2dA~~(pp + PR)
(II -S2)
On the x-t plot shown in Figure 11-10, consider JX>ints Rand S at which m
and p are known. By constructing the C+ characteristic line dxldt .. B
through R and the C- characteristic line dx/dt - - B through S, an inter·
section P is found at a later time and an intermediate value of x. Since both
Equations 11-S1 and 11·S2 are valid at P, they may be solved simultaneously
to yield the new values of m and p at this later time. In this way, the solution
can be obtained at a later time, from known values at the previous time
step. at all locations in the pipe.
e'-I
Pi>
(mrlmpl+mRlmHI)--+
(e'-l)=O
s
PP+PR
(ll-83)
Similarly, on using an explicit expansion scheme, the C- characteristic line
(Equation 11-S2) becomes:
B
fB2 6.x
Ag., (m, - ms) + (p, - p,) - 2dA'g1(p, + Ps)
.. - I
p!
(mplmrl + mslm~l) - - - - - (e' - 1) = 0
s
pP+Ps
(1l-S4)
562
In Equations 11-83 and 11-84, s is the same as in Chapter 7 for steady-state
flow (Equation 7~47), and s - 0 for horizontal flow. For this explicit
scheme, Streeter and Wylie (1970) have noted thato.t ~ .1.xfB for stability.
For an implicit finite difference scheme. the equivalent forms for Equa~
tions 11-83 and 11-84 can be derived similarly.
''ariation(J/\/ f'llwru
Rachford and Dupont (1974) have presented a variational method that
provides a fast and accurate means of simulating transient flow in gas pipe-lines and networks. Formulated as a Galerkin method, this approach offers
significant ad,antages in terms of computational cost and storage over other
methods. Readers are referred to the original paper for a detailed treatment
of this special method which is. perhaps. beyond the scope of our present
discussion.
Some Approximate Solutions for Transient FJow
There are many situations in pipeline engineering where the flow is unsteady. Approximate relationships have therefore been developed to enable
easy estimations for some special cases where it may not be necessary to generate very precise solutions to the unsteady-state flow relationships described earlier Some such cases are described in the following sections.
Blowdown and Purge
There are instances when it is necessary to blow down and purge a gas
line. lzawa (1966) provides some usefu1 solutions for this special case of unsteady-state flow. For subcritical flow (Pu!Pd < 2), lzawa (1966) derived the
following relationship:
v-
Gas Gatherl11J{ alld Trallsport
Cos Production EnginCt'rlng
SG3
Substituting for Rand &" and changing to customary units of V in Mscf. d in
inches and t in minutes, this relationship becomes:
(11-85)
For the case of critical flow (p" Pd > 2). lzawa (1966) has presented the
following relationship:
v '"' 0.4524 d2p.,til')~
(11-86)
where, as for the subcritical flow equation (Equation 11-85):
V ., gas ,·olume. Mscf
d - internal pipe diameter, in.
p., - average pressure. psig
t '"' time, min.
T *' temperature ("R)
Pressure Surges on Closing a Valve
A pressure surge OC(:urs when a \"alve on a flowline is closed, and the fluid
outflow is stopped. The kinetic energy of the flowing fluid is abruptly converted to internal energy, and a surge or wave travels back, countercurrent
to the direction of flow of the fluid. The pressure rise accompanying this
flow stoppage is highest at the valve. and decreases gradually towards the
upstream end of the pipe where the disturbance is attenuated. The greater
the compressibility of the flUid. the greater is the attentuation (or absorption) of the disturbance. Consequently, gas lines do not pose a problem,
whereas liquid lines, and sometimes high-pressure gas lines, pose a problem
of some concern. In most cases, pressure surges damage pressure-measuring
equipment only, but sometimes they may be powerful enough to even rupture the pipe. Stewart (1971) describes this problem and provides a method
for computing pressure surges for Iiqu.id lines,
(r!4)d't [2g..Z"RT(1 - Pdl",,)],"
Pressure Testing
where
V .... gas volume, ftl
d ,., internal pipe diameter, ft
t .... time, seconds
&, - constant relating mass and weight, 32.17 Ibm-ftlflbf.sec2
Z., - average gas compressibility factor
R .... gas constant, 85.56 ft-Ibf/lbm-oR
T ... temperature, OR
Pu. Pd - upstream and downstream pressures, respectively, psig
Pressure testing of a pipeline is commonly done for the detection of leaks.
This is a special form of unsteady-state flow where the pressure must be held
COnstant for a sufficient time, Campbell (1984) has given the following relationship for estimating the minimum vaJue of this testing time, (It)'dln. necessary:
(ll-S7)
•
564
Gas Gathering and Transport
Goa Production £'Igineering
where (~)min - minimum required shut-in time for the line. hr
d - internaJ pipe diameter. in.
L - length of the pipe section that is being tested for leaks.
miles
P, - initial test pressure. psig
565
Solving Equation 11·89 for PI:
p, ~ [Pi q~~·r
+
(11-90)
introducing Rp ., P l iP2 in Equation 11·90. we get:
A flo\\ line that has been shut-in for at least (~)mln hours is considered to hale
no leaks night"' line) if the pressure loss is less than the (aplmu psi gil-en
belo\\ (Campbell 19M):
(11-88)
(11-91)
Similarly, we can obtain an expression for P2 in terms of Rp:
p,-
where t - shut-in time, hr
Handling Variable Consumer Demand-Case of Constant Injection Rate
The two ways of handling daily fluctuations in consumer demand are
constant injection rate (but not necessarily pre<.Sure) into the pipeline. and
variable injection rates (and pressures), to ensure a constant pressure al the
delivery (outlet) end of the pipeline.
The advantage of constant injection rate of gas into a pipeline is the ease
of control. The pipeline functions as a buffer storage facility, accommodating the difference between the constant input and the fluctuating output.
The pressure at the delivery end of the pipeline varies from (Pl)m(n for the
highest delivery rate to CPz)mu for the lowe<>t delivery rate. Potential energy
(pressure energy) losses may occur at the delivery end where the pressure
will usuaJly exceed U>2)mi.D during most of the day. These losses can be
minimized by using a turbine driving a power generator. instead of pressure
reducers such as throttles, for reducing the outlet pressure.
Szilas (1975) presents the following procedure for designing a constant injection rate system for variable consumer demand, a modification of similar
developments by Smirnov and Shirkovsky in the USSR. Equation 11.30 is
written as follows:
q-
~
pj Pi]'·'
- -
Z"
(11-89)
r'
q "
'z
[P!-T
(11-92)
0'
The mean pressure in a gas line is given by (see Equation 7-32):
Pi]
•
p,"-,""-2 [PI+--3
PI + pz
- ~ [PI + p,p, + P!]
3
PI+P2
0'.
32"P.,,-P2 [R~ Rp+l
+ Rp + I]
Substituting for P2 from Equation 11·93 and rearranging, we get
3p."k
R~ + Rp + 1
2q~,~ - (Rp + 1)(R~ - 1)()S
(11-94)
A plot of 3p.,kJ2qZ~,S versus RI" as given by Equation 11-79, is shown in
Figure 11-11.
eo" Prodl4ctiQn Engineering
566
Go" Gathering arid Transport
567
the pipeline at the time corresponding to A must be equal to the minimum
output pressure, ~)mtn. From Equation 11-90, the pressure at the head end
of the pipeline, Ph i~ gi\'en by:
p, ~ [(P,).... q:H'
•
+
and the mean pressure in the pipeline. P., . is given by:
Figure 11·11. Szilas's method for
determining the buffer action of a
pipeline. (After Szilas. 1975_)
,
The volume of gas stored in the pipeline. V, can be determined as follows:
v~
"
"
"
p"T.,AL
P",Z., T.,
Solving for (Pa"/Z.,):
"
(11-95)
•
Agure 11·12. Szilas's method
for determining the buffer actioo
of a pipeline. (After Szilas, 1975.)
,1 • "'________,
.!"
where
,
•
__ ___________ c
,
P." T., ,. a\"erage pressure and temperature in the pipeline, respecti vel)
p",. T ... s< specified standard conditions of pressure and temperature, respecth'ely
Z~, ... a\erage gas compressibility factor (at PM" T.,)
A - pipeline cross-sectional area
L - length of the pipeline
o
TIN(.
IIOUR!
---_
Figure 11-12 shows the daily fluctuation of Rq, the percentage hourly
consumption referred to daily consumption. The dotted line parallel to the
abscissa indicates the average consumption Q..v' In segment A-B, consumption is less than q,." and gas accumulates in the pipeline. In segment S-C,
consumption is greater than q.". and the gas accumulated in the pipeline at
the earlier time is used to cater to this increased demand. Note that at point
A, the gas flow (supply or input) into the pipeline is exactly e<Jual to the
demand, and gas reserves are zero. Thus, the pressure at output (tail) end of
From Figure 11-12, we can determine the area embraced by the cun'eADB
and line AB by planimetering, and convert it to gas volume" This gas volume is the volume of gas stored in the pipeline during the slack-demand pe_
riod, VAB. This stored volume will be maximum at the time corresponding to
point B in Figure 11-12. Therefore, the head and tail end pressures, p! and
P2, in the pipeline will also be maximum at B. Using Equation 11-95,
P•• - p",T" IV + V
Z.,
T.,AL
A
1
AR
(11-96)
where VA is the volume of gas stored in the pipeline at point A.
The calculation procedure can now be described from these relationship"~"
First, a plot is made of the fluctuation in demand versus time, as shown in
•
568
Ga.f Gathering and Transport
Cos Production Engineering
Figure 11-12. Then, the volume of gas stored in the pipeline during the pcricx:l. of low demand is determined by measuring the appropriate area enclosed by the curve. Then, Equation 11-96 is used to calculate (p.vlZ..,) from
which p.,- and Z .. can be obtained by trial and error. Then, the value of the
expression 3p.,k/2qv,:,S is calculated. . Figure 11-11 can then be used to read
off the corresponding value of Rp. Knov,ring the ,,'alue of RI" P2 can be calculated using Equation 11-93, and then the required upstream pressure p! can
be obtained (PI ., Rpp~).
Let (PI)", .. be the maximum ftl<l!>ible pressure at the head end of the pipeline. Now, if PI :S (P')mu, then the quantity of gas V"8 stored in the pipeline
during the slack-demand period will be sufficient to handle the excess demand in the high-demand period Be. Otherwise, the pipeline must be redesigned.
Handling Variable Consumer Demand-Case of Variable Injection Rate
Bateyet al. (1961) described a method for obtaining solutions to the case
of varia.ble injection into the pipeline and conducted a sensitivity analysis of
the vanous factors that affect pipeJine performance. They represented gasconsumption variations in time by a Fourier function (Figure 11-13),
<l2 "" £(t). From this supply function and the constant supply pressure Pz, the
gas flow rate and pressure versus time functions can be calculated, proceeding step by step for various pipe sections backward along the line from the
tail to the head end. Such functions, represented as ql '" £I(t) and PI _ £2(t).
are sho"'Il along with the supply function <il .. £(t) in Figure 11-13. Any nu-
I INPUT PAI!:5SUFl[, 1:>,
II OJTPUT FLOW, '\12
m
INPUT FLOW,
0
I0
~
~.
,
,
•
0
0
•
0
o
3
to
,.
n
!;z::;
"
912151121243&912
569
merical technique may be used for solving the system of equ.ations £~r obtaining the £1 and P functions. The pipeline can then
prOVIded optlmum
control to meet the demand variation at a constant d.ehver y pressure P2·
Bateyet al. (1961) conducted a parametric anal~"S1S that enables one to
o'd the expensive numeric computations involved in solving the system of
:;;u~tions. To permit Fourier series exp~nsion, the load. Le .• the demand of
gas, is expressed in the following functIOnal from:
be:
(11-97)
Clo .. q,. + Qt sin (2,-t f l:t.)
where Qo - flow out of the pipeline section
q,. .. steady or a\'erage part of the flow
.
qt _ amplitude of the time-variable part of the flow out of the pipeline section
t _ time
I:t, - period of the time-variable output flow
Further, the input flow q; required for the given output boundary conditions
can be expressed as (Batey et aI., 1961):
~ _ q,.
+ ql sin (hlt,,)(t +
1"1)
(11-98)
where q .. sine wave amplitude at the input of the pipeline section
1"~ .. time required for the sine wave to propagate from input to
output
y - y-th harmonic
.
(h - amplitude of the flow corresponding to the y-th harmOniC
T, .. delay time for the y-th harmonic
Amplitude <h of the roth harmonic is generally less than 1% of the amplitude ql. Thus Equation 11-98 can be simplified to:
(11-99)
To specify how the sine wave propagates in the pipeline system. values of the
amplitude ratio, qtfqJ, and TI are required..
.
Batey et al. (1961) studied the effect of the three types of pipeline section
parameters that affect flow:
T 1101 I!: .HOURS
Figure 11-13. Simplified representation of the variable relationships for a line
section. (After Batey et al .. 1961.)
1. Parameters that depend upon line section geometry. such as length. diameter. and relative roughness (tid).
•
570
Cas Production Eligineerin,!iC
Go., Gathering and Transport
2. Parameters that depend upon the characteristics of the flowing gas.
These include molecular weight, pseudocriticaJ pressure, and the slope
of compressibility versus reduced pressure for the gas.
3. Parameters that depend upon the average operating conditions of the
pipeline. These are average line pressure, average flow, and avera~e
gas temperature.
Figures 11·14 through 1l~21 show the results of this parametric analysh
by Batey et aL (1961). In Figure 11-14. the amplitude ratio is shown as a
function of the period of the time yariable output pressure. The amplituJ,,;
ratio is less than 1, impJ}ing that the signal amplitude at the input is greater
than the output amplitude. Also, amplitude ratio decreases for high fr(>.
quencies, indicating that attenuation (damping) increases with frequenc~.
For a given frequency, damping increases as the output pressure decreases.
because damping results from energy loss, which is proportional to the
square of the velocity (and hence, inversely related to output pressure).
Damping also increases with increasing friction factor (Figure 11 -16), with
d(.'Creasing pipe diameter (Figure 11-18).
"
1"
~
,:
•
"0
h'
-.............
~
•
i
~
,
---
,
"(1'1 100
I
'"
P[ "100, HOURS
I
'"
rR[O UENC T , "hlt
I-
.,~~
•
Figure 11-1 4. Amplitude ratio of input upset to output upset versus period of
upset, as a function of the output pressure. (After Batey et aI., 1961 .)
The corresponding time deJa}'s for these variables are shown in Figures
11-15. 11·17, and 11-19. These figure; show that higher the frequency
(Io\\er the period on the abscissa), lower is the time delay or phase shift of
the demand wave (i.e., the phase velocity is higher). For a given frequency.
f'
•
["" ~ ~01
~
•
" .
HOURS - - - -
~~ ~
~ ~~
-••" "
Illl
'"
:-------; ~
'--.....::::
,,
,
al. . 1961 .)
-
,
~
Figure 11-15. Time delay 01 upset propagation from one end to the other end 01
a line section versus period. as a function of the output pressure. (After Batey et
,o
,,
.~
~ !--
"
roo
.,+-------~-------4------_+~'»
,,.
."",
"
-- ,. f--•"
I ,.
571
~.,'"
OO~
""
"",' ""
,
•
,
1'(1'1100, HOURS
""
----
'"
Figure 11-16. Amplitude ratio versus period as a function of the friction lactor
(After Batey et aI. , 1961 .)
phase shift decreases with increasi ng output pressure (Figure 11-15), decreasing friction factor (Figure II 17), and increasing pipe diameter (Figurc
lJ·19).
Figure 11-20 shows that the amplitude ratio decreases (or, attenuation in~
creases) along the pipeline length . Figure 11-21 shows that the phase ~hift
increases with increasing length along the pipeline. These figures can he
572
Gas Production Enginemng
Ga~
I, ""
t ",
7
""
•"
,•
•
~
~
•0"
f •
"
0
12 it!
40
20,"
••
•
'0
0-011
'0
""
0-007
'o>-______~--------L-----~~~~
•
"
1
573
d.
•
.;
•
Gathering and Trollsport
'0-1:-----1------:---=~-l
12
6
J
I-!\
j-:I
••_ _ _ _ _ _ PEIIIOO,HOURS - - -- --
PERIOD, HDUIIS
Figure 11-17. Time delay versus period as a function of friction lactor. (After
Batey et aI. , 1961.)
0'
"'- ~~
~
"'''''"
~
•"•
•o
,
·•"
0'
• ,
r
t
"'-.."'-.. ~
..... 07
"
•
_ ___
~uuoo
Figure 11-19. Time delay versus period as a function of pipeline diameter. (After
Batey et al" 1961.)
d,
.;:
;.-
~O'"
~ 06
•
)'Z,.~ "-
~
,
"""" i"o...
o
~,~
~
..
'0
f'a..
•
1'0..
~ c.
,'-....'""
'-<>.
,
~ °
°
°
'0
'0
'"
M
.0
_ __ _ __ L£NGTH,MIL£S - - - - - -.
,HOUJIS _ _ _ __
Figure 11-20. Amplitude ratio versus pipeline length. (Afler Batey et at , 1961 .)
Figure 11-18. Amplitude ratio versus period as a function of pipeline diameter
(After Batey el at , 1961 .)
used to determine the operating conditions necessary for meeting consumer
demand at a constant, specified contract (output) pressure.
The main advantage of satisfying consumer demand in this way is that no
pressure energy needs to be dissipated by throttling at the output end, and
the compressor requirements are therefore minimized. However, a sufficiently accurate foreknowledge of the demand wave is required.
Unsteady-State Flow in Pipeline Systems
We have so far described transient flow in a single pipeline. As discussed
earlier for steady-state flow in pipeline networks, this simple procedure mu~t
be modified for application to complex transmission systems where there IS
injection and o££take of gas at intermediate points along the line, or where
574
Ga s Gathering and Transport
,,.
,•
ap2
vv
"'"
"
--• ,.
•>
"
'7
,
0
>
o
-ax -
n
o
,./
~
Ag.,dx dP! =
B2 dt
"
'0
"
'00
the flows com-erge to, or di\"erge from. nodes. The node Jaw (Equation
11 -41 ) must apply to each of these nodes:
"
,
I
V,':' dp, ~ t
B- dt
m
I
•
- m...J
;.1
mi. -
rn...
(11-103)
w here mi.) ,. fl ow into node j from pipe leg i
mo.! = flow out of node j
(11 -100)
The values of mi. I can be calculated from Equation ll -102 as follows:
whe re m n ,. mass flow into or out of the node
m, = mass flow rate in pipe leg i meeting at the node for each of the
n pipe l~ meeting at the node
The m l values are computed from the non-linear algebraic equations
describing transient flow in a single pipe leg. This makes the description and
calculation for a transmission system of even a moderate size very complex
It is essential to incorporate some simplifications into the transient fl ow
equations. Guy (1967) has discussed some of these simplifications that ca n
be usually done without a significant loss in accuracy of the results. The first
simplification is to neglect elevation changes that are generally insignificant
for gas lines. Thus, the third term in Equation 11-71 can be omitted. Further. the second term, (piAg.,) (am/at ). describing the change in mass £10\\
rate per unit time, is in most cases smaller than the friction term in Equation
11 -71 by an order of magnitude and can also be dropped . The system of
equations describing transient flow (Equations 11 -66 and 11 -71 ) now sim ·
plify to:
ap _
at
t
0',
Figure 11·21. Time delay versus pipeline length . (After Batey et aI., 1961.)
,
(11-102)
dA ~g!
-
- - - - - L ENGTH, N ILES - -_ _ __
mn + Ern, - 0
fm l m lB2
Every node is assigned half the length of eac h pipe leg associated with that
node. Let V J be the \'olurne obtained on summing up the \-olumes of each of
the pipe legs that connect to node j. Equ ation 11 -101 can then be written for
node j as follows:
V
"
575
(11 -101 )
m _
1,1
[d,. ,A1.,g1 11'1 - Pflt' 5
f. B2
L .
..,
,.,
(11-104)
I.j
where L;.i represents the lengths of the indh'idual pipe legs. and S'.i is given
by
Substituting for m •. ) from Equation 11-104 into Equation 11-103, and multiplying by B2/Vig.,:
11'1 - PI'
j,5,.,- Vs' m..,
,I!<
0,
dp
n
';if - K, E
i _I
[J,.,(I p1-
Pl i)"'5q! -
= m..,
BK
g,
(11-105)
•
Gas Gathering and Transport
Cal" Production Engineering
576
, .. here K
--
Pipeline Economics
B
\'
and
J'.I - 1.
., dl.'Af.,
( 1t - 1{l6)
f. I
Applyinfot finite difference techniques.
d2.t ... P,tt + .11) + P,{t)
dt
dt
Using this and rearranging. Equation 11 -105 becomes
PI(t
577
+ ut) "" .l.tK.
It.
O,.(lpr - pr l)"S;.]- (B'I!J m".• ) + p,ll )
,-
Pipeline sizes are generally dictated by the available pressure drop, reo
quired flow rate, and the available pipe sizes. If two or more pipe sizes satisfy all the requirements and constraints, then one is chosen based on the
economics. An economic pipe diameter minimizes the (discounted or amortized) capital costs and operational (compression) costs. With increasing
pipe diameter d. the capital costs increase, whereas the operational costs decrease due to smaHer pressure losses. Thus, there exists an optimum d such
that the sum of the amortized and operational costs is a minimum.
It is obvious that for such an economic analysis, no general correlation or
equation can be easily determined for all possible cases because pipeline
costs, amortization (or depreciation) allowan~ within the corporate tax
framework , and operating costs vary widely. A simplified analysis by Peters
and Timmerhaus (1980) is presented here for determining the optimum ec0nomic pipe diameter for a single pipeline. The concepts developed are subse.
quently extended to the far more complex problem of the economics of gas
transmission systems.
IIt-I07)
A Simplified Analysis for Optimum Pipe Diameter
Equation 11·107 for node j can be expressed as:
•
Comprmon COS"
PI(t + .1t) - C 1 + Pi(t)
"here C, -
~IK,
It.
0, .• 1!pi' - 1'1 1)' '5, .• ]- (Bg.)m".• )
(it - lOS)
111-1091
Similar equations can be written for all the ot~er nod~ in the s:rste.m ,
Thus. we will have a system of non-linear algebraic equations ,:prescntmli!:
transient flow in the pipeline network. This syste~ ?f equaltons can i~
solved using finite difference techniques. For the explicit method. Equat
ll- IOS is expressed as:
PilI
\1
+ 61) - CIII) + p.ll)
whereas in the implicit method, C j is evaluated at time t
tion 11-108 is expressed as:
Pi{t
+ at)
- CJ(t
+ at , and Equa
+ 6.t) + Pi(t)
Other elements in the system, such as chokes and compressors, can also be
incorporated in the previous equations as done for steady·state networks.
II
The mechanical energy balance for a flowing system can be reduced to
the following form (see Equation 7-11):
w, _ fl."'ll
+ L,p) + B
2g.d
where
111-110)
w. - mechanical work added to the system by the compressor, ft.
Ibf/lbm
f - dimensionless Moody friction factor
L - length of the pipe, ft
v - flow velOCity, ftlsee
Lrp - frictional loss due to pipe fittin~ and bends, expressed as
equivalent fractional loss in a straight pipe
g., - conversion constant relating mass and weight (., 32.17 Ibmftllbf-""')
d '" inside pipe diameter, ft
B - a constant accounting for all other energy losses in the flowing
system
578
Gas GalherifJl!, and TranS1)Qrt
Gas Production Engineering
As discussed in Chapter 7 (see Equations 7-14 through 7-21), several relationships can be described for the friction factor, f, in terms of the Reynolds
number, !".Jlko Peters and Timmerhaus (1980) use the following equation for
turbulent flow:
(11-111)
Combining Equations II-Ill and 11-110, and applying the necessary conversion factors, the following equation can be obtained for the annual compression costs:
(11-112)
where
f'ixed
per foot of pipe length
C romp _ romp!eSion cost in dollars/vear
•
q _ gas £10'...· rate. fP/sec
p _ the gas density, Ibmfft'l
/.I ,. gas viscosity, cp
Ct = cost of electrical energy, $ kWh
H, so hours of operation per year
d ,. pipe diameter, in.
E _ compressor efficiency, fraction
B' _ a constant independent of pipe diameter d
emu Jor
where
579
Rp - ratio of total costs for fittings and installation to the purchase
cost for new pipe
C!'"p - annual fixed charges, including maintenance, expressed as a
fraction of the initial cost for a completeJy installed pipe
Optimum Economic
Pi~
Diameter
The total annual COSt CT for the compressor and pipin~ system can be obtained by adding Equations 11-112 and 11-114:
°
Gr- .-<)i3q2M P0,&-1IJ0 I~C r (I + L)H
Ip
)+Bo+(I+R)CdnC.
d4s.tE
II
II
Fp
(11-115)
Differentiating C T expressed by Equation II-liS with respect to diameter
d, setting the resultant expression to zero. and solving for d gives the optimum pipe diameter, d",pl in inches, as follows:
d". _ [1.32q2 ~po,SlJl.0-leC~(1
+
L,p)H~ll r~ M· n.
n(1 + Rp)CpEC Fp
(11-116)
The value of n for steel pipes is about 1.0 for d < 1 in ., and about 1.5 for
d ~ 1 in. Thus, for the commonly used greater than I-in. diameter pipes,
Equation 11-1l6 becomes (Peters and Timmerhaus, 1980):
~ _ qOH8p O1321J0025 [O.88Ce(l + L,p)HJIIS8
(11-117)
(1 + Rp)CpECpp J
Piping System
For most t)1>eS of pipe, the purchase cost per foot of pipe is related to the
pipe diameter as follows:
(11-113)
where Cp,pe _ purchase cost of new pipe of diameter d inches per foot of
pipe length, .$ 'ft
C p _ a constant equal to the purchase price per foot for a I-in.
diameter pipe, $Ift
d - pipe diameter, in.
The annual cost for an installed piping system can be expressed as (Peters
and Timmerhaus, 1980):
( 11 -114)
. An interesting fact to notice about Equation ll-lli is that the optimum
pipe diameter is relatively insensitive to most of the parameters involved.
Equation II-IIi can be simplified by assuming typical numeric values for
the terms involved. Using C e = $O.055/kWh, L,p - 0.35, H) _ 8,760 hr.;!
year, Rp - 104. C p - $0.45/ft for I-in. diameter pipe, E = 0.50,
C Fp - 0.20, and neglecting the viscosity term which is close to unity for
most cases for the small exponent involved, Peters and Timmerhaus (1980)
present the following equation for optimum pipe diameter:
d _
0.0039q0~5pO,1J
__ 0.OO22mo45lpo,31
(II-liB)
where m - mass now rate, Ibm/h r
p - £Iuid density, lbm/ftl
This equation is quite good for short pipelengths and where the pressure
drop in the pipelength is not large.
•
Ga! Production Engineering
Gas Gathering and Transport
581
Analysis Including Cost of Capital and Corporate Taxes
Gas Transmission Economics
In the previous analysis, a number of important factors were neglected,
such as the time value of money, corporate taxes, costs of compressors, and
the cost of capital (or return on investment). Including these factors and using a more accurate expression for the friction loss due to pipe fittings and
bends, Peters and Timmerhaus (1980) present the following equation:
It is relatively easier to estimate the economically optimal dimensions and
operating conditions for a Single pipeline. A complete transmission system or
grid, as described earlier, includes several producing wells, storage wells,
and a vast network of pipelines of different dimensions and requirements.
Designing such a transmission system to match the requirements is difficult
enough; economics introduces even more complexity.
The quantitative analysti described in the previous section assumes that
the gas throughput. m or q. is known. In dealing with natural resources
such as gas, one soon realizes that throughput is not easy to specify. Some
important factors, besides the ones discussed earlier, that playa role in determining the design capacity and size of a gas transmission system are:
d~pt' .. n
'1-;-+.,;O~.;""94"L-,,"d..,.-1.046 x
where
+ (l - t.)[l + (ioc + imc)MJ]
n(1 + Rp)Cp[i· + (1 - t,)(io p + i",p))Ep2
1O-IOH)C.,m2M,...016[~W
(11-119)
~t
- optimum economic inside pipe diameter. in.
m - mass flow rate, Ibm' hr
Lf<j ., frictional lass due to fittin~ and bends expressed as equivalent pipe length in pipe diameters per unit length of pipe
(L" - L,,Jd..,.)
M - ratio of total compressor installation cost to yearly cost of
compression power required
i· .. rate of return (or cost of capital before taxes) on incremental
investment, fraction
t, ., taxation rate, fraction
i.lp .. depreciation rate for the installed piping system, fraction
ioc .. depreciation rate for the compression equipment, fraction
imp - fraction of initial cost of installed piping system for annual
maintenance
imc .. fraction of initial cost of compression installation for annual
maintenance
p .. gas density, Ibm/fil
All other terms have similar meaning as before.
Thus. for a given throughput, we can compute the optimum pipeline diameter using the relationships given here. But the pipeline chosen may ha\'e
optimum behavior at some other throughput (that is, it may be able to handle a different throughput more economically). This is an interesting point
to note about pipelines: a pipe1ine's optimum throughput is not the same as
the throughput for which it has the most economic diameter.
1. Available supply of gas: the amount (reserves), current production
rate, growth rate in supply due to field development activities and/or
new discoveries.
2. Rate or growth in gas demand. The economics of the variation in pipeline capacity factors· has to be evaluated.
3. Availability of capital.
4. Technical problems or feasibility of transmission line construction,
such as difficulties in increasing line capacity by installing a second
pipeline.
Supply and demand projections are made using complex computer mod-
els that aerount for the vast number of factors that influence such predictions. The supply model involves reservoir modelling for production rrom
known reserves, geologic information for predicting the growth of these reserves, and field development plans. The demand model is even more complex. It deals with global (or local, as the case may be) economic growth,
expected energy consumption. energy consumption patterns (share of gas as
an energy source), price of gas and its effect on gas production and use, etc.
It is thus clear that supply and demand predictions are rarely accurate; some
commonsense analysis may often prove more reliable.
Availability of capital is usually not a serious constraint, but may preclude overambitious, ultra-large projects. Technical problems may be too
overwhelming in some cases, resulting in alternative feasible designs that
may not be optimum. It is easy to imagine how several other factors may
also become important in a given situation.
• Capacity factor l~ the ratio of the actual a"eragl:! discharge to the design capacity.
•
582
Cas Production Engineering
Gas Gathering and Transport
The two major features of a transmission system that is operating in an
optimum manner are high load and capacity factors··. and assured, uninterrupted gas supply throughout the range of the demand cycle. A high capacity factor will be obtained if the demand (and supply) is close to design
capacit}'. The load factor can be increased by using underground gas storage, by using some type of gas reserve such as high-pressure gas storage to
ensure an excess supply during peak demand. or by using the pipeline as a
buffer stora~e facility. An uninterrupted gas supply to meet varj;n~ demand
is ensured by considering two factors: availability, defined as the fraction of
the total time that an uninterrupted supply is achieved, and reserve factor,
which accounts for gas reserves provided in the form of additional parallel
lines. underground storage. pipeline buffer capacity. or other standby sup+
ply systems. Higher the availability, lower is the reserve factor required.
Solve this expression for the case where: gas gravity - 0.81, gas inlet
pressure in the sytem - 950 psig, input gas flow rate = 4 MMscfd,
and flowing temperature _ 78°F.
5. An 8,OOO-ft we11 is equipped with a 3-in. tubing. What minimum size
of surface flowline would be required to enable gas production at a
rate of 1 MMscfd, with a guaranteed pressure of at least 100 psia at the
separator? Use the following data: 1'11: - 0.6. bottom-hole pressure - 2.()(X) psia. bottom-hole temperature = 250°F, surface temperature - 82°F,
Can this surface flo\\.. line diameter be considered economic?
6. Write a computer program to solve Equation 11+48 for loopless pipeline systems. Use this program to solve for steady-state flow for a simple pipeline system.
Questions and Problems
References
1. Derive the coefficients indicated in Table 11-1.
2. A 7-in. ID pipeline transports a 0.68 gravity gas from a distance of 22
miles to a liquefaction plant in Saudi Arabia. The first 10 miles of the
pipelinp is looped with a 4-in. line, the next 5 miles is looped with a 3in. line, and the last 7 miles is a single unlooped line. The inlet and
outlet pressures for the system are 530 psia and 130 psia. respectively.
The flowing temperature is 95°F, Calculate the gas flow rate using at
least two £low relationships.
3. Two lines AC (5--in. lD, 4.5 miles long) and BC (5--in. ID. 3.8 miles
long). emanating from leases A and B, respective1y, terminate at tht,
gathering station at C. From C, a single 11.5-mile, 8-in. ID pipeline
leads into the regional trunk line at D. where the gas must be delivered
at 520 psig. Lease A produces 5 MMscfd of 0.65 gravity gas, while
lease B produces 7 MMscfd of 0.68 gravity gas. To what pressure
should the gas be compressed at (a) lease A, and (b) lease B. to enable
delivery of gas to the trunk line? Assume f - 0.008, ambient and flowing temperature of 85°F, and a perfectly horizontal flow system.
4. A 5-mUe long, 8-in. 10 pipeline is at an average inclination of 30
from the horizontal, with uphill flow. At a distance of 2 miles from the
inlet, it branches out into another 4-mile, 4+in. ID line. Derive a relationship to express the flow rate in the 4+in. line in terms of the £10\\
rate in the 8-in. line.
e
•• Load factor is the ratio of the 8"erage rate 10 Ihe muimum houri), rale of flo,",
583
Ariz, K. and Settari, A., 1979. Petroleum Reservoir Simulation. Elsevier Ap.
plied Science Publishers Ltd., England, 476pp.
Batey, E. H., Courts, H. R., and Hannah, K. w., 1961. "Dynamic Approach to Cas-Pipeline Analysis," Oil l,- Gas 1.,59(51, Dec. 18),65-78.
Campbell, J. M., 1984. Cas Conditionillg and Processing, Vol. 2. Campbell
Petroleum Series, Norman, Oklahoma, 398pp.
Cross, H., 1936. "Analysis of Flow in !\'etworks of Conduits or Conductors,"
Bulletin oj the Univ. oj Illinois, 286.
Distefano, C. P., 1970. "P1PETRAN, Version IV, A Digital Computer Program for the Simulation of Cas Pipeline Network Dynamics;' Cat. No.
L20000, March.
Coacher, P. S., 1969. "Steady and Transient Analysis of Cas Flows in Networks," paper CC157 presented at the Research Meet. of lost . of Cas
Engrs. , London.
Cuy, J. J., 1967. "Computation of Unsteady Cas Flow in Pipe Net\I.'orks,"
paper presented at the Inst. of Chern. Engrs., Midlands Branch ConL, U.
Nottingham, April 14.
Hain, H. A., 1968. " How to Determine the Maximum Capability of a Complex Pipeline System," Pipe Line News, 9.
lz~wa:, H. S., 1966. "How to Calculate Cas Volume in Blowdown and Purg109, Oil & Cas 1.,64(19, May 9), 118-123.
Peters, M. S. and Timmerhaus. K. D., 1980. Plant Design and Economics
JOT Chemical Ellgineers, 3rd ed. McCraw-Hili Book Co., New York, N, Y..
973pp .
or
,
584
GaJ Production Engineering
Rachford, H. H., Jr. and Dupont, T., 1974. "A Fast. Highly Accurate Means
of Modeling Transient Flow in Gas Pipeline Systems by Variational MethoW," Soc. Pel. Eng. f., 14(2, April), 165-178.
Stewart, T. L., 1971. "Computer Speeds Surge Calculations;' Oil & Gas J.,
69(47, Nov 22), 55-60.
Stoner, M. A.. 1969. "Steady-State Analysis of Cas Production, Transmission and Distribution Systems," paper SPE 2554 presented at the SPE 44th
Ann. Fall Meet .. Denver. Colorado. Sept. 28-0ct. 1.
Stoner, M. A., 1972. "Sensitivity Analysis Applied to a Steady-State Model
of Natural Cas Transportation Systems," Soc. Pet. Eng. J., 12(2, April).
APPENDIX A
General Data and Unit
Conversion Factors
115-125.
Streeter, V. L. and Wylie, E. B., 1970. "Natural Cas Pipeline Transients,"
Soc. Pet. Eng. J't 10(4, Dec.), 357-364.
Szilas, A. P., 1975. Production and Transport oj Oil and Gas. Developments
in Petroleum Science, 3, Elsevier Scientific Pub!. Co., Amsterdaal.
630pp.
Taylor, T. D., Wood, N. E., and Powers. J. E., 1962. "A Computer Simulation of Cas Flow in Long Pipelines;' Soc. Pet. Eng. J.• 2(4, Dec.), 297302.
Tuppeck, F. and Kirsche, H., 1962. "Ein Numerisches Verfahren zur Berechnung Instationarei Stromungs\,organge in Ferngasleitungen," Dos Cas
Und WasserJach, 103(21, June}, 523-528.
Wylie, E. B., Stoner, M. A., and Streeter, V. L., 197 1. "'Network System
Transient Calculations by Implicit Methods," Soc. Pet. Eng. J., 11(4.
Appendix A·1
Some Useful Physical Constants
Absolute zero temperature
Avogadro's number
Gas constant (R)
Dec.),356-362.
Density of dry air
(at 60°F, I atmj
Density of dry air
(at O°C. I atm)
Velocity of sound In dry air
(at O°C, I alm)
Acceleration due 10 gravity (g)
0.0'
- 273.15'
0.0'
- 459.Si·
6.022 169 E + 23
0.082057477
0.084 784
1.987
8.3145
1.9859
1545.3
10.732
0.730 24
0.001 223 2
0.076362
0.001 293
0.080 719
33.136
1,089
9.806 65
"'.665
Dimensional constant (g.)
•
•
• Indicates that tM
num~
In uni ts ot
Magnitude
Quantity
3217405
1.0'
10'
32.17405
22"1'
3.141 593
2.718282
,,""act
.85
"R
C
F
mole
(atm Iiter)/(gmmole K)
(kg/cmlliter)/(gmmole K)
(gm cal)l(gmmole K)
Joulesi(gmmole OR)
Btu'(lbmole OR)
(ft Ibf)/(Ibmole OR)
(psi ft"')/(Ibmole 'R)
(aim ftl)/(lbmole R)
gm/cml
Ibm/hl
gmlcml
Ibm'ft'
cm'sec
ft'5('C
m"'"
cm"~
ft . . ~
(kgm)I(N~
(gm cm)l(drne ~
(Ibm ft)I(lbf sec')
dimeruionless
dimensionless
dimemionle5lii
•
586
Gas Production Engineering
Appendix A
Appendix A-2'
General Data for Natural Gas Constituents
Appendix A·2 Continued
General Data for Natural Gas Constituents
~n,11y
Compound
~
,
,•
I
;
....
~...,.
0<.
"
C,H.
,~.
P'OfW'~
'.041
Xl0711
"'097
-}S8119 (SOXII
127.<18 1Il001
,.lU
1900
.
-~~
-297 ""
C,H"
12 lSI
1.~\f'hyTpent.~r
86 111
86.175
J.."V'hllpen'.~
N~ .. ~
4'1 .•
116178
"S19
c.H ..
116.178
111 52
2. }'()',.,...,h\'lbu II""
CoIl"
86.171
1)6.]6
209.17
1901 ,0'9
n-"'ep .. ~
(,H .. 100205
l-MeIIlyIM .......
C,tl" 100 205
)·Melh~·lhe'.~e
CH" 100.205
}.UhVTpenl."t
C.H" 100 lOS
2,1·00_,n,'po-n,.ne C.H., 100 205
2.4-0, mel h~ 'po! nl. nt C.H" IIl0.205
J.l-Oune\hrlp<!nl~t C.H,. 100 20S
'
...-
C ...... 100 205
,HXlOne
CoH" l1'2Jl
Col'" 114 111
CoH" 114211
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tsooe'."e
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(table contilluetl)
•
588
Appendix A
Ca.t Production Engineering
Appendix A·2 Continued
General Data for Natural Gas Constituents
Appendix A·2 Continued
General Data for Natural Gas Constituents
Den~n'l
c..·l-"'~
,'''',_
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(table continued)
\
I.
Coos Production
590
Appeudix A
En~in(,l',jllg
591
Appendi x A·2 Continued
General Data for Natural Gas Constituents
Appendix A-2 Continued
General Data for Natural Gas Constituents
CilO"hc: .. alue. 6O"f
AST\\
OC1~ne
Number
~
Compound
:
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•
Appendix A·3
An Overview of the SI System of Units
H,l
'00
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no
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ill
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974
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10 '8
15
10
12
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00'
00'
00'
00'
00
...
Svmbol
,
peta
tera
T
gigs
G
mega
,
P
M
10-'
10- 2
k.ilo
heCla
deka
deci
centi
10- 3
milli
10- 8
micro
,
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"p
1 0· t
10- 12
",no
1 0- 1S
femta
10- 11
.tto
h
"
,d
m
•
(table cQntinucd)
592
Gas Production Engineering
Appendix A
Appendix A·3 Continued
An Overview 01 the SI System of Units
51
a.. s.
Appendix A·4
An Overview of the Commonly Used OIl·Fleld Units
Quan t It i es " nd Uni t s
au.nu~
SI unll
~bol
lenglh
mISs
meter
m
kilogram
tim.
second
,kg
lemperature
emount of substance
kelvin
K
mole
mol
The two other bUill SI un'l$ are
ampere
for electric current. ancl
candela
QUlntity
Unit
Symbol
~ivalent
length
Inch
f OOt
yard
mile
h
yd
'"
12 In
m'
'"
Volum e
lor luminous Intensity
squ.re (sq) fOOt
sq yard
h'
.cre
Icre
sq mile
mi 2
plnl(U 5.)
quart(U.S.)
9allon(U 51
""
",
cubiC Icu ) foot
h'
barrel(U 5)
bbl
Sam. Commo n 51 Derived Uni t s Use d In G,u En gine. ring
ICceleration
"1;1
meter pe r second squired
squire meIer
density
kilogram per cubic meter
acre- f oot
Time
energy, work.
qu.nlitv of h,.t
joule
entropy
joule per kelVin
force
newton
Irequlncy
power
pressure
J
Nm
N
kg rnls 2
H,
11,
W
JI,
J/K
p,
specIfic heat
thetmel conductivity
velOCity
joule per ki l ogram kelvin
Witt per me Ier kelvin
meltr per second
viSCOSity, dynamic
IIlsCOsit y. kinamatlc
volume
pucal second
square meIer per second
Cubic meter
593
Velocity
N/m2
second
minute
hour
yd'
acre -ft
,
m,"
d.,
"'d
ye,f
Y'
feet par second
hI.
feel per mln\.ue
millS per hour
ft/mln
mph
cu
fillS
J/(tg K)
W/!m K)
ml,
p"
m 2/s
m'
Flow rau
(IIOIUme tr iC)
faet pe f sacond
gallons pef hour
b.rrels per day
to
5280 It
144 1n 2
9 h'
43560 ,,2
4840 Vel 2
640 acres
27.878.400 ,,2
2"
4 q'
01336806 ttl
1728 in l
7.480 520 gal
5614584 ttl
4 2 g al
43560 ftl
'0.
3600 s
24 hr
1440 min Of 86,400 s
36525 d
(1150 takan as 365 d)
60 fUmin
06818182 mph
60 ft/s
1466 667 hIs
88 hlmln
3600 fl 3/hr
26929872 gph
15388.495 bpd
gal/hr (gph) 3.713 34 £-05 "l/s
bbl/d (bpd) 6498 36 £-05 fillS
(table continued I
•
59.
AJlIJrndix A
GO\ ProJrlcticm Ellgillt'erilli!,
Appendix A·S
" Memory Jogger" for Metric Units
Appendix A-4 Continued
An Overview of the Commonly Used OIl·Field Units
MISI
gr,In
gl,m
ounce (.v)
ounce (Irov)
0'
0'
pounds (mus)
Ibm
ton f"hnr'fl
'0"
ton (long)
Density
liquids
Fore.
Pressure
pounds per tu Inch
pounds per tu foot
pounds per gallon
API gravity
'M
Ibm/in l
Ibmtrt J
Ibm/gal
°API
480 gtains
.,"
{ '000
16 oz (11111')
2000 Ibm
2240 Ibm
barrel
Bulish IherlT'al uo,1
Bntish thermal uM per pound·mass
{ 2300
o 133 660
6 Ibm/g.1
] 480 520 Ibm/It]
141 S/(specll,c 9ravltv)
- 1315
pdl
Ibl
0031 081 Ibl
3217405 pdls
pOunds per sq Inch
Iblfin z
144 Iblilt 2
pounds per sq loot
Ibflft z
0068 045 7 IUm
Viseosity
(dynamic)
46330632 Ibm/lft-s)
32174 05 Ibm/{M-sl
2.15839 £-04 Ibm/(ft-s)
Viscosity
(kinematic)
.q 1001 per second
.q inch pllr second
ftI/s
,.4 in 2/S)
6944444 E-03 in 1/s)
Temperature
absolute. de9rees Rankine
degrees FahrenheIt
",
Ener"". work
foot-pound (Iorca)
Blltlsh thermal unIt
horsepower-hour
therm
quad
ft-Ibl
hp-hr
therm
quad
7781692 ft-Ibl
1 98 E ·06 ft-Jbf
'.0 e.05 Btu
1.0 e.,o therm
horsepower
hp
550 It-Ibl/s
Btu/min
]3.000 ft-Ibl/mill
42 407 Btu/mIn
778.169 2 ft-lb1lmln
Power
Btu par minute
/s
"R
""
'000
OF. 45967
°R-45967
•,.,.
,
05
,.
calorie
centipoise
centlstokes
darey
degree Fahrenheil (Iemperalure difference)
dyne per cenllmeler
'001
cubic 1001 (cu tt)
cubic 1001 per pound-mass 1t1"lbm)
square 1001 (sq tt)
loot per minule
0.006 944 Ibfllnz
pounds-second per sq inch Ibl-sJin2
pounds-second per sq loot Ibf-slft 1
pounds (mass) per ft-s
Ibm/ft-s
In
square meters
hectare
0.16 ctJblc meIer
04
23
poundal
pound lorca
2
'BaIlParlt" Metric Values;
(Do Not Use As
COflverSlOfl Factors)
Customary Unit
4375 g"ms
595
loot-pound-Iorce
lool-pound-Iorce pel mlnule
lool-pound-'Ofce per second
holsepowef
horsepower, boiler
"'"
IuIowatthour
mile
ounce (avolldupols)
ounce (fluid)
pound-force
POUnd-force per squale Inch tPfessure, psi)
pound-mass
pound-mass per cubIC 100\
section
ton. long (2240 pounds-mass)
Ion. melllC (Ionne)
Ion. short
{
{
lou!es
joules per kilogram
klloJoules per kilogram
JOules
mrilipascal-second
square millimeter per sacond
square mlCromeler
kelvin
mlliinewton per meIer
cenllmelers
30
03 meIer
0.03 cubiC meter
006 cubic meIer per kilogram
0' square meIer
03 meier per minute
millimelers per second
5
)Oules
0,02 wan
waUs
wans (~.:. kilowatt)
750
10
kilowatts
25 centImeters
3.6' rnegaJoules
IS
kilometers
grams
28
cubic C1tnlJmelers
30
newtons
kliopascals
7
05 kilogram
kilograms per cubic meIer
hectares
260
26 million square melers
26 square kllomelefS
kilograms
'000
kilograms
'000'
kIlograms
900
,..
"
"
{ "
'U.a lqUnoal_
• (From Tluo 51 Metric Sy., ..m of l'"lu t)nd SPI;; Metric Sltmdord. 1984, CQlJrtesy of Sod!>ty of P.. ,r,,/...,'"
Eng;"........ Richardoon. 1~n~, I
•
596
Gas Prod'lelio/! Engilleering
---.......
597
Appendix A·6
Alphabetical List of Units (all Field to 51 Units Conversions)
T9~Ffl!'!'
......"
_.........
---...
..._'m')
""
_,m')
r.+.!!II(/IyB ..'
£.01
£+01
.<
.<
".
".
".
".
".
"'"
".
".
".
-,~
-....o(S)
_(fl)
(U $ .......-vI'"
ICI'.(U$_I'"
lO'e b:lt
..
4~'J'3
""-Ic)
••
........ (""1
-I"')
....'.. '1111
puctI (PI)
I>UC"I (p.)
pascal (pal
...-I .... 1m')
~.(~
~.(~
• 1
~gl'='l
MIl" (lot ~1toINn, 42 ~
BM!,oI'I"'.,m.'_(II'It~)
1Int,1II ",.,mtl_IWF)
6otllllo ",.,mll ..... IWF)
I""""" COIIOUCIMIyI
a...( ...... ~.I\.(I'ofIl''Fj
(...... mtI~1
-,.
1IIu1~)'''1'''1I''f1
l ...... mtI~)
IIIu I~ ' _ I.... ·l'II'·'Fj
llIItrmli ~I
..
jOule (J)
10!.9 '1
t 0!.4 68
1 730 715
,.~
.....n per _
1121511
,.~
81u1~'.
IlluI~T"')1I'
1 "'41314 [-01
81u 1_',0iU--""1I'
81u 1... "OiU>WroU!VllI'".,)
81u 11I'lefmott'....ot.HIl'-.)
... 1.... _ _ .r)Itor'I·_.)
81u 1 - " ' _ TtOIto).1rw--II'-'f}
f1r*""'-..;!_)
9IJ 1"'~"',I!'.'fl
(....... - 1
8Iu 1.......... _ l .... j.1.II','fl
IIIu (...... _ _ tII)Il.II'-'f1
5 112 2001
E.~
S lee 132 e.~
2i30711 E-O'
2 t2tI 151 f-O'
1151250 e.o,
"'''''' ""
jcuIIt 1* ......,. (JIm')
JOUIt 1* ........ 1..I;m')
..lIt flotl ........ CWm')
..on per ........ (W'm')
..., per ",.,... (W m')
...n _",., ... (W'm')
"'1-_1-'111'''''1
_-......
1 442219 [-01
k-. rw I.... K)I
(W (....1<))
1135~
,.~
1 ,,. 1S13
3 '~4&1
,.~
,.,"
,.~
,.~
I 134 1S13 E'~
2~5
,."
5618 2e3
,.~
1 &34
per ",.,... ktlwl (W ("""1())
per ",.,... ktlwl (W1"""1Q)
.......III,"a per....,'"
ktlwl (W 1m'1<l]
per",.,.,. k....... (W (m'I<I)
...n
581~*
21lo114115
20421!101
E.~
E·~
,.~
.. _ _
... u .',_ .. _ _ _ _ _ _ _ _ .. ,_ . _ _ _ _ .... _
. . . , ....... _
..... _. ____ .. __ ....,., ...... '.. m.__ ,... _ .. _____
..... _ ...
_............ _--_ ..
~_,..,
-
__ ,_...........--
..... _ _ . _ ... _ _ ...... _
.. _ _ _ _ _ .......... _
......... _
. . U l _ ' _ _ ...... _
(I'.
,.... ."..,_ ....... _ ",, ___ .. VS ........ _ ........... u l _ ...._
.. '" _ _ .. _ .. _ _ ......
... " _ ..... _ - . .. _ _ ... _ _ .... _ , ,. _ .... U ......... _ , _ _ ... _ _ _
.." " _ .... _
.. , ... _
... -,_·._t.·_
..,_
,_.,
t. _
,n. .... _ _ .' .... HlU'( ...
• (From TM SI Mdric S!fIt('71O oj t'"Ie....J SPE Merric Sr..nd..rd. 198-4. COIIrtl'$)' of S«ktv oj hrrcHf"t""
E.n$!in«Tf. Rlchlrdton. Te.u.)
CllDriet_1
....... (I5"C)
....... (lIiIogr .... - - . . . T....)
caIoIIe (loIogr .... _ 1
........ (ltiIogI'1n\. .... " ........-..')
CIII (.... "'od,..nicaljlem'
cool tlnl_IIOIWITIICIt~'g
cool t_"iOChemic;I/)Ig
cool (lnlemalionej Tabie~(g·"C)
cool (IhtoOIoochtmocllll(g'"C)
...
pM 1* '*9.... ~1IMn ~I
pM_"*'9<.... _...... I.lt(~1
4 llot 000
_'m')
......
....
..,.
......
....
....
......,,
....
_t'")
~("""""""T"")
pM!J)
..
joule PI< ........ (Jim')
pM per 1009'.... (.II"g)
jotM per 1dIogr.." IJllcg)
lOt'"' IIe/ klIDgr..,,".,..,., (J.(Kg'K)(
~ per klIDgrern k _ (JllkgI())
...nlWl
(~~".,
'11168'
350231101
Z.SoI'
.1."
'19002
"14'
4115 . .
4'8190
4 1.1"
4111002
4114"
4.1 84'
...~ (W)
...., IIe/ melt<' (Wlm')
"'(_OI",,", ... ,oI<tI~Icm'-s)
( .I Ilo11·
e.IIPftIr1IlriI(t_II.• 10 'em-')
...., per ....!tt"(wm')
..1ft per _ _ rw;(m-Kl)
per_(m-')
.,...t: ("*"<)
-......
1oIogt.." (kg)
2.0'
1.33322
UII06 :JB
city 1 - ""'1
city
MOIlI'd lsi
MOIlI'd Is)
,,_')1(..........)
"'1_OI~ ,lictI).1aT11··C)
_ _ al .. _We)
........
-...
.....
dtgNeF. ._
--,
..............
---
dtgNeF...........
"~
I~
Tabie)
1........- 1
EMU oI~
EMUalcun...,
EMU aI Netrie pa/"EMU oIlncIuctanot
ESU d _
ESU aI CU'r ....
ESU aI eItctnc poItr'IWtI
ESUol~
ESUal....unoo
,,~
,.~
,,~
E·"
E·"
,."
,."
, .,
,."
,.~
.
41M'
•.<
,.~
,.~
E-Ol
E·~
....
E."
E.Ol
,."
.r
.8
.......
,."'''''
1745321l
,.~
,.~
,.~
,.~
-11<)
r • • r"," 21315
-""'-
r", - Ir. - 32)11'
r • • IT~ ••Si57)11 .5
T•• ',/1.
....
,~
ktHln il()
'fiY'I!','8!u Ilhtornoc:l'>tn'liea
,.~
QIvIn mettr" fIotI ...... (lI<-m')IW]
. . . . 1·-.1}
_ _ '*"'11'_ (_ "... c:.-..I
,.~
5.051gn E-l0
2.003112 E-Ol
2.366 8&2 ,.~
E,,'0
_IHI)
('"'*""
oMgrM (qlil
,.~
•. <
•. <
-''''
-~-
,.~
puCoII.-.d (1""1
. . - - fIotI NCOnd (m',s)
_'m')
_'m')
-~
"Ftor.ft'o9Iu
PI"'" 11'.)
I>MCIoI If'.)
,."
4UIIS'
E+03
.'M'
41868'
4.1M·
6113333 ,.~
,.~
41M'
U13333 ,.~
"'I~)/I
... 1....
""'"-
' ... ·IO'••
.. ... _ _ , _ _ ... _ ' _ ... I ...
DUSI'IIII(\I.S.)
_ _ aI mtteUIY IO'CI
wan per mel., k-' rw 1.... 1<))
....-..,..,..,
-..,
81u~T_."
81u t. ." .... ..-ouo'IW
81u 1_"OiU*""-II)1'I'IIn
[ '03
.....n per mel ... kelYln rw'(m-Kl)
...., 1*""'" _
Ilhtomtl~1
...,
,.~
H.
,..,
,."
"" , ,."
wall 1* met...- . (W (m«))
9IJ 1.... ~ .... 1.-1I'-'fl
_--,.....,
~~'F)
...... 8Y ..
,."
''''.
232.·U
,""
."
jOoMl* ......... (.l'kg)
pM 1* Wogr_ (J.'I<g1
T_~(_'F)
'*'"- (2O"C,
)O'JIt (..I)
...., per _
",jWwoji~
1G13~E.05
',OM 350
k _ [W'lm'I<))
8Iu ~ r_VI>toI
... (_ _
<=*ill (l.i'iOChM'oeaI)
oe.o
I<"M (J)
JOUIt (J)
T_I ..... 1"'-11'·'1'}
INtmtI~)
,."
,..,
,."
15811'13 £-01
2 JSi 131
1 0!.5
E."
, 0!.5 81 E • .,
JOUIt (Jl
BooIllIlltlm., ..... leI:ff)
BIll (lnt...... ~ lllClt)·"'II'ofIl'·'Fj
E"
E."
H.
E· ..
"
To (:or-. From
E .02
E·l0
H'Sert E+lI
".
".
mel'" 1m')
Bti\loI'I ..., ....... , ~ (In!et<1alQ'lll T.t>I.)""
6o~,"" "'.,m.' """ (mean)
,."
• 1108 850' E. 04
_,m')
W
Btu rlttt .. _
"
~'N
""-ICI
\ar.., IF)
Appendix A·6 Continued
Alphabetical List of Units (011 Field to 51 Units Conversions)
IotMn mtItf' 1*"'" UII-m').W)
1.711102 E-Ol
_"'""'",., ... per ... ft l(K-m'YW!
1oIogt.." per _
(kg!m)
1.7$2 250 E-O'
1.111 II I E-01
_IN)
.8
.8
pUCtllf'.)
1,0'
".,..IJ)
1.602 IV
1.0'
1.0'
_",.,.. rN....)
rtttdlF'l
..... 1"')
"'M
'*""Y lMI
"""'III)
!lttd IF)
... ""
~.I"'I
-~,
""'" III)
.8
1.0'
1.0'
,.~
E-01
E-Ol
E- ,g
E.~
E·Ol
E·"
,.~
,.~
, 112 &SO E_12
E-l0
3.3355
,."
2991V
'9111155<1 E. 11
'.911115501 e ~ 11
(table continued)
•
598
.....
To COf!!!I! F¥"
..-'"""
....,.,
.... I * _ _ (W'm')
_Iq
_Iq
,....,.'~111'...-'2'1
...
"""_IU$)
M'
....
1!"~
'* _
---..................
fMler _ oecond 'tnI$l
....Ier _ oecond ("",.j
IMler PI<"""" (mi.)
fMI .. PI< oeconcI' ("... '1
-"11>.1
CMdN 1* met... (C<),II'I')
."
jouII {JI
_. ""
"",.
...nfW)
.nlWl
11·"',,_
mew 1* I«»IIIl' (mit')
_
PI<.,..;o:wI' I"n,)
....... ..-.,,10'1
-,
-,.,
_,m')
_,m')
gIIonl~1oQo,od)
-I.,
geIcin IU It 11Ipj)
~IUS
,....'.)
....1... (""1
cI ,",,*,"j'.
dryl
........ _ _ (m'.)
. . - ' _ _ Im',")
IU 5 fIrpIl
gII(US Ii_n~
"" (U,S Iop;If....
gIII(USIop;I~
_ _ _ jDI<II lm'iJ)
_ _ _ _ tAml
tSFC. specoIicUol_I
v-r"'I ,....- fiiIIoI ......1
o-r-- t....- ... .-....yJ
....
-...
--""
.-....-..
_.
._---_.,
__._-_._
........-. -_.__m
_m
_,m')
..... ,m')
..... ~I
gil IU It)
,,(U,S.,
.U IWl
_1Wl
_1Wl
_1Wl
-""""
'"""-- 1".Nf)
~(UK)
hourI ..........)
Nu"1_1
.
........
,
."'. ,."
,,."
."
,.,.""
,."
,."
,·ro
....... ,."
,·ro
,·ro
,."
,-"
"'''' ,."
,."
,
• 41161167
E-Ol
30<1.·
E~OI
30<18·
E -01
1016:J111 E .01
34282'511
1,)Sstl,
,.~
37M
'"
22'511697
1 l~'"
421·0"
980& 650" E ~ DO
,.
4 ~'OIO
4~092
·,.
3185412
431!11284
14100M
7 ~7 741
7157747
1420 5501
1,182941
...
,...
,.~
E~OI
,.~
,.,.roro
".
".
e eoe 650· E. 01
-,m')
ho!H\lO'I'I''' (550 ~·IbIIlo)
l'IotHpower I~)
\IotMI>O'Wer 1-';)
ho!_I_)
...
1290:JO.t- £-02
2131 &liS E -02
• 71,.,.
2131 &115 E -02
.630875 E~OJ
Idiogr_ PI< ....... (kWm')
Idiogrom (l<g)
Idiogrom 1* ....... (kvIm'l
~'P.I
",-",,".~~~
"' ..... ~c;m'
e-O!I
••
~I
(U,S IquldJ
2~&40'
,_(,Id)
.,... 1.......)
",loin (11'7tIOO Ibm
,~
,2903(1" E-02
.........1*_(.... ,.)
,.,..... (m')
meier'
....Ier' PI< _
, .... '.)
N ft I......... MebOn /IIOOUIUI)
E-
~
....... 1 * - 1....".1
••
..
...
,-"
-,m')
roo. 01 .,.IM Ill! 2'F)
...,,' ,,,.........
r.;7 3!03
~(p.)
II'..... ( -..... ~)
,E-01
·ro
E-01
", ,."
z".
,,.... ,."
E -0'
E-O.
,.ro
....... (m)
- 1m )
IocJIIUS~
".
".
".
Toc-lFtQm
8C
• &oIUT
_1m)
_ 1m )
...... (*'*"-1
fl!y!!F!!J
• &Sa .,
~(Cl
'*..,.,.~)
--..........
"
IICIDf"d (I)
-(II
E-OI
1 SI'019I E-Ol
14711H1I" E-OS
1111 eoe E-Ol
·
,.~
10'
74S11 8VII E. 02
,."
"''' ,,."
."
,."
,."
,."
'460·
1354"
7 460.3
7 457 0
'''''
3
~eo
..
11'0
599
Appendix A·6 Continued
Alphabetical List of Unit. (011 Field to 51 Units Conversions)
Appendix A-6 Continued
Alphabetical List of Units (Oil Field to 51 Units Conversions)
----
'*'"
Appendix A
Ga$ Production EFlgim'erilig
,.ro
--""
tvO~(~l
!oUdtSy"
"
kIIog< .... fOol
1UICtt_.... flonQI
pUUlIP.,
rdI III rnIfCUIY 1l2"F)
rdI III .-cury lWf')
" " aI ..._ (J'J.rFJ
I'IdI aI ....al.. \6O'F)
~IP.)
cuiIL(....--. MCIICn~) ..
-,"
-,,,
iIL'~aI_r"
-I""')
,",'
...-.. "' - " " 1m")
...
....
~,~T
IIiIocaIDM
~
(m".)
....... 1* _
_Plt.-.:lI"'I)
..".
__)
'IlherTrocI>tmocall
me...)
Ii;Ioc8Iori4I llI\em>OCIIerr'I.I)'"..,
--
~ (ltMo"oocn.o,iO;.Il~'1
1dIogf..... ~,1Igf)
..m
kV""!m (maa)
...:::::...
...
249082
paulIP-)
a_
E.O •
,."
"",. ,,.ro
.ro
,-, ,,,."
."
"s.,"
,_ roo ,."
,."
331!as
1IMQI1P.)
M"
E+Ol
.~t2.
>M'
_1"'1
""
,_m
......
"",.
1 ",lMlerl''''')
"""",,",
joule (J)
...n fW)
...n fW)
~I~
.....- .... Ierl~...,)
1dIog'.... llo,gl
plIC;Ij IPI)
palCel(PII
PIIICeI(PI)
_ _ _ (oM)
2731117 E-01
• 162 31' E-07
2!i<1'
£-02
W
".
E.02
' .. _ r. - 273,IS
4,186'·
4,19002
411W
6973)33 E~OI
411W
98O&6S·
9110665·
911066S·
9110665·
980&65·
9_80& 65·
2771718 E-OI
,·ro
,."
,."
,."
,."
,."
,."
,
,."
...
....
---- ......
......
--.............
...
.
..
.........__ _--_ _ __ _-_.--_ -1oIow_ _
IoIpllOOOItJ/j
1dp1n.' (Qi)
~
....)
......
~I~
,.. ,."
,.,.
,·ro
c.MCltllPI<"-- 1"""11'1')
II.·
'1108 M-
"...,...,(N)
_I.
pueeI
__
(PI) _ I.... )
'*"""'''
1",,"'11'1')
jlUlPI< """'" IJom'I
_,,,,)
_,m')
-"""
1*"--
_ _ (5)
..,.,
",*,-(p.o.'1I1
-1"'1
"<iCOIII:I4-""".. t~)
_1m)
~
_1m)
.... '--1
_1m)
_1m)
_1m)
.... (U.S.........,)'"
.....
r~~
..... (U It nauIicII)
..... {U.S,~
III .... (InI....,.bOnIIj
Oq .... IUS ...-..rl'"
.. . _
........ ..:::.=:=.-.
"':.:;:....
\"o,w (kmIIi)
.......... __ .......
...- -.... _
_. ._(,Id)
,~'"
'·ro
,."
,."
,
,."
,.,.
,-"
,·ro
,.ro
,.ro
2~lI9I
rnIoi"l*
("".)
_ _ leocond
MCO"Id (""')
--"cI~(O"C1
....... (angIt)
""..
'M'
,
, ,
,.".
....,... (11'1')
pltclllPI)
I)UCII IPI)
E.,S
2.S89 983 E ~ oe
............ \inlerllrionlQ
""'" (\I'iIemaIionII)
E~OI
1609347 E .. 03
1.152·
1.85311-10' E+ro
....1.. 1* MCO"Id I""')
.-
,,.ro
,
1 &09~. E+03
mila.twl~
.....,..r~
,.,.
I_F""--l)
>~.
_(m)
rnIoi .. ,ml
II*.. (ml
....,... (m')
kIomeI.. _
3 113 099
4 11-10'
,
-I""
~
4448 222
.894751
5144444
E~oe
4 470 4·
E-01
1.609344· E+OO
2.611224' E+OI
1609~· E~03
1.0·
1 333 22
...
2~182
(table
E.02
E+02
E-04
Clm/illlled)
•
600
Gas Production Engineering
Appendix A-6 Continued
Alphabetical List of Units (Oil Field to $1 Units Conversions)
To CC!'/W!!'! F!Q!!!
........ t_fOIw)
........ ('"*NIl
_...
--
rno;dI( ........ ~)
ohm ckvIIt ..... per ft
........ (1-.!upcIo1
_(woyor~
_ ( U K IIuid)
_(US~
...~"
0. (~).gII (\IK kpI)
QZ (~)Ip(l).S kp;I)
-......-
OI(~)/W1'
QZr~~11'
QZI~yYd'
~IU.S)
_re)"
PtITII Iz:l"Cl'''
"
~('l
.-.d(11
NCOr'ICI II'
""'*' f* ........ (Ai"',
ohm ........ (0 .... )
ohm'-""'" p e r _
(10........,..,1
1I:IIDvr.",(~)
_'m')
_,m')
1ubgI.... I..,)
~,~
_
..... (1+<>1)
1dIogI .... .,.. ...... ~m'J
kIogf .... 1* .......
11<9...,
......... (\0.""
kiogf .... _
Ir/Iovr- _ ......... !k9m')
1IiogI_ 1*....t"'!kWm'I
_1m)
....tr(m')
kq ..mlkg)
lUIogr.m _
PfoQ MCIDfId....,....
I"QI(P'''-m')(
perm-.! (O"C)'"
1o;lIoQi"" per ~ MCIDfId met.'
IkgIIP ...1TI')(
kiogIr.." per p.IIQI MCIDfId _
1*"'1'9\ (23"C)'"
tiogr.... _ PQCaI MCIDfId_
-
IX8 (prIr-..1
dry)
.... (1) S IcIudl
.... f\I 5
"'*"
IP'I"Itr'I
~I-""""")
po<n:I {11m awwdupcn)'"
po<n:I (\roy or~)
_.
-.
.....
tom-II'I"""'*" 01_,
'.00
_1m)
_1m)
- " M<:ond (P"'I
tiogr-11I91
kIiogr .... I~1
kIIogf .... mN<' 1"vm'J
"*'""
........ 1* ....... !I<9'm'I
1IIIogI.... I*"...cond (\G.'I)
___ .... _10'-'1
_ _(\g.J)
11<9-.....
.........
'*9.... _ _ (IogI1)
1IJOgr.... 1* _
(ko.s)
~ 1* "-"\19m')
~,~
-.~
~''--(toIJ'"
IbU....
1II1\.... "~
I'ItWIOn IN)
I'ItWIOn "",erl""")
...-....,.. 1* _(I"""')/Inl]
.•
...-''''''-_'''_''''05_1-':
. . .....
. ---. -.
.....-.
................. {'for.. '
7.0111 5S2
e.2lli021
1"" l!02
1729_
3 OSI 517
3 390 515
30115 e78
88091&8
1.55517'
, '00
'·00
,."
,."
,."
,."
E-Ol
E+ Ie
5.72135
E - 11
57'525
E-ll
•.
'Sf 29
,.~
• 211518 '·00
5!iO$ 105 ,.~
'731 765 E-Ool
351'59I·E-00l
E-Ol
'535 112. E-Ol
3,~"7 E-01
'2"01\ '·00
2.28391 ,.~
" ) 3 189 ,.~
\'81 1501 . . 00
' .11112 '28 "00
1 $01 \143 E+Ol
.1771133 E+OI
1111126'
1.2511.19 ,.~
".
.... '"
2c 781 190
,."
E-01
..~
755.ln '·00
4535 i2. E-Ol
5.1132 764 E-Ol
I 382 550 E-Ol
'.00
lqe 1501 '.00
....em . . 00
1.355 818 . . 00
5.331_ E+OI
,_,&0\
...,,"
-.
~IVS."'YI
..-
"*"'1""1
."" '" ,."
.-(,_Iion_~
gr.,.(Gy)
11* pucIII NCOr'ICII1-(P"')1
1.0'
.....
1d1ogr.... !l<9)
pucaI noand (P"I)
1<iIog<am 1* ....,.... ('o.g.m')
1tII11'" (psi)
.."
3110344 . . "
2,'" 307
2 9!i7 35.3
Z 710 139 E-OI
~!r"
\.lZi&ol& !-OI
. . 00
. - ....... 1* ...... [(r+mymJ
~ NCOr'ICI (""")
.........., IM" ....... (N.m)
1tII..;"m.·tII-.'!!'
""
,."
""~
,."
,."
,."
"
ConY!<! From
1 562 '211
E-12
-'m')
_'m')
To
IbI.....P •
11511'7 E.O!
1.0'
'·00
,1
puaoI (PI)
pucIII M<:ond (P ... )
~--
2.6211 000
[lvnI{PaflTIn
- _ ........ cml'n')
.....
_---- --- --
E .. O!
5ta3&11 E .. O!
E-12
1iJIoVr..... ~I"vm'J
(SI'C. tpeaIIc \ w I _ )
'¥P'Y9y"
' .0'
"53 22
I>UCtI MCIDfId (Pu)
p..ell MCIDfId (PI'S)
1oiIogr.... 1* ........ f1<9i1Tl')
1dIDgr.... 1*
{logim')
1IIogr- _ . . - fII9Im')
....
_.-........... ""
..........
...-...
_..._-_-.....--_..,..,., .
.......
Appendix A-6 Continued
Alphabetlca' List 01 Units (Oil Field to 51 Units Conversions)
(\giIP.......)1
tnHn.'(rnor-.Iof_)
tIrftItaI f\I K Iiqujd)
IIrWgtIIU,$. kp;I;
601
Appendix A
~rp.)
",.
.......... 1M" ....... (NIrn)
to/IbII (1NUI~-....gI'II I_I "110)
..., fU S liQuid)
n
-"'1-'11)
.-...
........,
.......
----...
",lImpe ••
""
-
_(UwN\Ie~)
luDgf_tc'kgl
_,m')
'-I'M!)
-"'(I)
....,...(...,
coulomb (C)
,•• Iid IF)
-,~
......... (5)
'*'" In)
"'M
....,
... Im')
CIIndIlIa
_ _ _ loo.1TI')
mtMr'" _
..."..., I.... I)
_'m')
mel.... (m')
1IIogr.... _ ....... f\<g.m)
••
.....
""" IJ)
"'"('SUY)
10>\ flonsI. 2.2~ Ibm)
"'" IIM1ricI
"'" lnudear MI\III'...... 01 TNT)
"'" Ifllrigerltian)
"'"I. . . .)
"'" Ishoft. 2000 Ibm)
~-",..
~'t.-
Dt-tDIaI (2000 1l1li
IOn I""" H;. O'C)
-"...,
w.
.....-,-",,-W'"'
W...•
1\01
Id\oot..... I~)
1IJogr....
1d\ogI1m (kg)
""" (J)
...IH(W)
meI"'(m,)
ldIogr_ ('leg)
1<Jogo".... 1* mt1 .... (lo.g 1TI')
1dIogr.... PI< MCIDfId (kg.")
-..........,
.....-IN)
1oIIogr.... (kg)
_,m')
~IPII
jDultlJ)
wtll_~{W"'"
wJII
_ _ {W 'm ')
,~
IMler,,,,)
~.
........ (m')
mtter' _ --.oj (m'JI)
\'M"I~)
--.oj (I)
.,..,11icIer.'"
mtle<' (.....
....",...a (I)
-"'Ill
.~'"
'·00
".
,...
,.~
...,."..s (I)
IUilft·.j
,."
E_g!
(_~_')
~I*
..-....
--...
_,m')
E _01
1,101221
-1m)
- "'lang")
"'"I __
paSQI (PI)
newton 1* ~ .... (N.'I<g)
~,78802e
, 'Sf)9() E.O!
'.7811 0211 E .01
US! 2M E.02
'54 751
'.00
,.~
~6oI813T
E-OII
'!iI121ilM1 E -Ol
(_F_,)
1 000000· E-OI
1(59390 e.Ol
, 788026 E _01
5.1537N E.02
33356'0 E-l0
3.3356'0 E-l0
1112650 E-12
'.111175~ E. II
U12650 E-12
111117 S50I E.-l1
2"1.25
'.00
..
".
,
,."
..... ...
1.0·
"11678
,.~
,.~
,."
",
"
". ,'·00
'·00
,."
,."
,
."
".
"M
,~
2.11166el
1.018 ()47
E tot"~·
3516800
2 631 6B5 , .00
.0716017 E .02
,."
,."
",,'"
....
."
,
,,, ."
.=" '00
,..,. ,."
".
._•.
2_5111158 E-OI
I_F_'I
1.258637 E-OT
10·
1550003
.1 ... •
• 361 27.
760155<10
1.27' 258
3 153Il00
3.155115
3155 fi3
"00
,.~
E.03
E-Ol
E-Ol
E-Ol
,·00
E.-01
E.07
E_07
•
602
Gas Producliall Engineering:
Appendix A
o~, 08
38 8 0 80
'. ,. •
, .,
L
I
603
8
"'''' "'''' "' .................. '"
.....
~
.. -- ..... ..
~-
,!." ',e
I~
!
;;;
t
I
! i IHI~ll I~ '. Ii I!
.
:.:.
, I' I~
,
1
I
I{ ,. If Ii
11 II
t
i If ~
, I'
II
-...
... ...
ze ,.,
•
Appendix B
605
General Nomenclature for FORTRAN Code
APPENDIX B
Computer Programs
(FORTRAN Subroutines)
This section presents a few subroutines in FORTRAi'\' that find use in developing any computer program for computations related to gas properties.
production. and flow. Readers are encouraged to use these programs as they
are, and also as a part of mOTe complex programming effort~.
Subroutines
CRIPT
CASCOM
CASVIS
FRICF
HORIZF
CSMITH
VERTF
HACBR
BEGBR
Critical pressure and temperature.
Cas compre:;.sibility, and compressibility factor.
Gas viscosity. Uses subroutine VISCOR for viscosity correction.
Moody friction factor calculation.
Horizontal steady-state Single-phase flow using various
methods.
Cullender & Smith method for determining bottom-hole
pressure.
Sukkar & Cornell method for non-horizontal steady-state
single-phase flow.
Hagedorn & Brown method for multiphase flow in pipes.
~ & Brill method for multiphase flow in pipes.
Al.1Xiliary (Service) Routines
INTPI
INTP2
~U\tlNT
Linear interpolation for a single-variable dependent parameter.
Lagrange interpolation for a parameter dependent upon
two variables.
Romberg numericaJ integration.
604
APR ..
ANC ..
APCR ..
CR ..
DENL ..
DELTAP ..
DND ...
DNFR DNCV ..
DNL ..
DNLV ""
DP ,.
DPH '""
DR '""
EPCR ..
FF ..
FLH ..
FNSLH ,.
FPCR ..
CCRA '"
GDEN ..
GVIS ..
IERR,.
I FREG IOU ,.
ITER
MITER
MW
P
PI
P2
PBH
PC
PL
PR
PWH
QCSC
R.."JUM
..
..
..
..
..
..
,.
..
..
..
...
..
..
Absolute pipe roughness, inches.
Inclination angle of pipe from horizontal, degrees.
Acceleration pressure gradient, psi/ft.
Reduced gas compressibility. dimensionless.
Liquid density. Ibm/cu bic ft.
Pressure difference between inlet and outlet for gas flo\\~ psi.
Dimensionless pipe diameter number.
Dimensionless Froude number.
Dimensionless gas vclocity number.
Dimensionless liqUid viscosity number.
Dimensionless liquid "elocity number.
Inside pipe diameter, inches.
Depth of well. or elevation difference, ft.
Reduced gas density, dimensionless.
Elevation pressure gradient. psi/ft.
Moody friction factor.
Liquid holdup, fraction,
No-slip liquid holdup, fraction.
Friction pressure gradient. psi ft.
Gas gra\'ity (air .. I basis), dimensionless.
Gas density, Ibm/ftl.
Gas viscosity, cpo
Error indication in subroutine execution.
F10w regime indicator.
I 0 code for device on which output is desired (a file, line
printer).
Iteration counter.
Maximum number of iterations allowed for a trial and error.
Molecular weight, Ibmllbmole.
Pressure, psia.
Pressure at inlet end of pipe, psia.
Pressure at outlet end of pipe, psia.
Bottomhole pressure, psia.
Critical pressure. psia.
Length of pipe, ft.
Pseudo-reduced pressure, dimensionless.
Wellhead pressure, psia.
Gas flo\l,'rate at standard conditions (14.73 psia, OR) . Mscfd.
Reynolds number. dimensionless.
•
606
Ga~ Production Enf!,ill(,l.'rin~
SICMAL
T
Tl
T2
TBH
Te
TOt.
TPGR
TR
TWH
\'ISL
Y\1
y
Z
ZC
- Liquid interracial tension, dynes/em.
... Temperature, R.
Temperature at inlet end of pipe, R.
. Temperature at outlet end of pipe. R.
- Bottomholc temperature. cR.
.. Critical temperature. - R.
.. Error tolerance between succes.-.in~ itcrati"e solutions.
• Total pressure wadient. psi rt (nel.!ative) = - (EGR
+ FeR + AeR).
.. P<;cudo-rcduCE'd temperature. dimensionless.
.. Wellhead temperature. 'R.
.. Liquid ,·isca.ity. cpo
.. Fluid (mi..:durc) \elocity. ftsec.
~ Gas oompmitioo (mole fractions in the ~luence of Table 3-1)
array.
.. Ca.~ compressibilit~ factor. dimensionless.
.. Gas compressibility factor at the critical point (assumt.'<i O.2i)
Appendix B
607
c
IF(INDEX.EQ.2) GO TO 40
SUMA-OO
PCM" 00
TCM-ao
00201·1.18
SUMA" SUMA • Y(I)"MW(I)
PCM - PCM • Y(I)"PC(I)
TCM - TCM • Y(IJ"TC(I)
20 CONTINUE
GORA .. SUMA/28.97
00 TO 60
C
40 PCM .. 709604 - 58118*GGRA
rCM - 170491 • 307344'GGRA
c
C Apply Wichert 8.
AliI
(1972) coneclion for sour gases
c
60 A - V(14) • V(IS)
S - VIIS)
EPS ·1200·tA·'09 -A U I6)' 150"tS"OS - 8'·40)
TCM - rCM - EPS
PCM • PCM'TCMI(TCM"EPS • B·EPS"(1 O-B))
c
_ _ _ _ _ _ _ F·~O~R,-,T",R~A'C"~'S~u~b~,"~u~ti~ncs=---_ _ _ _ _ __
RETURN
END
c
c
SUBROUTINE CRIPT(lNOex.Y.GGRA.PCM.TCM)
c
c---------·
C
C
C
C
C
C
C
C
C
C
This subroutine Iinds the crlticel pressure and temperature 01 a gu
Irom its (II COmPOSitiOn. or (ii) gravity
INPUT Y or GGRA. and
INDEX" I II gas composition Y 15 provided (GGRA 15 computed).
.. Z If GGRA is prOVldlld,
OUTPUT
MllI1ure critical pressure. PCM (psi.) .• nd temper.ture. TCM (Rankine).
DATA USED (lor each component)· MW. PC•• nd TC lor IIch component
Note If the gl$ 15 sour. supply the mole fraClions
Y(14) of C02•• nd Y(IS) ot HZS. to enable Wichert 8. Allz correction
C-----------------------------------------------------------------------
SUBROUTINE GASCOM{PR.TRLCR)
c
C ---------------------------------------------------------------------C
C
C
C
C
C
C
C
C
C
METHOD USED Equation of stete methods as follows
For TR < > I, use DRANCHUK 8. ABOU-KASSEM's (l97S) procedure
for TR • I •• nd PR >- I, use YARBOROUGH 8. HALL's (1974) method
For TR" 1•• nd PR < I, use ORANCHUK ET AL's (1974) eQulllon
INPUT PRo TR
OUTPUT Z. CR
C ---------------------------------------------------------------------C
C
REAL Y(18), MW(18), PC(18), TC(18)
DATA MW/16043.30.070.44097.58124,S8.124.72151.72ISI.86.178.
, 100205.114232.128.259.142286.28013-44 010.34 076.31999.
, 2016.IB0151
DATA PCI 6678.7078.6163.550.7.529.1.4886.4904.4369.3968.
I 3606.3320.304.0,4930.1070.9.13060.7371.1882.32036 I
DATA TCI 343 1.5498,6657,765 4.734 7.845 4.8288.913.4.972.5.
# 1023.9.10704.11118,227.3,5476,672.4.278.6.599.1165 I I
This subroutine cllculates: (i) 9U compressibility I'ctor Z
and (ii) reduced 91S compressibIlity CR
in the f.nge 02 <- PR <- 20.0. 0.7 <- TR <- 3.0
c
IF(TRNE 10) GO TO 103
If(PRGE. 10) GO TO 102
C----- DRANCHUK 8-COEff -------------C
CAll ZFACT1(PR,TR,Z.CR)
RETURN
c
C----- HALL 8. VARBOROUGH -------------
•
6<)8
Cas Production Engineering
AppeTldix B
609
c
c
102 CALL ZFACT2(PR,TRLCR)
RETURN
OR... OR··'.O
oZDR .. Al • A21TR • AlITR3 .. 2.0·CA'.ASITR)·DR
, • SO·AS·A6·DR.ITR • (20·A7·DRfTR))
, ·(10<-M·DR2-CA8··2 0)·oR4)*EXP(-AS·OR2)
CR .. , O/PR - (ZC/IIZH20)-TR))·(DZDR/CI.0+CDRIZ)·OZOR))
C----- ORANCHUK l1-COEfF _____________ _
C
c
103 CAll ZFACT3(PR.TRLCR)
RETURN
'NO
c .................................................................... ..
c
c
c
RETURN
'NO
c
...................................................... .
C···············
c
SUBROUTINE ZFACT2CPRTR.l.CRj
SUBROUTiNE ZFACT1(PR,TRl.CRj
c ------_______________________________________________________________ _
C Applies Oranchuk'l ,I (1974) B-coeH equalion
C Uses Newton-Raphson method for guessing reduced denSIiV OR
(r.presented here bV the symbol VJ, then calculates Camp laCIor Z.
eC -------________
• _________________________________ . ___________________ •
c
C --- --- ----- - - -- - - --- --- - - - -. -- ----- - - -- - --- -----. - - - ------ - --- --- ----C Follows the procedure Irom Yarborough and Hall's (197') paper
C Nomenclature and melhodologV similar to subroutine ZFACTI
C ------.---------------------------------------------------------------
c
C
REAL Y(IOS), F(IOS). OFDY(10S)
REAL VIIDS). F(IOS). OFDY(105)
c
c
c
Y(1) .. 0.3723
TOl .. 0.0001
TRI .. 10fTR
TRI2 .. TRI**2.0
TRI3 .. TRI·"3.0
DATA. A I.AZ.AJ.A4.A5.A6.A7.A8! 031506237, -1 04670990.-057832729.
*053530771. -061232032. -0 10488813.068157001, 0 6S"6S'9/
YO)- 0372J
TOL - 00001
TRJ-TR··3
c
00 10 I - '. '00
c
c
c
FCI) .. YCI) • CA,·A2/rR.A3fTRJ)"CYClj·.2.0) .. CA4+ASlTR)
, ·(Y(I)··) 0) • AS·A6fTR·{Y(I)··6.0) • (A7 fTRJ).CY(ljU30)
, ·(10"AS·(Y(I)"'"2 0))·EXP(-AS·CY(I)o·2.0)) - o 27*PRfTR
OFOY(l) .. , 0 <- 2.0·CA '<-A2ITR+A3ITRJj"Y(I) <- 3.0.(A•• ASfTRj
, ·CYCW·20J - (6 0·AS·A6ITR)·CY{lj"SO) _ (A7ITRJ)"{YCI)
, "*20)·(3 0<-3.0·AS·CY(I)··20)_2 0·CASoo2 0).C YClj •• 4.0))
, • EXP f- A8·CYCI)"20))
YCI.,) - Y(I)- F(I)IOFOY(I)
ERR .. ABS{Y{I_I)_ Y(I))
IF (ERR LHOlJ GO TO 20
10 CONTINUE
c
c
c
C ----- Computations lor CR __________________________ _
C
ZC .. 0.270
DFoYCI)" (1.00 'O·Y(I) 6 '0·(YCI)h2.0) - '0*CYCI)U3.0)
, + YCI)··'.O)/((I.O- Y(II)··' 0) - CZ9 SZfTR-19 5Z*TRIZ
, 69.16*TRI3)"Y(I) • (2 18<-Z 8ZfTRJ"(907fTR-Z'2.Z·TRI2
, <-"Z.4*TRI3J·(Y(lj··C I. 18 .. 2.8ZITR))
Y(I+ 1) .. YO)- f(I)/ DFDY(I)
ERR" ABSCYU<-I) - Y(I))
If (ERR.lE.TOl) GO TO ZO
10 CONTINUE
c
20 OR,. Y(I.,)
OR2 ,. OR u 2 0
z .. '.0 <- CA1-A2ITR<-AlfTR3j.DR <- (A •• A5ITR)"OR2
, <- (AS*A6ITR)·COR"S 0) • (A7/CTR**3.0))"OR2
, "11·0. A8·0R2).EXP(-A8.0R2)
DO 10 I .. I, 100
F(I) .. -0 0612S·(PRlTR)·EXP(-1,2<-1I1.0-TRI)U2 0))
, .. C{Y(I)+YCI)··2.0<-Y(I)·"3 O-YCW·' 0)/((1.0-Y(I))··30))
, - (1'.76ITR-9.76·TRI2.' S8"TRI3)O(Y(I)d2.0)
, • (90.7fTR-242.2°TRI2<-'2.'''TRI3)·(Y(I)··CZ18o 2.82fTR))
ZO OR - YCt.,)
z .. (0.0612S·CPR/TRj·EXP(-,Z·C(I.0-TRI)"·ZOj))fDR
C
C ----- Computations lor CR --------------------------C
ZC- 0.Z700
TR2 .. TRuZ.O
TR3 .. TRO·J.O
OlDY" ('<-'·DR-Z*COR··ZO))/((I-OR)··' 0) - (1'.76fTR-9.76ITR2
, +4.S8/TRJ) 0 C90.7ITR-Z42 2fTR2.'2 'ITR3)
•
610
c
Ca., Production ErlKineeriug
Appendix B
, ·(1.1S-282ITR)*COR"*(O lS+Z.82fTR))
CR .. 10/PR - (ZC/((Z·oZO)OTRWfOZOY/(10o(DRlZloDIOY»)
70 PRCAl-P/0.27
IF(ABS(PRCAl-PR)-OOOI ) 170.170.80
80 IF (PRCAl-PR)ISO,170.90
90 DR .. DRI
OElDR .. DELOR/2 0
00 TO 160
100 ORI .. OR-(P-O 270'PR)/OP
IF (ORI)110.nO.120
110 ORI - OS-OR
120 IF{DRI-22) 140.1'0,130
130 ORI - ORo09"{22-0R)
"0 IF{ ASS/DR-OR I )-0 0000 1 ) 170.150.150
ISO DR-DR I
160 CONTINUE
170 Z .. 0,270 oPRI(OR"TR)
200 CONTINUE
RETURN
c
'NO
c ••••• ................ u
••••• u
........................................
c
SUBROUTINE IFACTJ(PR.TR.I.CR)
c
c -- '''''---. --------------------------________________________________
0
__
C Or.nchuk & Abou"Kusem-s (1975) procedure deroved from Starhng EOS.
e uSing' l-coef1s
C
C
---0------. --------------------____________________________________ 0__
c
611
DATA Al.A2,A3.A4.A5A6,A7.A8A9,A10A11 /0.3265.-10700,-05339.
1001 S69. -005165.05475,-07361,0.1844,0.1056,0 6134, 07210 I
C
ITeR .. 0
J • 1
OR" '.0
C ----- Computations for CR ---------------------------
C
ZC .. 0.2700
OR2 .. ORO"2,0
OR4" DRh,.O
OZOR .. A I .. A2ITR .. A3/TR3 .. A'ITR ... As/ITR"OS 0)
, .. 2.0"(AS+A7ITR_A8/TR2)"OR - s.0"AS"(A7{TR-A8/TR2j"OR'
, .. (A 10"(OR2ITR3)-A I 0°.0, II O(DR'fTR3),"(-2 0".0, IIOOR)"EXP(-A II-OR2J
, .. (2.0"A I 000RITR3_' 0-.0, 10°.0, 11"(OR--3.0)/TR3)"EXP(-A II"OR2)
CR .. I,O/ PR - (ZC/((Z**20)"TR))" (OZORl{1.0-(ORIZ)*OZOR))
TRl • TRuZ
TRJ .. TRo'J
TR4 .. TR"·.
Cl .. A7.ABITR
CO ..
C2 ..
C300
C4 •
Al*TR -A2 *AJITR2 -A4tTR3 +ASfTR4
ASoTR .Cl
-CI*A9
AIOITR2
c
c
RETURN
IF (PR-30 0) 10.10.200
10 IF ITR-10) 20.20.30
20 J • 0
DRooOO
DElDR" 01
30 IF (TR-3.0) 40.'0.200
.0 DO 160 ITER· 1.100
IF (J) 50.50,60
50 ORI • OR
DR • DR.OELOR
60 DR2 .. ORu2
DRS· OR-oS
TI • CO"OR
T2 • C2"OR2
T3 .. C3°DR5
T• • C,oDR2
T5 .. AnoOR2
T6 • EXP(-TS)
P - ITRoT1-n-T3)OOR -T4"DRO(10_T5)"T6
DP .. TR·200T '-30"T2oS 00T3.T'"TSO(30_3,0"Ts-2,0*TsOTS)
IF (J) 70.70.100
c
'NO
SUBROUTINE GASVIS(PR,TR,T,INOEl(Y.GGRA.GVIS,IERR)
c
C-------------------------------------------___________________________ _
C Cllculltes the viscosity at I 915 from liS
(i) composition, using Stl,1 ,nd Thodos (1961) 'qullion.
C
C or (ii) gravity using Clrr .t.1 (1954) method
C
Pressure correction by C,rr.t ,I. (195') is used
c
C
V.lid in the rlnge of 105 <'" TR <'" 30, 0.10 <- PR <'" 20,0,
SOD < .. T <- 860 (Rlnklne). Ind 0.55 <oo OGRA <- 1,50.
C
C INPUT'
CPR, TR, T.
C
INOEX .. I If gas compOSition Is known
C
.. 2 It gas grlvlty only is known,
C
Component mole frictions, y,
C or GORA Ilongwith the mole Ir.ctlons 01 N2. C02 Ind H2S.
C OUTPUT: On viSCOSity OVIS It PR, TR, Ind
C
IERR .. Error indlClllon - beyond rlnge a. method
C SUBROUTINES USED, VISCOR. INTP2.
C------------------------______________ ______________________ ____ _
•
612
Gal Production Engineering
c
REAL VIIS). MW(18), PCPS). Te(18). VCQMP(18)
Appendb:: B
C
150 IERR '"' 1
GVlS '"' 0,0
RETURN
OATA MWI 15043.30070,44097,58 124,58,124,72.151.72 151.86.178,
c
, 100.205.1'4232.128259,142286,28013.44.010,34076.31.999.
, 2.016,180151
DATA PCI 6678.7078.6163.550.7,529 1,488 6.490 4,436 9,396 8,
f 3608,332 0.304 0,493 0.10709.1306.0,737,1,1882.32036 I
DATA Tel 343 1.549 8.665 7.765.4,734 7,845.4,828 8.9134.972 5,
I 1023910704,11118.227.3.547.6.612.4,278.6,599,1165.1 I
C ---- VISCOSITY AT 1 ATM & GIVEN TEMP T ----------------
C
c
C --GIS "'Iscoslty II 1 81m & gtven temp Tusing componenl data __ _
C
C ---- VISCOSITY AT GIVEN PRESS & TEMP
C
200 CALL VISCOR{PA, TR,GVISA,.GVISJERRj
RETURN
END
c
51· TC(I)"(1./6.)/( (MW(I)"*{O.5})*(PC(I)H(2./3.)))
TRI • TITCII)
IFITRt,OE.1.S)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ••• . . . . . . . . . . . . . . . •• . . . . • . . •
c
SU8ROUTINE VISCOR(PR,TR,GVISA.GVIS.IEAR)
c
C-----------------------------------------------------------------------
00201-1,18
ao
TO 10
VCQMP(I) • (34E-4)*(TAl u O.94)/SI
GO TO 20
10 VCOMP(1) - (1.778E-4)·( (4 58"TAI - 16W·{5/8,) )/51
20 CONTINUE
c
c
c
C .. u
IF(INOEX,EQ.2) GO TO 100
613
SUMA" 00
SUMB - 00
00301-1.16
SUMA .. SUMA .. VCOMP(I)"Y(I)*(MW(I)··05)
SUMB .. SUMB - Y(I)·(MW(I)**O 5)
30 CONTINUE
OVISA - SUMAfSUMB
GO TO 200
C ---- Gu VISCOSity .t 1 .tm & givln tamp, Tusing GGRA -----
C
100 IF( GGRA LT 0,55 .OR GGRA GT, 1,50) GO TO ISO
IF! T .LT. 500 0 ,OR. T GT, 8600) GO TO 150
T-T-460,0
GORA2 .. GGRA'''20
OGINV - 1,0/(1.0-GGRA)
VBASIC" 0.0126585 - 0.00611823"GGRA ... 0,0016457.·GGRA2
, - 00000164574"T - (0.71922E-06j"GGRA"T - (0.609046E-06)·GGRA2"T
CH2S· 1.0E-6 - ((1.13E-4)"YHZS*GGRA -(3.BE-5)"YH2S .'.0E-6)"OGINV
CC02 .. (0,000134"YC02"GGRA - 0000004·YCOZ + 0,000004·GGRA)*GQINV
, - 0.000003
CN2 - (0.000170·YNZ"GGRA _ 0.000021"YN2" O,OOOOI·GGRA).GGINV
, - OOOOOOB
GVISA - VBASIC + CHZS .. CCOZ + CNZ
T-T+480.0
GO TO 200
C Calculates 91S viscosltV at PA, TR from kJlown viSCOSity GVtSA at
C
1 atmosphlre. using Carr It.1 (1954) method.
C
valid in the renga of 1,05 <- TR <- 3.0. 0 10 <- PA <- 20,0
C INPUT:
CPR, TR, OVISA
C OUTPUT:
C
GVIS .. Gas visCOSI!V at PR, TA
C
IERR - Error Indication - tlevond fange of !Itlte values
C SUBROUTINES USED INTP2.
C DATA USED
C
VlSTBl .. Tebla of viscosltv ratios .5 • function of PA. TA.
C
TRTel - Tamplrlture values In thl viscoSity tebla
C
PRTel" Prlssure v.lues In thl viscosity t.bla
C---------------------------------------------------------------------c
DIMENSION PRT8l(22), TRTel(13). VISTBl(Z2.13)
INTEGER HP, HT
DATA PRTBU 0,1.02,03.04.05.06,0.7.08.09.10.12.14.16,
, 1.8,2.0.30,4,0.60.80.100.15 O.ZO 0 I
DATA TRTeU
, 1.05.1.10.1 15,1 ZO,I ,30,1 40,1 50, 160.1.75.Z00.ZZ5.Z50.3 01
DATA VISTBU
, 1.000,1012.1,025,1 050.1 075,1.10.1 145.1 195,1285.1.415.1.76.
, 2.285.2865.3 29.3650.4 760,5 5.6 460.1 150.7.680.865.9370,
, 1.0.1011,1 023,1043,1065,1 086.1 120.1 150.1 195.1255. I 435,
, 1.70,2.070,2 465,2.B,3 85,4 655.5.72.6.50,7 06,8.1,888,
, 1.0,1.01.1.021,1 036,1 055.1073,1.095,1 12,1145,1.175,1.28.
, 1.42,1.59,185.2 16,3.225,3.975,5,030.58Z,6.385,7410.8 lB.
, 1.0,1009,1019,1.03,1.045.106.1,01.1.085.1 11,1 135.1.195,
, 1.285,1.425,1.57.1.75.2 6.335.438,5 125.5 74.6.75,7.5,
, 1.0.1.008.1 017.1,027,1.04,1.054,1,063.1.075,1.1.1.12.1.155.
, 1.215,1.285.136,1,46,2.02,2 56.3.5.4 185,4 755,5,79,65.
, 1.0.1.007,1.015,1 024.1 035.1048.1 056.1 061.1.089.1 1.1.135.
I 1.185,1.235.1.28,1335,1.69.21\.2.19.338.3.86.4.79.541.
I 1.0.1.006,1 013.1,021.103.1 042.1,049, 1059.1.078,1 1.1 12,
•
614
Gas Production Engineering
# 1.15,1.185,122.126,1.5,1.785.2.325,2.82,323.4.06.4.6 I,
c
I 1.0,1,005, 1 011.1 018,1025,1.036.1.042.1.051,1,067,1 07.1 095,
, 1 12.1.15.1 18,1215.1385,1595,2030,2425.2.77,349. 4025.
, 1 0.1 004. '.009.1.015, 1021,1 ,03, 1 035,1 043.1 056.1.065,109,
I 1 11,1.125,1 145.1 165.128.1435,1.77,2.095.2.375,299,3.5.
, 1 0.1 003.1 007.1012.1,017,1024.1,028,1035,1045.1 055, '.06,
f 1070,108.1095.1.11.1205.129.1.5.1.725.1,955.2.48,2925
, 101002.1005.1009.1013.1018,1021.1027,1034,1040,1,045,
, '.055.1 065. I 075.1.085.1145,1 21,1 34 I 485.1 665.2.085,2 46,
I 1 0.1 001.1 003. t 006.1.009.' 012, I 015.1 019.1,023, '.025. '.03,
• '04,105.1 06.1 065.1.105.1 155.1.245.1 36. ! 485.! .8J.2.! 5,
I ! 0.1 0.1.001, 1003.1005.1007. 1009,1.011.1013.1,015, 1020,
I 1025.103,1 OJ5, 1,04.! 06,1085.1.14, 1205,1265,1495,1.75 I
Appendix B
615
c
C ---- VISCOSITY AT GIVEN PRESS eo TEMP ---------------C
60 GVlS - VlSGR·GVlSA
RETURN
C
100 IERR - 1
GVlS .. 0,0
RETURN
END
c
c.. •.. •.... •.... •• .... ••·••• .... •·•••••••••••• .. •••• ........ •• .. •• ......
c
SUBROUTINE INTP2{X)(I,X2)(3.X4 YY1,Y2,Y3,Y4)
IERR "0
IF{ TR LT, 1.05 OR TR GT 300) GO TO 100
IF{PR LT DOlOR PR GT.200)GOTO 100
c
C ---- VISCOSITY RATIO ----------------------- ____________ _
C
lP .. 2
HP - 21
c
C----------------------------------------------------------------------C This subroutine finds the value Y for a given X IVlng In the range
C
of four points (Xl.Yl). (X2.Y2). (X3,Y3), and (X4.Y4),
C
using the generalized Lagrange Interpolalion equation
C----------------------------------------------------------------------C
AI-XI-X2
A2 -Xl-X3
A3 - Xl -X4
A4 .. X2- X3
AS .. X2- X4
AS .. Xl-X4
Bl .. X- Xl
- X- X2
83 - X- X3
B4 - X- X4
Y .. B2JA1'B3/A2 'B4/A3 'Yl - BlIAI'BJ/A4'B4/AS'Y2
I + BlIA2'B2JA4'B4/AS'Y3 - BlIAJ'B2JAS'B3/A5'Y4
LT - 3
HT .. II
DOIOJ-LT.HT
IF{TRTBL{J).GE.TR) GO TO 20
10 CONTINUE
J-HT"
20 IF{PRTBL{lP - l)lT PRJ GO TO 30
I • I
CALL INTP2{TR.TRTBl{J- 2), TRTBl{J-I), TRTBl(J), TRTBl(J" I.
I VISI. VlSTBl{I.J- 21.VlSTBl{I.J-l ),VISTBL(tJI,VI STBl(I,J'I))
VlSGR - 1.00 • (PR '(VISI-I,D))
GO TO 60
c
.2
C
RETURN
30 IF(PRTBL(HP • ').GT.PR) GO TO 40
, - HP • 1
CAll INTP2{TR,TRTBl(J-2), TRTBl(J-I).TRTBl(J), TRTBL(J" I.
I VlSI,VISTBL(I.J-2),VISTBL(1.J-I),VISTBL(I.J).VISTBL(I,J"II
VISGR .. VISI
GO TO 50
c
4000451-LP.HP
IF(PRTBL(I) GE PRJ GO TO 50
45 CONTINUE
I .. HI'. I
50 CAll INTP2{TR.TRTBl{J-21.TRTBl(J-l1.TRTBl(J).TRTBL(J"),
I VISJ. VISTBL(I.J- 2),VISTBl(I,J-! I.VISTBl(I,JI, VISTBl(I.J -, I)
I .. I - ,
CAll INTP2(TR.TRTBl{J - 2), TRTBL(J-I), TRTBL(J).TRTBl(J" I,
I VISI, VtSTBL(I,J- 21,VlSTBL(I,J-I ),VISTBL(I,J),VI STBl(I,J' , I)
VISGR - VlSI' (VISJ-VISI)'(PR -PRTBLUl)/(PRTBl(I'I)- PRTBl(I))
END
C
SUBROUTINE FRICF(OP.APR,OGSC.GGRA.GVIS.FF)
C
C----------------------------------------------------------------------C This subroutine finds the MoodV friction lactor lor gas flowing in
C • pipe. using Colebrooke's equation, With Newton-Raphson itlrltion
C INPUT:
COP, APR, OGSC, GORA, QVIS
C OUTPUT:
C
FF (MoodV Irlctlon faClor)
C---------_____________________________________________ ----------------C
REYN - 20 123·0GSC·GGRAI(GVIS·OP)
A - APR/(37'OP)
FF" 0.030
TOl .. 0.000005
•
616
Gal Production Engineering
e
108" A +
o 62S1(REYN*(FF
Appendix B
e
U
DELTAP .. PI - P2
PRI .. PIIPC
PR2 .. P2IPC
PAV" (20130)*(pl"30 - P2*~0)/(PI··20 - P2"2.0)
PRAY .. PAV/PC
CAll GASCOM(PRAV.TRAV.ZAV,CRAV)
CAll OASVIS(PRAVTRAV.TAVJNDEX,Y.GGRA.GVISAV.IERR)
COEF4 .. (OP"S O)/(GGRA"TAV*Pl)
RHS4 .. 7 969634*PC*(S20 0/14 73)*(COEF4"OS)
COEF" (PI"20 - P2·*20)*(COEF4IZAV)
RHS .. S.63S3821*(S20,0114.13)*(COEf**0 S)
O 5))
GO" 1.0/(FF""O 5) + 2.0"AlOGIO(S)
C .. O.314/(REYN"{Fp·'511
OOOF .. -05/(FF"·'.5) - (2 O/ALOG(10.0))"(C/8)
ffN .. FF - OQIDGOF
IF(ABS(FFN-Ff).lE,TOL) GO TO 20
Ff " FFN
GO TO 10
e
20 FF .. FFN
RETURN
END
e
SUBROUTINE HORIZf(DP.PLAPR,INDEX Y.GGRA.PC,TC.T1.T2.lFINO.
, IMETH,OOSC,Pl,P2.0ElTAP)
e
C---Thll unknown rate must be guessed to enable calcn of FF-C
except tor thl clSe of IMETH .. 1.
e
e
fF .. 0.0321(OP"(1013 0))
OGSC .. RHS / FF·*O,S
tF(IMETH,EQ.l) RETURN
c----------------------------------------------------------------------C
This subroutine finds the pressura drop or 'Iownle
C tor steady-state ,Ingle-phas, ;1$ flow in I horllontal pipe. using
C
(I) If IMETH .. 1, than Weymouth equltlon
C
(iI) If IMETH .. 2, Ihln Plnh.ndle-A aqUlllon
C
C
617
e
C ---Iterate for Flow rate and frIction factor ----------
e
(ill) If tMfTH .. 3, then f.nhendll-B equation
(iv) If IMETH .. 4, then Clinedlns! equltlon,
e
e
It IFIND .. 1. then compute 'iowrelil (Irom known PI and P2)
.. 2. ttlen compull pressure drop (from known OOSC and PI)
.. 3. ttlen compute pressure drop (from known CGSC and P2)
e INPUT
OP, Pl, APR, INDEX, Y, GORA. PC, TC, Tl. n, IFIND. IMETH,
.nd ani of thin threl
(i) PI and P2. or (ii) cose and PI, or (II) OOSC and P2
C OUTPUT
One of thase threll. dilpendlO9 upon input
(i) OOSC. or (Ii) PI and DELTAP, or (iii) P2 and DELTAP
SUBROUTINES USED:
C
GASCOM, OASVIS, FRICF. NUMINl. INlPl
e
e
e
e
e
e
e
e
C----------------------------------------------------------------------e
COMMON TRAV
DIMENSION Y(18). DATARA(100,2)
e
ITER - 0
IF(IMETH,EQ.4) CAll NUM1NT(PR2.PRI ,V1NT)
10 ITER" ITER" 1
IF(tMETH,EQ.4) GO TO 20
REYN .. 20.123*OGSC·GGRA/(GVISAV·DP)
IF{IMETH Ea.2) FF .. 0 0768/(REYN u O 1461)
IF(IMETH Ea.3) FF .. O,003S9/(REYN**003922)
OGSCN .. RHS/fF"O,S
00 TO 40
20 CAll FRICF(OP APA.OGSC.OORA.OVISAV.FF)
OGSCN .. (RIIS4/fF u O,5j-(VINT**O S)
40 ERR" ABS(OGSCN - oosq/OGSC
OGSC - OOSCN
IF(ERR.m .TOLANDITERlE MITER) GO TO 10
RETURN
e
C--- CASE OF PRESSURE DROP CALCULATION ------------ __________ _
e
e
100 COEF .. (GGRA·TAV*PlI/(Op··S 0)
TOl .. O.OS
MITER" 20
TAV" T1
IF(Tl.NE.T2) TAV" (Tl - T2)/ALOG(T11T2)
TRAV .. TAVrrC
e
IF(IFIND,GT.I) 00 TO 100
e
e
e
C--- CASE OF FLOW RATE CALCULATION -----------------------
RHS" COEF*, 14.13*OGSC/( S.6353821·S20.0) )··2.0
RHS4 .. COEF-, 14 73-0GSC/(7.969634·PC*S20 0) )U2.0
C--The unknown pressure must be guessed to enable calculation 01
C Iverage Z-factor. and also friction flctor (except IMETH-I)
C which dapends upon gas viscosity
FF .. O.0321(OP·-O.333)
D2P .. RHS·FF
•
618
Ga3 Production Engineering
Appendix B
IF(IFINO E0-2) P2 .. (P,U20 - D2P)**Q 5
IF(IFINOeG.3) PI" (DlP. PZ**ZO)**Q.5
200 PRI .. X
PI .. PR1·PC
ITER .. 0
C
110 ITER -ITER. 1
PAV· t2013 OjO(P,U3,O - P-'·o30}/(P\--ZO - fZ
U
210 DElTAP .. PI - P2
RETURN
2D)
PRAV .. PAV/PC
CAll GASCOM{PRAV.TRAV.lAV.CRAV}
END
CALL GASVIS(PRAV,TRAV,TAv,INoex,Y,GGRA,GVISAV,IERR)
cC
REYN .. 20 123*OGSC"GGRAI(GVISAV"OP)
c
GO TO (140.120.130,1S0j.IMETH
c
c
619
._uu............... ·..........·······u............................
SUBROUTINE NUMINT(A.B.VIND
120 Ff" O,0768/(REYN··O 1461)
GO TO 140
130 FF .. Q,Q0359/(REYN-"O,03922)
c
140 D2PN .. RHS"Z,AV"FF
IF(IFIND E0.2) P2 .. (p,uZ.O - D2PN)**Q.5
IF(IFIND,Ea.3) PI .. (02PN • P2*-2.0)··O.5
ERR" A8S(02PN - D2P)/02P
D2P .. 02PN
C ---------------------------------------------------------------------C
C
C
C
C
C
C ------------------ ---------------------------------------------------C
IF(ERR GT,TOL.AND.lTERLT.MITER) GO TO 110
COMMON TR
DIMENSION T(I1.11)
DELTAP .. PI - P2
RETURN
c
C
TOl" 0 OOOS
MITER" 10
C-B-A
FA .. FUNCG(A)
FB .. FUNCG(B)
ITER - 1
lVl- 1
KMAX" 1
T(ll) .. (CI2,O)*(FA • FB)
VlNTO" T(l . l)
C ---- For IMETH .. 4 ------------------------
C
150 CALL FRICF(OP,APR,aGSC,GGRA,GV1SAV,fF)
VINT .. RHS.oFF
PfU .. PIIPC
PR2 .. P2IPC
IF(IFINO_Ea.3) GO TO 160
PflGl .. PRI
PftQ2 .. osapR2
GO TO 170
160 PRG2 .. PR2
PftGl .. osapRl
C
c
170 DO 190 I - I,SI
CAll NUMINT(PRG2,PRG1.0ATARA(I.2))
IF(IFINO.EQ3) GO TO 180
OATARA(I.l)" PRG2
PRG2 ,. PRG2 + 002·PR2
GO TO 190
180 OATARA(I,I)" PRGI
PRO 1 ,. PRQl + 0.02 apRI
190 CONTINUE
C
CAll INTP1(2.I.DATARAXVIND
IF(IFINO Ea.3) GO TO 200
PR2 - X
P2 - PR2·PC
GO TO 210
-
...
This is I gener,1 subrouun. for per10rmlng numerical integration
using th, fISt Ind accurat' Romberg's method
INPUT: Integrltion limits lower' A to higher B
OUTPUT: Value of the Integrated funct ion. VINT
FUNCTION used: FUNCG. which evelue,.s the Integrand lor the
ClinedinSI equation in this elSe
c
10 ITER - ITER" 1
lVl .. lVl • 1
KMAX .. KMAX .. I
OX - C/(20· 0 (KMAX-Ill
l .. IFIX( 2.0*"CKMAX-l) - 1 )
SUMF - 0.0
DO 20 J .. l ,l
SUMF .. SUMF + FUNCG(A .. J·OX)
20 CONTINUE
T(1.KMAX) .. (O)(l20)*CFA + Fe .. 20*SUMFI
00 40 l .. 2,lVL
0030 K" KMAX-1.1.-1
EX .. 4.0"(L-l)
FAC .. 1.0/(EX - II
T(L.K) .. FAC*CEX·T{L-l.K.') - T(L-l.K))
30 CONTINUE
40 CONTINUE
•
620
Appendix B
Cas Production Engineering
50 IF(IEa.M.ANOAGT 1.0) GO TO 80
IF(A.lT.I.O) GO TO 100
IF(A.EQ.l0J GO TO 70
60 CONTINUE
c
'lINT· T(lVL 1)
ERR'"' ABS(VINT-VlNTO)1V1NT
IF(ERR.LE.TOLANOHER.LE MITER) RETURN
VlNTC • YlNT
C
70 Z .. DATARA(IJHV}
GO TO 100
GO TO 10
'NO
SO Z • OATARA(M.lHV)
A .. 1.0
cc ....................................................................... .
C
c
100 IF(INDEQ.Z) GO TO 110
y .. DATARA(I-l,ZJ .. A-(OATARA(I,2) - OATARA(I-I,2)1
FUNCTION FUNCG(PR)
COMMON TR
RETURN
110 X - OATAM(I-I ,I)" A*(DATARA(I,I) - OATARA(I-I.l))
IF(PR l1.0.2) 00 TO 20
CALL GASCOM(PR.TR.l.CR)
C
FUNCO • PR/Z
RETURN
20 FUNCO '"' 00
RETURN
'NO
cc ..................................................................... .
RETURN
c
SUBROUTINE INTP1(IND,M.DATARA,X,V)
c
c----------------------------------------------------------------------This I•• IIne'f interpolation routine.
c
C
For INO '"' 1. Y Is dlllirmined for' glvefl XC
INO • 2. X Is determined for. given Y
C INPUT:
C
DATARA· Arr • ., 01 (X.V) dall points
e M . number of dIll points (Iangth of arr • ., DAlAMI,
C----------------------------------------------------------------------C
DIMENSION OATARA(100,Z)
SUBROUTINE CSMITH{OP,PLDPH,APR,INOEX,Y,GGRA,PC,TC,OGSC,PWH,TWH,
# TBHJSFCON,PBH)
c
C----------------------------------------------------------.-----------This subroutine finds Ihe bottomhole pressure for static or
C steady-Slate single-phase flow of gas through I non-horizontal pipe,
using Culiender & Smith (1956) method
C
C A third-order numerical integration Is used insteld of Simpson's rule.
C INPUT:
COP, PL DPH. APR. Y, INOEX, GGRA. PC, TC,
C
OGSC, PWH, TWH. TBH (if 0, then It Is estlmlted by this pro9ram).
C and ISFCON .. 0 for stltic (no flow) well
.. 1 for flowing weil.
C
C OUTPUT: PBH
C
C SUBROUTINES USED GASCOM. GASVIS, fRICf
C----------------------------------------------------------------------C
c
IF(INO EQ.Z) GO TO 10
IHV" 1
c
l·X
GO TO ZO
10 IHV - Z
c
'NO
c
c
C
621
l·Y
c
DIMENSION Y(IS). A(4)
DATA AI 0125, 0375, 0375, 0 125 1
TOl .. 0.001
MITER - 20
C--Inltlll guess of PBH, TBH if unknown --C
Z000601-Z,M
A- IZ - OATARA(I-l,IHV))/(OATARA(I.IHV) - OATARA(I-I,IHV))
IF (A) 30,40,50
30 Z· DATARAll ,IHV)
A- 00
GO TO 100
40 Z .. OATARA(I-I,IHV)
A" 00
GO TO 100
If(PBH.EQ.O.O) PBH - PWH • 0.00002s oPWHoDPH
If(TBH.EQ.O.O) TBH - TBH .. O,OlsoDPH
c
Gl - 0.0187S-GGRA*DPH
IF(ISfCON.Ea.I) Gl- Gl*IOOO.O
PRWH .. PWHIPC
TRWH - TWHITC
CAll GASCOM(PRWH,TRWH,l,CRWH)
PTZ .. TWH*VPWH
,
622
Gas Production Engineering
c
ITER-a
IF(ISFCON Eo.O) GO TO 20
PTZ .. lOIf'TZ
CALL GASVISjPRWH.TRWH.TWH,INDEX,Y,GGRA,GYlSWH.lERA)
CALL FRICF(OP.APROOSC.GGRA.GVISWH.FF)
FQ2 .. 2.6957*(1 OE-6)*(FF/4 OJ*(QaSC"*20j*PU(DPH*{OP'os.O))
TKENER .. 1 11\*\ 815*(1 OE-S)*GGRA"(OGSC**2 O)l(PWW(OpU4 0))
PTl- (PTZ ~ TKENER)/(FOZ • 000I"(PTZ**ZO))
20 VINTGl .. A(l)'PTZ
PRES" PWH
TEMP" TWH
VlNTG I .. V1NTG2
C
C-----Integr.tion loop ---------------
C
30 ITER" ITER· 1
PINeR" (PBH - PWH)130
TINeR" fTBH - TWH)/30
c
00501-2,4
PRES" PRES + PINeR
TEMP" TEMP. TINeR
PRED .. PRES/PC
TRED .. TEMPITC
CAll GASCOM(PREO.TAEO.Z,CRED)
PTZ .. TEMP'VPRES
IF(ISFCON Eo.O) GO TO 40
P11 .. 1.0/PTZ
CAll GASVIS(PREO,TRED.TEMP,INDEX.Y,GGRA,GVISCOJERR)
CAll FRICF(DP,APR,OaSC,GGRA,GVISCO,FF)
FQ2 .. 2.6957*(1 OE-6)*(FF/40)*{OGSC"2.0)·PlI{DPW(DP"S 0))
TKENER .. 1 '1'·'.875*( IOE-6)·GGRAO(OGSC**2.0)/{PRES*(DP·*4.01)
PTZ - (PTZ * nENER)/(F02 .. a 001*(PTZu2.0))
'0 VlNTG I • VINTG 1 .. A(1)-PTZ
50 CONTINUE
C
C-----Newton-Raphson il.ullon-----
Appendiz B
c
SUBROUTINE VERTF(DP.PLOPH,APRINOEX,V,GORA.PC.TC.Tl.T2.
IIFINO.OOSC,PI.P2.0ElTAP)
c
C----------------------------------------------------------------------C This subroutine finds the pressure drop or IlowUtl for sleady-stale
C single-phase gas flow In I nOn-hOfl20ntal pipe using Sukklf-Cornell
C (1955) method. with the integrand evaluated bV numenCII Integration
C
C II IFINO .. 1. then compute lIawrale (Irom known PI Ind P2)
C
.. 2. Ihen compute prlssure drop (Irom known COSC and Pll_
C
• 3, then compute pressure drop (Irom known COSC and P2)_
C NOTE
C (1) Pl,T1 Is upstre.m. P2,r2 Is downstream OPH Is pOSitive
C
lor upwlfds Ilow from I to 2, negative otherwise
C
So. lor. flowing well, 1 is bonomhole, 2 Is wellhead
C (2) Subroutine NUMINT should be suitably mOdified to ICcept
C
Function FUNCSC (instead of FUNCG), Also. the COMMON
C
declaration In NUMINT should include vlriable BB
C
C INPUT:
COP, PL DPH, APR. V, INDEX, GGRA. PC, TC, n, r2. IFINO, IMETH,
C
Ind one of Ihese three
C
(I) Pl Ind P2, or (Ii' COSC and PI, or (ii) CGSC Ind P2
C OUTPUT:
cane 01 these three. depending upon Input
C
(i) aGSC or (il) PI Ind DELTAP, or (iii) P2 Ind DELTAP
C SU8ROUTINES USEO
C
GASCOM, GASVIS. FRICF. NUMINT, INTP1.
C----------------------------------------------------------------------_
C
COMMON TRAV, 88
DIMENSION V(18). DATPOO,2)
c
TOl - 0.001
MITER" 20
c
TAV· n
IFrnNE.T2) TAV· (1"1 - r2j/AlOG(T11T2)
TRAV .. TAVITC
RHS • 0,01S7S"GGRA"DPHITAV
ERHS • EXP(20 0 RHS)
C
FUNC • Gl - (PBH - PWH)*VINTG 1
PNEW • PBH .. FUNC/PTZ
ERR" ABS(PBH - PNEW)1P8H
P8H .. PNEW
IF(ERR.lT.TOLOR,ITERGT MITER) GO TO 100
PRES· PWH
TEMp .. TWH
VINTG 1 • VINTG2
GO TG 30
c
c
IF{IFIND.Eo.I) GO TO 100
C--- CASE OF PRESSURE DROP CALCULATION --------- __ ___________ _
C
C Assume I v.IUI for unknown pressure to enlble IV viSCOSity cllcn.
C
C
100 CONTINUE
RETURN
'NO
623
FF .. 0.0321(OP"P 0130))
XX .. (2_S272E-OS)"FF"OGRA*TAV"PL *(ERHS-l 0)*(QGSC**2.0)
XX· XX/(2.0"RHS"(Op·*S 0))
•
624
G(U Product/on Engineering
Appendix B
If(lFINO.EQ.Z) pz .. ((P'--2.0 - XX)/ERHS )**0.5
IF(IFINOEa.3) PI .. ( (PZ**2.0)+ERHS + XX )*'"0.5
c
C A$Suml a vatul for unknown fall to Inabll calcn 0' FF and B
c
c
C ---iteration proceClure for Preuure and friction faclor ----C
rTER .. a
10 ITER" ITER" 1
PAY" (2 013 0'''(P'··3.0 - P2··3.0)/( PI**2.0 - P2"*20)
PRAll .. PAWPC
PAl .. PI/PC
PR2 .. P2lPC
FF .. 0032/(OP*"(1.0/3 0))
XX .. 2.0"RHS"CDp··S.O,"(P'··2 0 - (P2"2 O)"ERHS )
YY .. (2.S272E-OS)·FF·GORA·TAV·PL ·(ERHS - 10)
OOSC .. (XX/YY)··O 5
c
C ---Iteration procedufe for Flow ratl and friction factor -----
c
OOSCO .. O.S"OOSC
DO 110 ,- 1,51
CALL FRICF(DP.APR.OGSCO,GORA.G"'SAV.FF)
BS" (6.6663E-04,·FF·PL·(00SCO··2.0,"(1A"··2 0)
B8" BS/(OPH·CDp··S.0)·(pC"2.0) ,
CALL NUMINTCPR2,PR1,DAT(I,2))
OATCI,
OGSCO
OGSCO .. OOSCO .. 0.02·00Se
110 CONTINUE
CALL INTP1(2,I,DAT,X,RHS)
oose .. X
OELTAP .. P' - P2
CAll GASVIS(pRAV,TRAV,TAV,INDEX. Y,GGRA.GVISAVIERR)
CAll FR1CF(OP,APR,OOSC,GGRA.GVtSAVfF)
BB .. (6.6663E-(4)*FF"PlO(QGSC**2.0)"(TAV**2.0)
BB .. 881(DPH"(Dp·"S O)"(PC··Z.Q) )
c
I, .
IF(IFINO eUZI GO TO 20
PRO ... Q,S"PRI
0015'·1.51
•
625
CALL NUMINT(PR2,PRG1,DAT(I.2))
OAHI,I) .. PROt
PRG 1 .. PRG 1 .. aOZ"PR I
c
15 CONTINUE
CAlL INTPl(2.I.DAT)(,RHS)
PRI .. )(
RETURN
END
c
PIN" PR'''PC
ERR .. ABS(PIN - Pil/PIN
C.. • ...... ••• .... • ..• .. ••• .. •••••••• ....................................
c
PI" PIN
GO TO 50
•
FUNCTION FUNCSC(PR)
COMMON TR, BB
IF{PRLT.0.2) GO TO 20
CALL GASCOM(pRTRl..eR)
FUNCSC .. V(PR • BS·(Z··20)/ PR)
RETURN
20 FUNCSC .. 00
RETURN
c
20 PRGZ .. OS"PR2
00 25 I .. 1.51
CAll NUMINT(PRG2.PR1 .DAT(I.2))
OAT/I,ll .. PRG2
PR02 - PR02 • 002·PR2
25 CONTINUE
CALL INTP'(2.l.OAT,X,RHS)
PR2 .. X
P2N .. PR2·PC
ERR" ABS(P2N - P2)/P2N
P2 .. P2N
c
c
END
SUBROUTINE HAGBR(DP.ANGAPR,GOEN,O"IS,DENl.VISl.SIGMAl.VM,FNSLH,P,
, IFREG,FLH,EPGR,FPOR.APOR,TPOR)
C---- _______________________________________________________________ _
c
C This subroutine calculates thl liquid holdup and prl!lSsure gradient
50 IF(ERR OT TOLANO.ITERH.M1TER) GO TO '0
OELTAP" PI - P2
RETURN
C for mul1lphue flow using the Hagedorn Ind Brown (1965) correlation
C The Duns Ind Ros C'961) IIquulon Is used for computing the
C ,cceleration pressura gradient.
C INPUT:
c
C--- CASE OF FLOW RATE CALCULATION -----------------------
C
C
C
'00 PAV" (2013.0)·(PI·~.0 - 1'2"3.0)/(1""2.0 - P2"2.0)
PRAY .. PAwpe
PRI .. P1IPC
PR2 .. P2IPC
CALL GASVl5(PRAV,TRAV,TAV,INOEX,Y,GORA.OVISAV,IERR)
C
C
C
C
p
OP, ANG, APR, ODEN, 0"15, OENl. "ISL SIOMAl. VM, FNSLH,
and Pressure P .t which the gr.dlent Is dlsired to be computed
OUTPUT~
IFREG .. 1 for single-phlse liquid
.. 2 for slngil-phul gu
.. 3 for two-phUI bubbll flow
,
l
626
Appendix B
Gal Production Enf{inemng
OENMIX .. GOEN
GO TO 50
.. 4 for other type of two-phu' flow.
e and fLH, EPGR. FPGR. APGR. and TPGR.
c
C
c
C SU8ROUTINES USED' INTPI
\
C----------------------------------------------------------------------C
DIMENSION OATHL(12.2). OATCNl(10.2). OAT51(12.2).
, DATHl1(100.2j, DATCN1(IQO.2). OAT511(100.21
c
COlt. trrlVS for liquid hOldup correlatiOn
c
C
IFREG - 3
VS '" 080
FGH" 0.5·( 1.0 .. VMIVS - ((I 0-VMIVS)·"2.0 - 4.0·VSGIVS)·oO.5 )
fLH'"10 -fGH
IF(fLH LTfNSLH) fLH .. fNStH
OENMIX .. FLH"OENL - fGH"GOEN
RNUM .. 1488 0·OENlO(VSUFLH)-(OP/12 O)IVISl
fF" 114 - 20-ALOGIO(APR/OP • 2.125/RNUM oo 09J
ff - 1 0/ff u 2 0
EPGR " OENM1X"SIN(ANGR)f144 0
fPGR .. FF·OENL "(VSUfLH)··2 0/(2 0'32.2"12.0·01')
CFf-OO
GO TO 70
DATA OATHU
, 02.0 5,1 0.2 0,50.1 0 0 20 0,50 0,100,0.200 0,300 0.1000,0.
, 0 Q.4.009,O 15,0 18.0 25.0 34.0 44,0 65,0 82.092,096,10 I
DATA OATCNU
, 0,002.0005.001,002,003.006.0 1,0 15,02,04
, 000 19,0,0022.0 0024.0 0028.0 0033.0,0047.0 0064,0 008.0009.
0,01151
DATA OATS"
, 001,002,0025.0,03.0035.°_0 4,0,045,005,006,0 07,0 08,009,
".0,11,123,1,4,1.53,16,165,1681,74,118.18,'83/
I
cC Calculat.
C
VSL
liquid (VSl) and gills (VSG) supIHficl., vllocities
~
\/M·FNSLH
VSO" \/M - VSl
c
C C"cu'ate the required dImensionless numberS
C
C 1 .. IDENUSIGMAl)UO 5
C2 .. IDENUSIGMALj*"O 25
C3 _I DENL·(SIGMAl·"30) )"025
DND" 100727*OP'CI
ONGV" 1.938"VSG*C2
ONLV" 1,938"VSl"C2
ONL .. 0 15726"VISUC3
c
C ANGR Is the inclination .ngtl in radians
20 A" 1 071 - 02218"120"(Vw o2.0)/OP
IF(A.LTO 13) A" 0 13
B" 1.0 - FNSlH
IFl8.GEA) GO TO 30
C-- Griffith (1952) correlation lor bubbl. Ilow -----
c
,
c
C-- Hagedorn & Brown correlallon -----
C
30 If REG .. 4
0040 I .. 1,10
OATCNI(I, I) .. ALOG(OATCNL(I.1))
OATCN1(1,2j .. ALOG{OATCNL(12))
40 CONTINUE
•
00501-1.12
OATHlI(1.1) - ALOG(I.OE-OS"OATHL(II))
OATHL 1(1.2) - OATHl(I.2)
•
OAT$ll(I.1)'" OATSI(I.I)
OATSll(I,2)" OAT51(1,2)
50 CONTINUE
C
~-- Uquid holdup calculations -----
C
c
C-- Oltlrminl flow rlglm. tvp' -------------------C
IF(FNSlH.lTI,O) GO TO 10
FLH'" 1,0
lFREG .. 1
OENMIX .. OENt
GO TO 50
c
10 IF(FNSlHGT,O 0) GO TO 20
FLH .. 00
lFREG ... 2
627
X ... AlOG(ONL)
CALL INTPI(I.IO.OATCNI ,)(. Y)
~;~~~(,0NLV.EXP(YJ*((P/14 73)··0 \)/(O NO"(ONGV·"0575)))
! 1.12,OATHlI.)(.FLH)
~ .. ONGV·(ONl··0.38)1(ONO··2.14)
ALL INTPI! 1.12.0ATSll,)(.SI)
IF(SILT.IO) 51 .. 10
FlH - flHOSI
IFlfLHLT.OOJ fLH .. 00
IfIFLHGT.IOl flH .. 1 0
IF(FLHGTFNSlH) GO TO 60
FLH .. FNSLH
•
628
Appendix B
Cas Production Engineering
c
629
c
ANGR" ANG*nO/(7 0*180.0)
60 OMIXNS .. FNSLWOENl .. (1.0 - FNSLH)*GDEN
DENMIX" FLH"OENl ... {I.O - FlHJoGDEN
c
VISMIX" (VISLUFLHjO(OVIS··p 0 - FlH)J
C-- Determine flow regime type --------------------
RNUM .. 14880"DMIXNS"VM*(OPI12.0)IVISMIX
Ff .. I ' . - 2 O"ALOG10(APRIDP • 212S/RNUM u O.9)
C
IFREG .. 5
IF(FNSLHGT.0.99999) IFREG .. 1
IF(FNSLH.LT I .OE-05) IFREG .. 2
IF(IFREG GT2) GO TO 10
FLH .. FNSLH
GO TO 100
FF .. 1 O/fF"2 0
EPOR .. OENMIX·SIN(ANGR)/l44 0
FPGR .. FFO(OMIXNS"2 O'°(V",o·2.0)/(2 0"32,2*'2 O"DpODENMIX)
VSG .. (10 - FNSlH)"VM
eFf .. OENMIX*VM"VSG/(32 2·'44 O·P)
c
IF(eFFGT 0 95) aD TO 80
70 TPGR .. - (EPGR ... FPGR)/( 1 0 - eFF)
APGR .. - TPQR*CFF
RETURN
c
80 WRITE{IDU.200)
200 FORMAT(/2X:CRITICAL FLOW REGION IS BEING APPROACHEO
, , ABORTING SUBROUTINE HAGBR.'/)
c
c
INDIC .. 0
AINDIC .. All
IF(FNSlH.LT,O.Ol) GO TO 20
IF(FNSLH.GT.O.4) AINOIC .. AL4
IF(ONFR.GE.AL2.ANO.ONFR.LT.AL3) INOIC .. 1
IF{ONFR.GEAl3.ANO.ONFR.LT.AINDIC) IFREO .. 4
IF(ONFR.OE.AiNOIC) IFREG .. 3
GO TO 30
20 IF(ONFR.GEAL 1) IFREG .. 3
30 IF(INDIC,Ea.1ANO.IFREG.EQ.5) IFREG .. 6
'I7X,
RETURN
'NO
SUBROUTINE BEGBR(DP,ANG,APR.GDEN.GVIS,DENLVISL,SIGMAL, VM,fN 5lH,P,
I IfREG,FUUPGR,FPGft,APGR.TPGR)
c
c-----------------------------------------------------------------------
C This subroutine celculates the pres5ure gradient for multiph.5e flow
C
using Beggs .nd Brill (19731 correlation.
C INPUT'
COP, ANQ, APR. GOEN. GVIS. OENL VISL SIGMAL VM, FNSLH,
C
.nd Pressure P .t which the gr.dient is desired to be computed
C OUTPUT:
C
IFREG .. 1 lor slngll-phesl liquid
C
.. 2 for slngle-phese 9es
C
.. 3 for distributed (multlphese) flow
C
.. 4 for Intermlnent (multlphese) flow
C
.. 5 for segregated (multlphlSe) flow
C
.. 6 tor trlnsitlon flow (Treeted IS intermittent)
C Ind RH, EPGR, FPGR. APGR, Ind TPGR
C
C-----------------------------------------------------------------_____ _
C
C Cllcul'te liquid (VSl) Ind gls (VSG) superficill velocities
C
VSL .. VM-FNSLH
VSG .. VM - VSL
c
C Cllcullte the required dimensionless numbers.
C
DNLV .. 1 93B""VSL e((DENVSIGMAL)UO.25)
DNFR .. lZ.0-(VM-"Z.0)/{3Z.Z*DP)
c
C ANGR I, the Inclination Ingle in r.dians
10 ALI .. 316 O*{FNSL"'""O 30Z)
ALZ .. 0,00092521{FNSlH·*Z 46842)
AL3" 0.10/{FNSLHool.45155)
AL4 .. 050/{ FNSLH 0 067380)
C
1I-IFREG-2
GO TO (40,50.60,SO), II
c
C-- For distributed flow ----40A-l065
B - 0.5824
C .. 0.0609
o .. 1.0
E .. 0.0
F .. 0.0
G .. 0.0
GO TO 70
C-- For Intermittent flow ----50 A .. 0.845
B· 0.5351
C .. 0.0173
o .. 2.96
E .. 0.305
F .. -0.4473
G .. 0.0978
GO TO 70
C-- For segreg.ted flow ----60 A .. 0.98
B .. 0.4846
C .. 0.0868
•
Gas ProdUClion Engineering
630
Appendix B
0-0011
-3.768
F" 3.~9
e ..
FPGR .. FF"OMIXNS"(VM o '2 0)/ (2 0"32 2"12.0"DPI
erF .. DENMIX"'VM-VSG/ (32 2* 144.0·P)
G .. -1614
IF(CfF.GT 095) GO TO 140
TPGR .. - IEPGR .. FPGR)/ (l 0 - CFF)
APOR .. - TPQR"CfF
c
70 FLHO .. A"(FNSlH·oSjIONfR··C
If(FLHOLT.FNSlH) FLHO" fNSLH
IF(ANGR.Ge,O 0) GO TO 80
C--For all Ilow types 'or downh,ll lIow--
a ..
470
E .. -03692
F-01244
0-·05056
GO TO 90
631
RETURN
c
140 WRITE(IOU.200}
200 FORMA T(nX:CRITICAl FLOW REGION IS BEING APPROACHED
, '.. ABORTING SUBROUTINE SEGaR '1)
:nx,
RETURN
'NO
C
80 IF(ANGR,NE.O 0) GO TO 90
FlH .. fLHO
GO TO 100
C
C--flow is non-horizontal ------
C
90 X .. O"(fNSLHUE)"(DNtV"Fj"(ONFRuG)
CFAe .. (1 a - FNSlH)"ALOG(X)
IF(CFAC.lT.Q,O) CFAC .. 00
x .. SIN(lS"ANGR)
51- 1,0" CFAe "IX" o 333"X··3 0)
IF(51.lT.0.0) 51 .. 00
flH .. FLHO*51
IFjFLH.GT.l.0) flH .. 10
c
C Mixture properties .nd ffictlOn f.ctor
C
100 OMiXNS .. fNSLH"DENL + (1 0 - FN5LH)*GOEN
DENMIX .. FLH · OENl + (1 0 - FLH)'"GOEN
VMIXNS .. FNSlH"ViSl • (1.0 - FNSlH)'"GVIS
RNUM .. 14880·0MIXNS*VM'"(DP/lZ.0}NMIXN5
FF" 1.14 - Z.0 '"ALOG10(APR/DP + ZI.Z5/RNUM'"·0 9)
FF .. 10IFf**Z.0
IF(IFREGU.Z) GO TO 130
c
v .. FNSLH/(FLH*" 2.0)
IFtyGT.l.0ANOV.lT 12) GO TO 110
YLN .. AlOG(Y)
S .. VLN/(-00SZ3 • 3 18Z'"YLN - o 872S'"(VLN'"'"Z 0)
, .O.018S3'"(VLN'"*40))
GO TO lZ0
110 S .. ALOG(ZZ·Y - 1.2)
lZ0 FF .. FF'"EXP(S)
C
C C.lcul.tlon 01 prusure gr.di,nts
C
130 EPGR" DENMIX·SIN(ANGRI/144 0
•
Index
A
API gravity, 366
Aquasorption, 261
Average pressure in gas pipe,
Abandonment pressure, 32
Abwd,." 212-213, 218-226,
261-262, 265-267
Absorption, 260-262, 263-271
B
Absorption dehydration. See
Beam pumping, 389
Dehydration.
Acentric factor, 44-45, SO, 64
Acid gases, 7, 255
removal of. See Desulfurization
P""""'" .
Additive injection, 208-2lO
requirements, 209-210
techniques , 208-209
type., 208
288-290
Binary interaction coefficient, 44
Slowdown of pipe, 562-563
Boiling point
cubic-average, 35
molar-average, 35
normal, 34, 35
Bottom-hole pressure
flowing. See flowing
bottom-hole pressure.
Adiabatic exponent, 358. 407,
static. See Static bottom-hole
pressure.
409-412
ADlP process, 264
Adsorption dehydration. See
Dehydration.
Aerosols, 128
Alkanol-amine process, 263-267
Alkazid processes, 268
Allowable pressure in pipes, 284
Brake horsepower, 423-424, 440,
448
Brown's chart, 48
Bubble point curve, 22, 31. 36
prediction of, 36
c
Allowable velocity in pipes,
284-285
Alumina. 236
Amine:s, 263-267
Annular flow, 347-348
Campbell method, 171, 174- 178
Centrifugal compressors, See
Compressors.
Centrifuge, 96-98
633
•
Gas Productioll Enginel'ring
63'
Characteristics. See ~tethod of
characteristics.
Chemical absorption, 263-271
Chemical potential, 26-27
Chokes, 101, 126, 250
flo\\
lhrou~.
354 ·359
purpose, 354-355
subsurface. 354-355
surface. 354 ·355
Cleaninf?;_ See Gas cleaning.
Clearance. -126-428
Clinedinst equation. 292
Commercial fuel costs, 4
Composition-composition
dia!{l'ams. 23
Compressibility, 68- 71
Compressibility factor. Sec
Z.factor.
Compression
adiabatic, 406-408
efficiency. 411. 423-424,
426-428
isentropic, 406-408
isothermal. '00
optimum ratio, 425
pol>1ropic, 408
406-412
pr~,
characteristics, 408-409
stages, 413. 424-425, 440
Compressors
aftercooler, 422
axial-flow, 401
centrifugal. 400-401. 403-406,
438-447
design, 438-447
continuous-flow, 394-395,
400-403
design
analytic method, 414-417,
438-439
centrifugal,438-447
charts. 423, 428-435, 441-445
Index
Mollier charts, 417-423, 439
reciprocating. 424-438
rotary, 448-449
dynamic, 400--402
intercooler, 413. 421
efficiency. 423-424
ejector. 402-403
mixecUlow. 402
multistae:e. 413. 424-425. 440
posith'e-displacement, 394-400
reciprocating. 396. 403-406,
424-438
clearance. 426-428
horsepower required. 426,
428-435
speed/stroke length, 435
volumetric efficiency, 426-428
rotary, 396-400
design, 448-449
helical-lobe. 400
liquid-piston, 399
sliding-vane, 398
spiral-lobe. 400
h"'o-impeller, 399
selection. 403-406
thermaL 402
types. 394-403
Computer programs, 604-631
compressibility and Z-factor,
607-611
critical pressure and
temperature, 606-607
friction factor. 615-616
interpolation
Lagrange, 615
linear, 620-621
multiphase flow
Beggs-s,m, 628 631
Hagedorn-Brown, 625-628
nomenclature for. 605-606
numerical integration, Romberg,
619-620
steady-state flow
horizontal, 616-619
vertical: Cullender-Smith,
621-622
vertical: Sukkar-CorneU.
623-625
viscosi~~
611-615
Concentric orifice. 462-463
CondensatE'S. See Gao: ('Ondf>no:~tt'"
Conservation of mass, law of, 29
Constant pressure process, 20
Constants, physical. 585
Contactor, 212-213, 218-226.
261-262, 265-267
Contaminants. 4
Convergence pressure. 135-136,
164
Conversion factors. 593-603
oil-field to SI. 596-603
Corresponding states. law of. 44,
50
Cricondenbar, 22, 34-35
Cricondentherm. 22, 34-35
Critical
compressibility factor. 45. 50
flow, 357-358. 456. 543, 563.
See also Flow, regimes.
locus, 23, 136
point, 20-23. 35
pressure. 20, 45, 46-49
saturation, 32
temperature, 20. 45, 46-49
Critical-flow prover, 456-457
Cullender-Smith method, 338-340.
345-347
Cunningham correction, 129
Cyclone, 98
D
Daltons' law, 29
DEA. See Amines.
635
DEC. See Glycol.
Dehydration, 207-208, 208-251.
521
absorption. 210-235
flow scheme, 211-213
plant design. 215-232
plant problems. 213-214
additive injection, 208-210
ad~rption, 235-250
adsorbent (desiccant) capacity.
242, 244-245
adsorbent (desiccant)
properties. 242
adsorbent types, 236
analysis of proces.~, 240-241
bed design, 243-250
bed regeneration cycle, 238.
239-240
breakthrough time, 245-246
chemical, 235
cycle time, 242
design variables, 241-242
flo\\' scheme, 237-239
minimum bed length, 246
physical, 235
regeneration calculations.
247-250
expansion refrigeration. 251
soh-ent properties, 210
Densitometer, 524
Density. 66
Desiccants. See Dehydration.
adsorption.
Desul£urization processes
alkanol-amine process, 263-267
alkazid, 268
Benfield, 267
carbonate, 267-271
Catacarb, 267
chemical absorption, 263-271
G-V, 267-268
Holmes-Stretlord. 268-271
•
636
Gas Production Engineering
hot carbonate, 267-268
iron-sponge, 258-259
molecuJar sieves. 259-260
physical absorption, 260-262
selection, 257-258
selectivity. 257
se1exol, 261-263
solid·bed (adsorption). 258-260
types. 256
water wash (aquasorption). 261
Dew point, 22, 36, 170
curve, 22. 36
depression. 170
prediction of, 36
Differential liberation, 116-117
Differential pressure. 454-457
Diluents, 4
DIPA. See Amines.
Directional flow. See Multiphase
flow.
Distribution coefficient. See
Equilibrium ratio.
Drag coefficient. 97
Dry ice. 20
E
Eccentric orifice. 462-463
Economics
gas transmission, 581-582
optimum pipe diameter, 577-580
EC. See Glycol.
Ejectors, 402-403
Elbow meter, 459
Electric precipitators, 134
Embrittlement. of steel, 128
EMR. See Eykman molecular
refraction.
EMR index, 57
Ener~y balance, 275-277
Index
Energy consumption, worldwide,
2-3
Enhanced oil recovery. 33
EOS. See Equation of state.
Equation of continuity, 552
Equation of motion. 552
Equation of state, 39-46
Benedict-Webb-Rubin. 42-43, 56
general form. 43-45
hydrate prediction. 206
Peng-Robinson, 43
Redlich-Kwong, 43
solution methods. 45-46
Starling-Carnahan, 55
Starling, 56
Van der Waals, 41-42
water content, 178-181
Equilibrium ratio, 27-29. 36. 45.
135, 189-193. 194-197
charts, 137-163
thermodynamic criteria of.
25-27
vapor-solid, 189-193, 194-197
Equilibrium vaporization ratio. See
Equilibrium ratio.
Equivalent diameter of pipe, 532.
538
Equivalent length of pipe. 532. 537
Erosional velocity, 284-285
Expansion factor, 67
Expansion refrigeration. 125-128,
250-251
Expansion, temperature drop due
to. 127
Eykman molecular refraction. 50.
57-62
F
Fanning friction factor. 282-283
Fillers, 4
Filters, 133
diatomaceous earth. 267
Finite difference methods.
555-562. 576
backward difference, 556
central difference, 556
explicit, 555-559
forward difference, 556
implicit. 558-559
Flange taps. 463
Flash calculations, 29-31.
134-136,164-166
Flash liberation. 117
F1ash tank. 212, 261-263
Flow
annulus. 347-348
liquid present in small amount.
366-367
modeling of, 532-550. 551-576
multiphase. See Multiphase flow.
nozzle;, 455
pipe
steady-state. See Steady·state
flow.
unsteady-state. See
Unsteady-state flow.
pipeline systems. See Pipeline
systems.
pressure profile. 289
regimes, 277-281. 282-283. 368
restriction/chokes, 354-359
critical flow, 357-358
subcritical £low, 357-358
steady-state. See Steady-state
flow.
temperature profile, 359-362
unsteady-state. See
Unsteady-state flow.
Flowing bottom-hole pressure,
341-347
average approximate. 341-342
637
Cullender-Smith method,
345-347
Sukkar-Cornell method. 344-345
F10wing temperature in pipe. See
Temperature profile.
F10w measurement
mass. 523-524
methods. 454-461
natural gas liquids, 524-525
problems. 521-522
two-phase. 525-526
F10wmeters
attribute;, 452-453
accuracy, 452-453
calibration curve, 453
linearity. 453
precision, 452-453
rangeability, 453
repeatability, 453
critical-flow prover, 456-457
differential pressure. 454-457
elbow meter, 459
flow nozzles, 455
mass, 523-524
inferential, 523-524
true, 523
natural gas liquids, 524-525
orifice meter, 454. See also
Orifice meter.
orifice well te;ter, 456
pitot tube. 455-456
positive-displacement, 457-458
reciprocating-piston, 457-458
rotameter, 459-460
rotary meter, 457-458
selection, 454
turbine meter, 458
two-phase, 525-526
ultrasonic meter, 461-462
venturi meter, 455
vortex-shedding, 460-461
•
638
Index
Gas Production t;nginFcring
Formation \"olurne factor, 67
Fortran programs. Sec Computer
programs.
Fracturing:. 13. 14
proppant. 13
Friction. 276
Friction factor. 282- 283
chart. 278
rU~ddty. :!7 -~, ';.5, 46. 179-181
Fugacity coefficient. 28, 29, 45.
46. li9 181
chart. 181
G
Cas cleaning. 128- 134
methods, 130
steps in, 128
Gas compressibility. 68-71
Cas compressibility factor. See
Z·factor.
Cas condensates, 11, 32
reservoir. 32
Cas constant, 26-27. 40, 79
Cas density. 66
Gas deviation factor. See Z-factor.
Cas drive reservoir
dissolved. 31
internal, 31
solution. 31
Gas formation volume factor. ()f
Cas gravity of total wellstrcam,
366
Gas horsepower, 423-424. 439-440
Cas hydrates. See Hydrates.
Gas lift, 390
Cas-liquid £low. See Multiphase
flow.
Ca .• ·oil ratio, 32-33
producing. 32
Gas production
system optimization, 33
worldwide, 5-6
Gas relief valH~:S. 91
Gas resen·oir. 32
Gas specific heat. See Specific
heat.
Gas transmission economics.
581 582
Gas. type of
condensates. 11
dissolved or associated. II
free gas. 9
in brine, 14
in solution, 9
non-associated, 10
Gas viscosity. 72-79
Carr et al. method, 72- 75
dynamic. 72
kinematic. 72
Lee et al. method. 7S- 79
single-component, 75-76
Gathering systems. 529-531
axial. 529-530
common-line, 530-531
radial. 529-530
trunk-line. 530-531
well-center, 530-531
Gels. 236-237
Giammarco-Vetrocoke process.
267-268
Gibbs free energy. 25
Gibbs phase rule, IS- 19
Glycol, 208. 210-232
contactor, 218-226
corrosion, 214
decomposition, 214
flash separator, 231-232
injection pump. 209
10=;,213
plant design, 215-232
plant problems. 213-214
pump, 214. 230-231
reboiler. 226-228
reconcentration. 214
stripping still. 229-230
vapor flooding. 214
GOR. See Gas-oil ratio.
Gravity settling. 98-100
H
Hammerschmidt's equation, 209
Holmes-Stretford process, 268-271
effluent stream. 270-271
Stretford solution, 269
Horizontal flow, 285-305, 368-371
Horizontal separator. See
Separators.
Horsepower. 416. 423-424.
438-440
Hydrates, 183-20S, 521
conditions promoting, ISS-1S6
curve, 184-185
formulas, 184
from sudden expansion. 186
phase behavior. IS4-ISS
prediction. 186-207
approximate. 186-187
equations of state. 206
Katz et aL, IS9-193
McLeod-Campbell . 2O-t-206
Trekell-Campbell , 193.
197-207
prevention. See Dehydration.
without sudden expansion, IS6
Hydraulic radius, 277-279
I
Ideal gas, 40
deviation from ideality. 40-41
639
Ideal gas law. 40
Ideal horsepower, 416. 423-424.
438-440
Impingement. 100. 130-133
Inclined rIow. 305-348, 381-383
Inhibitors_ i_ 208-210. 521
Intensive properties. 20
Iron-sponge process. 258-259
l<:<'ntropic exponent. 358 . ..Wi
409-412
Isobaric process. 20
Isobaric specific heat. See Specific
heat.
J
Joule-Thomson effect. WI. 126,
250, 360-361
temperature drop upon
expansion, 127
K
Katz et al. method. 189-193
Kay's rule. 46. 51-52
Kirchhoff's laws, 543-544, 574
K-values. See Equilibrium ratio.
L
Laminar flow. See Flow. regimes.
Latent heat
fUSion, 20
vaporization. 20
Law of conservation of mass. 29
Law of corresponding states, 44. 50
Lever's rule. 24
Liquid
discharge valves, 91
loading. See Liquid loading.
recovery maximization, 116
•
640
641
Cas Production Engineering
settling volume, 103-104, 114.
ll7. 119. 121-122
s1ugs. 91
surging. 90
Liquid loading, 385-391
minimum rate for prevention.
386-388
prevention, 386-388
unloading, 388~391
beam pumping. 389
gas lift. 390
plunger lift, 389-390
small tubing. 391
surfactantisoap injection. 391
Lockhart-McHenry method,
165-166
Log-mean temperature, 286
Looped pipes. See Pipeline systems.
Low temperature separation.
Molecular sieves, 237, 259-260
acid-resistant, 237
poisoning, 260
MoHier charts, .117-423, 439
Moody friction factor, 278.
282~283
~Iultiphase
flow. 365-391
directional wells. 381
hilly terrain' inclined. 382-383
horizontal,368-371
liquid loading. See Liquid
loading.
pressure traverse curves. 369-379
small liquid presence, 366-367
vertical, 372-380
Multipole correction factor, 64
N
125-128.250-251
LTX units. 125-128, 250-251
M
McCabe-Thiele diagram. 220,
226-227
McLeod-Campbell method.
204-206
McKetta-Wehe correlation, 171.
172
MOEA. See Aroines.
MEA. See Amines.
Measurement. See F10w
measurement.
Measurement devices. See
F1owmeters.
Method of characteristics, 559-562
MFH. See Fracturing.
Miscible injection, 33
Mist extractor. See Separation.
Xatural gas
constituents, 4, 7
physical data, 586-591
consumption, 2-3
contaminants, 4
"""'. 4
development, 1-4
diluents, 4
field processing, 89
fillers, 4
history, 1
hydrate;:, See Hydrate;:.
occurrence, 9~14
coal, 14
geologic structures, 8-10
geopressured aquifers, 14
reservoirs, 10
tight sands, 13
tight shales, 13-14
origin, 8
production, 5-6
production system, 14-15
water content, 169-183
Newton's law, 129
Non-ideal gas, 40
Nozzles, 455
o
Oil-field units, 593-594
conversion to Sl, 596-603
Optimum pipe diameter, 577-580
Orifice meter, 454, 462-522
accuracy, 520-521
calculations, 467-519
installation, 465-466
factors, 470-519
basic, 470-475, 486-489
expansion, 479-485, 494-497
flowing temperature. 498
gauge location, 517-518
manometer, SOl. 517
orifice theTmal expansion,
518-519
pressure-base, 489
Reynolds number, 475-479.
490-493
specific gravity, 498
supercompressibility. 498-516
temperature-base, 498
pressure measurement/recording,
466-467
direct-reading chart, 466
square-root chart, 466
pressure tap locations, 463-464
corner taps, 464
flange taps 463
pipe taps, 463
vena contracta, 463-464
rounded-edged. 457
selection, 518-519
sha~edged, 456-457, 462
square-edged, 462
straightening vanes, 464-465
t}1)E$, 462-463
concentric, 462-463
eccentric, 462-463
segmental, 462-463
Orifice well tester, 456
p
Panhandle A equation, 291, 537
Panhandle B equation, 291, 537
Paraffinic, 35
Parallel pipes. See Pipeline systems.
Partial pressure, 28, 170
Particulate matter, 128
Peng-Robinson equation, 43
Phase behavior
applications, 31-33
multicomponent systems, 21-25
single-component systems, 19-21
Phase diagrams, 18-25
pressure-temperature diagram,
19. 21-22
pressure-composition diagram,
24-25
ternary diagram, 24
Phase rule, 18-19
Physical absorption, 260-262
Physical constants, 585
PhYSical data for gas constituents,
586-591
Pipeline
advantages of, 275
aging/corrosion, 531
allowable pressure, 284
allowable velocity, 284-285
average pressure. 288-290
blowdownlpurge, 562-563
capacity factor, 581
closing valve, 563
•
64.
Cas Production Enginet'Ting
economics, 577-582
efficiency, 292, 303
flow modeling, 532-550,
Polytropic head. 438-439
Positive-displacement. 394-396,
551-576
flow through
Pressure traverse curves. See
Multiphase flow.
Processing of natural gas
dehydration. See Dehydration.
desulfurization. See
Dcsuifurization processe<>
Pseudocritical, 34
pressure. 46-49
temperature, 46-49
Pulsating flow, 521-522
steady-state. See Steady-state
flow.
•
bide,;
unsteady-state. See
Unsteady-state flow.
load factor, 582
pressure deration. 531
pressure profile, 289
pressure testing, 563-564
reserve factor, 582
roughness, 281
storagefbuffer capacity, SOt, 582
transmission factor, 303
trash. i, 128
variable demand. See Variable
consumer demand.
Pipeline systems, flow through
steady-state, 532-550. See also
Steady.state flow.
looped, 535537
networks. 541-550
looped, 545-550
loopless, 544-545
parallel, 533-535
series, 532-533
unsteady-state, 551-576. See also
Unsteady-state flow.
approximate solutions,
562-572
networks, 573-576
pipes, 551-562
Pipe taps, 463
Pitot tube, 455-456
Plunger lift, 389-390
Poi).tropic efficiency, 411
Polytropic exponent, 409-412
457-458
R
Real gas behavior. 40
Reciprocating compressors. See
Compressors.
Reciprocating-piston meter,
457-458
Redlich-Kwong equation, 43
Reduced density, 56
Reduced pressure, 50
Reduced temperature, 50
Refrigeration. See Expansion
refrigeration.
Regeneration, 239-240, 258-261
Relative paraffinicity, 35
Reserves
classification, 11
possible, 13
potential, 1\, 13
probable, 11
proved, 11-12
worldwide, 12
Reservoir
abandonment pressure, 32
condensate, 32
engineering, 33
gas, 32
oil, 31, 32
undersaturated oil, 31
Residence time, 96, 104
Restrictions. gas flow through,
354-359
critical,357-358
subcritical. 357-358
Retrograde
condensation, 32
region, 22
Revaporization, 32
Reynolds number, 129, 277-281
Robinson et al. correlation, Iii,
173-175
Rotameter, 459-460
Rotary meter. 457-458
Roughness, of pipe, 281
S
Scrubbers, 133-134, 211-212,
215-218
cartridge, 134
dry, 134
oil-bath, 134
specifications 216-218
Segmental orifice, 462-463
Selexol process, 261-263
Separation
baffle
angle, 92
centrifugal, 91
conical,91
plate, 100
centrifuge, 96-98
coefficient, 99, 102
differ