TOPIC
Gas Pipeline Flow
•
Gas gathering Systems
•
Gas Flow Equations
•
Gas Pipeline Flow Calculations
•
Corrections for Elevation Changes
•
Multiphase Flow in Pipe
Expected Outcomes
Students should be able to
• Explain different types of gas gathering system
• Identify various types of gas flow equation
• Calculate various gas flow parameters using
suitable gas flow equations
• Explain different types of flow pattern in pipes
2
Natural Gas Flow System : Gathering & Transmission Lines
3
Gas Gathering System
•
Consists of :
–
–
–
•
•
•
Size and complexity (separator, dehydrator, sulfur plant, etc.) may vary both within
a gas producing area and from one area to another.
Smallest gathering system consists simply of two or more gas wells interconnected
by a pipeline system and tied directly into a distribution system.
A dry gas field :
–
•
may have no processing equipment except drips at each well and in low places in the line.
For a wet gas field :
–
•
piping between individual wells in a gas field,
processing equipment and
compressor station at the inlet to the transmission or distribution system.
drips, separators, heaters, and a gasoline plant may be required.
For large fields and several interconnected fields :
–
–
Involving hundreds of miles of piping, gathering system
May include, beside piping and valves, such equipment as drips, separators, meters, dehydrators,
gasoline plant, sulfur plant, cleaners and compressors.
4
Gathering System Layout
• Layout of the gathering system is influenced by
several factors. Among the most important are:
–
–
–
–
–
Overall economy
Shape of the field
Future development
Roughness of the terrain
Required system reliability, etc.
• Three commonly used layouts are loop, radial and
lateral.
• Generally one or a combination of these layouts will
be selected for most gathering systems.
5
Gathering System Layout
Well
Loop
Separator or satellite
gathering point
Radial
Compressor station
(central facility)
Lateral
6
Loop Gathering System
• Main gathering lines laid in the form of a loop
around the field.
• Individual well flow lines connected to the
main gathering lines
• Not economical i.e, pipe costs, however it
permits system operation while a part of the
loop is being repaired
7
Radial Gathering System
• Main gathering lines laid radially out from a central
processing facility near the field center
• Gas collected from several wells at a common point
where it may be transported directly to a central
facility or partially processed and then transported to
a central facility
• Generally applicable when :
– moderate to large amount of liquids are produced
– two phase flow of liquids, and
– gas would cause excessive pressure drops in the individual
flowlines
8
Lateral Gathering System
• Main gathering lines :
– runs through the field, and
– wells are produced directly into the main line from
either side
• Generally restricted to:
– dry gas fields having short individual well flow
lines, and
– usually represents the minimum pipe cost system
9
Gathering System Selection
• For small gas fields:
– relatively simple, because ;
• All three plans probably suitable, and
• little difference in initial cost will be apparent
• For larger fields :
– difference in cost between all three plans can be considerable
• Necessary for economic study :
– flowline cost and
– processing facility cost
to determine which plan will result in the best economic ?
10
Main Gathering System Sizing
Depend on the following factors:
•
•
•
•
•
•
•
•
Number & design of compressor stations
Anticipated peak day demand
Safety at maximum pressure
Initial reservoir pressure of wells
Expected production of wells
Whether liquid condensate, water & hydrate may be present
Line pressures to be maintained as well as future lower pressure
Allowable pressure drop when producing the field with
compressors
• Final abandonment pressure
11
Gas Flow Equation
• Many formulas can be used in gas flow
calculations:
–
–
–
–
–
–
–
Weymouth
Panhandle
Oliphant
Smith
Sptizglass
Gustafon
Various companies, etc
• Most of these formulas are relatively satisfactory
for use within the range of:
– line sizes,
– lengths and
– flowing pressures for which their empirical constants
were determined.
@ Sometimes the errors are too large
12
Gas Flow Equation - General
Derived from basic mechanical energy balance (Bernoulli’s theorem)
 Tb
Q  K 
 Pb
Q
K
Tb
Pb
P1
P2
d
gg
T
L
f
=
=
=
=
=
=
=
=
=
=
=


  P12  P22 d 5 
 


  g g TLf
1
2
flow rate (SCF/D)
Valid for:
constant
• Compressible fluids flow
base temperature (oR)
• Isothermal
base pressure (psia)
• Steady state
• No work done upon gas by
inlet pressure (psia)
external means
outlet pressure (psia)
• Gas @ Boyle’s law
ID of pipe (in)
• Pipeline level
gas SG (air = 1.0)
average flowing gas temperature (oR)
length of pipe (miles)
coefficient of friction (friction factor) - dimensionless
13
Factors Affecting Flow
Can be divided into two main classes:
1.
Factors which are inherent in:
1.
2.
pipeline such as length, diameter and wall roughness and
flowing gases such as density, viscosity and velocity
(the relationships between these factors form the bases for all
pipeline flow formulas)
2.
Factors which are due to:
1.
2.
3.
construction characteristics and
operation of the line and
which are largely undetermined in nature e.g. the presence of
rust or liquids in the line, bends, valves, drips, lack of roughness
of the pipe, construction joints, river and road crossing, etc.
Therefore, an average efficiency factor (E) based on
operating experience is applied to the flow formula
14
Flow Formulas Different ?
•
Various flow formulas may be classified into three
main groups on the basis of how the friction factor
is determined:
1.
2.
3.
•
Formulas in which f is constant
Formulas in which f is a function of the diameter of the
pipe (ex: Weymouth’s formula & Oliphant’s formula)
Formulas in which f is a function of Reynold’s number
(ex: Panhandle Eastern formulas)
None of gas flow formulas recommended for field
gas operations fall in the first category
15
Weymouth’s Formula
• Used for sizing gas lines operating at pressures
from 35 – 100 psig without modification (i.e.
without za). The degree of error increases with
pressure
• By including za (a gas compressibility factor)
evaluated at the average pressure and
temperature of the gas in the line, the formula
is used for the design of short pipelines and
high pressure gas gathering system (P > 100
psig), injection system and gas lift system
16
Weymouth Formula Assumption
Weymouth assumed that f varied as a function of the
diameter in inches as follows:
0.008
substituting the value of f 
inthe general flowequation :
1
d 3



2
2
5 
 Tb   P1  P2 d 
Q  38.77  

 0.008  
 Pb  
g g T L 1 

 d 3  




1
2
d
8
3
1
2
2
5 2

P

P
d
8
 Tb 
1
2
 d 3
Q  433.5   
 Pb   g g T L 
17
Weymouth Formula with Za
With the gas compressibility factor included, Weymouth
formula becomes:
 Tb 
Q  433.5  
 Pb 
1
 P  P  2 83

 d
 g g T L z a 
2
1
2
2
where: za =
gas compressibility at average T and average flowing
pressure (Pavg)
Pavg
2

3
P P 
 P1 P2 
2 

 

 P1  P2  
3 
P P 
 P1  P2 
3
1
2
1
3
2
2
2
1
2
To get za :
 Fig. 16-6: gg  Tpc , Ppc  Fig. 16-3: Tpr , Ppr  z
 or use Fig. 10-5  (1/z)1/2
18
Pseudocritical Properties @ Natural Gas
19
Natural Gas Compressibility Factor
20
Deviation Factors
21
Gas Flow Based on Weymouth Formula @ Low q System
22
Gas Flow Based on Weymouth Formula @ High q Gathering System
23
Gas Flow Based on Weymouth Formula @ High Pressure
Gathering System
24
Gas Flow Based on Weymouth Formula @Cycling Plant
Gathering System
25
Gas Flow Based on Weymouth Formula @Cycling Plant Injection System
26
Oliphant’s Formula
• Recommended for design of low pressure gas gathering
system
• Extensively used for designing vacuum and low pressure
(25 – 35 psig)
 5 2  d   14.4   Tb   0.6   520   P12  P22 
 

Q  1008 d    
   
 
 30   Pb   520   g g   T   L 

3
1
2
27
Oliphant’s Formula
Low P Gas System (100 psia & less)
28
Panhandle’s Formula
•
Recommended for large diameter and long pipelines (transmission and gas
delivery)
Panhandle A
Panhandle B
0.085
f  f  Re   f 
Re0.147
0.5394
1.07881
2
2
 P1  P2 
 Tb 
Q  435.87  
d 2.6182 E
 0.8539

 g g T L z 
 Pb 
0.015
f  f  Re   f 
Re0.0392
0.51
1.02
2
2
 Tb   P1  P2 
2.53
Q  737    0.961
 d E
 Pb   g g T L z 
where :
E  efficiency factor (average = 0.92, based on experiment)
E  0.92 for large diameter: e.g.for d = 36"  E  0.98
E  0.92 for small diameter : e.g . for d 16"  E  0.828
29
Panhandle Formula @ Gas Transmission System
30
Correction for elevation changes
• In actual practice, transmission line often deviates
considerably from the horizontal.
• There are several methods to make correction for
elevation changes including the configuration layout of
the pipeline.
• Some methods are very simple, but only applicable for
certain situations  Method 1.
• Some methods are very complex, mostly in practical
usage it requires a special computer programming to
solve the problem.
31
Panhandle Equation
Correction for elevation changes
Panhandle A
 2
(0.0375g g (h2  h1 ) P
2
1.0788
 P1  P2 
Tavg zavg
 Tb 
2.6182

Q  435.87  
d
E
0.8539

P
g
LTavg zavg
g
 b


2
avg






0.5394
Panhandle B
 2
(0.0375g g (h2  h1 ) P
2
1.02
 P1  P2 
Tavg zavg
 Tb 
2.53

Q  737   d E
0.961

P
g
LTavg zavg
g
 b


2
avg






0.51
32
Gas flow in series, parallel, and looped pipelines
•
Flow in series, parallel, and looped are necessary to:
– increase pipeline throughput while maintaining same pressure drop and level
– repair old pipelines, broken, corrosion, etc. without reducing required gas
amount to be transferred
– develop new gas wells in existing area
•
Philosophy involved to solve complex transmission system:
– Equivalent length of a common diameter
– Equivalent diameter of a common length
•
Equivalent: both lines will have the same capacity with the same total pressure
drop
•
Note: All the examples that follow will be based on the Weymouth’s equation
33
Series Pipelines
Weymouth eq:
 Tb 
Q  433.5  
 Pb 
Original
1
 P  P  2 83

 d
 g g T L z a 
2
1
2
2
Total equivalent length:
LAeq = LA + LB(DA/DB)16/3
Flow Rate change (%):
Modification to series with B line
 capacity ?
dQ = {(1/ LAeq )0.5 – (1/L)0.5}/(1/L)0.5
34
Parallel Pipelines
Original
Percent increase in capacity :
% dQ = 100(DB/DA)8/3
Modified to parallel with line B  capacity ?
35
Looped Pipelines
Only a part of line parallel
% increase in capacity:
% dQ = 100[(q – qo)/qo]
= 100[(Lo/L’)0.5 – 1]
Where;
qo = original flow rate before looping
q = flow rate after looping
Lo = original pipeline length
L’ = equivalent of pipeline after looping
= L’AB + Lc
L’AB = [1 / (1/LA)0.5(1 + {DB/DC}8/3)]2
LA = length of looped section
DB = ID of looped section
DC = ID of series section
36
Formulas Comparison
37
Correction for elevation changes
• In actual practice, transmission line often deviates
considerably from the horizontal
• For elevation changes:
P  e P 
Q  A

Le


2
1
s
2
2
1
2
where :
e  2.7183 (base of natural log )
0.0375 g g h
s
Tz
h  change in elevation, ft (h is positive if outlet is higher than inlet )
Le  effective length of pipeline, miles
 Tb 
A  K  
 Pb 
 d

g T
5


f
1
2
38
Correction for elevation changes
• Effective length, Le of the pipeline is based upon the profile of the
line between pressure-measuring stations
• If the slope is uniform:
 e 1 
 L  JL
Le  
 s 
s
 e 1 

where : J  
 s 
s
39
Correction for elevation changes
• If the slope is not uniform, the profile should be divided into
sections of nearly uniform slope
• The effective length is then calculated as follows:




 e s1  s2 e s3 1 
 e s1 e s2 1 
 e s1 1 
 L1  
Le  
 L3  ......... 
 L2  
s3
s2


 s1 




 e  sn  1 e sn  1 
 Ln

sn


 J1 L1  J 2 e s1 L2  J 3 e s1  s2 L3  .........  J n e  n 1 Ln
s
hn
where : s1 
s2 
sn 
0.0375 g g h1
h4
Tz
0.0375 g g h2
Tz
0.0375 g g hn
Tz
h3
h2
h1
40
Pressure Drop in Pipe
As much as 80% total pressure losses @ flowing well
Pressure drop as a function of:
– Wellbore mechanical configuration
– Fluid properties
– Production rate
• Based on energy equation:
P1
g
v12
P2
g
v22
--- + -- Z1 + a ----- = --- + --- Z2 + a ----- + W + El
r
gc
2 gc
r
gc
2 gc
•
•
41
Pressure Drop in Pipe
•
Based on energy equation:
P1
g
v12
P2
g
v22
--- + -- Z1 + a ----- = --- + --- Z2 + a ----- + W + El
r
gc
2 gc
r
gc
2 gc
where;
a = kinetic energy correction factor for velocity distribution
W = work done by flowing fluid
El = irreversible energy losses @ system (friction losses, etc)
42
Pressure Distribution in Pipe
•
For most practical application:
– No work done on/by the fluid  W = 0
– Kinetic energy correction factor = 1.0
 Energy balance between two points @ system:
/\P / r = (g/gc)/\Z + [/\(v2)]/2gc + El
•
El = energy loss per unit mass, ft-lbf/lbm
Total /\P = /\potential energy + /\kinetic energy + energy losses (friction)
– /\potential energy  elevation
– /\kinetic energy  acceleration
dP
g
rvdv
f r v2
--- = -- r sinq + ----- + -----dL
gc
gc dL 2 gc d
 Pressure transverse/distribution curve @ condition (q, GLR & pipe size)
43
Pressure Drop in Pipe
•
SINGLE PHASE LIQUID FLOW
dP
g
rvdv
f r v2
--- = -- r sinq + ----- + -----dL
gc
gc dL 2 gc d
– f = friction factor  Moody friction factor (function of NRe)
44
Single phase gas flow
Gas density = PM/zRT
Where P = pressure, M = molecular weight, z = compressibility factor, R = gas constant
Pressure drop :
dP/dL = 5.057x10-17 { f SGgas Qsc 2 zT/d5 }{1/P} + 0.01875 P SGgas sinq / zT
Where;
dP/dL = pressure drop, psia/ft
M = 29 SGgas
Psc = 14.7 psia
Tsc = 520 oR
R = 10.732 cuft.psia/lb-moleoR
Qsc = scf/d
P = pressure, psia
d = diameter, ft
T = temperature, oR
L = length, ft
f = friction factor
To solve the equation  assume that z, T and f constant  defined by average value  rewrite dP/dL & integration from P1
to P2 and define C1 & C2 = constant
C1 = 5.057x10-17 f SGgas Qsc2zT/d5
C2 = 0.01875 SGgas sinq /(zT)
(C1/C2) + P12 = {(C1/C2) + P22}exp(2C2L)  C1/C2 = 2.6977x10-15 f(QscZT)2 / d5 sinq
45
Two-phase flow
• Gas reservoir may produce liquids (condensate or water)
• Gas pipelines may carry some liquids  affect pressure drop (more complex)
• Two important characteristics (multiphase vs single phase flow)
• Existence of slippage (gas-liquid)
• Presence of flow regimes
• Drops in transmission pressure in a horizontal two-phase gas condensate line are
greater than in a dry gas line
• Even relatively small amounts of liquid increase such pressure drops considerably
• Contributing factors are:
– energy lost in accelerating and transporting the liquid
– increase roughness caused by wetting the pipe wall and by waves on the surface
of the liquid
– reduction in available flow area due to introduction of a liquid phase
•
•
In hilly terrain, even more energy is lost in lifting the liquid over individual rises
The additional pressure drop appears to depend largely upon the gas velocity in the
pipeline
46
Pressure Distribution in Pipe
MULTIPHASE FLOW
• Pressure calculation depend on predicted flow pattern (bubble, slug,
transition or mist)  iterative & trial & error
•
Many researchers have proposed method to estimate pressure drop, i.e.
– Poettman & Carpenter – earliest researcher  pressure-traverse curves for oil
wells
– Gray – gas well
– Brown & Beggs
•
Pressure-traverse curves for particular tubing diameter, production rate &
fluid properties (mixture)
dP
g
rmvmdvm
fm rm vm2
--- = -- rm sinq + --------- + ----------dL
gc
gc dL
2 gc d
47
Reynolds Number
In field units:
Re = 1488Dvr / m
D = diameter, ft
m = viscosity, cp
r = density, lbm/cuft
v = velocity, ft/s
D = diameter
m = viscosity
r = density
Re < 2100 : laminar flow
Re = 2100 : turbulent flow first apparent
Re = 2100 – 3500 : transition flow
Re> 3500 : Turbulent flow
In petroleum :
•Water-like viscosity : turbulent flow
•Viscous oil : laminar flow
48
Velocity Profiles in Laminar & Turbulent Pipe Flow
•Laminar flow:
•Individual fluid particles moving only in flow direction with no fluid movement across pipe
•Turbulent flow:
•Rapidly fluctuating flow velocity components in random directions
•Newtonian fluid:
•Viscosity independent of shear rate
•Non-Newtonian fluid:
•Viscosity shear rate dependent
•Apparent viscosity decreases as shear rate increase
•Very different velocity profile across tubing
•HF stimulation & gravel packing operations
49
Frictional Pressure Drop
Fanning eq:
fm = Moody friction factor
Moody friction factor diagram or Chen eq:
•Laminar flow (Re < 2100):
•Frictional pressure drop independent of tubing roughness & proportional to fluid velocity
• fm = 64/Re
•Turbulent flow (Re > 3600):
•Frictional pressure drop very sensitive to exact inner pipe wall nature & fluid flow conditions (Re)
•Important factor : relative pipe roughness (e/D)
•e = absolute roughness, which depend on:
•Pipe metallurgy
•Coating material
•Fluid velocity (corrosion @ high rates)
•Fluid corrosivity (pH, solid, CO2, H2S)
•Deposits (hydrates, paraffin, asphaltenes)
•Years in service (used tubing :@numbers of years, 15 x roughner than newly installed tubing)
•Jain eq: 1/ f0.5 = 1.14 – 2log{(e/d) + (21.25/Re0.9)}
50
Moody Friction Factor Diagram
51
Flow Regime of Mixing Fluid in Pipe
•Not mix fluids:
•Turbulent flow : mixing zone between fluids will be small
•Laminar flow: trailing fluid centre portion penetrate a long way into leading fluid  two fluids arriving
simultaneously at tubing bottom & being mixed during injection into perforation
•Mixing fluids:
•Turbulent flow: mixing of two fluids stream occurs rapidly
•Laminar flow: concentration gradients occurring in transverse direction across pipe for substantial distance
52
Multiphase Flow In Pipe
•
•
•
•
•
•
When there is great density difference  slip & hold-up phenomenon
Slip:
– Less dense (lighter) phase ability to flow at greater velocity than denser (heavier) phase
Hold up:
– Consequence of slip
– Volume fraction of pipe occupied by denser phase is greater than would be expected from (relative)
in – and outflow of two phases, since its velocity slower than light phase
Superficial phase velocities (VSL & VSG)
– Liquid: VSL = qL / Ap
– Gas : VSG = qg / Ap
– q = phase volume flow rate
– Ap = pipe cross sectional area
In situ or actual velocity (VL & VG)
– Liquid : VL = qL / AL = qL / HL Ap
– Gas : VG = qG / AG = = qG / HG Ap
– AG = actual area of pipe occupied by gas
– AL = actual area of pipe occupied by liquid
Slip velocity : Vs = VG – VL = (VSG/HG) – (VSL/HL)
53
Hold-up Factor
•
•
•
•
•
To combine physical properties of phases flow in multiphase flow in pipe
4 types:
– Liquid holdup – HL
– No-slip liquid holdup – lL
– Gas holdup – HG
– No-slip gas holdup - lG
Liquid holdup:
– HL = liquid volume in pipe / pipe volume
– If HL = 1.0  only liquid flow in pipe
–
HL = 0  only gas flow in pipe
Gas holdup:
– HG = 1 – HL
No-slip liquid holdup:
– Ratio between liquid volume in pipe volume and total pipe volume when liquid & gas flow in the same velocity
•
•
lL =
qL / ( qL + qG )
No-slip gas holdup:
– lG = 1 - lL = qG / ( qL + qG )
54
Multiphase Flow In Pipe
55
Segment of Vertical Pipe Flow
56
Multiphase Fluid Properties
•
Liquid/gas mixture density:
rm = rLfL + rG(1-fL)
fL = liquid volume fraction
No slip flow:
rm = rLlL + rG(1-lL)
Slip flow:
rm = rLHL + rG(1-HL
• Viscosity of liquid/gas
mixture:
mm = mLHL + mg ( 1 – HL)
Slip viscosity:
mm = mLHL + mg ( 1 – HL)
No-slip viscosity:
mm = mLlL + mG(1-lL)
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Oil/Gas Flow @ Pipe
• Flow pattern @ pipe function of:
– Gas & liquid flow rates
– Pipe inclination angle
– Pipe diameter
– Phase densities
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Flow Pattern in Vertical Pipe
•
•
•
•
At c : 1st gas bubbles appear  fluid mixture velocities increases & average fluid density decrease
Formed bubbles widely dispersed in liquid
Continued flow upward :  further pressure reduction, more bubbles created – still remain widely dispersed in
continuous liquid phase  “bubble flow regime” : low density gas bubbles flow rate > liquid  slip occurring & HL
increases
Further upward flow : gas phase volume & mass increases, corresponding to reduction in liquid phase volume & mass.
Intense mixing ensure gas & liquid phases in equilibrium as P reduces Gas phase composition changes with evaporation
of higher molecular weight HC.
•
More gas bubbles  bubbles coalescence  fill entire tubing cross section & form slug (very large gas bubbles @
constant size separated from each others by areas of liquid containing smaller gas bubbles.  “slug flow regime” : gas
slugs act as efficient mechanism to lift liquid to surface (slip minimised).
•
Velocity increases @ gas expansion & volume increases  large gas slug breaking up into wider gas bubbles sizes range
 “churn flow or froth flow ” : highly turbulent flow pattern dispersed within one another.
•
Further upward flow: gas liberation & expansion continue  phases separate into central, high velocity core of gas
with continuous liquid film on tubing wall  “annular flow regime”
•
Shear at gas/liquid interface from gas velocity continue to increase, destroy annular ring of liquid on tubing wall &
disperse it as “small droplets mist”  “mist flow regime”
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Flow Regime Mapping @ Vertical Pipe
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Multiphase Flow in Inclined Tubing
• Much easier for gas to separate from liquid as in vertical
• Much greater difference between actual & superficial phase
velocities than vertical
• Alters flow regime as inclination angle (q) increases from
vertical
•  tubing length (L) greater than vertical tubing depth (H)
L = H/ cos q
•  hydrostatic head component of total downhole increases
with angle (q) increases due to HL increases
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Flow Pattern @ Horizontal Pipe
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Horizontal flow pattern
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Vertical Flow Pattern
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THANK YOU
FACULTY OF PETROLEUM & RENEWABLE ENERGY ENGINEERING (FPREE)
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