Celculation of Static Press',,;re Gradients iu Gas WelliS
By M. J. RZASA· AND D. L. KATZ,· MEMllER A.I.M.E.
(New York Meeting. February 1945)
P2 = picssure at boUma (/ w;;'I,
ABSTRACT
lb. per sq. in. abs.
'i'm;; derivations of three methods of com·
G = gas gravity
puting the :;tatic pressure gradients in n~tural
have been presented to show the
aS3umptions made. Charts were developed from
which the pressure gradients may be read when
the .vell·head pressure, the well fluid gravity,
depth, ~ nd the average wdl temperature are
given. A chart for estimating the well fluid
gravity from the condensate content and separatlJC gas gra.vity is included. The effect of the
increased average well temperatuce after flow
on the calculation of the static pressure
gradient is discussed.
X = depth of well, ft.
Au alternate method is to compute the
average density of the gas in the w.::ll and
multiply by the well depth ill a ms.nncr
similar to that used for liquid gradients.
gas wp.l1s
INTRODUCl'ION
Reservoir pressures have been calculated
A static pressure gradient is a special
case of the general fluid-flow equation.
Consider a pound of fluid flowing in a
vertical column from point I to point 2,
Fig. I. By an energy balance for fluid
flowing from ! to 2:
.;com weil-heed pressures for gas wells for
'11any years. As tne pressure measurements
become more accurate, the need for a
:-eH!l.blc calcdation of the static pressure
c(rac1ient ofle!l arises. This paper will
develop the several methods for computing
the pressure gradient in gas wells and make
'l. comparison between them.
The method of calculating static pressure
gradients in common use is Eq. I (ref. I)
or its counterpart which includes a factor
for the deviation of the gas from the ideal
gas law.
in which PI = pressure at well head, lb.
per sq. in. abs.
Manuscript received at the office of the
Institute Nov. 6. 1944. Issued as T.P. 1814 in
PETROLEUM TECHNOLOGY. March 1945.
• University of Michigan, Ann Arbor.
Michigan.
in which U = internal energy, ft-Ib. per
lb.
P = pressure, lb. per sq. ft.
V = volume, cu. ft. per lb.
u = average linear velocity, ft.
per seC.
X = height above datum, ft.
q = heat absorbed by fluid, ftlb. per lb.
W = work done by system, ft-Ib.
per lb.
An energy balance on the fluid itself gives:
U = JTdS - fPdV
+ etc.
bJ
in which T = temperature, deg. R.
S = entropy, ft~lb. per deg. R.
per lb.
leo
COPYRIGHT, 1944 AND 1945, BY THE
AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS
(INCORPORATED)
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DERIVATION OF FORMULAS
,
,
!
1
. '--1- H
t+t- "1
"
, .~
I
....
w
2000
.,
w
: ,
!--+-t-t--'-.1......l-j.--I-+-+-I-4-++-++--'-++-~~~-:++-t-lM E THO
~
.
b'
I
I' II
,
~
j
i
,
,
!
i
!
~
~
.E,~ ~~ RIM ~ NTA ~r+-t
j/---t-+-+-'l'-<:!-'+"I~#-....-+-++++--H-t--++++-+-+-~'=t~t-ttt"i=~.::;~-tti
4000
i
'"
~~~ ~~~~~~~Hr.i4-~+~~:4-~,~~~~~4~~~++~-~~Hr~-~+~
....-or
H-i-H-+++-t-H-t-+-!-H-+++-H M E ~ HOD . 1 II '
,
,
k.II
a 6000
2100
2800
PRESSURE:
-t,-++--+--1"~N--H--H-t-+-!-t-t-++--r++-H
-j'
2900
3000
LBS,jS~.IN.
Fw. r.-DEPT.H-PF,ESSURE GRADIENT IN GAS WEH..
3100
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~
I02
CALCULATION OF STATIC PRESSURE GRADIENTS IN GAS WELLS
etc. = increase in all forms of
energy other than heat and
. compression
If friction losses are defined as W" then
fTdS = WI
+q
A combination of Eqs. 2, 3, and 4 gives the
general fluid-flow equation:
J
VdP
2
+ Au
+ AX + W, + W.
2g
+ etc. =" [sl
This equation gives the true pressure
gradient as a function of the specific
volume of the fluid throughout the wen.
If actual values of V were available
throughout the well, the solution for P
would be found such that the area under
the curve of V versus P from PI to P 2 would
equal the depth of the well X. In the
absence of experimental values for V, the
gas law and compressibility factor may be
used to compute the specific volume.
The limitations that may be placed on the
general equation when considering a static
or motionless column of fluid are:
With these limitations, Eq. 5 reduces to
Eq.6:
h
2
(2ZNRT dP = X
[6]
VdP +AX = 0
TABLE
in which P = pressure,
V = volume,
Z = compressibility factor,
N = number of mols per lb ..
R = gas constant per mol,
T = absolute temperature.
Combining Eqs. 6 and 7:
it
[81
P
I.-Example Calculltion for Method I
(2 ZNRT dP = X
]I
P
[81
Given: Well A
PI = 2600 lb. per sq. in. abs.,
Depth-temperature data,
X = 7500 ft.,
PPe = 663.8 lb. per sq. inch,
pTe = 385.6° R.,
G = 0.744
By approximate methods, or a series of trials on this method, the depth-pressure curve is obtained.
Depth.
Pt ••
X
Well
Well
PresTemsure. p. perature.
Lb. fer
T.
Shs~' Deg. F.
T.
Deg.
R.
Pr
Tr
Z
0.498ZT
--p-
0.498ZT
M'
--P-
Av.
Cum.
Area, Area
Or
Sq. Ft. X
Calc.
- - - - - - - - - --- --- --- - - - - - - - - - - - - - - - - - 0
1.000
2.000
3,000
4.000
S,OOO
6.000
7.000
7.500
2.600
2.691
2.774
2.852
2.929
3.005
3.079
3.15 2
3.188
77
IIO
144
159
174
190
206
221
228
537
570
604
619
634
650
666
6SI
688
3.9 2
4.05
4.18
4.30
4·41
4·52
4.64
4·75
4.80
N=
I.39
I. 48
I.56
1.61
1.64
I. 69
I. 73
I.77
1.79
0.701
0.765
0.807
0.829
0.842
0.86!
0.~80
0.894
0.901
0.0721
0.0806
0.0874
0.0895
0.0906
0.0926
0.0947
0.0961
0.0967
I
=006
(0.744)(29.0)
. 4 3
R = 10.73
NR = 0.498
91
83
78
77
76
74
73
36
0.0764
0.0839
0.0887
0.0900
0.0916
0.0936
0.0953
0.0963
1,000
1,002
1,000
2,002
996
99 8
2.99 8
3.996
4.998
5.996
6.996
7.49 6
1,002
998
1,000
500
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u = o. No velocity.
W. = o. No work done.
W, = o. No friction loss.
Etc. = o. Energy other than heat and
compression neglected.
PV = ZNRT
PRESSURE
LBS./SQ.IN. ABS.
FIG. 2.-CURVE OF EQUATION 8.
H
o
w
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0.07t±±:tJ::tj:±±:j±±:±±tt±tltl±ttttttt::ttJ:t:J:j:tl:±±ttllitl±tl±tt±:t::ttJ:±t±±t±±t±:J:t:ttj
2600
2700
2800
2900
3000
3100
3200
3300
104
CAT,C'ULA'fION OF STATIC YRESSm:m GRADIENTS IN GAS WET.LS
Method I
{:T. ~.;;,J prc;sure pP•.
The well prC3"'lfCS ::;,t e'1::h depth in
r::bl,~ I were estimated by prior cdcuja-tifJt1S, The proof that they are correct lies
Jdeihod II
An equation may be derived that has the
form of .Eq. 1. if T and Z are assumed COT!gtant ~md may be removed f.rom the
mtegral:
R. earranging,
P2
X
In _po = Z~;;:;R7'
- 1
x
. P2 _.. PI = PI (eZoNP.T. - . )
Method III
o.o1874GX
---;r"z-;;- - ,)
(x -- 0.00931 -"~~-)
., Q,oT8'I4Pl i~52, IX3bl
1.
J'
<1Za
[n)
Given: Well A
1'1 = .600 lb, per sq. in, "bs.
G ~, 0.744
X = 7500, ft.
T" = 152.5° P. sa 61.2.5° R~
pp, ~ 663.8 lb, pel sq. ir.. rIbs.
-{I"'PC
3RS.6Ci R.
PI = 2600 lb. per sq. in. ah;,
G = 0,744
X ,...." 7500 f~.
T. "' r 52.5°)1'. = 612.SoR.
PP. ~, 663.;S Ib, per sq. in. "bs,
pT, .~ 385.6°R.
First TriQ.f
Assu:mc
P. = 3100 lb. per sq. in, abs,
P. = 2850 lb. per sq~ in. abs.
23
Pr"
5<?, = 4.30
T • •~ ~ •.?:'.2 ,-, L59
663.3
385,6
::::"'!
,';rsl Trial
: '5Sk,l.. '~
Zo ~ 0.820
P, ::....., ,::\:100 Ili. p:~r sq. i~. nbs.
P '-' 3.~,~~ ,~ /•. 30
T. =
6(>::t.~·
Z] =
_1100 _. 2600 =
Po = 285(,
XG
= (0. 018 74)(r1O.IO)(2600)
0.3960 AI' = 541
AI' = 604lb, per sq, in.
-- ,)
~ ..
I;'
500 .., ,,6o<>(o,?~.36) .. 53, lb, per St!.
5;uond Trial
A:;sufi.e
1', ,..~ .1I8.~ lb. per sq. ~n. 2'01.:;21
PI" ot:lI _~1 IV 4.,a6
6·)3_8
+
.~
Sc:;otuf 7 vial, since Za. t9.ken :~.t in.correct P n
As~-. ..1Il"C~
1', = 32(14 lb. per sq, in, abs.
P. l
290'2 Ih4 per sq. in, abs.
o;'";!.
P r ,-~ ~?~~~ = 4.17
P ... ~"! 7.'3~'~"
'J', =
J.~0
Z:J .:= t).8~I
(0,01&74) (0.744) (7500)
260c = 2600(. - ",;;"1)'(612.5)'-'"
582 ~ 2600(C.~2;j9)
P. -.~ 582
260\)
(612,5)(O-il~0) = IO [Q
AP(r _. (0,C0937)(Il<).ro»
O.~10
('l.O,87.I) (0.744) (7 $00)
26oo(e"----(u,iJ,.;;)-(f.;·~,Sr'-·
(7500) (0.744)
ToZ.
~~~ = 1.50
J8~,0-
"4,i,.~,(er
3r82 -
aZel
Given: Well A
Method 11
p, - 1', = Pl(e
r·,,]
TABLE 3 . --Example Calculation for
AP
'fABLE 2.-Example Calculation for
alV,!.. 4!:
or
T· 0'- I.~9
Za ..,. 0.821
-lE.•z. = {J.s_()&(0.~4;42.
=
JtO.09
(OIl.SJ\O .•,.!)
I)
""" 2(}'''''G(~ 0."010 ~. I~
582 lb. per sq, in,
TO 318a lb. P~" sq. in. abs. cakul",ted by methd, II.
Mt:a~u:~-~d .~H.-CfSU.Jf.! at 'j :-itt;} ft.
:.-~ 3193 lh. per s~. ~ti.• airs
',\1>(1 .- (O.O'l9.n)(1H) "0)
= (o .. oI874)(BO.09)(2~QO)
"·~96[ t!.P ~, 540.0
P, = 602 + %600 AP ~, 602 lb. per sq. in.
• ~ 320. lb. per sq. it). ~.b •• cnlc:ulated by m.ethod IH,
.l\.1casl.I,:t:{I, 1.-H"'cs~ur\! J,t 7Sou fL
-- 3 !93 lb. pcr ~lq. in. abf>~
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In Eq. 8, R is constant and N is constant
if the gas gravity is uniforrn throughout
the wdl, hIt Z, T, and Pare v?J'hbles. To
solve the integral, Z and T must he
evaluated for each preRsure. The solution
for this method requires the desired pressure---gradient curve to evaluate Z and
hellC!' b'~comes a trial and error solution.
Tahle I present1' the final soluthn a!t'2C" II
serbs of trials for the pll;:ssure gradient in ~,
g~s well using Eq. 8.
The data for well A from Eilel'ts and
Schellhardt 2 were used for the measured
static pressure and temperat1ue r,radi\,:llt.
The composition of the 'Nell fluid wes given,
which permitted calculatio71 of ltfl gravity
G ::tn,l the ps~udo(1itical te;'Tnatuf8
in the calculation by Eq. g of the correct
depth from the integral that is the area
under the curve of Fig. 2.
M:.
Jo RZASA AND D, L. KATZ
This equation may be simplified, since
I
sure constant or to use an average value of
V in Eq. 6.
>
G =< 9
N for one pound of flUId con:2 00
h2
VdP = Va
sidered, and R = 1544 with P in units of
pl)unns per square inch
O.01874~
P~ - Pl = P1(e
Z.T. - I)
lOS
f,2 dP = Vg(P: - PI)
= ['$ -:- P x = X
p ..
[12
[II
in which p" is the density of the fluid at the
average pressure. Since Po may be obtaine~
Table :2 gives an example calculation of this
I.
:-m
.1:;
1.5 ::;-
- .~
'!ci:
oc
".
~.j>'
10."
CII
0< 1.3
SCI
...1«
I&.~
.J~
T
w~
3:1.&.1
If)
U
1·°0
20
40
60
80
100
120
140
BARRELS CONDENSATE PER MILLION STD. CU. FT. GA.S
FIG. 3.--GRAVITY RATIO VERSUS S'l'QCK-T!l.NK YrELD 01' CONDENSATE.
method, using the same data as Table 1.
This equation must be solved by trial and
error for Zo since it depends on an assumed
average pressure.
by use of th~ comp1"cssibHity fa.<::tor, gP.;;
gravity, ten.perature, !.'md pres:~~re, thz
following equation results:
144(PI - PI) X 359 X To X 14.7 X Z«
29.0 X G X 492 X (PI
M/2)
= X [I3~
in which P represents units of pounds per
square inch,
.
Method III
If the temperature and compressibility
factor are assumed constant, it sbould
make llttle difference to assume the pres-
+
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.1!-t:
~~
~ .. ~ l' '\ +
....-- t
->
I
'~4f
106
CALCULATION OF STATIC PRESSURE GRADIENTS IN GAS WELLS
approximation is usually sufficient. If
P, T, and Z are stright-line functions of
depth, the equation is exact. If variations
occur, the solution may be made for
increments of depth with ·more accurate
results.
Table 3 gives an example calculation
for this method. The calculated bottomhole pressures (lb. per sq. in. abs.) by
the three methods are tabulated as follows:
This equation is relatively easy to solve
and involves a trial and error for the
Ct»J
Ct»..J
wo
a::Ct»
3 1 93
3 188
3 202
700
0.10
~<
..._z 65
"
0:-
Uej
Oct»
0':
JCt»
wlO
~..J
4
350
MISCELLANEOUS GASES (4)
• SATURATED GASES (3)
CONDENSATE WELL EFFLUENTS
~,~~~~~~IH~YH~m~m~m~1H~ml~HI~lll~IHi~mJ
Q50
0.55
0.60
GAS
0.65
GRAVITY
0.70
0.75
0.80
(AIR = I •
FIG. 4.-PSEUDOCRmCAL CONDITIONS AS FUNCTIONS OF GAS GRAVITY.
compressibility factor Zo. However, the
change in Z. with pressure at the usual
well conditions is not large and a second
The results indicate that the simpler methods II and III are essentially equivalent. *
• See Addendum.
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""O:w
J ...
Experimental Method Method Method
Pressure 2
I
II
III
M. J. RZASA AND D. L. KATZ
GRAVITY OF WELL FLUIDS
A dry g~s well producing no ,-ondensate
will have the same gas gravity in the well
as at the gas meter and presents no problem
2500
1000
PRESSURE GRADIENT
1750
7
quantity of condensate and gas-phase
composition in a well would be very
complicated, either the well-effluent gravity
or an average gravity for the well-fluid
gas phase will be used.
~P)
LBS./SQ. IN.
750
500
250
2000
3000
4000
5000
6000
7000
8000
AvERAGE WELL PRESSURE .~ +~) LBS./SQ. IN. ASS.
9000
10000
FIG. 5.-PRESSURE GRADIENT AS A FUNCTION OF AVERAGE WELL PRESSURE AND TEMPERATURE FOR
0.60 GRAVITY GAS.
in finding the correct gravity. The gas
composition in a well that produces
condensate may be computed by adding
the condensate to the gas separated. If
the well fluid were a single phase throughout the well, the molecular weight of the
well effluent gives the true gas gravity for
the static column. When condensation
takes place within the well bore due to
temperature and pressure changes, the gas
gravity G becomes a variable and N
in Eqs. 8 through 10 is also a variable.
Since the procedure for predicting the
A simple procedure for estimating the
well fluid gravity is desired. The information normally available for a condensate
well is the condensate yield in barrels of
stock-tank liquid per million cubic foot
of separator gas and the metered gas
gravity. Fig. 3 has been prepared using
actual data on 15 condensate wells for
which the well effluent and separator-gas
compositions were known in addition to
the stock-tank yield of condensate. The
curve appears to be of fairly general application, even though there are three vari-
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o
2000
10
108
CAi,CULATION OF STATIC PRESSURE GRADIENTS IN GAS WJ<;U,s
ables, separator pressure, liquid gravity,
and liquid molecular weight, which could
cause different .gravity ratios for a given
stock-tank yield of condensate. The IS
PRESSURE
pseudocritical temperatures and pressures
are a function of gas gravity for natural
gases. Saturated gases at high pressure
or condensate well effluents would have
GRADIENT CAP). LBS./SQ. IN.
;zsoo
1000
2000
3000
1;;t;'OO
. -- XI
AVERAGE WELl.. PRESSURil:
~
6000
1000
8000
"'"f-) LBS./SQ. IN. ASS.
9000
10000
FIG. 6.-PRESSURE GlU,mEN'l' AS A FUNCTION 0:" ,WERAGE WELL PRESSURE AND TEMPERATURE FOR
0.65 GRA'ITY GAS.
condmsa.te wells include a wide variety
d aU three of these variables, with no large
net deviation from a single curve.
PSEUDO CRITICAL CONDITIONS
In addition to the well fluid gravity, the
pseudocritical conditions must be known
to predict the compressibility factor for
any pressure-gradient calculation. If well
effluent analyses are known, the pseudQcritical conditions may be computed
directly as molal average critical temperatures and pressures for the pure
constituents. It has been shown. that
sligntly different curves of gas gravity
versus pseudocritical temperature and
pressure than single-phase natural gase~
at low pressure.
Fig. 4 gives the pseudocritical conditions
for saturated gases 3 and condensate weB
effluents. The curve developed for miscellaneoLls natural gases 4 is also shown.
CHARTS FOR CAI.CULATlNG GRADIENTS
Since any well having a fixed well-heat1
pressure, gas gravity, and well temperatures will have a definite static pre!lsnre
gradient, it wOl1ld seem that charts could
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o
M.
J. RZASA AND D. L KAT/,
be develop~d to give the gradient as a
function of well-head pressure Ph average
temperature T G, ga.s gravity G, and depth
X. By Eq. ISb, lli> is a function of average
2250
2000
o
1000
2000
represent tbe dendty of the well fluid but
on an odd scale to make the depth lines
straight. Since the average pressure in a
well. is not known, a trial and error soluti>JH
PRESSURE GRADIENT CAP) LBS./SQ. IN.
1750
1500
1250
1000
750
3000
4()OO
r.
.50 )0
'
t.vEHAGE WELL PRESSURE
6000
t.Ae'
o
600C:
LBS./SQ. IN. ASS.
2 J•
Fw. 7.-PRESSURE GRADIENT AS A FUNCTION OF AVERAGE WELL PRESSURE .'ND l'EMPEl?I'l:fLJli.E 1'O!:
0.70 GRAVITY GAS.
pressure P a , depth X, gas gr:wity G, and
average temperature T a , as Z. is a dependent variable.
Figs. 5 through 9 have been prepared
using Eq. ISb for gases of gravities 0.60,
0.65, 0.70, 0.75, and 0.80 with AP (l
function of depth at t.he average pressure
and the avcrage temperaiure in the well
These gases are assumed to follow the
pseudocritical conditions of Fig. 4 and ti)
have compressibility factors of referencell
?, !'lld 1. 'T'he onUn~ tcs Oll thCcf' cr.arts
is involved when computing the bottomhole pressure P2 from the well-head
pressure Pl,
To assist in this calculation, Fig. Ie>
has been prepared.. The d:art gives th"
pressure gradient bY for gasef o~ 0.70
gnwity, using a diiIerent avenge temperature for tach depth. '.Uw depth-temperature relationship used is l:t3"F. at 4000 ft .•
208''F. ;;.t 8000 ft .. lol.nd 282~F. at 1:2,000 it.
For wells that have this temperlltur~
gmdient and ". wdl fllli,l Itr:lV;ty of ,> ';0.
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2.500
109
IIO
CALCULATION OF STATIC PRESSURE GRADIENTS IN GAS WELLS
By Fig. 10, the approximate gradient
corresponding to 2600 lb. per sq. in. abs.
is 610 lb. per sq. in. and p .. = 2905 lb. per
sq. in. abs. From Figs. 7 and 8,
Fig. 10 gives an accurate calculated gradient. For wells having different temperatures
ur gas gravities, Fig. 10 should be used
only to approximate the IIp in order to
2000
2500
1000
2000
3000
AVERAGE
WELL
5000
PRESSURE
LBS./SQ. IN.
1000
750
<6000
7000
o
8000
(1'1 t ~ LBS./SQ. IN. ABS.
9000
10000
FIG. 8.-PRESSURE GRADIENT AS A FUNCTION OF AVERAGE WELL PRESSURE AND TEMPERATURE FOR
0.75 GRAVITY GAS.
+
obtain the average pressure (Pi
M/2)
= P .. in the well, which in turn is used in
Figs. 5 through 9.
EXAMPLE USES OF CHARTS
Using the data. on well A, compute the
pressure at 7500 ft. for a well having a
tubing-head pressure of 2585 lb. per sq.
in. gauge. The well fluid gravity is 0.744
and the average well temperatur~is 153°F.
IlP for 0.70 gravity gas = 565 lb. per sq.
in.
M for 0.75 gravity gas = 615 lb. per sq.
in.
Interpolatingforo.744gravity,IlP = 609
lb. per sq. in.
P 2 at 7500 ft. = 320y lb. per sq. in. abs.
Experimental value = 3193 lb. per sq. in.
abs.
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o
PRESSURE GRADIENT CAP)
1750
1500
1250
M.
J. RZASA AND D. L. KATZ
As a second example, compute the
reservoir pressure at 8000 ft. for a well
producing 40 bbl. of stock-tank condensate
per million standard cubic feet of gas.
From Fig. 9 at 135°F. and 8000 ft.,
t:.P = 820 lb. per sq. in.
Repeating at PIS of 3225 lb. per sq. in.
abs., /l.P = 825 lb. per sq. in.
PRESSURE GRADIENT CAP)
1000
LBS./SQ.
2000
17~0
ISOO
1250
1000
2000
3000
4000
SOOO
eooo
AVERAGE
WELL
PRESSURE
(F: +~)
7000
8000
2S0
o
9000
10000
LBS.lSQ. IN. ABS.
FIG. 9.-PRESSURE GRADIENT AS A FUNCnoN OF AVERAGE WELL PRESSURE AND TEMPERATURE
FOR 0.80 GRAVITY GAS.
The well-head pressure is 2800 lb. per sq.
in. gauge, the separator-gas gravity is
0.670, and the temperature of the well
bore at 4000 ft. is 135°F.
From Fig. 3, the well fluid gravity is
estimated to be I.I9 X 0.670 = 0.789.
From Fig. 10, the approximate gradient
corresponding to .2815 lb. per sq. il,l. abs.
is 765 lb. per sq. in. and PIS = 3198 lb. per
sq. in. absolute.
Reservoir pressure = 2815
lb. per sq. in. absolute.
+ 825 = 3640
EFFECT OF FLOW ON EARTH-TEMPERATURE
GRADIENT
In estimating the average well temperature, the usual procedure is to assume a
straight-line relationship between the reservoir temperature and a well-head temperature of 60° to 70°F., depending upon the
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o
III
112
(;Ai,-:LiI,A:fION OJ!' STATIC PRESSURE GRAL)U:N'fS IN GAS WELL"
locality. If the well bore is in thermal
equilibrium with the earth, this procedure
give~ results little uifier"nt from the
measured temperature gradient,
800
PRESSURE
1000
1200
1400
1800
1800
2000
2200
GRADIE:NT 'loP) L,BS./SQ. IN.
FIG. lO .. --PRESSURE GRADIENTS FOR 0.70 GRAVITY GAS AND CIVEN EARTH-TEMPERATURE CRADIENT.
During flow, the well bore and surrounding earth gradually increase in temperature
over the normal earth gradient. Harbert,
Cain, and Huntington b have indicated the
;,;atuT':' of this problem by la.i)oratory
!U"asllreme::lts. A well that has been
fiC)wing prior to mea~urement of the
well-hc:1d pressure will have a higher
a\""rage ",'en t,emperature than at thermal
equilibrium. Ft!rther reiinemellts in the
calcuiation of pressure gradients in gas
wells that have been flowing just prier to
measurement of well-head preszure will
include some procedure for estimating the
from the natural gas may be shown by
using higher average temperatures for
well A. For a well-head pressure of 2600
lb. per sq. in. abs., a gas gravity of 0.744
and a reservoir temperature of z23°F.,
the following values for /J.P
ASSt1nled Surface
Temperature,
Deg. F.
Average Wen
Temperature,
Deg, F.
_._---- - - - - -
liP fro . .l1 Ili~s,
7 and 8
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800
average weH temperature from well history
and flowing well-head temperat.ure,
The effect of a change in the a wrage
well temperature due to heat tr:ll1;>Icl
M.
J. RZASA AND n. L
are found by interpolating between Figs. 7
and 8 for a series of well temperatures.
These results indicate fnat the l~.lt:tl­
la.don of pressure gradients in Eas well~
I>:~ ,l.l.ve been shut in only 24 hr. after a
period of flow may not be accurate if the
equilibrium earth-temperature gradient is
used.
2.
R.a\,ylins and Schellhardt: U. S. Bur. Hine,;
Monog:'aph 7 (19.16).
Eilmts and Schellhardt: U. S. Bur. Mines
R.I. 3402 (1938).
KATZ
II;
factors by which 1'1 is multiplied t.o givl'
P 2 - . PI. Let 0.oI~74
KG
r-7' = c, then tOl
.~~
method n the hctm b';c()!n~:: (.~<, -. tj . ; ,
.' \
for method III it becomes ..-.~--)
(
,1 -
0.5C
A direct compari:;on of the two faci"rs h;
several values of care ,,5 f(lJl0ws:
c
c
I
---~------.---
--~-.-.-----
..
--- -.---
-
0.5C
--------~-
0.05
0.05 1 3
146, 140.
0.10
0. 1052
0. X0 5 2
.1 (6), 58.
0.20
0.221
0.2222
3. Standing and Katz: Trans. A.l.M.E. (1942)
4. Katz: Ref. and Nat. Gasolille Mfr. (1942)
5. Hnrbert. Cain. and Huntington: ldd. and
Eng. Chem. (1941) 33, 257.
A more accurate comparison of methods
II and III may be made by comparing the
0.30
0.35 0
0·353
0.40
0.49 2
---~~-
0.649
0·500
c.o67
These prove that the two metho,1s
should give practically identical results.
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ADDENDUM
0.05 1 .3