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,(
=&m+--
/
,,
Rapid Methods for Estimating Reservoir
Compressibilities /
.,
H.J. SAMSY,JR.*
.,
MEMBERAIME
I
ABSTRACT ;
Conventional calculation of total system isothe~mai
compressibility for a system captaining a free gas phase
involves, among other things, evaluation of the change of
oil and gas formation volume factors and the gas in soh-
tion with pressure. Preferably, this information should be
obtained from laboratory measurements made with parti-
culirr oils and gases. Often, experimental
measurements
are not available. In this case, it is necessary to obtain
uressure-voiuns e-temperature relationshi~s from general
correlations such as~hose of Standing f;r Californ~a oils.
In order tospeed estimatesof compressibility, generalized
plots have been prepared of the change of both oil forma-
{ion volume factors and gas in solution, with pressure
frc)m Standings correlations. A generalized piot for esti-
tnating the change in the two-phase (oil and gas) formation
volume factor with pressure is also presented.
Usually, the ~fject of gas dissolved in reservoir water
upon the total s~stem compressibility is neglected for~gtw
saturated systems, due to the low sohtbility of gas in water.
Results o./ this study indicate that. the increase in total
system compressibility.caused by solution of gas in water
is often as large as thekcompressibility of water, and can
be magtiitudes Iargfr for low pre xure systems. General-
ized results for esthhating the change of gas in solution in
water with pressure are presented in tabular @ graphical.
form.
.
INTRODUCTION
During the prpt decade? pressure build-up and draw-.
down techrdques have gaine~an important pIace,inreser-
voirengineerikig. Build-up anddrawdown anrdysesareody
two special applications of tlie broad field of transient
fluid-flow theory. All solutions of transient fluid-flow prob-
lems contain a parameter called the total system isother-
mal compressibility. This property of fluids and porous
rockis a measure of the change in volume of the fluid
content of porous rock with a change in pressure, and it-
may vary considerably with pressure.
Evaluation, of total system isothermal compressibility is
not difficult, but it is tedious and time-consuming. Often
compressibilities are estimated roughly, or transient flow
methods are neglected completely, Y
The ber@M of using accy:rati?,riystern cornpremibiifty in
Properly-executed build?w or drawdown analjses are:
Original manuscript received in Society of Petro leum Engineers o ll ice
Ses)L 16, 196% Revised manuscript received Dec. W, 196S.
MOBIL O/L CO.
LOS ANGELES, CAIIF.
l. Better pkumirtgofpvssurebuild- upsmaybeachieved
to avoid uMecessar
Ior
ch, ,f ii ta marim-le
yig.u .-MW.W...W-.
2.
Better and mor= I WLLUIC GSUIIMWUL SL2SL1G 1U1111SLL1UIJ
pressures for reserves estimates kmd rate performance
estimates.
3. Reliable information for evaluation of well comple-
tion effectiveness, and planningand il;terpretation of well
stimulation efforts.
The purpose of this paper is to clarify the nature of the
totaf system isothermal compressibility, and to present use-
ful methods for estimadon of compressibility, particularly
for systems ,containing a gas phase.
DEVELOPMENT
Numero~ publications have presented solutions to
transient sin~e-phase flow of slightly compressible fluids,
stressing pressure build-up applications. In transient flow,
a compressibility* term arises to permit volume content
of fluids in porous rock to change as pressure changes.
The basic ,nature ,of the compressibility term is, usuallY
taken for granted, Problems arise in practical applications
of transient fluid theory because most published works con-
sider only one flowing fluid-in an ideai porous system
containing only one fluid. .
In 1956, rPerrine presented an intuitive extension of
single-phase flow pressure build-up methods to multiphase
Kow conditions. Later, Martin established conditims un-
der which Perrines multiphase build-up method had a
theoretical foundation. - -
Perrine has shown that improper use of single-phase
build-up amlysis in certain multiphase flow situations can
lead to gross errors in estimated static formation pressure, ~
permeability and well condition. It is likely that much
pressure build-up data for oil weHs should.be analyzed on
the basis of mukiphase flow.
For
both
single-phase and multiphase build-up analysis,
the isotherm+ compressibility term in dimensionless time
groups often shouId be interpreted as the
total system:com-
pnmibility, All real reservoirs dontain one or more corn-
pressible fluid phases. fn addition, rwk compressibility
can contribute in an important way to the total system
compressibility. The proper total. system compressibility.
- expression. may. contain terms. for. eompressibifi~=of oii,...
gas, water, reservoir rock. and terms for the. chatige of
solubiiity of gas in liquid phases.
*Now a professor of petroladm engineering at Texas A&M U., Cd-
Iege Station, Tsx .
preferences g iven at end of paper .
*It will be understrqd that thc term rmmrmrmWilitYref~ to isotk-
mnl compr.rsslbility in the following.
.
APR. IL, 1964
.,
47
..
...
~.
{
. .
/.. .
. .
-..
,- ,.. , . ,- - - .. ------ .. . ., ..1
8/10/2019 00000772 Ramey Compressibility
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r
.-
,
~
/
.
A general expression for total system compressibility
can be written in terms of separate phase compressibilities
by volumetric phase saturation weighting. That is: ,
f+= S,,c,, +s;c,c+s,c+c, . . . . . . . (1)
By definition, the isothermal compressibility of component
i is
C;=+-i+ -)...
- -
2)
Expressing volumes in terms of formation volume fac-
tors, and considering gas volubility effects, Martin pre-
sented essentially the, foRowing extension of Perrines ex-
pression for total system. compressibility.
.f=so[;(*)++(*)]T+ ~
w%-)+%(%)].-
()
, i3Bv
.
B,
a p ,
+C, . . . . . ...(3)
Eq. 3 ii deve~oped in the Appendix.
Practically speaking, the greatest uncertainty in estima-
tion of total system compressibility is estimation of the
proper liquid saturations for volumetric weighting. Uncer-
tainty in liquid saturations ofien overbalances uncertainty
in estimation of separate phase compressibilities.
In this connection, clarification of the basis for Perrines
multiphase build-up theory is important, The separation of
oil and gas nobilities proposed by Perrine is actually based
on the field producing gas-oil ratio. equation.
R= ( )+R. . . . . . . . .
(4)
f;
where R is the instantaneous field producing gas-oil ratio.
Consequently, Perfifses multiphase build-up method im-
f plies the existence of a .kO/k. vs. saturation relationship.
Thus, liquid and gas satumtions may be estimated from
rnatmials. balances, or from results of the build-up test
and existing k,,/k,,-saturation relationships.
Determination of total system compressibility from %.
3 depends upon the number of fluid phases pre.
448
As pressure is increased within the pores of the rock,
the rock grains are compressed, and the bulk volume of
the rgck is increased due to interaction of internal pressure
and the ,confining overburden pressure. The effect of both
factors is to increase pore volume as pressure increases.
.Thus by the general definition of compressibility given by
Eq. 2, rock compressibility in terms of change in pore
voiume
should be negative qua-ntity. I-Iowever, the effect of
an incr~ase in pore volume with an increase in pressure
can be pictured as an increase in the size of the container
holding reservoir fluids. If the container volume isheld
constant, the sanie effect could be achieved by additional
shrinking of contained fluids. Thus the
eflective
rock com-
Hall reported that rock compressibilities range from 3X
10- to 10- (pore volume/pore volume) /psi. Halls results
and tbi.?seof Fatt are summari~ed by Craft and HawkIns.
Rock compressibility covers a range in magnitude from
the compressibility of water to tha}~of some oils, and is
generally less than the compresslbdlty of gas. However,
rock compressibility is often an important component in
total system compressibility, particularly when gas, satura-
tion is small, porosity is small, or liquid compressibilit ies
are small; GeertsmaJ van der KnaapNand Dobrynin have
studied the effect of overburden and pore-space pressure
upon rock compressibili~y.
AQUIFERS
Water influx and material balance calculations often
require estimates, of the total compressibility of an aquifer,
system, i.e., porous rock totally saturated with water, In
this case, Eq. 1 becomes:
.;
(Cl=c,c+cj, ... . . . . . . . .
. (5)
Specific information on the compressibility o{the aqui-
fer water will generally not be available. In view of the
uncertain nature of other information on the aquifer (e.g., ,
porosity, permeability?, /he precision of estimates of com-
pressibility of the aqulfcr from existing correlations is ade-
quate. Available correlations are listed under Oil Rcser-
voirs. ~Water compressibilities range. from- 2X 10( to
4X 10-apsi-.
GAS RESERVOIRS
,,
There may be two or more phases present in a gas, re-
servoir: natural gas, comate water, and occasionally con- -
densate, tar or other forms of liquid hydrocarbons. For the
present, consider only gas and water to be present. The
effect of a liquid hydrocarbon phase will be discussed un-
der Oii Reservoirs. The compressibility of natural gas is
large and ranges from 1,000X 10 psi- at 1,000 psi
pressure, to about lOOXJ0 psi- at 5,000 psi pressure.
The effective compressibility of water with dissolved gas
ranges from 15X 10- psi- at 1,000 psi, to 5X lo-~,psi-
at 5,000 psi. Rock compressibili ties range from 3X 10to
10X 10 psi-. Thus compressibilities of rock and water ..
are often negligible compared to the compressibility of
gas. Eq. 1 becomes:
,.
,. .
,
Ct=suc,, .,..., . . . ..-.
; (6)
In certain cases; e.g., high pressure and high connate
water saturation, water and rock compressibilities are not
negligible. In this event, Eq. 3 must be used to evaluate
total compressibility. It is recommended that the magni- -
tude of water and rock compressibility contributions be
checked quantitatively before Eq. 6 is used.
Clearly, measured gas compressibilities should be used
if available. If measured values are not available, estimates
can be made by one of several acceptable correlations or
methods. For example, cotipressi13ility of gas for Eqs. 3
or 6 can be computed from the real gas law (see Trube,:
or Craft and Hawki@l ~~ rube has published reduced
compressibilities for natural gases in convenient graphical
form. His corndation is usually the best source for esti- ,
mation of gas compressibilities.
/
Often the reciprocal of absolute pressure is used ap an
estimate of gas compressibility. This approximation is
rigorously true for a per ect gas, and should not be used i
.foEprE.ss,ures above 5 20 psi. -., ..-. _:. . ~. ._. ,:.-..:-,
OIL f&5ERVOIRi
1,
OH reservoirs contain two or more fluid phases in addi-
tion to roclc oil, water and possibly gas, Although gas
compressibility is much larger than oil, water, or rock
JOURNAL OF
PETROLEUM TECIIXiJLfl GV
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,. -,, ,.
,
.
. .
,
r
compressibilities, gas saturations may be small and it otten
is necessary to consider contributions from each fluid
phase and the rock. Eqs, 1 or 3 ,are generally applicable.
in regard to the formation water contribution to total
compressibility, the correlations of Dodson and Standing,r
or Culberson and McKetta ~
may be used.
The compressibility data presented by. Dodsors and
Standing provide only the effect of the change in liquid
water volume, the first term in the water contribution in
Eq, 3. In order to obtain the second term involving the
pressure differential of the gas in solution,
(aR.,./@),,
either the Dodson and Standing, or Culberson and Mc-
K&tta solubility data can be used. Since this term is
often
numb larger than the water compressibility, gas-in-water
solubi[ity, data ,have been, differentiated generally and re-
sults are presented in Table 1, and Figs. 1, 2 and 3, Table
.
1 and Fig. 1 present, the pressure differential of gas in
solution fbr a single nati.rral gas containing
88.51
per cent
methane and 6:02 per cent ethane, This system was stud-
ied by Dodson and Standing.
For this system, the pressure differential does not
change much with temperature over the range lQOF to
250F as shown by Table 1, Thus a single, average fine is
shown &i Fig. 1; to cover the &tird temperature range.
Correction for total solids in the brine should be made
by usingthe lower graph
oh
Fig. 1. If temperature is above
250F, Fig, 1 should not be used. Figs. 2 and 3 can be
used to estimate the pressure differential of soh ion gas
for mixtures of methane and ethane in water. -These fig-
ures were prepared from the Culberson-McKetta data and
cover a more extensive range in temperature and pressure
than the Dodson-Standing data. The expression for the
pressure differential of any mixture of ethane and methane
is:
feren~iations indicated by Eq, 3 are not difficult, but arc
tedious and subject to the usual errors inherent in differ-
entiation, It is often necessary to smooth original data and
final results.
Assuming that experimental information is no~ avail-
able, the change in oil formation volume factor and gas in
solution with pressure required for ~q. 3 can be obtainer-i
from Standings correlations for California oils, Fig, 4
presents the change of gas insolution inoil with pressure
as a. function of gas i q solution and pressure. Fig. 5 pre~
sents, the change of oil formation volume factor yith- gas
in solution as a function of oil formation vokrme factor.
These figures are general and, in. conjn~ction with Figs, 1, ,
I
ii
m
\
I
v
m
o 1000
2000
3000 4000 5000
PRESSURE, PSIA
%.
(%).=1(2).+2%-),~~-7)
COkRECTION FACTOR FOR SALINITY
1.0
(
CORRECTION
FACTOR
0.s
0.8
0
10
20 30 60
where the subscript 1 re ers to methane, and 2 refers to
ethane, Becatke the sol@ilit y of hydrocarbons in water
decreases rapidly with increasing mofecular weight, con-
tributions to the pressure differe ltial from propane and
higher molecular weight cornponenfs can often be neg-
lected. Again, correction for total solids in ,brine should
be made by using the lower graph on Fig. .f. Eq. 7 is not
rigorously correct, but provides a very good approximation
as can be shown by comparison of Do~son-Standing data
from Table 1 with results from Eq. 7 and the Culberson-
McKetla data from Figs. 2 and 3, Eq, 7 was derived as-
suming both the mol fraction water in the vapor ~hase
and mol fraction gas in the liquid phase are quite small.
1n regard to oil and gas contributions to the total sys-
tem compressibility, it is possible to determine total com-
pressibility from Eq. 3 provided formation volume factors
and, gas volubility data are ~~lailable as a function, of pres-
sure at the desired system temperature, The numerous dif-
TOTAL SOLIDS IN BRINE, PPM n 10-3, -
G
a
._
TABLE I-CHANGE OF iOLuiSi LITY OF A NATURAL GAS IN PURE WATER
WITH PRESSURE,(FROM
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{
,/
.
,/
,.
?.
2 and 3 and Table 1, provide a rapid means for evaluation
of total system compressibility from Eq. 3 for any system
containing a gas phase. Note that the change of oil forma-
tion volume factor with pressure is obtained from results
of both Figs. 4 and 5 and the expression:
,Development of the relationships shown on Figs. 4 and
5 from Standings correlations is presented in the Appen-
dix.
Gas Saturatiotr Less Than Crit ical Saturation
For the conr ition that gas saturation is less than the cri-
tical saturation for free gas flow, it is possible to rearrange
Eq. 3 to avoid much of the differentiation associated with
oil and gas phase data. The result i~ ,
= -+[(%)l.+s[=(%)+
B. 3R.w
(
)1
.T +-c 9)
where B, is the total, or two-phase (gas and oil) formation
volume factor:
B, = B. + (R.,R,)B, . . . . . . . . (10)
Derivation of Eq. 9 is presented in the Appendix.
It should be clear that use of Eq. 9 is limited to systems
where the gas phase saturation
is less
than the critical gas
saturation for ftow of free gas. For this reason, use of Eq.
9 is quite, restricted. But, for systems wher~, Eq. 9 does
apply, considerable simplification results. It IS possible to
obtain @B,/~p), directly from Standings two-phase vol-
ume factors, or from experimental data by methods ,which
do tinvolve differentiation. These features are presented
in the Appendix.
Undersaturated Systems A hove the BubbIe Point
Compressibility of undersaturated oil and formation
water above the bubble point cah be estimated readily
from existing ,correlations. The required information can
be found in the following -sources: for oil~see Trube~
for reservoir wa~ersee Dodson and Standing.
-,
.
,,
0.010
0.000
g
1.
0.006
d
m..
k.
u.
u
w.
.
0.004_+
3
a
e ~ ~02
.
.- . .-
.0
a-
,, -
,.
{
,,
,
DISCUSSION
The main purpose of this paper is to clarify the nature
and importance of total system compressibility for tran-
sient flow problemsand particularly pressure buiid-up
analysis. Often, specific PVT data ard not available to the
field engineer. It is likely that Eq. 3 and Figs, 1 through
5,, and Table 1 will be of most use for field calculations,
with the Dodson-Standing water compressibility correla-
tional Trubes3 correlation for gas compressibility, and the
,..
R;, 13AS IN SOLUTION, S .)YF/STB
,,
Fm.
4-CHANCE OF GAS IN SOLUTION IN
OIL wrrw I?RESSUHE vs
GAS IN SoLuTIo~. ,
,-
/
.
,
0 .: 000
4000
6000 8000
10,000
FoRMAT ION VOLUME FACTOR OF
i. RESSRE-PSY
OIL, Ba, RES. SBL/STB/
,
FIG,3-CHANGE OF %LuBu,IrY OFETNANEIN PU REwAIER T?ITN
FIG,
5CNARGEOF OIL FORMATION VOLUMp FACTORWITH GAS IN .
.
PRESSURSvs PRESSURE,
SOLUTIONvs OIL FORMATION VOLUMEFACTOR.
\
460
JOURNAL OF PETROLEUM TECHNOLOGY
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i
. .
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, ,, .
,, .
R
,. =
t
/
,
.
solubi.lit y of ga s in w a ter , scf/S TB w a ter ,
cor r el a ti ng f un ct ion , s ee Ap pen di x,
rea l ga s la w
deviation factor,
specific gravity of tank oil at 60F (to water),
gas gravity (to air),
SUBSCRIPTS
1 = methane,
2 = ethane,
b = bubble poin:,
= denotes phase
i.
0
.
,,,
/
.,
.,
.,
,.
.
Ha;l correlation of rock compressibility. An example
estimation of total system compressibilityy is presented in
the Appendix, Fig. 7 will be of limited hse for reservoirs
at pressures below the bubble point, but still producing at
or near the original solution gas-oil ratio.
CONCLUSIONS
One result of this study of compressibility is worth
emphasis. The (OR,,./3p)* term wtich appears in Eqs. 3
a nd 9, repr esent s t he incr ea se in effect ive ga s com pr es-
sibilit y result ing fr om solut ion of ga s in w at er .
This term
is usually neglected in estimation of total system compres-
sibility. It should beility of Reservoir Rocks: Trusts.,
AIME (1953) 198,309.
5.Fatt, I. : Pore Volume Cmnpressi lr il it it s of %ndstone Keservoir
Rocks, Trans., ~IhfE (1958) 213,362. /
6. Craftj B. C., and Hawkins, M. F.:
Applied PefI-olIw/m Ik.seruoii
Engineering, Prentice.HaR, Iuc., E n g le w oo (l C l if f, . N .1. f 1959)
.132.
7. Geertsma, j,:
4TIw Effect of Fluid lresmre Declilie ou VolmnW
tric .Changes of Porous Rocks , Tram., Ali[fl (1957) 210, 331. .
8..van der Knaap, W,:
*Nonlinear Behavior of, .hrs~ie Porous
1
edia,
Trans.,
AIME [ 1959) 216, 179; fl Influence nf :1 ,;
Pore Volume Change an, he E, tinmtion of Oil Resemes.
Erdol urrd Kolde ( 1960) 13, 305.
9.lMmytin, %. M.:, -Effect rrf O{erhurden l+ressure on %me
Properties of .%mrlstmws. Ser. Pet. En,g.
jour. (Dec. .
1962)
360.
Ftc. 7lSOITiERMAL Pakssma D~FERENTML OFTWO-PHASE
VOLUME FACTOR.
, .
8/10/2019 00000772 Ramey Compressibility
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--
I
10.
Llodson, C. R, and Standing, h . B.: Prwsure-Volume~Tempertr-
ture and Solufrility Rela tions for Natural GBs-Water Mixtures,
Drill. & Prod. Prrrc.,API (1944) 173.
11.
Culberson, O.
L, and McKetta, J.
J.:
Phase E uilibria in
\
drocarhorr-WaterSystems,Part II.. ., Trans., AI IE (1950)
ld9, 319,
19 r..ll.--.m n r .. AM,.v...,.
1,
J,:
Phtr* Equilibria in Hy-
11.,...
Trans., AIME (1951)
1Y4, 24s.
Uu,,,s , .>v,, , v . AA @,, u , MJ S.G .,-, . ,
droearfron-WaterSystems,Part I
. , .* -.
k%Jrnbe, A. S.: Compressibi lity of Natural Gases,
Trurrs., AIME
(1957) 210, 61.
14. lhbe, A. S.:
Colz]llressil]ility of Underwtwrted Hydmearhon
Reserroir F1nids, Trans., AIME (1957) 210, 34.1.
APPENDIX
DERIVATION OF GENERAL TOTAL SYSTEM
ISOTHERMAL COMPRESSIBILITY EXPRESSION
Eqs. 1 and 2 state:
c, = .sOc,,s,rc,r+sycr+c, . . . . . . . (1)
and
()
a vi
(., ______
v,
ap t--...
.
, 2
.
Since a normal fluid decreases in. volume with an in-
crease in pressure, the definition of compressibility given.
in Eq. 2 indicates a normal fluid will have a positive
compressibi lity. We can write the following expressions
tor the separate compressibilities in Eq. 1:
r,, =
-w%=
-k(%) ~
Since gas is soluble in b&h oil and water, as well as conl-
pressible, the total compressibility term must be considered
an effective- compressibility which ran account for. solu-
tion effects. Oil and water formation volume factors con-
.taiin the effect of solution gas on the change in liquid
phase volumes. Thus terms to reduce the gas phase volume
by the quantify of gas going into solution as pressure is
raised must be added. The change in gas volume due to
soiution of gas in c ~iis (aR./ap), scf/STB-psi, or in terms
of reservoir barrels per unit pore volume-psi:
()
B,, res bbl/scf) ~f?,
.
. .
S es bbires bb] v)(B,,- res bbljSTB)
ap ,.
A similar term may also be written for effect of solution
of gas in watec
()
~ ~ aR6.
B,, ~ y.
Thus we may combine the previous to obtain Marti&
expression for total effective isothermal compressibility
for a mukiphase system of oil, water and gas:
,
[
1 aBr,
1
,, aR..
c, .= S,, -
.
B,, a p -f-z@- ,
DETERMINATIONOF (2R./~P) , FROMSTANfUNGS
PVTCORRELATIONSFORCALIFORNIAOILS .
Standingsi Fig. 1, a correlation of bubble-point pres-
sure and gas-oil raticr, may be expressed analytically by
()
R,- n
~oosw ,
~ ~ kol :. . A1.1,
=
tL0537p +
1.408
Y.
-.
where y, is the gas gmvity (to air), T is temperature, F,
and (API) is the tank oil gravity, Taking the natural
logarithm .of b?th sides of this equation, and differentiat-
ing analytically with respect to pressure leads to:
()
aRa
R8
~,
= (0,83p i- 21.75) .
Solutions of this equation are presented on Fig. 4.
l)EfERMINAHONOF (W./tUt,) r.FRON S~A.~lHN[;.S ~~
PVTCORRELATIONSFOR
Cc4LJ f?0RhlL4ILS ,
[4
1
tandings Fig. 3* presents
B,, vs R. ~ + 1.25 T s
1.
~ J%(:)
raphical differentiation yields
(, ..
vs B,, sIS
. r
shown on Fig. 5. Note that y,, is the s~ecific gravity of
tank oil at 60F, and temperature T is in F.
SAMPLECALCULATIONOF TOTAL
SYS1EhfCOMPRESSIBILITY
Given the properties of an oil zone in Table 2, (1) find
all quantities needed to estimate total system compressi- ,
bility as a function of pressure, and (2) estimate the total
system compressibility at a pressure of 1,500 psia assunl-
ing pore volume saturatioris ofi oil57 per cent; water-
40 per cent; and gas3 per cent.
The oil formation volume factor B,, may be estimated
from Standing: Chart 3,* and the solution gas-oil ratio
R.
may be estimated from Standing, Chart 2.* The iso-
thermal change in solution gas-oil ratio
(N?./ap.)r.
is ob-
..
tained from tFig. 4 of this paper. .The quantity [Vy.,/y,,
(i3Bt,~aR.),] may be obtained from Fi~. 5. and
Then
(M,,/ i3p)r may
be obtained as indicated by-.Eq. 8:
The c&ipressibility of gas-saturated water may. be esti~
mated from Dodson and Standing. Tlie quantity
(aR,,, /
Z?p),
may be taken from Table 1 or e~timated from Frg. 1,
this paper, because no information was given on detailed
giis composition. The. compressibility dof, gas may be ob-
tained from Trubes pseud&reduced compressibilities.
The gas formation volume factor may be computed from:
1
z(T+ 460) res bbl
B,, = 0.00504 --- .
P
Scf
Thus~
B,, = 0,00504 (155 -k 460) ~ = 3.1;.
~.
From :he pseudo+ritical properties. of natural gases. at u
gas gravity of 0.83, the pseudo-critital temperature and
pseudo;critical pressure are 432R and 664 psia. Thus
pseudo-reduced temperature and pressure are:
,,
-
I .* 1,1 ,
P
s,
()
~g
,.
. .
._
B,,
+ C,.. ,. .. .
~1 .,
(3)
*Ref. 1 fimrre numbers refer to the
AP I wblication:
.Chart mrmbers
refey tn the pm-ket rhwts xttached to the Reinhold rmbhcutkrfi .
.,~~
.
JOlll{N. i J, OF PETltsJt .EIJM .fEf: l{NOI,OGY
8/10/2019 00000772 Ramey Compressibility
7/8
,
I
TABL142-01 L zONE PROPERTIS3
Porosity ; i: per cent
Fermatlen temperature
011
sravlW
Gas eravi ly
39,8 API (0.S26 to water]
1308: P;:)
Formation water salinity
From Hall the
rock
compressibility is estimated to be
3 X 10-0 pore volume/pore volume-psi.
Table 3 summarizes calculation bf
. .
TA8LE 3-CALCULATION OF TOTAL SYSTEM COMPRESSi81Ll lY FOR SAMPLE PROBLEM
A. OiL AND GAS
,
m+),
(&&) ,
(+2)
+ -{*)T ,,,
[-war,
Pressure
R.
scf/ST8
-(~)= f,.,
~ *K*); %%%.1 &
p+io
pT
~=
--w-- j:\
1]
1
29
0.0 %45 O. O %}l29 0.0001175 0.754 0.910 0.~7~65 0.00149
[s)
500
126
0.29
0.001372
1000 280 1.173 0.23
5:00
v 0.000500 0.000145 0.0001236 1.51
0.828 0.00257 0.000723
0.000599 0.79
1500
460.
1.267 0.37
5.41
0.000541 0.000157 0.0001238 2.26
0.762 0.00157 0.000458
0.000334
0.53
1900
60
1.3A0 0.38
5.56
0.000556 0.000161 0.0001201 2.86
0.733 0.00120 0.000341
0.000221 0.375
NOTES
(1) From R ef. 1, Ckrt 3,
Reinhold publication
i21
From Ref. 1 , Chert 3 , Reinkld pub lication
[3) From f% . 4 , This Paper
[4) From Fig. 5 , This Poper
(5) Vwo s 1
.
(6) UseEa.8. ThisPowr
(71a = 3.1
21P
(8) From Ref. J 3 , cq pm c cmr
(9) co ~ 1/500 = 0.002 for 500 PSiO
,.
8. RESERVOIR WATER
/
3
K:T, uf/bbl*
[-+++) ~
-+(%: %%7 +( .L) ~ , -= ,::;; % ~,yw) ,>(&J) ] r
Preisure ,. Pure
Pure
Far Gas
.
ps a
Water
8rine
Wafer
in SOlutiOn*
8rine
Water 8rlne
bbl
6P ~
+.
P
,,
4.3
4.1
.ji 12 x 10-6
~ ~~
-. E .1.019
33,sxlfl-3
37 .0 x 1o-u
3 to x 10-S . .I.obo
1000. .. 7.5. . , 7.+. .,3:03 ~.,o:o
3.26 x 10-. 0.0057 0.0Q54. - 1.017
13.6x 10-n s
16 .9x 10-n
-,;053. ..
&29 X 10= -
U.00.65-- 0:0043- ~.FJJ:- - 6 .6SK10-a --- -- 9.94x ~0a- ----~ - - - -
1500
10.0
1900
11,3
10.9 : 3.01 x 10P
1.095 3.30 x 10-0
0.003S 0.0036 .
4
8/10/2019 00000772 Ramey Compressibility
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Sa
[
1
+ R,,R,)~+B, - . .
B.
But
by d~firsition, the two-phase volume factor
B, is:
B, = B, + (R,, R,) B,
and by differentiation,
- )=[- -R-R +B*17
Thus
- )T
sO[-+ + - ( ),
which may be substi~uted in Eq. 3 to yield Eq. 9.
E VAL L J ATI Ok O F aB,/ijp .
The change of the two-phase vph.srne.factor with pres-
sure may be evahsated in severaI ways other than direct
differentiation. One way is by means of the empirical Y
correlation. oThat is, from
=ix:)=ap+d
We achieve
=1{(%9+
}=B1{ P=+ +l}
and
m,
7 (%-l)(Y*P)I
=-pY
.
. J
and
()
1 aB,
B,b -i- B,
-B,J 2Y -d
.E FT.
BopY
or
.( )
a, = B,b + (B, B,J(Y +~)-,
T~r
B,, Y
Either form may be used. The interesting feature is
that the oil and gas compressibility terms including the
solution effect may be ldetermined as a function of pres-
sure without differentiation. This procedure permits
smoothing data since values of Y should ,be determined
from the best straight line through the data points. Cal-
culatioris are tedious, however. This method is probably
of most use in connection with experimental data and for
application to some forms of the rntiterial balance.
The partial
(aB,/i3p)r
can also be eva lua ted by direct
I
d if fer en t ia t ion of S t a n din gs B, correlation; Standings cor-
relation of
B, vs
pressure can. be differentiated generally
to yield Fig. 6. Fig. 7 presents a nomographic solution
of results on Fig. 6 to aid determination of (aB,/i3p)T. It
shouId be emphasized that Fig. 7 is of only limited use
in determination of total system compressibility due to
the restriction of gas saturation to less than the critical
value for free gas flow. However, Fig. 7 may be of con-
siderable use in connection with certain material balance
calculations. :
.-.
.
,
\.
i
,
. .
.,
.>
.,
,.
?
**
,
f
.
