S 80 T pressibility Factors in Predicting Gas Cjdxy.cup.edu.cn/ngcupb/Files/FilesUploaded/spe...2003...
Transcript of S 80 T pressibility Factors in Predicting Gas Cjdxy.cup.edu.cn/ngcupb/Files/FilesUploaded/spe...2003...
S
TCI
C T Treore
AGser UfDsa IcPor TsdKe IGrdpprbcoc Apc
SPE 1590
The Use oCondensnese Ntuk Ar
Copyright 2012, Society
This paper was prepare
This paper was selecteeviewed by the Societyfficers, or members. Eeproduce in print is res
Abstract Gas condensatesystems. The eestimation, gas reservoir is ther
Underestimatiofactors that do nDuring isothermseparation in thaccount for the
Ideally, Z-factochanges duringPVT data acquior gas gravity oretrograde cond
This paper descsingle phase Z determined fromKay (1936) mixestablishes that
ntroduction Gas condensateretrograde conddewpoint. Gas prediction earlyphase Z-factor reservoir. GIIP below the dewpcompositional cor gas gravity tconsuming proc
A generalised phase systems critical propert
080
of Two Pate Perforukhe, SPE an
y of Petroleum Enginee
ed for presentation at t
d for presentation by ay of Petroleum EngineElectronic reproductionstricted to an abstract o
e reserves are teffect is worse
reserves, petrorefore crucial i
on of reserves onot consider twmal pressure rehe reservoir. C
phase changes
ors for gas reseg reservoir deplisition campaigof reservoir fludensate system
cribes a correlafactor from Ram Dranchuk Axing rules. Thet the two-phase
e reservoirs repdensate due to compressibilit
y in the life of a(Z2p) is introdufor a rich gas
point value. Prchanges duringo obtain the twcess and cost.
compressibilityencountered i
ties, pseudo-re
hase Comormance nd W.E.Maso
ers
he SPE Annual Techn
an SPE program commeers and are subject ton, distribution, or storaof not more than 300 w
typically underin rich gas conoleum accountiin reaching dev
often results frowo-phase regioeduction below
Consequently, ths in the reservo
ervoirs are deteletion. Sometimgn. A methodoid to obtain tw
ms.
ational researchayes et al (1992
Abu-Kassem (19e paper compare Z-factor shou
present a signifits ability to foty factor (Z-faca reservoir is cuced to accouncondensate sysreferably, Z2p -g reservoir depwo-phase Z-fac
y factor chart n gas-condenseduced proper
mpressib
on, Ph.D., SPE
ical Conference and E
mittee following review o correction by the autage of any part of thiswords; illustrations may
restimated whendensate systeming, and pipelinvelopment deci
om approximatons that retrograw the dew point
here is need tooir.
ermined from cmes the CVD teology that emplwo-phase Z-fact
h design with t2) to determine975) correlatiores Z2p, Z-factould be used for
ficant part of worm a liquid phctor) is essentiacrucial in reachnt for liquid drostem will be se-factor is determletion. Numero
ctor to compens
for natural gasate reservoirs.rties and subs
bility Fact
E - Robert Go
Exhibition held in San A
of information containthor(s). The material ds paper without the wry not be copied. The ab
en single phasem with adversene designs. Acisions and cont
tions based on ade condensatet phase change introduce a tw
onstant volumest reports are loys a suitable tors (Z2p) is des
two-phase Z-fae GIIP for gas cons using pseudors, GIIP valuemore precise e
world gas reservhase in the reseral for accurate
hing developmeop-out during periously underemined from coous correlationsate for CVD t
ases presented . Many authorsequently Z an
tors in Pr
ordon Univers
Antonio, Texas, USA, 8
ned in an abstract submdoes not necessarily reritten consent of the Sbstract must contain co
e compressibilite implications fccurate predictitractual agreem
single phase (e reservoirs exs occur leading
wo phase Z fact
me depletion (CVnot readily avacorrelation devscribed. This c
actor derived frcondensate resdo-reduced proes obtained fromestimation of G
ves. A gas conrvoir by an isoprediction of i
ent decisions aphase changes estimated if theonstant volume ns have been detests report not
by Standing ars have develond Z2p-factors
redicting
sity.
8-10 October 2012.
mitted by the author(s)eflect any position of tSociety of Petroleum Eonspicuous acknowled
ty factors are afor gas initiallyion of GIIP ear
ments.
(Standing and Kxhibit at pressurg to liquid and tor in material
VD) tests that ailable or plansveloped using
compares quite
rom the real gaservoirs. Z-facoperties presenm the CVD tes
GIIP in gas con
ndensate reservothermal pressuinitial-gas-in-pand contractual(liquid and gas
e (Z2p)-factor isdepletion (CV
eveloped usingt readily availab
and Katz makeoped correlatios. Dranchuk a
Gas
). Contents of the papehe Society of PetroleuEngineers is prohibitedgment of SPE copyrig
applied to two-y in place (GIIPrly in the life o
Katz) compresres below the dgaseous phasebalance calcul
simulate comps are non-existfluid molar co
e well with actu
as law equationctors were also nted by Sutton (st and correlatindensate reserv
voir is also knoure reduction bplace (GIIP). Gl agreement. Tseous phase) ins not used at pr
VD) test which g fluid molar coble due to its ti
es no provisioons to determinand Abu-Kasse
er have not been um Engineers, its ed. Permission to ght.
-phase P)
of a
sibility dew point. e lations to
positional tent for mposition
ual data for
n and
(1985) and ons and
voirs.
own as below the
GIIP The two-n the ressures simulates
omposition ime
on for two-ne pseudo-em (1975)
2 SPE 159080
presented a correlation to directly determine gas compressibility factor using reduced gas density. The correlation closely represents the Standing and Katz (SK) chart and is recommended for a majority of natural gases. Sutton (1985) studied gas condensate with high gravity and modified Stewart-Burkhardt-Voo (1959) mixing rules in order to minimize the large deviation observed in gases with high heptanes plus concentration when applying Kay’s mixing rules (1936). Rayes et al. (1992) presented a correlation to calculate Z2p-factor based on 131 CVD data with C7+ ≥ 4% collected from reservoirs worldwide. The correlation was expressed as a function of pseudo-reduced temperature and pressure. Wichert and Aziz (1972) examined natural gases with significant amounts of carbon dioxide and hydrogen sulphide and presented correlations to yield accurate Z-factor by correcting the pseudo-critical properties. This is a comparative analysis that utilized compositional wellstream data to determine GIIP for gas condensate reservoirs using two-phase Z-factor derived from the real gas law equation and correlations from Rayes et al (1992), Dranchuk Abu-Kassem (1975), Sutton modified SBV (1985) and Kay mixing rules (1936). Methodology This study compared GIIP estimated using Z2p-factor obtained from correlations to estimation with CVD test. The selected correlations are as follows:
1. Kay mixing rules 2. Sutton modification of SBV (SSBV) 3. Dranchuk-Abou-Kassem (DAK) 4. Rayes et al.
Data used for the analysis were obtained experimentally from CCE and CVD test performed on gas condensate to simulate fluid production by reservoir depletion. The dewpoint pressure Pd was used to determine the dewpoint Z-factor (Zd). A typical CVD report provides the following parameters required for subsequent calculations of two-phase compressibility factor (Z2p):
1. Molecular weight of heptanes plus (Mc7+) 2. Density of heptanes plus (c7+) 3. Two – phase deviation factor at dewpoint (Zd) 4. Well stream produced, cumulative percent of initial (np/n) 5. Liquid volume reported as a percentage of cell volume (SL %) 6. Fluid molecular weight.
At pressures below dewpoint, heavier hydrocarbons condense out of the gas phase. Hagoort (referenced in Walsh and Lake 2003 p. 529) proposed the modification of Havlena and Odeh (1963) equation for volumetric reservoir by replacing the single-phase Z with two-phase Z-factor (Z2p).
= - …………........Eq. A
= ……………… Eq. B Cumulative gas production (GP) becomes the sum of dry gas from separators (Gp(surf)) and gas equivalent of stock tank liquid (GE). Where Gp = Gp (surf) + [GE*Np] Np = the volume of stock tank liquid.
GE = 133,000 o is the specific gravity of condensate given on the compositional analysis report. Mwo is the molecular weight of fluid determined experimentally. If not available it could be determined by the relationship below:
Mwo =
PZ
Pi
Zi
PZiG
G p
PZ2p
PdZd
1GpGIIP
oMwo
42.43 o1.008 o
SPE 159080 3
Two-phase compressibility factor (Z2p) becomes:
= ……………….Eq. C
Where Gp = cumulative gas produced at pressure p, scf
GIIP = gas initially in place, scf P = reservoir pressure, psia Pd = dew-point pressure, psia Zd = gas deviation factor at the dew-point pressure. Pd
The predetermined dewpoint pressure is use in calculating the dewpoint compressibility factor (Zd) using the real gas law presented below:
Zd = ………………..Eq. D
Where Vi = volume of initial gas occupied, ft3 Pd = dewpoint pressure, psia ni = moles initially at the reservoir, lb-mole T = temperature, °R R = gas constant, 10.730 psia ft3/lb-mole °R A cross plot of average reservoir pressure (P/Z2p) against cumulative production (Gp) has become a widely accepted method of estimating GIIP and reserves. Gas compressibility factor is generally estimated from the Standing and Katz (SK) chart, this chart has been reproduced for spreadsheet application by Dranchuk and Abou-Kassem (DAK)(1975). Z-factor is expressed as a function of pseudo-reduced temperature (Tpr) and pressure (Ppr) which requires the use of pseudo-critical temperature (Tpc) and pressure (Ppc) for multi-component mixtures. Z = f (Ppr, Tpr) where
Ppr = ………………..Eq. 1
Tpr = ………………..Eq. 2
The commonly used methods for calculating critical properties are Kay’s mixing rules and Sutton’s modified SBV method (Sutton, 1985) in combination with Wichert and Aziz for acid gas content. Kay’s rules Kay’s (1936) mixing rules for pseudo-critical properties expressed as the molar average of critical constant is adequate for gas mixtures with known composition and non-hydrocarbon content. Ppc = Σ yi Pci ………………..Eq. 3 Tpc = Σ yi Tci ………………..Eq. 4
Where yi = mole fraction of the ith component in the mixture Pci and Tci = critical pressure and temperature for the I component Stewart-Burkhardt-Voo mixing rules (SBV) Stewart et al (1959) presented a correlations derived from combining 21 different rules of pseudo-critical properties prediction and introduced the pseudo-critical Z-factor as a third constant. These correlations were accepted for high molecular weight gases.
Z2pZdPd
P
1Gp
GIIP
Pd
Vi
niRT
pppc
TTpc
4 SPE 159080
J = i ………………..Eq. 5
K = ………………..Eq. 6
= ………………..Eq. 7
= ………………..Eq. 8
Sutton’s modified SBV mixing rules Sutton’s (1985) mixing rules derived from modifying the SBV rules to minimize the large deviation of high molecular weight gases from SK chart. The new mixing rules introduce FJ, EJ and EK as empirical adjustment factors for heptanes-plus content in the hydrocarbon mixture. This is recommended for gases with specific gravity greater than 0.75.
= c7+
………………..Eq. 9
EJ = 0.6081 FJ + 1.1325 FJ2 – 14.004 FJ y
c7+ + 64.434 FJ yc7+
2 ………………..Eq. 10
Ek = (Tc/Pc0.5
)] c7+ [0.3129 yc7+
- 4.8156 yc7+
2 + 27.3751 yc7+
3] ………………..Eq. 11
J’ = J – EJ
K’ = K – EK
T’pc = K’2/J’ ………………..Eq. 12 P’pc = T’pc / J’ ………………..Eq. 13 Where J and K are calculated from equations 5 and 6. °R/psia. Wichert – Aziz correction method The correlations presented by Wichert-Aziz (1972) accounted for the non-hydrocarbon impurities in natural gases such as CO2 and H2S. The previously mentioned mixing rules did not account for the presence of these fractions in gas mixtures. The correction factor below is applied to the pseudo-critical properties of sour gases to obtain an accurate Z-factor.
Ε = 120[A0.9- A1.6] + 15 (B0.5 – B4.0) ………………..Eq. 14 T’pc = Tpc – ε ………………..Eq. 15
P’pc =
…………………Eq. 16
A = y
H2S + yco2
……………….. Eq. 17 B = mole fraction of H2S ε = pseudo-critical temperature adjustment factor and is defined mathematically by the following expression. T’pc = corrected pseudo-critical temperature, °R P’pc = corrected pseudo-critical pressure, psia
13y i
TcPc
i
23
y iTcPc
0.5
i
2
yiTc
Pc
0.5
i
TpcK2
J
PpcTpcJ
FJ13
yTcPc
c7 .
23
yiTc
Pc
0.5
2
S
DDRtr
ρ
ZT f
W
R
R
R
R
R
TgT
T
ρ
I
ρW
f
T RTp
Z
T
SPE 159080
Dranchuk-AbuDAK (1975) pReduced gas deemperature an
reduced pressur
ρ.
Z.
ρThe equation-o
f ρ R ρ
Where coefficie
R A
R.
R A
R A
R
The constants given below: Table 1. Consta
The initial simp
ρ.
If the initial gue
ρ ρWhere
f ρ R
This equation i
Rayes-Piper-MThe correlationpseudo-reduced
Z2p = A0+A1(p
Table 2. Consta
u-Kassem (DApresented an eensity by defin
nd pressure. Thres 0.2 ≤ Pr ≤ 2
of-state for redu
R ρ
ents R1 to R2 a
A1 to A11 dete
ants A1 to A11 d
plified guess of
ess substituted
2 R ρ
s solved by app
Mccain-Postonns developed byd pressure 0.7 ≤
pr)+ A2( )+
ants determined
1
Tr
AK) correlatioempirical correnition is the rathe correlations 25 to 30 and tem
uced gas densit
ρ R ρ
are expressed b
ermined by a n
determined by
f reduce densit
d in equation 3.
5 R ρ
plying the itera
n (Rayes et. al)y Rayes et al (≤ Pr ≤ 20 and t
+A3(pr)2+ A4(
d from Rayes e
on elation to detetio of gas densrequire iterati
mperatures 1 ≤
ty calculation a
R 1 A
elow:
nonlinear regr
a nonlinear reg
ty (r) is:
16 gives a non
2 R ρ exp
ation method o
) correlations(1992) for rich temperature 1.1
)2 + A5(
et. al correlatio
1
Tr
p
T
ermine compresity at a specifiive solution to≤ Tr ≤ 3.
…
as proposed by
ρ ρ exp A
…
…
…
…
…
ession model
gression mode
n-zero value, th
A ρ 1
of Newton-Rap
gas condensat1 ≤ Tr ≤2.1
) …
ons
pr
Tr
essibility factofic temperatureo determine Z-
………………
………………
y the DAK is gi
A ρ 1 0
………………
………………
………………
………………
………………
of data points
el of data points
he enhanced gu
2A ρ A
phson.
te from CVD s
………………
or directly usie and pressure factors. These
…..Eq. 18
….Eq. 19
iven below:
0…Eq. 20
….Eq. 21
….Eq. 22
….Eq. 23
….Eq. 24
….Eq. 25
obtained from
s obtained from
………
uess of (r) bec
………
A ρ 1 A
studies gas com
….Eq. 29
ing reduced gadivided by gas
e are suitable f
m SK Z-factor
m SK Z-factor
………….Eq. 2
comes:
………….Eq.
ρ …..Eq.
mposition is ap
5
as density. s at critical for pseudo-
r charts are
charts
26
27
28
pplicable to
6
SWpScZ SSdSpSSSth RApw RHIc T
6
Summary of AWellstream complace and reservStep 1: Pseudocalculated usingZ-factors were
Step 2: The twStep 3: Suttondetermination oStep 4: Rayes properties fromStep 5: Gas iniStep 6: AnalysStep 7: Compahe base case (Z
Results A total of five Cprimary aim of were applied us
Reservoir descrHydrocarbon RInitial reservoirconditions of 6
Table 3: Summ
Approach for Emposition fromves estimation
o-critical tempeg equations 3 –established usi
o-phase comprn’s modified Sof Z-factors.
et al correlatim Sutton’s moditially-in-place e the behavior are and analysZ2p obtained fro
CVD report frof using the corrsing Microsoft
ription: CVD dRecovery” (War pressure is 650°F and 15.025
mary for Case 1
Estimating GIm five reservoir. The steps pro
eratures and pre– 4. Equations ing DAK equa
ressibility factoSBV, equation
ions, equation dified SBV equ
(GIIP) is estimof Z2p and Z we the variationom CVD test).
om gas-condenect Z-factor to excel spreadsh
data from the Nalsh and Lake 2500 psi with tem5 psia.
IIP rs was used in
oposed in this wessures at spec14 – 17 were t
ations 18-28.
or starting fromns 9-13 were
29 was appliuations 9-13. mated from a crwith pressure ren in estimated
nsate fields in tdetermine acc
heet. Step-by-s
North Sea reser2003). mperature of 2
n calculating cowork are outlincified pressure then applied fo
m the dewpointused to calcu
ed to estimate
ross plot of P/zeduction. gas-initially-in
the North Sea acurately gas inistep calculation
rvoir as publish
75°F. The dew
ompressibility ned below: drop starting f
or non-hydroca
t pressure was ulate pseudo-cr
e two-phase Z
z versus Gp at a
n place (GIIP)
and Middle Eaitially-in place.n is found in A
hed in literature
w point pressur
factors which
from the dewpoarbon correction
determined froritical propert
-factors direct
an extrapolatio
using Z2p and
st were selecte. Correlations s
Appendix 1.
e “A Generaliz
re is 4536 psi, s
S
is vital for ini
oint pressure wn.
om equation Cies and DAK
tly using pseud
on of P/z equal
d single-phase
ed for this studyselected for the
zed Approach t
standard reserv
SPE 159080
itial gas-in-
were
. for direct
do-reduced
s zero.
Z-factor to
y with the e project
to Primary
voir
S
F
F
SPE 159080
Figur
Figure 2: Cros
Figure 3: Cros
re 1: Plot of z-
ssplot of Two
ssplot of Z2pA
-factor vs. Pre
phase Z2p, Sin
and Z2pR (Ca
essure for rich
ngle Phase Z (t
ase 1)
h gas condensa
test) and Z (D
ate (Case 1)
DAK) and Gp%
% (Case 1)
7
8
RT
F
F
8
Results for resTable 4: Summ
Figure 4: Plot
Figure 5: Cros
servoir samplemary for Case 2
of Z-factors v
ssplot of Z2p(a
e: case 2 , Reservoir tem
vs. Pressure fo
actual), Single
mperature: 305
or Lean Gas C
Phase Z (test)
oF
Condensate (C
) and Z (DAK
ase 2)
K) and Gp (Ca
ase 2)
S
SPE 159080
S
F
T
DGGgTthpcS
SPE 159080
Figure 6: Cros
Table 5: Summ
Discussion Gas CompressGas compressibgraphically. VaTwo-phase Z-fahree step proce
pseudo-reducedcorrelations weStanding and K
ssplot of P/Z, Z
mary of GIIP
sibility Variatibility factors obalues from CVDfactors were caless. First, the pd properties weere used to calcKatz chart (1942
Z2pA and Z2pR
Analysis and A
ion Based On btained from thD test are usedlculated from C
pseudo-critical ere determinedculate compres2) hence it was
R vs. Gp (Case
Absolute Ave
Alternative Mhree correlation
d as the base caCVD test resulproperties wer
d and thirdly, Dsibility factorss chosen to esti
e 2)
rage Error.
Method. ns and laborato
ase for comparilts and Rayes ere estimated fro
Dranchuk Abu-K. DAK correlatimate Z-factor
ory test are preing the accuracet al correlationom Kay’s and Kassem (DAK
ations give the cr values.
esented above icy of values obns. Z-factors wSutton mixing
K) (1975) and Rclosest fit and
in tables 3 – 4 btained from co
were determinedg rules. SecondRayes et al. (19representation
9
and orrelations. d from a ly, the
992) n of
10 SPE 159080
The summary of gas-initially-in-place for all methods and the summary of AAE are presented in table 5. Significant variation observed in Z-factors can be attributed to different methods used for estimation. This variation affects the accuracy of GIIP prediction either by overestimation or underestimation. P/Z versus cumulative gas production (Gp) plot repeatedly showed that the Z2p -factor gives an accurate GIIP estimate when the linear plot produced is extrapolated to zero P/Z. The single phase Z-factor underestimated GIIP with an Average Absolute Error (AAE) of 9.76%. Rayes correlations gave the closest match with an AAE of 2.33% The relationship between the two-phase Z and single Z-factor at each depletion pressure shown in figures 1 and 4 indicates that at higher pressures gas compressibility factors converge when the system is in a single gaseous phase. As pressures decrease, deviation occurs and single Z tends towards the value of 1.0 while two-phase Z decreases as a result of the condensed heptanes plus fraction in the reservoir. This is signifcant in rich gas-condensate reservoirs. On the contrary, figure 4 in case 2 shows the Z2p -factor approaching 1.0 at low pressure, with the sample gas-condensate acting as if it were a wet gas. The single-phase Z in figure 5 shows a close estimate of GIIP with absolute average error (AAE) of 0.89% to Z2p prediction. The summary of AAE can be found in table 5. The degree of deviation indicates the richness of the reservoir fluid; if the deviation is less or the Z2p -factor is tending to the single phase Z-factor value, it verifies that the fluid is a lean gas-condensate with heptanes plus content less than 4 mol%. Following the conclusion made by McCain (1994), the reservoir can then be treated as a wet gas reservoir notwithstanding condensate drop-out at surface. Comparing Rayes et al. Correlations with CVD Z2p – factor (Actual). Gas compressibility factors predicted by Rayes et al. correlation have close comparisons with the actual Z2p – factors. With slightly lower values of Z in rich gas condensate and higher values in lean gas condensate, overall estimation of GIIP has an absolute average error (AAE) of 2.33%. For the lean gas-condensate in case 2, an AAE of 4.28% was observed, it can be deduced that the correlations are not fit for gases with low mole percent of heptanes plus. Comparing Single Phase Correlations with CVD Z2p – factor (Actual). The single phase Z-factor from the CVD test and Z-factor obtained using Kay mixing rules (1936) repeated gave higher Z-factor values which resulted in consistent under-prediction of GIIP. The non-linear plot showed an overall AAE of 6.14% and 9.76% for test Z-factor and Kays mixing rules respectively. The exception to this was seen in case 2 (figure 6) where an extrapolation of P/Z to zero gave a perfect linear plot in a lean gas condensate reservoir. Sources of Error Determining close approximation of Z2p - factor for estimating GIIP is dependent on the following:
Data accuracy and computation. Sampling Error In-adequate amount of representative fluid sample. Insufficient PVT analysis: Compositional analysis measurement is commonly done to C7 instead of preferably C20,
Conclusion The effect of two-phase compressibility factor in estimating gas-initially in-place (GIIP) for a volumetric retrograde reservoir was presented and its importance cannot be over emphasized. It was observed that the Z-factor is a significant contributor to the estimation of GIIP. Hence, applying the correct compressibility factor to a two-phase system is vital. Ignoring the use of two-phase compressibility factor results in high values of Z giving low values for p/z in a rich gas condensate reservoir systems hence seriously underestimating the initial-gas-in-place (GIIP).
• The variation plot of single Z and Z2p - factor versus pressure confirms the reservoir type such as lean, conventional
or very rich reservoir (near critical fluid) depending on the degree of deviation. • The P-Z plots of CVD (actual Z2p ) values predicts GIIP accurately and is used as the base case. Rayes et al correlations
presented the closest match to the actual Z2p -factor with Average Absolute Error (AAE) of 2.33. • From this study, Rayes et al. correlations are recommended when CVD report is not available. • Dranchuk Abu-Kassem (1975) and Rayes et al (1992) correlations both require input of pseudo-critical temperature and
pressure. Therefore, care must be taken to compute these parameters accurately. Kays mixing rules presented the largest deviation resulting in serious underestimation of reserves. The resulting errors could lead to ignoring potential profitable assets.
The single phase Z-factor repeatedly underestimated GIIP in the range of 5 – 12% when compared with the actual two phase Z-factor. This method presents unsatisfactory results in a two-phase system and should be avoided except in lean gas condensate reservoirs.
SPE 159080 11
The study establishes the importance of applying Z2p-factor in GIIP estimation for rich gas condensate reservoirs and for developing more precise compositional correlations to minimize or eliminate deviations between correlations and the actual Z2p-factor (CVD test).
Possible sources of error to note include difficulties in obtaining representative fluid samples, incorrect CVD composition reports and failure to recognize the effects of pressure interference from a mutual aquifer.
Nomenclature γg Gas specific gravity ε Wichert and Aziz acid gas correction term AAE Average Absolute Error Bg Gas formation volume factor GE Gas equivalent GIIP Gas initially in place Gp Gas produced at surface EJ Sutton SBV parameter EK Sutton SBV parameter FJ Sutton adjustment parameter, temperature J́ ́ Sutton parameter Mc7+ molar mass of heptanes plus fraction P Pressure Ppc Pseudo –critical pressure Ppr Pseudo- reduced pressure R Universal gas constant = 10.731 T Temperature Tpc Pseudo – critical temperature Tpr Pseudo- reduced temperature We Water influx Wp Water produced yc7+ Mole fraction of heptanes plus fraction. Z Gas compressibility factor Z2p Two-phase gas compressibility factor Z2pA Two-phase gas compressibility factor (Actual) Z2pR Two-phase gas compressibility factor (Rayes) Acknowledgements Appreciation goes to Mr. James Arukhe, Lead Petroleum Engineer with Saudi Aramco for his insights and helping to proof read this paper. References AHMED, T.K., 2006. Reservoir engineering handbook. New York: Gulf Professional Publishing. CORREDOR, J.H., PIPER, L.D. and McCAIN, W.D. Jr., 1992. Compressibility factors for naturally occurring petroleum gases. SPE 24864. In: Proceedings of Annual Technical Meeting and Exhibition, 4-7 October. Washington, DC: Society of Petroleum Engineers. CRAFT, B.C and HAWKINS, M., 1991. Applied petroleum reservoir engineering. 2nd Ed. New Jersey: Prentice Hall Publishers. CRAFT, B.C and HAWKINS, M.F., 1959. Applied petroleum reservoir engineering. 2nd ed.: Englewood Cliffs, NJ: Prentice-Hall Inc DAKE, L.P., 1998. Fundamentals of reservoir engineering. 12th Ed. New York: Elsevier Publishing. DAKE, L.P., 2001. The practice of reservoir engineering. New York: Gulf Professional Publisher. DRANCHUK, P.M. and ABU-KASSEM, J.H., 1975. Calculation of Z-factors for natural gases using equation of state. Journal of Canada Petroleum Technology, July-September 1975, pp.34-36. Eilerts, C.K., 1959. Phase relations of gas-condensate fluids, vol. II: Monograph 10. Bureau of Mines, American Gas Association. Pp.764-770. FAN et al., 2005.Understanding Gas-condensate Reservoir. Oilfield Review, winter 2005/2006, pp. 14-27. HAVLENA, D., and ODEH, A. 1963. The Material Balance as an Equation of a Straight Line. Journal of Petroleum Technology, (15)8, pp. 896-900. KAY, W.B., 1936. Density of hydrocarbon gases and vapour at high temperature and pressure. Ind., Eng. Chem., (28) 1014-1019.
12 SPE 159080
McCAIN, W., D 1994. Heavy components control reservoir fluid behaviour, SPE 28214. In: Proceedings of the SPE Technology Today Series Conference. Richardson TX. Society of Petroleum Engineers. McCain Jr., W.D. and Bridges, B., 1994. Volatile oils and retrograde gases-what’s the difference? Petroleum Engineer Journal. January 01, pp. 35-36. McCain Jr., W.D. and Piper, L.D., 1994. Reservoir gases exhibit subtle differences; Part 4. Petroleum Engineer Journal. March 01, pp. 45-46. RAYES, D.G. et al., 1992. Two-phase compressibility factors for retrograde gases. SPE Formation Evaluation, (7)1, pp. 87-92. SUTTON, R.P., 2005. Fundamental PVT calculations for associated and gas/condensate natural gas systems. SPE 97099. In: Proceedings of the SPE Annual Technical Conference. 9-12 October 2005. Dallas, TX: Society of Petroleum Engineers. SUTTON, R. P., 1985. Compressibility Factors for High-Molecular-Weight Reservoir Gases. SPE 14265. In: Proceedings of Annual Technical Conference and Exhibition, 22-26 September 1985, Las Vegas, Nevada: Society of Petroleum Engineers. STANDING, M.B., 1977. Volumetric and phase behaviour of oil field hydrocarbon systems. 9th ed. Dallas: Society of Petroleum Engineers of AIME. WALSH, M.P. and LAKE, L.W., 2003. A generalized approach to primary hydrocarbon recovery: A handbook of petroleum exploration and production 4. Amsterdam: Elsevier Ltd. WHITSON, C.H., FEVANG, O. and YANG, T., 1999. Gas condensate PVT -what's really important and why. In: Proceedings of IBC Conference, 28-29 January 1999, London. WHITSON, C.H and BRULES’, M.R., 2000. Phase behavior; SPE monograph series, volume 20. Richardson, TX: Society of Petroleum Engineers. WICHERT, E., and AZIZ, K., 1972. Calculation of Z’s for sour gases. Hydrocarbon Processing, (51)5, pp.119-122.
SPE 159080 13
Appendix Computation of Two-Phase Compressibility Factor Sample calculation of two-phase Z-factor at different pressures using the real gas equation (eq. C) and different correlations used in this study will be shown in this section. Subsequent results were generated from Microsoft excel. Reservoir description: CVD data from the North Sea reservoir as published in literature, Walsh and Lake (2003). Initial reservoir pressure is 6500 psi with temperature of 275°F. Standard reservoir conditions of 60°F and 15.025 psia. Table 6: CVD Report of a North Sea Reservoir at 275o F
Components 4521 3900 3200 2500 1800 1200 700
Hydrogen sulfide 0 0 0 0 0 0 0
Carbon Dioxide 2.42 2.44 2.46 2.48 2.53 2.55 2.6
Nitrogen 0.47 0.49 0.5 0.51 0.52 0.51 0.48
Methane 68.22 69.9 71.3 72.41 72.85 72.46 71.01
Ethane 11.8 11.85 11.96 12.04 12.16 12.35 12.53
Propane 5.46 5.4 5.34 5.28 5.36 5.49 5.9
Iso-butane 0.83 0.8 0.78 0.76 0.77 0.81 0.91
N-butane 1.74 1.66 1.61 1.56 1.59 1.68 1.87
I-pentane 0.72 0.68 0.64 0.61 0.6 0.65 0.74
N-pentane 0.74 0.69 0.65 0.62 0.61 0.66 0.75
Hexanes 1.07 0.97 0.87 0.8 0.78 0.81 0.93
Heptanes plus 6.53 5.12 3.89 2.93 2.23 2.03 2.28
Total 100 100 100 100 100 100 100
Mol. Weight of C7+ 148 134 124 117 111 108 107
Density C7+ 0.793 0.776 0.767 0.76 0.754 0.751 0.75
Deviation Factor - Z
Equilibrium gas 0.950 0.908 0.876 0.873 0.890 0.917 0.949Wellstream produced, Cum.% of initial, Mscf
0.00 8.761 21.717 36.857 53.451 67.933 80.041
Composition of Produced Wellstream - Mole Percent, Reservoir pressure, Psig
CONSTANT VOLUME DEPLETION STUDY AT 275°F
Using the formula derived from the real gas equation above: AT PRESSURE, P = 4521psig (DEW POINT PRESSURE)
=
Zd = 0.950 determined during CCE test with dew point pressure and recorded in the report. Gas initially in-place (GIIP) = 1000Mscf.
Cumulative production of initial gas-in place = 0
Z 0.950
4521 15.0254521 15.025
1 0.
At dew point pressure, the Z-single phase equals Z2p as there is no liquid-dropout. As discussed earlier, the CVD test begins at the dew point pressure and the report is made on the bases of 1000Mscf of initial gas-in place at that pressure. AT PRESSURE, P = 3900psig (FIRST STAGE DEPLETION)
Z 0.950
4521 15.0253900 15.0251 0.08761
.
AT PRESSURE, P = 3200psig
Z 0.950
4521 15.0253200 15.0251 0.21717
.
AT PRESSURE, P = 2500psig
Z 2pZdPd
P
1Gp
GIIP
14 SPE 159080
Z 0.950
4521 15.0252500 15.0251 0.36857
.
AT PRESSURE, P = 1800 Psig
Z 0.950
4521 15.0251800 15.0251 0.534.51
.
AT PRESSURE, P = 1200psig
Z 0.950
4521 15.0251200 15.0251 0.67933
.
AT PRESSURE, P = 700psig
Z 0.950
4521 15.025700 15.0251 0.80041
.
Application of Kay’s Mixing Rules and DAK Correlations Single phase Z-factor is calculated to compare with the test data. Kay’s mixing rules is applied to determine pseudo-critical properties and Z will be determined directly by Dranchuk Abu-Kassem correlations (DAK). Table 7: Critical properties of fluid molar fraction
ComponentsCritical Pressure, Pci psia
Critical Temp.Tci °R
3900 3200 2500 1800 1200 700
Hydrogen sulfide 0 0 0 0 0 0 0 0
Carbon Dioxide 1071 547.6 2.44 2.46 2.48 2.53 2.55 2.6
Nitrogen 493 227.3 0.49 0.5 0.51 0.52 0.51 0.48
Methane 666.4 343.33 69.9 71.3 72.41 72.85 72.46 71.01
Ethane 706.5 549.92 11.85 11.96 12.04 12.16 12.35 12.53
Propane 616 666.06 5.4 5.34 5.28 5.36 5.49 5.9
Iso‐butane 527.9 734.46 0.8 0.78 0.76 0.77 0.81 0.91
N‐butane 550.6 765.62 1.66 1.61 1.56 1.59 1.68 1.87
I‐pentane 490.4 829.1 0.68 0.64 0.61 0.6 0.65 0.74
N‐pentane 488.6 845.8 0.69 0.65 0.62 0.61 0.66 0.75
Hexanes 436.9 913.6 0.97 0.87 0.8 0.78 0.81 0.93
Heptanes plus 360.6 1023.9 5.12 3.89 2.93 2.23 2.03 2.28
Total 100 100 100 100 100 100
CONSTANT VOLUME DEPLETION STUDY AT 275°F
Composition of Produced Wellstream - Mole Percent Reservoir pressure, Psig
AT PRESSURE, P = 3900 Psig (FIRST STAGE DEPLETION) Ppc = ∑yi ∗ Pci = 654.116 Psia Tpc = ∑ ∗ 446.940 °R Applying Wichert-Aziz correlations to correct for non-hydrocarbon component presence, gives:
ε = 120[A0.9- A1.6] + 15 (B0.5 - B4.0)
ε = 120[0.02440.9- 0.02441.6] + 15 (00.5 - 04.0) = 3.93 T’pc = Tpc – ε = (446.94- 3.93) = 443.01°R
P’pc =
=
. ∗ .
. . = 648.365 Psia
Calculating the pseudo-reduced properties:
Ppr = = .
. =6.04
pppc
SPE 159080 15
Tpr = =
. = 1.66
Z-factor determined from DAK correlations:
ρ0.27PZT
From iteration, ρ = 1.092
Z.
= . .
. . = 0.899
AT PRESSURE, P = 3200 Psig Ppc = ∑yi ∗ Pci = 658.472 Psia Tpc = ∑ ∗ 437.377 °R Applying Wichert-Aziz correction factor for the presence of non-hydrocarbon:
ε = 120[0.02460.9- 0.02461.6] + 15 (00.5 - 04.0) = 3.96 T’pc = Tpc – ε = (437.377- 3.96) = 433.42°R
P’pc =
=
. ∗ .
. . = 652.52Psia
Therefore
Ppr = = .
. =4.93
Tpr = =
. = 1.695
Applying DAK correlations:
ρ0.27PZT
From iteration, ρ = 0.863
Z.
= . .
. . = 0.909
AT PRESSURE, P = 2500 Psig Ppc = ∑yi ∗ Pci = 661.89 Psia Tpc = ∑ ∗ 429.86 °R Using Wichert-Aziz correction factor:
ε = 120[0.02480.9- 0.02481.6] + 15 (00.5 - 04.0) = 3.98 T’pc = Tpc – ε = (429.86- 3.98) = 425.88 °R
P’pc =
=
. ∗ .
. . = 655.75 Psia
TTpc
pppc
TTpc
16 SPE 159080
Therefore
Ppr = = .
. =3.84
Tpr = =
. = 1.73
Applying DAK correlations:
ρ0.27PZT
From iteration, ρ = 0.637
Z.
= . .
. . = 0.942
AT PRESSURE, P = 1800 Psig Ppc = ∑yi ∗ Pci = 664.25 Psia Tpc = ∑ ∗ 425.65 °R Wichert-Aziz correction factor application:
ε = 120[0.02530.9- 0.02531.6] + 15 (00.5 - 04.0) = 4.05 T’pc = Tpc – ε = (425.65- 4.05) = 421.59 °R
P’pc =
=
. ∗ .
. . = 657.93 Psia
Therefore
Ppr = = .
. =2.76
Tpr = =
. = 1.74
Applying DAK correlations: From iteration, ρ = 0.435
Z.
= . .
. . = 0.983
AT PRESSURE, P = 1200 Psig Ppc = ∑yi ∗ Pci = 664.567 Psia Tpc = ∑ ∗ 426.350 °R Correcting for non-hydrocarbon content using Wichert-Aziz correlations.
ε = 120[0.02550.9- 0.02551.6] + 15 (00.5 - 04.0) = 4.078 T’pc = Tpc – ε = (426.350- 4.078) = 422.27 °R
P’pc =
=
. ∗ .
. . = 658.21Psia
The pseudo-reduced properties become:
pppc
TTpc
pppc
TTpc
SPE 159080 17
Ppr = = .
. =1.845
Tpr = =
. = 1.74
Applying DAK correlations: From iteration, ρ = 0.280
Z.
= . .
. . = 1.022
AT PRESSURE, P = 700 Psig Ppc = ∑yi ∗ Pci = 662.970 Psia Tpc = ∑ ∗ 432.651 °R Applying Wichert-Aziz correction factor:
ε = 120[0.02560.9- 0.02561.6] + 15 (00.5 - 04.0) = 4.145 T’pc = Tpc – ε = (432.651- 4.145) = 428.506 °R
P’pc =
=
. ∗ .
. . = 656.619 Psia
With these properties, the pseudo-reduced properties become:
Ppr = = .
. =1.089
Tpr = =
. = 1.715
Using DAK to determine Z-factor for this pressure: From iteration, ρ = 0.161
Z.
= . .
. . = 1.062
Application of Sutton Mixing Rules for Pseudo-Critical Properties Estimation. Sutton mixing rules (1985) is a modification of Stewart-Burkhardt-Voo (1959) (SBV) correlations. Component J and K are first determined from SBV and then substitute in Sutton’s correlations. Equations 5 – 13 are used in the calculation. Detailed calculations for all depletion stages are not included here. Referring to table 7 above for the critical properties, the following are obtained: AT PRESSURE, P = 3900 Psig (FIRST STAGE DEPLETION) J 0.7488 0.8304 = 0.7093
K ∑ = 18.1564
Sutton’s modification for heavier hydrocarbon (C7+)
F 0.145 0.086 = 0.0534
E 0.6081 ∗ 0.0534 1.1325 0.0534 14.004 0.0534 0.0512 64.434 0.0534 0.0512 = 0.0064
E.
√ .0.3129 ∗ 0.0512 4.8156 0.0512 27.3751 0.0512 = 0.38126
J J E 0.7093 - 0.0064 = 0.7029
pppc
TTpc
pppc
TTpc
1
K
T
P A
ε T
P
T T
Te T
TT(S
Z
A
8
K K E
T
P .
.
Applying Wich
ε = 120[0.0244
T’pc = Tpc – ε =
P’pc =
The Table belo
Table 8: Pseudo
The pseudo-redet al correlation
Table 9: Pseudo
Two-Phase Z-FThere are many(1992) correlatSutton mixing r
Z2p = A0+A1(p
AT PRESSUR
2.24353
0.000829231
= 18.1564 - 0..
.= 449.5
= 639.488 Psi
hert-Aziz corre0.9- 0.02441.6
= (449.50- 3.92
=
.
.
w show a sum
o-critical prope
duced pressurens to calculate t
o-reduced prop
Factor Using y ways to calcutions has been rules.
pr)+ A2( )+
RE, P = 3900 P
3 0.03752
1 6.176 1
1
Tr
38126 = 17.77
50°R
i
ction factor: 6] + 15 (00.5 -
29) = 445.571 ∗ .
. = 6
mary for subse
erties from Sut
calculated fortwo-phase com
perties from Su
Rayes Correlaulate compresschosen to calc
+A3(pr)2+ A4(
Psig (FIRST ST
281 ∗ 6.176
1.53428.
752
04.0) = 3.929
°R
633.898Psia
equent depletio
tton mixing rul
r each depletionmpressibility fa
utton correlatio
ations sibility factor fculate the two-
)2 + A5(
TAGE DEPLE
– 3.56539 ∗
0.131987
1
Tr
p
T
on stages calcu
les
n stage is preseactor.
ons
for gases. For -phase compre
) …
ETION)
∗1
1.649
7.
.= 0
pr
Tr
ulated on excel
ented in table 9
this study, Rayssibility factor
………………
0.940
sheet. Reservo
9 below, these
yes-Piper-McCr using pseudo
….Eq. 29
S
oir temperature
will be inpute
Cain-Poston (R-reduced prope
SPE 159080
e is 275°F.
ed in Rayes
Rayes et al) erties from
S
A
A
A
A
A
T
T
SPE 159080
AT PRESSUR
2.24353
0.000829231
AT PRESSUR
2.24353
0.000829231
AT PRESSUR
2.24353
0.000829231
AT PRESSUR
2.24353
0.000829231
AT PRESSUR
2.24353
0.000829231Table 10 below
Table 10: Summ
RE, P = 3200 P
3 0.03752
1 4.983 1
RE, P = 2500 P
3 0.03752
1 3.849 1
RE, P = 1800 P
3 0.03752
1 2.754 1
RE, P = 1200 P
3 0.03752
1 1.84 1.5
RE, P = 1200 P
3 0.03752
1 1.087 1w summarizes t
mary for Case
Psig
281 ∗ 4.983
1.53428.
Psig
281 ∗ 3.849
1.53428.
Psig
281 ∗ 2.754
1.53428.
Psig
281 ∗ 1.84
53428.
Psig
281 ∗ 1.087
1.53428.
the Z-factor val
1
– 3.56539 ∗
0.131987
– 3.56539 ∗
0.131987
– 3.56539 ∗
0.131987
– 3.56539 ∗
0.131987
– 3.56539 ∗
0.131987lues obtained f
∗1
1.686
7.
.= 0
∗1
1.715
7.
.= 0
∗1
1.731
7.
.= 0
11.726
.
.= 0.7
∗11.7
.
.= 0.7
from both corre
0.892
0.850
0.809
767
722
elations and CVVD test for res
servoir case 1.
19