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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