20055-Two-phase Compressibilility Factors for Retrogade Gase

7/24/2019 20055-Two-phase Compressibilility Factors for Retrogade Gase

1/8

TYuo-Phase Compressibility Factors

for Retrograde Gases

D.Q. Raayes

SPE, and

L.D. Piper

SPE, Texas A&M U ;

W.D. h4cCairr Jr.

SPE, Cawley,

Gillespie & Aasocs.; and

S.W. Poston

SPE, Texas A&M U.

.,

~

Summ a rY. The t w o-pha se com pressibilit y fa ct or should be u sed in m a t er ia l-ba la nce ca lcula t ions for rich-ga s-condensa t e sys,t im s.

This pa per present s a correla t ion for est ima t ing this fa ct or from field da t e. The correla t ion, w hich is ba s~ on 67 fluid-deplet ion st udies

w it h C 7+ concent xa dons 24 m ol% a lso a pplies to r ich ga ses w it h la rge a mount s of C 02, H2S, a nd N2. The correla t ion gives a n a ver-

a ge error of 3 .66% but ma y resuJ t in la rger errors for som e rich ga ss?..

Introduction

The Standing

.md Ka tz] correla t ion for the ga s compressibility fa c-

tor is vslid only, for dsy-ga s sy st ems. Ret rogra de ga s-condensa t e

reservoirs exper ience liq uid fa llout dur ing deplet ion befow the dew -

point . The t yo-pha se com pressibilit y fa ctor a ccount s for t he. for-

ma t ion of a liq uid pha se.

C om pressibilit y fa ct ors a re used in m a ter ia l-ba l~ ce eq ua t iom

to est im a t e init ia l ga a in pla ce a nd reserves.. G a s compressibilit y

fa ctors norma lly , a re used w hen a reservoir fluiddeplet ion study

is not a va ila ble. This pra ct ice is a ccept a ble for remogra de ga ses

if the ga s condensa t e is lea n ; how ever, if the g~ is rich, the reserves

ma v be ser iouslv underest ima t ed if t he t w c-uha se comrm= wibt i~

fa ck is not u st i.2

FfE . 1 show s the rdationshb of t he cmm ressibfit v fa ctors of

a r icfi ga s condensa t ea s a t iurkon of presske. 3 I n&s syst em,

the tw o-pha se com pressibilit y fa ct or is uniformly less t ha n the ga s

compressibilit y fa ct or , a nd t ie tw o compre?.sib$lt y fa ctms diverge

a s the pressure deplet es. S yst em s t ha t exist a t higher pressures a nd

tempera t ures m a y displa y a different beha vior nea r the dew point .

H igh-pressure regio~ ha ve been observed in w hich the t w o-pha se

com pressibilit y fa ctor is greiter t ha n the ga s com pressibdity fa c-

tor . At low pressures, how ever, t ie t w -pha .se compressibilit y fa ct or

is less tha n the ga s com pressibilit y fa ctor a nd both diverge a s the

pressure decrea ses. For the ca se in Fig. 1, fa iluze to usc the tw o-

phw e.compressibilit y fa ctor w ill ca useph tobe tea low , underes-

t im a t ing the init ia l ga s in pla ce a nd the reserves.

This pa per present s correla t ions t ha t a id in det ermining w hen a

tw o-pha se comprsssibt ity fa ct or should be used a nd how to ca lcu-

la t e t his fa ct or from field da ta . The correla t ion for the tw o-pha se

compressib?t y fa ctor is ba sed on the pseudoreduced proper t ies of

t he prcduced ga s t ha t ca n be ca lcula ted from the w elM.r Wn ga s

com posit ion or the pr im a ry-sepa ra t or w specific gra vity correct-

ed to w ell st rea m. The pseudoreducxd pressure a nd pseudoreduced

t em pera ture w ere ca lcula ted w it h t he met hods present ed by Sut-

t on. 4 These m ethods include correla t ions for ca lcula t ing the pse:-

docr it ica l proper t ies of t he hept a ne-plus fra ct ion,s a djusbnent of

the pseudccr it icd proper t ies for impt it ies,e a nd use of the m odi-

fied St eya r-B urkha rdt :Vco7 mixing rules. S ut t on a lso gives a cer-

rela t i.on for ca lcula t ing pseudoreduced pressure a nd tempera t ure

fm m &e w eif-st rea m ga s specific gra vit y. The correla t ion for de-

termining w hen to uset i t w o-pha se compressibility fa ct or is ba sed

on the .jnit ia l w &t rea m ga s specific gm vi~ t ha t ca n be ca lcula -

ted from surfa ce sepma t ion da t ig-l~ if w ell-sma rn-comp.xit ion da t a

a re not a va isa ble. fbe correkv.ions w ere veriil~ w ith simula t ed prw

duct ion da t a .

Theory -

The

ma t eria l-ba la nce eq u a t ion for volumet ric perforkce of a

ret rogra de ga s reservoir is derived ea sily from the rea l ga s la w .

Initially the reservoir mmins n, m oles of ga s:

n~=p~VJztRT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(I)

Now at Shell western E&P l.c.

, .Now al S.A. Hold( ch ~ ASSOCS,

Copyright 1932 Sccle y of Petroleum En@wers

Assuming tha t only ga s is produced, a liq uid pha se condenses in

the reservoir a s the pressure deplet es below the dew point , lea ving

n, m oles of ga s a nd liq uid rema inin g in the reservoir :

~r=ntnp=pVl/zpRT. . . . . . . . . . . . . . . . . . . . . . . . . . ...(2)

B eca use t he compressibilit y fa ctor in E q . 2 now a pplies to bot h ga s

a nd liq u id, it is a t w o-pha se compressibilit y fa ct or .z.lz

D ividing E q . 2 by E q . 1 gives, a ft er subst it ut ion of

GP/G

for

nplnt a nd rea rra ngement ,

L=_ L

(3)

ZW I (G P /G ) :;,

a form of t he ma t er ia l-ba la ms eq ua t ion simila r to tha t &en by

pa lm. 13

Rea rra ngement a nd expa nsion of E q . 2 to account f or t h e, v? lu me s

occupied by the ga s a nd liq uid rema ining in the reservou give a

rela t ionship bet w een the t w o-pha se compressibility fa ct or a nd the

compressibility fa ct ors of t ie eq uil briuro ga s a nd liq u id,

(4)

~ . 4, recent ly given by Vo et a l., 14 indica t es t ha t t he tw o-pha se

com pressibilit y fa ctor is a w eight ed a vera ge of the liq uid a nd ga s

com pressibilit y ft iors a nd a simcdon of premue, tempmt ure, com-

posit ion, a nd the a m ount of liq u id rema ining in the resew oir .

Development of Correlations

Our correla t ions w ere developed w it h da t a from 131 consta nt -

voleme deplet ion st udies per formed on r@xogra de ga s s~ ples co-

Iected w or ldw ide. Tsble 1 show s the ra nge of t ie da t a a t dew point

~ ndit ions. The da t a w a s pa r t it ioned on.t he ba ses of C 7+ concen-

fmt ions a nd bnpm bies f.Ta bIe 2). A sensit ively study w a s per formed

w ith the t ia l correla t ions t ha t support ed t hese pa r t it ions.

The tw o-pha se com pressibilit y fa ct or w a s correla t ed w ith psw -

dor.deed pressure a nd pseudoreduced t em pera mre. ~ : compo-

sit ions of t ie produced ga s from ea ch st ep of t he const a nt -volume

deplet ion st udies w ere u sed to ca lcula te bot h t hs pseudoreduced pres-

sure a nd t empera ture w it h the met hods present ed by Sut ton. Fig.

2 show s t he Ia bixa torydet ermined tw o-pha se compressibility fa c-

t or for the ent ire da t a set a s a funct ion of pseudoreduced pressure:

.4khough the da t a sprea ds a t low pseudoreduced pressuzes, a g@era l

linea r t rend is a ppa rent .

F igs. 3 t bIOU gh 6 show S illlib2 plot s for D a ta SetS 1 @OU @J

4. These figures in~ ca t e t ha t the da ta ha ve tw o different t rends

a s a result of C 7+ concent ra t ion. The W&pha se compressibilit y

fa q or for the r ich ga ses (Figs. 3 a nd 5) show s a genera l lin ea r t rend

w ith pseudoreduced pressure, w hile the tw o-pha se compressibilit y

fa ctor for the lea n ga ses (Figs. 4 a nd 6) show s a qw a hme simik?r

to tha t of a singkpha se ga s. While not indica ted in Figs; 2 through

6, the t w o-pha se com pressibiMy fa ctor w a s found to be a linea r

funct ion of the inverse of pseudoreduced t em pera ture. I n fa ct , t he

va r ia t ion in pseudoreduced tempem mre pa rtkdSy a cmu+ ts for t he

sprea ding of da ta not ed a t low va lues of pseudoreduced pressure.


2/8

.

I

I

Compressibility Factor

:

~: .

e


3/8

2.0.

0.0

04 s 12 16 20 2

P seudoreduced. P ressure

Fig. 3Two-phase compressibility factor as a function of

pseudoreduced pressure for Data Set.1.

2.0-

:

~ 15-

g.

. .

.

...-

~

.

.-.. . . :

~ Lo-

~ >j,>:., ,.~ -:,

- .. . .. , :. . .

=

e

F . : . : . .-. : .

. . . . . .

~ ,. .

z o,3-

.0.01

04 8.12 16

20 2

P sendoreduced pressu~

Fig. 4Tw o-pha se compresolblllt y factor as a function o

pseudorsduced pressure. for Data Set 2.

4

If

w hile the fina l correla t ion is ba sa l on the 67 deplet ion st udies

of D a ta S et 1, a pproxima t e tw o-pha se compressibilit y fa ct ors @so

ca n be obt a ined for D a ta S et 3. Fig. 7 show s the a ccura cy of the

correla t ion w iih D a ta S et s 1 a nd 3 compa red w ith the a ctua l iw o-

pha se compressibility fa ct or . These a re the r ich ga ses, incklng

t hose w it h la rge concent ra t ions of impurit ies . As Ta ble 1 show s,

@ese da ta sets include a sa mple w it h more tka n 63 % C 02 a nd a

sa mple w ith more t ha n 28% H 2S .

.F ig. 8 show s t he a ccura cy of the correla t ion w ith Da @ S et s2

a nd 4 compa red w ith the ,a ct ua l t w o-pha se compressibilit y fa ctor.

F ig. 8 illust ra t es t ha t the tw o-pbsss compressibilit y fa ctor of a lea n

ga s ca nnot be predict ed by E LI . 5. The a vemge a bsolut e error for

D a ta S ets 2 a nd 4 combined is 7.35% La ter , w e show t ha t t he

singkph?,se ga s, compressib,t ity fa ~ r l shot id be used in t ie

m zter ia l-ba lpce eq ua t ibns for lea n ga ses.

E q . 5 is mcm mnendid for use w it h ga ses ha ving CT+ concen-

t ra t ions of 24.0 m ol% C onseq ~ nt ly, a met hod is needed w est i-

ma te t he concentra t ion of the C 7+ fra ct ion w hen the w ell-st rea m

ga s-com posit ion da t a a re not a va ila ble. We us~ the ent ire da ta set

to develop the follow ing correla t ion to ca lcula t e the concen~ a t ion

of the C 7+ fra ct ion from the w ell-st rea m ga s specific gra vity

nc,+ = O.0885119+ 0.141013(~ .J . . . . . . . . . . . . . . . . . . . (6)

Fig. 9. show s the a ccura cy of t his w rrela t ion w it h t he a cb.d C 7+

fra ct ion. Thus, if @e w ell-st rea m ga s specit ic gra vity is


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TABLE 3PERCENT ERROR OF SELECTED DATA SETS

P ercent Error

D a ta S et Avera ge Ma ximu m

Rz

3.3s 34.95 =

;

7.95 34.51

NA

3 4.81 27,58 NA

6.55 25,39

NA

& 4.98 34.95

NA

NA. no t appmabl e,

1. C a lcula te pseudoreduced propenies of the produced ga s fmn

w ell-st iea m ga s com posit ion or w ell-st rea m ga s ~ pecific gra vity

2. I f t he concent mt ion of C ,+ is 24.0 m ol % (or if t he w ell

st rea m ga s specific gra vit y is > 0.911), me E q . 5 to ca lct ia t e t h

tw o-pha se com pressibil@ fa ctor .

3. K t he w eu-st rea m ga s, com posit ion a nd the w el-st rea m ga

specit ic gra vity a re bot h unknow n, a s w ill be the ca se w hen pre

dict ions a re ma de of r esemes a t a n a ba + dom nent pressure, u:e t h

la st know n ga s com posit ion or specific gra vit y.

VerIficatbr of COrrelatIOn

The correla t ion w a s t est ed by simula t ing na t ura l reservoir deple

t ion t irocesses w it h the VI P -C OMP ~ module of the VI P

E XE &YLIVE TM simula t or . 16 The r&ervoir simula t or w a s set up

a s a n r-Z m odel w ith one producing w ell in the center of t he reser-

voir. The sim ula t ed reservoir w a s 150 fi Odck w it h a 440-ft dia met er .

The porusit y w a s 0.13, a nd the perm ea bilit y w a s 400 md in me

ridia l direct ion a nd 40 md in the vert ica l direct ion. The grid for

the sim ula t ion model ha d nine concentr ic r ings a round the producer ,

w ith ext erna l pdii a t 10, 20, 30, 40, 70, 100, 130, 170, a nd 220

ft und ha d nine la yers, ea ch of eq w d t biclmess, p.omsiV, a nd per-

m ea bt ity . The consta nt flow ra te w a s 4,C X30 Mscf/D . Alf ot her pa -

ra m et ers, including sa t ura t ion da ta , rock a nd fluid properdes, a nd

sepa ra t or t empera mres a nd pressw es, w ere t a ken from Ref. 3.

C onsta nt -volum e deplet ion da m from a richq a n d a lea n 17 ga s con-

densa t e w ere m a tched w it h t he P eng-Robinson 18 eq ua t ion of st a t e

(EOS) &d t he sim ula t ors E OS-P AKTM. Ta ble 4 show s the fluid

analy s es .

The siimda t ed da t a w ere a na lyzed tw o different w a ys. B ot h a ma f-

ysis met hods used the ps-eudoreduced proper t ies of t ie produced

2.0

,.

g

~~

.

LO-

~

H

z

~

:

~

0s

0.0.

0.0 0.5

1.0 1.5 2

Actual Two-Phase z Factor

Fig. 7Accuracy of Iwo-phase compressibility correlation f

Dafa Sets 1 and 3.

>

N

m

g

.

:

.~r.,

.s

%

OS.

2

,.

0.0

.0.0

0.5 1.0 1.5 2

Actual Two-Phase z F a ct or

Fig. SAccuracy for two-phase compressibility correlation

for Data Sets 2 and 4.

ga s a t severa l pressures to ca lcufa t e the tw o-pha se compressibilit y

fa ct or. The ma jor @Terence in the tw omet bods is that, in the tint

m eth od, the w ell-st rea m ga s composit ions w ere used to culcula t e

t hepseudoreduced proper t ies, a nd in the second met hod, t he w elf:

sw a m ga s specific gra vit ies w ere used. The G old et a l. 9 comela -

t ion w a s used for the la t t er ca lcula t ions.

Ffg. 10 shows the results ,of these calculations in the form of a

m a ter ia l-ba bmce plot for the rich ga s condensa t e. For com pa r ison,

Fig. 10 a lso show s t he a ct ua f da t a from the const a nt -volum e deple-

t ion st udy. As expect ed, the a ct w ?l Pkw extra pola t es to 1.0, a nd

the a ct ua l p[z ext ra pola t es to = 0.9, indica t ing t ha t in$ia l ga s in

pla ce a nd feserves a re underest ima t ed by 10% The ca lcula t ed

pI zWe&t iS in it ia l gm in pla ce a nd reserves w it h a n error of

+3.0%.

Ftg. 11 show s sim ila r ca lcula t ions for t ie Lea n-ga s-w m densa t e

sy st em. For this sy st em, the a ctw a l

p/z

ext ra pola t es to = 0.98, in-

0.15

.5

6.12-

a

2

k

:

z o.~

g

=

0.05-

~ .

:

~

0.W3

Actua l H epta ne P lu s Fraction

lg. 9Accuracy of C,+ correlation fOr initial cOmP~ltiO~.


5/8

,

mm -

0 Cnliulated (p/z)2ph (mm x.sitk?m)

Calculated (tiz)20h (Cold, et al)

. Actual ($.lz)%,h

Actual P/.

3W+3 -

N

L

Zooil ~

161n3 -

0-

0.0 0.2 0.4

0.6

0.8

1.0

Cumulative Gas Produce4 Fmctiori

lg. 10Material.balance plot for a rich-gas-condensate

;ystem.

dica t ing t ha t m a ccept a ble est ima te of init ia l ga s in pla ce a nd

ressrvez ca n be obt a ined w ith t ie ga s compressl% fity fa ctor.

@mcluslOns

1. An est ima te of the t w o-phme com pressibility f6ctor ca n be

ma de w ith the correla t ion present ed if t he C,7+ C 0U G 5n@It i0U of

t he init ia l ga s i3 =4.0 mol or the wdhtmam g33 specific grwi-

I J i3 >0.911.

2. When the init i21 C 7 + concentra t ion is


6/8

B

.

e

:

Rayes

Poston

Piper McCain

D.G. Rayes Is an associate reservoir

en91neer fOr Shell Western E&P Inc. In

the Kemrldge ProductIon Div., Bakefs.

field, CA. Rayes holds BS and MS

degrees In petroleum engineering from

Tex8s A&MU. ~ D. Piper is a ssnlor

Iecturw [n petroleum engineering at

Texas A&M U. In College Station, TX.

His research interes@ Include phase be-

havior, reservoir englneerlng, and r88w-

volr simulation. He holds BS, MS, and

PhD degrees in petroleum epglnfering

from Tes8s A&M U. and an MS degree

In operations research fmm the U.S. Naval Po8fgraduate

School. WfNIam D. McCaIn Jr. is an executive consultant

at S.A. Holditch & A880cs. in College Station. Previously, he

was a petroleum engineer with Cawley, Gillespie & Assocs.

In Foe Worlh and taught petroleum engineering at Texas ASM

u. and Mississippi State U. He holds a,BS degr.se frOIII M18-

si88ippi Sf8fe U. and MS and PhD degrees from the Georgia

Inst. of Technology, all In chemical englnewlng. McCain

8ewed on the 19 S6-89 Career Guidance Committee, the

1972-75 Textbook Committee, and the 1967-71 Education

8nd Accre@tation Cammlttee, which ha chaired during 1967-

70. McCaln was the 1972 Mis@lppl Section chairman and

an SPE Short Course instructor from 1984 to 1991. S.W.

Poston is a professor of petroleum engineering at Texas A&M

U. Previously, he worked for 14 years at Gulf 011 E&P Co. in

various positions h U.S. and international 10catlOnS. POStOn

holds SS and ME degrees [n gealcgkal engineering and a PhD

degree In pettuleum engineering, all from Texas AgM U. He

sefved ori the Editorial Review Committee during 1974-75,

I

1976, and 1980-84.

5. Kesler , M.G . m d Lee, B . I .: J mprove P redk+ ion of E nt ba fpy Fra c-

tions, Hydrocarbon Processing flvfa rch lP 7 Sl 153-58.

6. Wicher t , E . a ndt i, K: Ta kuMe2s for Sour G a ses, H ydmca r fmn

Froces ng (hfa y 1972) 119-22.

7, S t ew a xt . W.F. . B urkha rdt . S .F . . a nd VW. D .: pTdiC t iO l of P seu-

docr it i~ P t ietm for h; pa ~ r~ ent ed a t t ie 1959 AfC hE

Meet ing, Ka m a s C ily, Ma y 18.

8. 3heoV a nd

Pratice of the Tesdng of s Welfs,

t id edit ion, P ub.

ERCS-75-34, tiasy

Resmuces & Consermdon B-m& w,

(1975).

9.

Gold. D.K.. McCain. W.D. Jr.. and Jeminm. J.W.: h Inmmved

Met h;d fort be Dk t ion of the Res*G ss S@fic t%w ity

for Re@?a .de G a ses, JPT@ly 1989) 747-5Z Tram., AJMB, 2S7.

10. Whitscm, C.H.:

&Discussion

of An Improved Met30d for the De&r-

@nation of the Rmerv&Gas @iic Gravity for Relrogmde flays,

JPT (NOV. 19S 9) 1216 Tram., AJME, 287.

11. Gold, D.K., McCain, W.D. 1.., ard Jennings,

J. W.: Authom Re-

ply fa Discussion of An fmpmved Methcd for the Determination of

the Reservoir-Gas 2p@c Gravity for R&mgmde Gases, JPT(Nov.

19S9) 121 Trans.; AIME, 2S7.

12. Craft, B.C. and Hawldm.,

M. F.;

Applied Pet roleum Resem .r Eng i-

neering

P@@Hefl h., New York City

(1959) 59-P 6.

13. D a l% L. P .: Fundamwtak of Reservoir Engineering, Elsev ie r Scien -

d6C Fubfisbi 12 Co., Oxford

(1P 78) 37-43,

14. Vo, D . T., J ones, J . R., a nd Ra gba va n, R.: P er forma nce. P redicdom

for G as-C om f ema te Resew oki, SPEFE (De+. 19S9) 576-84 Trans.,

ATMF 3R7.

.-.. -, ---

15. SM U serk G ufde: S t a risdcs, Version 5 eibion , S .42 I nst . la .. , C a y,

N C (1985).

16. Reference M-1 for EOS-PAK and VfP-EWXOTJW Western At-

lw i&rdted Tehologies,

H ou st on (1987).

17. Firooza ba @, A., H ekim , Y., a nd Ka tz, D . L.: Reservoir D eplet ion

C a J mla t iois fork C on&nsa fm U sing Extended AmlYses m t he P eng-

R obim m E q w ,fion of Sa t e:, r% J. Chem. Ens. (Oct. 1978) 56,

610-15.

18. P eng, D .-Y. a nd Robinson, D . B .: A New Tw o C onst a nt E q ua t ion

of S ta te, Im i. & Eng. C hem . Fundanwnrafs (1976) 15, No. 1,59-64.

S[ Metric Conversion Factors

II

X 3.048* E 01 = m

ft~ X 2.831685 E02 = rn3

F ~F32)/l.8

= .C

md x

9.869233

EO-I = mz

psi x 6.894757

E+OO = kpa

.Coversion factor 1s wad,

SPEFE

Or lglml SPE nmn.wrl p rece ived fo r revl ow Awl 16 ,1990. Rev ssd nmnusc rl fl r ecei ved

Aug. 13,1691. Pew+ aaaP@4f0rPubllcMb SaPt.4, 1S91. P.Qwr(SPE2C@53 flrsl -M.

ed at the 1990 Call f.arnla Re91.nal Meeting held . Ventura APIU 4-6..


7/8

, *

W 20055

N

2.0

1.6

1.2

0.[

0.

0

0 0

0.4

0,8

1.2 1,6 2.0

ActualTwo-PhaseZ Factor

Fig. 8 Accuracy of Two=Phasc Compressibility Correlation for Data Sets 2 and 4.

0,15

0 0

0 0

0 03

0,06

0,09

().i2

0,15

ActualHeptane PlusFraction

Fig,

9

Accuracy of Heptane

Plus Correlation

for Iu tial Compositions,

117


8/8

5000

4000

3000

N

Q

2ootl

lC Q(

O p/ Z2phCalC,(Composition)

D P/

Z2phCalc,(Goldet al.)

~ p/ Z2phActual

pJZActual

c

O O

0:2 0.4

0.6

0 8

1.0

1.2

CumulativeGas Produced,Fraction

Fi& 10. Material Balance Plot for a

Rich t3as=Condensate System,

5000

4000

3000

N

la

200(

100(

\

0 p / Z2phCalc.(Composition)

p / z2ph (Mc, (Gold et al.)

m p/ Z2phActual

p/Z

Actual

(

0 0

0,2 0.4 o~6 o.8

1,0

1,2

CumulativeGas Produced,Fraction

Fig.

Material Balance Plot for a Lean Gas=Condensate System.

118

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20055-Two-phase Compressibilility Factors for Retrogade Gase