spe76752 Establishing Gas Phase Well Performance for Gas Condensate Wells Producing.pdf

Copyright 2002, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the 2002 SPE/AAPG Western Regional Meeting, 20 - 22 May 2002, held in Anchorage, Alaska, U.S.A. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract

This paper provides a new method of forecasting natural gas production of gas-condensate wells that flow under three phase conditions. Such wells include gas condensate wells that produce liquid condensate and water along with gas phase, their main production. Mathematically treating such systems can be very demanding. A new tedious, but simple method of projecting the gas phase production is proposed. In this method we integrate reservoir production data and the pressure transient data to forecast well performance without prior knowledge of relative permeability as function of saturation. Since pressure transient well test data is usually available on yearly basis, effective permeability as a function of pressure can be updated. It is the true representative of the reservoir conditions of heterogeneity, geometry, and resident fluids.

The total gas production in a gas condensate reservoir is contribution of all the three regions that might exist at certain stage of depletion. Free and dissolved gas in both oil and water in Region-1, free and dissolved gas in water in Region-2, and free and dissolved gas in water in Region-3. Thus to project the production, along with the physical properties of fluids in all the three regions, their phase change with pressure also has to be handled.

It is observed from the solved examples that buildup of condensate liquid phase reduces the gas production as well as water production, a favorable situations. Partially the gas production loss is recovered in form of condensate while reducing water production.

Finally, few examples with simulated data are analyzed to show the use of new method. A step-by-step procedure is also devised to establish the well performance. Small operators will benefit from this method at the most, since data acquisition like relative permeability curves requires to laboratory experiments on cores. Introduction

We are extending our understanding of the retrograde gas-condensate systems lately. Recently many good papers have been published that treat gas-condensate systems. Retrograde gas-condensate reservoirs are primarily gas reservoirs. A zone of liquid begins to form as the dew point pressure is reached. The liquid keeps accumulating and does not flow until the critical liquid saturation is reached. Once critical saturation of the liquid phase is reached, it begins to flow towards the wellbore along with the gas. Pressure at this point in the reservoir is termed as P*. Interestingly, this liquid may re-vaporize as the pressure further crosses the lower line on two-phase envelope of phase diagram. This behavior of re-vaporization of the oil phase is called the Retrograde behavior. Fig.1, Fig.2, Fig.3, and Fig.4 show the schematics of such a phenomenon in vertical wells and horizontal wells.

Fig.1 Phase behavior of the condensate fluids.

SPE 76752

Establishing Gas Phase Well Performance for Gas Condensate Wells Producing Under Three-Phase Conditions Sarfraz A. Jokhio*, Djebbar Tiab*/University of Oklahoma, and Arshad Anwar * SPE MEMBERS

2 S. A. JOKHIO, D. TIAB, AND A. ANWAR SPE 76752

P e

P dP *

P w f

S w c

Fig.2. Three regions in a gas condensate reservoir with vertical well. Deliverability loss in such conditions is mainly due to two reasons: a) Gas undergoing liquid phase and b) permeability impairment by the liquid. Thus both have to be handled mathematically to predict well performance with reasonable accuracy.

Pi PdP*

Pwf

Fig.3 Three regions around a partially penetrating horizontal.

Pi PdP*

Pwf

Fig.4 Fluid and pressure distribution around the fully

penetrating horizontal well. Literature Review

Depletion of gas-condensate reservoirs has been a topic of continuous research. Quantitative two-phase flow in the reservoirs was first studied by Muskat and Evinger14. They were the first researchers who indicated that curvature in IPR curve of solution gas drive reservoirs is due to decreasing relative permeability of oil phase with depletion. Based on Wellers2 approximations of constant de-saturation of oil and constant GOR at a given instant (not for the whole life of the

reservoir) in the reservoir, Vogel1was able to develop an IPR that would revolutionize the performance prediction of solution gas drive reservoirs. Fetkovich23, Camacho19 and Raghavan, Wiggins18, and Sukarnos16 work on IPRs follows the Vogels1 work.

Gilbert correlation for productivity index estimations for oil wells (J = P/q) was being used until 1968 for solution gas reservoirs too. Vogel1, 1968, first published IPR for solution-gas reservoirs, which handles the two-phase flow of oil and gas. Vogel using Wellers concepts was able to generate family of IPR curves in terms of only two parameters, flow rate and BHFP.

Recently Raghavan and Jones13 discuss the issues in predicting production performance of condensate systems in vertical wells. Fevang and Whitson5 model the Gas-Condensate well deliverability using simulator and by keeping the track of saturation with pressure and relative permeability. We need an analytical IPR for gas condensate wells to be able to use it in optimizing production equipment including tubing, artificial lift systems, pumps, and surface facilities. Three Phase Systems

Figure 5. Thee-phase system with developing oil phase Producing Gas Oil Ratio in Three-Phase Systems (Rpgo) in Region-1 By Definition

ofreegfreeo

sgwwSfreeofreeg

oT

gTPgo Rqq

RqRqqqq

R,,

,,

+++== (1)

+

+

+

=o

gg

rg

oo

ro

sgwww

rws

oo

ro

gg

rg

oT

gT

RB

kkB

kkC

RB

kkR

Bkk

Bkk

C

qq

..

...

(2)

ESTABLISHING GAS PHASE WELL PERFORMANCE FOR GAS SPE 76752 CONDENSATE WELLS PRODUCING UNDER THREE-PHASE CONDITIONS 3

On simplification

+

+

+

=o

gg

rg

oo

ro

sgwww

rws

oo

ro

gg

rg

Pgo

RB

kkB

kk

RB

kkR

Bkk

Bkk

R

..

...

(3)

Simplifynig and solving for individual phase effective permeabilities, yields

( ) ( )

+

=oo

rwsgwPgoso

Pgoo

oo

ro

gg

rg

Bkk

RRRRR

Bkk

Bkk

.

1 (4)

( )( )

+

=gg

rg

ww

rwsgwPgoso

Pgoo

oo

ro

Bkk

Bkk

RRR

RRB

kk

.

1 (5)

( ) ( )sgw

PgosoPgooro

rg

gg

oo

ww

rw

R

RRRRkkkk

BB

Bkk

=1

(6) Producing Oil-Water Ratio (Rpow) in Three-phase Systems (Region-1) Assuming that the oil and water phase are completely immiscible, the two-phase system equation for production oil-water apply.

w

freeoofreeg

w

oPow q

qRqqqR ,,

+== (7)

+

==

ww

rwoo

roo

gg

rg

w

oPow

BkkC

BkkR

Bkk

CqqR

.

1.. (8)

On simplifying, results

+

==

oo

ww

rw

roo

gg

ww

rw

rg

w

oPow B

Bkkkk

RBB

kkkk

qq

R

.

...

(9)

Solving for water, gas, and oil effective permeability respectively.

+

=

oo

roo

gg

rg

Pow

wwrw B

kkR

Bkk

RB

kk ..

. (10)

( )

=

o

gg

oo

rorw

ww

Powrg R

BB

kkkk

BR

kk

.

.. (11)

( ) ( )ooogg

rgrw

ww

Powro BRB

kkkk

BR

kk

= ... (12)

Producing Gas-Water Ratio (Rpgw) in Three-phase Systems (Region-1) Similarly

w

sgwwsofreeg

w

oPgw q

RqRqqqqR

++== , (13) Where Rsgw is the solution gas-water ratio expressed as SCF /STB. For two phase systems Rsgw = 0.

+

+

==

ww

rw

sgwww

rws

oo

ro

gg

rg

w

gTPgw

Bkk

C

RB

kkR

Bkk

Bkk

C

qq

R

.

...

(14) Simplifying

sgwsoo

ww

rw

ro

gg

ww

rw

rgPgw RRB

Bkkkk

BB

kkkk

R +

+

=

.

...

(15)

Solving for water and gas effective permeability respectively.

( )

+= soo

ro

gg

rg

gwsPgw

wwrw RB

kkB

kkRR

Bkk

... (16)

( ) ( )ggsoo

ro

ww

rwgwsPgwrg BRB

kkB

kkRRkk

= ... (17)

( )

=

s

oo

gg

rg

ww

rwgwsPgwro R

Bx

Bkk

Bkk

RRkk

..

. (18)

Producing gas water ratio (Rpgw) (Region-2 and Region-3)

w

sgwwfreeg

w

gtPgw q

Rqqqq

R+== , (19)

++

==

ww

rw

sgwww

rw

gg

rg

w

gtPgw

BkkC

RB

kkB

kkC

qq

R

.

..

(20)

Simplifying

sgwsoo

ww

rw

ro

gg

ww

rw

rg

w

gTPgw RRB

Bkkkk

BB

kkkk

qq

R +

+

==

.

...

(21)


Solving for water and gas effective permeability respectively.

( )

=sgg

rg

gwsPgw

wwrw B

kkRR

Bkk

.. (22)

( ) ( )ggww

rwgwsPgwrg BB

kkRRkk

= .. (23)

Modeling Relative and Effective Permeability as a Function of Pressure Vertical Wells (Pressure Drawdown)

The effective oil and gas permeability during pressure transient period can be expressed as follows, respectively7:

( )

==

tP

h

Bqkkk

wf

oofreeoroo

ln

6.70 , (24)

( )SP

wf

freegrgg

tmP

h

qkkk

=

ln

6.70 , (25)

( )

==

tP

h

Bqkkk

wf

wwfreewrww

ln

6.70 , (26)

Above equations are valid for a fully developed semi-log straight line. Several algorithms are available in literature for estimationg the log derivative of the pressure recorded during a pressure test.

Pressure Buildup

+

==

ttt

Ph

Bqkkk

ws

oooroo

ln

6.70 (27)

Similarly

SP

ws

freegrgg

ttt

mPh

qkkk

+

==

ln

6.70 , (28)

+

==

ttt

Ph

Bqkkk

ws

wwwrww

ln

6.70 (29)

To be more accuarte following equation can be used.

( )SPtigi

tg

ws

freegrgg

ctctt

d

dmPh

qkkk

+

==

ln

6.70 , (30)

Modeling 3-Phase Pseudopressure

Flow of real gases in porous media in presence of more than one phase can be expressed using Darcy's law. Under pseudo-steady state conditions and in field units it is expressed as follows:

TgT mPCq = . (31) Or sgwwsogfreegT RqRqqq ++= (32) For vertical wells

+

=a

w

e Srr

Ln

hC

75.0

.00708.0 (33)

And for horizontal wells

++

=aH

wSLnC

rALn

bC75.0

.00708.02/1

(34)

mP, the pseudopressure for condensates can be written as:

++=

r

wf

P

Psgw

ww

rws

oo

ro

gdgd

rg dpRB

kkR

Bkk

Bkk

mP ..

..

..

(35) Total gas flow at the surface in three phase systems is the contribution of all the three phases. It comprises of free gas flow, dissolved gas in oil phase, and dissolved gas flow in water phase. Mathematically, Region-1:

++=

*

..

..

..

1

P

Psgw

ww

rws

oo

ro

gdgd

rg

wf

dpRB

kkR

Bkk

Bkk

mP (36)

Substituting Eq. 18 in Eq. 36 and simplifying it results the gas phase pseudopressure function in terms of water phase properties.

=*

..

1

P

Ppgw

ww

rw

wf

dpRB

kkmP (37)


Substituting Eq.16 in Eq.36 and simplifying results

+

=*

..

..

1

P

Ps

oo

ro

gdgd

rg

sgwpgw

pgw

wf

dpRB

kkB

kkRR

RmP (38)

Above equation eliminates the water phase properties required in Eq. 36. Now substituting Eq.10 in Eq.38 and simplifying results

( )( )

+=

*

11

1k.kPP

P so

oso

ggsgwpgw

pgwgg

wf

dpRB

BRR

BRRR

mP (38a) Where ( )sgwpwopgo RRRB = Region-2: Since oil phase is immobile in Region-2, therefore, only gas and water phase are mobile.

+=

dP

Psgw

ww

rw

gdgd

rg dpRB

kkB

kkmP

*2 .

..

. (39)

Where Rsgw is the solution gas water ratio. Substituting Eq.22 in above equation results

=Pd

P gdgd

rg

sgwpgw

pgw dpB

kkRR

RmP

*2 .

. (40)

Now substituting Eq. 23 in Eq.39, results

( ) =Pd

P ww

rwpgw dpB

kkRmP

*2 .

. (41)

Region-3: Above both equation can also be used for Region-3 since gas and water phase are mobile in it but with different pressure limits on the integral.

=P

P gdgd

rg

sgwpgw

pgw

d

dpB

kkRR

RmP .

.3 (42)

( ) =P

P ww

rwpgw

d

dpB

kkRmP .

.3 (43)

In Eq.41 the term

gdgd

rg

Bkk.

.defines the dry gas flow. The

term

sgwpgwpgw

RRR

is the additional gas that is dissolved in

the water phase and will be produced.

If more than one regions exist at the same time then total pseudopressure is given by

321 mPmPmPmPT ++= (44) Estimating Effective Permeability Using Surface Measured Rate Eq.37 and 38a, represent the pseudopressure for gas condensate in Region-1 in three phase flowing conditions. Eq.40 and 41 represent the gas condensate pseudopressure in Region-2. Eq.42 and 43 represent the pseudopressure for gas condensates in region-3. Now the pressure transient response in terms of pseudopressure for region-1, Region-2, and region-3 can be expressed as follows. Region-1:

( )( )

+

+

=

+

SrcPk

t

dpkkh

q

dpRB

BRR

BRRR

wt

e

P

Prg

measg

PP

P so

oso

ggsgwpgw

pgw

wf

wf

8686.02275.3

)(log)log(

.

6.162

11

2,

*

*

(45)

Gas effective permeability integral has been re-arranged such that it can be estimated from well test analysis. Region-2:

+

+

=

SrcPk

t

dpPkkh

q

dpBRR

R

wt

e

Pd

Prg

measg

Pd

P gdgdsgwpgw

pgw

8686.02275.3

)(log)log(

)(.

6.162

.1

2

*

,

*

(46)

Region-3:

+

+

=

SrcPk

t

dpPkkh

q

dpBRR

R

wt

e

Pd

Prg

measg

P

P gdgdsgwpgw

pgwe

d

8686.02275.3

)(log)log(

)(.

6.162

.1

2

*

,

(47)


The effective permeability integral now can be estimated by analyzing well test data as

( )

=

)ln(

6.162k.k ,*

rg

tdmPd

h

qdpP

g

measgP

Pwf

(48)

( )( )

= hq

tddmP

dpPkk measgg

P

Prw

wf

,

)ln(

6.162. (49)

The effective permeability is the derivative of above equations 48 and 49. Establishing IPR Rawlins and Shellhardt17 equation can now be used to establish the well performance.

( )nTgT mPCq = . (I-1) Procedure To Establish IPR

1. Convert the most recent pressure transient data into pseudopressure using Eq.38a without gas effective permeability term. Also calculate the

time log derivative

)ln(tdmPd

of the transient

pseudopressure data. 2. From the well-developed semi-log straight-line

portion, estimate effective permeability integral using Eq.48. Select the proper equation depending on the region that exists.

3. Plot the effective permeability integral estimated in Step-3 Vs pressure get a good curve fit such that ends at zero. This is as if both the limits on the effective permeability integral were zero. Get a simple algebraic equation. For detailed analysis paper SPE 75503 can be referred.

4. Now convert the production pressure, Pwf, into pseudopressure using Eq.38a again without effective permeability term. In the next column, calculate the effective permeability integral for same Pwf values. Multiply the pseudopressure with integral values to get final pseudopressure values.

5. From the log-log plot of mP, estimated in step-4, vs. rate estimate the C and the n. C is the intercept and n is the slope. These are the parameters of Rawlins and Shellhardt17 equation, I-1.

6. Establish the well performance using Eq.I-1. Conclusions

1. A new method of establishing well performance of gas condensate wells that produce under three phase conditions have been introduced.

2. This new method does not use relative permeability curves as a function of saturation, instead, it uses pressure transient data to get effective permeability as

a function of pressure and then use it to project well performance.

3. A new definition of pseudopressure for gas condensate reservoirs has been introduced that does not require relative permeability curves for three phase gas condensate fluids.

4. Well test pressure data is used to estimate the effective permeability as a function of pressure that includes the phase change that occurs in the gas condensate reservoirs with depletion.

5. Effective permeability of either phase can be calculated from the surface measured gas rate.

6. Concept of free gas rate that is required to calculate relative permeability in multiphase systems has been completely eliminated.

7. The effective permeability of one phase can also be used to convert the pressure data into pseudopressure of other phase. This is very useful in case only one phase production data is available.

8. It has been observed that the wells that produce under three-phase condition, developing condensate (liquid) phase reduces both gas deliverability (considered to be negative impact) and water production, a positive impact.

Nomenclature Bo = Oil FVF, RB/STB Bgd = Dry gas FVF cf/scf kro = Oil relative permeability krg = Gas relative permeability qg = Gas flow rate, scf/D Rs = Solution GOR, SCF/STB Rsgw = Solution gas water ratio, scf/STB Rp = Producing GOR, scf/STB (qg/qo) Rpgw = Producing gas water ratio, scf/STB Rpow = Producing oil water ratio, STB/STB S = skin SSL = Semi-log straight line. SOC = Critical oil saturation, fraction mP = pseudo-pressure function, MMpsia2/cp o = Oil viscosity, cp g = Gas viscosity, cp Subscripts g = Gas o = Oil w = Water r = relative e = effective meas = Measured 1 hr = One hour w = wellbore (In well testing equations) cor = Corrected b = Bubble d = Dew s = shut-in


t = total 1 = Region-1 2 = Region-1 3 = Region-1 g1,o = gas phase in Region-1 using oil effective permeability g1,g = gas phase in Region-1 using gas effective permeability o1,o = Oil phase in Region-1 using oil effective permeability o1,g = Oil phase in Region-1 using gas effective permeability References 1. Fevang, O. and Whitson, C.H. Modeling Gas-Condensate

deliverability, Paper SPE 30714 presented at the 1995 SPE Annual Technical Conference and Exhibition, Dallas, Oct. 22-25.

2. McCain, W.D. Jr.: The Properties of Petroleum Reservoir Fluids, Second Edition, PennWell Publishing company.,

3. Craft, B.C. and Hawkins, M.F: Applied Petroleum Reservoir Engineering, Second Edition, prentice Hall PTR Publishing Company.

4. Gopal, V.N.: Gas Z-Factor Equations Developed For Computer, Oil and Gas Journal (Aug. 8, 1977) 58-60.

5. Standing, M.B. and Katz, D.L.: Density Of Natural Gases, Trans., AIME (1942), 146, 140-149.

6. Penuela, G. and Civan, F.: Gas-Condensate Well Test Analysis With and Without Relative Permeability Curves, SPE 63160.

7. Serra, K.V., Peres, M.M., and Reynolds,. A.C.: Well-Test Analysis for Solution-Gas Drive Reservoirs: Part-1 Determination of Relative and Absolute Permeabilities SPEFE June 1990, P-124-131.

8. Economides M.J. et al. The Stimulation of a Tight, Very-High-Temperature Gas Condensate Well SPEFE March 1989, 63-72.

9. Guehria, F.M. Inflow Performance Relationships for Gas Condensates, SPE 63158.

10. Lee, A.L., Gonzalez, M.H., and Eakin, B.E.: The viscosity of Natural Gases, JPT (Aug. 19966), 997-1000 Trans. AIME, 237.

11. Al-Hussainy, R., Ramey, H.J.Jr., and Crawford, P.B.: The Flow of Real Gases Through Porous Media, JPT (May 1966), 624-36; Trans., AIME 237. 12. Jokhio, S.A. and Tiab, D.: Establishing Inflow Performance

Relationship (IPR) for Gas Condensate Wells, Paper SPE 75503, presented at SPE Gas Technology Symposium, Calgary, April 30-May 02, 2002.

13. Jones, J.R., Vo, D.T., and Raghavan, R.: Interpretation of Pressure Buildup in Gas Condensate Wells, Paper SPE 15535.

14. Evinger, H.H. and Muskat, M.: Calculation of Theoretical Productivity Factors, Trans.,AIME (1942) 146, 126-139.

15. Jones, L.G., Blount, E.M. and Glaze, O.H.: Use of Short Term Multiple Rate Flow Tests to Predict Performance of Wells Having Turbulence, paper SPE 6133 presented at the 1976 SPE Annual Technical Meeting and Exhibition, New Orleans, Oct. 3-6

16. Sukarno, P. and Wisnogroho, A.: Genaralized Two Phase IPR Curve Equation Under Influence of Non-linear

Flow Efficiency, Proc. of the Soc. of Indonesian Petroleum Engineers Production Optimization International Symposium, Bandung, Indonesia, July 24-26, 1995, 31-43.

17. Rawlins, E.L. and Schellhardt, M.A.: Backpressure Data on Natural Gas Wells and Their Application to Production Practices, USBM (1935) 7.

18. Wiggins, M.L.: Inflow Performance of Oil Wells Producing Water, PhD dissertation, Texas A&M U., College Station, TX (1991).

19. Camacho V. and Raghavan R., Inflow Performance Relationships for Solution-Gas Drive Reservoirs. JPT (May 1989), P-541-550.

20. Forchheimer, Ph.D.: Ziets V. deutsch Ing., (1901) 45, 1782.

21. Al-Hussainy, R., and Ramey, H.J. Jr., Application of Real Gas Flow Theory to Well Testing and Deliverability Forecasting, JPT May 1996, 637.

22. Guehria, F.M. Inflow Performance Relationships for Gas Condensates, SPE 63158.

23. Fetkovich, M.J.: The Isochronal Testing of Oil Wells, paper SPE 4529 presented at the 1973 SPE Annual Meeting, Las Vegas, NV, Sept. 30-Oct. 3.

Examples Vertical Wells-Pressure Drawdown Example-1

This example was generated using Sapphire Well test Software. Since reservoir pressure is above the dew point pressure, therefore, only Region-3 exists. Only water and gas are mobile in this region.

Table 1. Well and reservoir data.

Data Pi 8,000 psi

GWR 50,000 CF/STB WGR 20 STB/MMscf

SG 0.75 Pd 5,000 psi tp 500 hrs Cr 3.00E-06 1/psi T 212 F

GOR 8000 cf/STB r

w 0.3 ft

h 100 ft C 0.2 STB/Psi S 5 kh 2,000 md-ft k 20 md qg 2 MMcf/D q

w 40 STB/D

API 45


1. Following the procedure given earlier, pressure data were converted into pseudopressure function ignoring the effective permeability. Using equation 42, pressure test data is analyzed, (without gas effective permeability term.)

=Pd

P gdgd

rg

sgwpgw

pgw dpB

kkRR

RmP

*g .

.

2. Using Eq.43 well test data is analyzed for water

phase effective permeability

( ) =Pd

P ww

rwpgw dpB

kkRmP*

g ..

3. Using Eq.48 and Eq.49, the gas and water phase

effective permeability integrals were estimated.

( )( )

= hq

tddmP

dpPkk measgg

P

Prg

wf

,

)ln(

6.162. (a)

( )( )

= hq

tddmP

dpPkk measgg

P

Prw

wf

,

)ln(

6.162. (b)

4. Now the production data can be converted using

equations in Step 1 and 2, this time with effective permeability integrals for both gas and water phase.

5. Since we did not have production data, therefore, values of n, and C were assumed.

Table 2. Pressure, Pseudopressure and Effective Permeability Integral Data for the Straight line Region

Time P mP mP t*d(mP)/dt Integral-Keg hrs psi Psi2/cp 106

10.09817 7930.564 337.0989 2420990 100616.5 32.32073 11.33033 7930.236 337.0874 2432498 99991.36 32.52281 12.71284 7929.91 337.076 2443942 99429.37 32.70663 14.26404 7929.586 337.0646 2455328 98920.97 32.87473 16.00452 7929.263 337.0533 2466661 98469.72 33.02538 17.95736 7928.941 337.042 2477949 98063.72 33.16211 20.14849 7928.621 337.0307 2489195 97706.82 33.28324 22.60698 7928.301 337.0195 2500406 97386.73 33.39264 25.36545 7927.983 337.0084 2511583 97106.81 33.4889 28.4605 7927.666 336.9972 2522733 96856.47 33.57545 31.93321 7927.349 336.9861 2533857 96637.74 33.65145 35.82965 7927.033 336.975 2544959 96442.7 33.7195 40.20152 7926.717 336.9639 2556042 96272.07 33.77927 45.10685 7926.402 336.9528 2567107 96119.87 33.83275 50.61072 7926.087 336.9418 2578157 95986.79 33.87966 56.78616 7925.773 336.9307 2589194 95867.68 33.92175 63.71512 7925.459 336.9197 2600218 95764.11 33.95844 71.48954 7925.146 336.9087 2611232 95670.81 33.99156 80.21258 7924.833 336.8977 2622237 95590.1 34.02026

90 7924.52 336.8867 2633233 95515.49 34.04684 100 7924.233 336.8766 2643290 95453.31 34.06901 110 7923.974 336.8676 2652383 95403.34 34.08686 120 7923.738 336.8593 2660680 95362.9 34.10131 130 7923.521 336.8516 2668311 95329.73 34.11318 140 7923.32 336.8446 2675373 95300.94 34.12348 150 7923.133 336.838 2681947 95276.85 34.13211 160 7922.958 336.8318 2688094 95255.95 34.1396 170 7922.794 336.8261 2693868 95237.43 34.14624 180 7922.639 336.8206 2699311 95221.56 34.15193 190 7922.493 336.8155 2704459 95207.51 34.15697 200 7922.354 336.8106 2709341 95194.65 34.16158 210 7922.222 336.806 2713985 95183.93 34.16543 220 7922.096 336.8015 2718413 95173.42 34.1692 230 7921.975 336.7973 2722643 95164.82 34.17229 240 7921.86 336.7932 2726693 95155.8 34.17553 250 7921.75 336.7894 2730577 95148.54 34.17814 260 7921.643 336.7856 2734309 95141.84 34.18054 270 7921.541 336.782 2737899 95135.07 34.18298 280 7921.443 336.7786 2741359 95130.31 34.18469 290 7921.348 336.7752 2744697 95123.81 34.18703 300 7921.256 336.772 2747921 95119.59 34.18854 310 7921.167 336.7689 2751040 95114.55 34.19035 320 7921.082 336.7659 2754060 95110.61 34.19177 330 7920.998 336.7629 2756986 95107.22 34.19299 340 7920.918 336.7601 2759826 95102.81 34.19457 350 7920.839 336.7574 2762582 95100.32 34.19547 360 7920.763 336.7547 2765261 95096.58 34.19681 370 7920.689 336.7521 2767867 95093.7 34.19785 380 7920.617 336.7495 2770403 95090.75 34.19891 390 7920.547 336.7471 2772873 95088.61 34.19968 400 7920.478 336.7447 2775280 95085.38 34.20084 410 7920.411 336.7423 2777628 95083.48 34.20152 420 7920.346 336.74 2779919 95081.98 34.20206 430 7920.282 336.7378 2782156 95078.69 34.20325 440 7920.22 336.7356 2784342 95078.56 34.20329 450 7920.16 336.7335 2786479 95075.38 34.20444 460 7920.1 336.7314 2788568 95074.1 34.2049 470 7920.042 336.7293 2790613 95072.39 34.20552 480 7919.985 336.7273 2792615 95070.08 34.20635 490 7919.929 336.7254 2794575 95069.65 34.2065


Table 3. Pressure, pseudopressure, and water effective permeability integral data.

Time P mP mP t*d(mP)/dt Integral[Keg] hrs psi Psi2/cp 106

11.33033 7930.236 1263.714 42746.01 8.756184 12.71284 7929.91 1263.671 42503.26 8.806073 0.153006 14.26404 7929.586 1263.629 42286.31 8.8517 0.140655 16.00452 7929.263 1263.587 42090.73 8.892656 0.126844 17.95736 7928.941 1263.545 41918.08 8.929868 0.115727 20.14849 7928.621 1263.503 41762.76 8.962863 0.102996 22.60698 7928.301 1263.462 41626.73 8.992707 0.093466 25.36545 7927.983 1263.42 41504.77 9.019016 0.08264 28.4605 7927.666 1263.379 41397.93 9.042699 0.074583

31.93321 7927.349 1263.337 41302.42 9.06355 0.065817 35.82965 7927.033 1263.296 41218.78 9.08227 0.059212 40.20152 7926.717 1263.255 41143.99 9.098748 0.052214 45.10685 7926.402 1263.214 41078.33 9.113536 0.046936 50.61072 7926.087 1263.173 41019.58 9.12656 0.041398 56.78616 7925.773 1263.132 40967.99 9.138269 0.037264 63.71512 7925.459 1263.091 40921.62 9.148551 0.032761 71.48954 7925.146 1263.05 40881.11 9.157835 0.02961 80.21258 7924.833 1263.009 40844.51 9.165967 0.025961

90 7924.52 1262.969 40812.47 9.173505 0.024085 100 7924.233 1262.931 37324.01 9.179859 0.022196 110 7923.974 1262.897 33745.15 9.185001 0.019869 120 7923.738 1262.867 30792.85 9.189191 0.017747 130 7923.521 1262.838 28315.74 9.192667 0.016007 140 7923.32 1262.812 26207.98 9.195692 0.015051 150 7923.133 1262.788 24392.12 9.198265 0.013756 160 7922.958 1262.765 22811.59 9.200489 0.012714 170 7922.794 1262.744 21423.76 9.202498 0.01223 180 7922.639 1262.723 20194.99 9.204213 0.011069 190 7922.493 1262.704 19099.59 9.205767 0.010615 200 7922.354 1262.686 18116.98 9.207178 0.010157 210 7922.222 1262.669 17230.45 9.208386 0.009138 220 7922.096 1262.652 16426.85 9.209558 0.009307 230 7921.975 1262.637 15694.69 9.210544 0.008192 240 7921.86 1262.622 15025.12 9.211553 0.008758 250 7921.75 1262.607 14410.18 9.212403 0.007695 260 7921.643 1262.594 13843.75 9.213176 0.007278 270 7921.541 1262.58 13320.34 9.213967 0.00775 280 7921.443 1262.567 12834.74 9.214543 0.005849 290 7921.348 1262.555 12383.57 9.215298 0.007949 300 7921.256 1262.543 11962.78 9.215808 0.005563 310 7921.167 1262.531 11569.89 9.216419 0.006893 320 7921.082 1262.52 11201.9 9.216898 0.005576 330 7920.998 1262.509 10856.6 9.217346 0.005373 340 7920.918 1262.499 10532.03 9.217858 0.00635 350 7920.839 1262.489 10226.11 9.218212 0.004506 360 7920.763 1262.479 9937.667 9.218656 0.005835 370 7920.689 1262.469 9664.996 9.219032 0.005064 380 7920.617 1262.46 9406.799 9.219413 0.005292 390 7920.547 1262.45 9162.033 9.219695 0.004012 400 7920.478 1262.442 8929.915 9.220106 0.005996 410 7920.411 1262.433 8709.011 9.220364 0.003868 420 7920.346 1262.424 8498.799 9.220594 0.003529 430 7920.282 1262.416 8298.758 9.220993 0.006279 440 7920.22 1262.408 8107.584 9.22108 0.001386 450 7920.16 1262.4 7925.276 9.221466 0.006361 460 7920.1 1262.392 7750.793 9.221661 0.003283 470 7920.042 1262.385 7583.872 9.221877 0.003704

7910

7920

7930

7940

7950

7960

7970

7980

7990

8000

8010

0. 01 0. 1 1 10 100 1000

T i m e [ h r s ]

P d =

Fig.6. Pressure behavior during three phase well test. Since the test last up to 7910 psi and the dew point pressure is 5,000 psi, therefore, only one Region-3, single-phase gas region with water production was observed during this test.

0

0 . 5

1

1.5

2

2 . 5

3

0 . 0 1 0 . 1 1 10 10 0 10 0 0

T im e [ h r s ]

Fig.7. Semi-log plot pseudopressure Vs. time.

0. 01

0. 1

1

10

0. 01 0. 1 1 10 100 1000

T i m e [ h r s ]

Fig.8. Pseudopressure and its derivative against time.


32

32 . 5

33

33 . 5

34

34 . 5

79 18 79 20 79 22 79 24 79 26 79 28 79 30 79 32

P r es su re [p si ]

Fig. 9. Gas phase effective permeability Integral, Eq.a.Step-3.

8 . 6

8 . 7

8 . 8

8 . 9

9

9 . 1

9 . 2

9 . 3

7 9 18 7 9 2 0 7 9 2 2 7 9 2 4 7 9 2 6 7 9 2 8 7 9 3 0 7 9 3 2

P r e s s u r e [ p s i ]

Fig. 10.Water phase effective permeability Integral, Eq.b. Step-3.

0

0.1

0.2

0.3

0.4

0.5

0.6

7918 7920 7922 7924 7926 7928 7930 7932

Pressure [psi]

Gas

Pha

se E

ffect

ive

Perm

abili

ty [m

d]

Fig. 11. Gas phase effective permeability, derivative of Eq.a.Step-3.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

7918 7920 7922 7924 7926 7928 7930 7932

Pressure [psi]

Wat

er P

hase

Effe

ctiv

e Pe

rmea

bilit

y [m

d]

Fig. 12. Water phase effective permeability, derivative of

Eq.b.Step-3.

Well Performance Assumed values: C = 0.5, n = 0.8

5000

5500

6000

6500

7000

7500

8000

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Flow Rate [MMscf/D]

Pres

sure

[psi

]

Fig.13.Gas Phase IPR against pressure, in Region-1, Pd = 5,000 psi.

Table 4. Gas effective permeability Integral.

Pressure Integral (keg) 5000 30.476471637928624 5200 30.631891184301181 5400 30.795983644540905 5600 30.969129442903928 5800 31.15174520450631 6000 31.344289374502508 6200 31.547270060542279 6400 31.761256836033446 6600 31.98690025784522 6800 32.224968032864444 7000 32.476421828527052 7200 32.74261028416964 7400 33.025876464272628 7600 33.332271093338032 7800 33.696972432023308 8000 33.688467604648922

Table 5. Water effective permeability Integral.

Pressure Integral(kew)

5000 10.116158420583201 5200 10.044798023019742 5400 9.9734377384218023 5600 9.9022283647546126 5800 9.8313100887163723 6000 9.7608134581254411 6200 9.6908609278103778 6400 9.6215694038350044 6600 9.5530547391367231 6800 9.4854404920007789 7000 9.4188772084256887 7200 9.3535920091200848 7400 9.2900466165207281 7600 9.229646563845015 7800 9.1813748736733521 8000 9.0312612761992642


5000

5500

6000

6500

7000

7500

8000

0 20 40 60 80 100 120 140

Flow Rate [STB/D]

Pres

sure

[psi

]

Fig.14. Water Phase IPR in Region-1.

Example-2: Vertical Wells-Pressure Buildup This example was simulated with reservoir pressure just above the dew point pressure to simulate the Region-1, Region,2 and Region-3 together. But the pressure did not drop far below to see all the three regions together. The lowest pressure is 3,500 psi. Initial data is masked by the wellbore storage effects, but the region-1 P > Pd = 4,800 psi is well developed. After 100 hours, we are in radial portion and are in the Region-1.Thus using same procedure as in example 1, well performance is established.

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

0.01 0.1 1 10 100 1000

Time [h rs]

Fig. 15. Semilog Plot of pressure Vs. Time.

Table 6. Well and reservoir data. Pi 5,000 Psi GWR 10,000 CF/STB WGR 100 STB/MMscf SG 0.7 Pd 4,800 psi tp 1,000 Hrs Cr 3.00E-06 Psi-1 T 250 F

GOR 20,000 cf/STB rw 0.35 Ft h 100 Ft C 0.2 STB/Psi S 3 Kh 50 md-ft K 0.5 Md qg 1 MMcf/D qo 50 qw 100 API 50

100

110

120

130

140

150

160

170

180

190

200

0.01 0.1 1 10 100 1000

Time[hrs]

mP

[MM

psi2

/cp]

Fig.16. Pressure behavior during three phase well test.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

4650 4700 4750 4800 4850 4900 4950 5000

Pressure[psi]

Inte

gral

[Keg

]

Fig. 17. Gas phase effective permeability Integral.


0

0.5

1

1.5

2

2.5

3

4650 4700 4750 4800 4850 4900 4950 5000

Pressure[psi]

Inte

gral

[Kew

]

Fig. 18. Water phase effective permeability Integral.

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

4650 4700 4750 4800 4850 4900 4950 5000

Pressure[psi]

Kew

[md]

Fig. 19.Water phase effective permeability.

0

0.005

0.01

0.015

0.02

0.025

4650 4700 4750 4800 4850 4900 4950 5000

Pressure [psi]

keg

[md]

Fig. 20. Gas phase effective permeability.

0.1

1

10

100

0.01 0.1 1 10 100 1000 10000

Time[hrs]

mP[

MM

psi2

/cp] Pd = 4800 psi

Fig.21. Pseudopressure and its derivative against time.

4800

4820

4840

4860

4880

4900

4920

4940

4960

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Gas Flow Rate [MMscf/D]

Pres

sure

[psi

]

Fig. 22. Gas Phase IPR.

Table 7. Gas effective permeability integral.

Pressure Integral[Keg] 4650 0.29762045799890937 4670 0.3634043918298419 4690 0.43596219600121575 4710 0.51181576975883678 4730 0.58665922703122982 4750 0.6561523280790823 4770 0.71689985846021637 4790 0.76735591174235665 4810 0.8084286250357622 4830 0.84372127405466752 4850 0.87956986766447234 4870 0.925261217962693 4890 0.99405023518172253 4910 1.1060116957040951 4930 1.2948447155669481 4950 1.6238079244197225

Table 8. Water effective permeability integral.

Pressure Integral[Kew] 4650 0.44302027417364041 4670 0.54102367599140588 4690 0.64930281931686321 4710 0.76265680812973728 4730 0.87462474391444535 4750 0.97867937420967451 4770 1.0697047931514044 4790 1.1453612878255373 4810 1.2069959437796109 4830 1.260001519200659 4850 1.3138657315396646 4870 1.3824893833407772 4890 1.4857006838184235 4910 1.6535103105320569 4930 1.9362592834488127

4950 2.428352358662414 4951


4600

4650

4700

4750

4800

4850

4900

4950

5000

0 50 100 150 200 250Water Flow Rate [STB/D]

Pres

sure

[psi

]

E ffect of Condensate Deposition on W ater Phase IPR IPR

Pd = 4800

Fig.23. Water phase IPR.

Comments on Fig.23: Although dew point pressure is 4800 psi, its impact on water production is felt much before. The upper line is the water production trend if dew point pressure was not reached. After dew point pressure, water production declines sharply. Thus it is clear from Fig.23 that the condensation helps reduce water production. The second dotted line is the water production trend if P*was not reached. After P* is reached water trend stabilizes and shows linear decline. Example-3: Horizontal Well

Table. Well and reservoir data.

Pi 3,000 psi GWR 10,000 CF/STB WGR 100 STB/MMscf

SG 0.7 Pd 4,800 psi tp 1000 hrs C

r 3.00E-06 1/psi

T 200 F GOR 20,000 cf/STB

rw 0.3 ft

L 1,000 ft C 0.1 STB/Psi S 0

Kh 30 md-ft K 0.5 Md qg 5 MMcf/D q

o 250 STB/D

qw 500 STB/D

API 50 h 60 Ft

Zw 30 Ft

Since reservoir pressure is less than dew point pressure Region-2 and Region-1 might exist. In this example we do not know P*, so it is assumed that only Region-1 exists. Using Eq.38a, pressure test data is analyzed, ignoring the gas effective permeability term.

( )( )

+=

*

11

1k.kPP

P so

oso

ggsgwpgw

pgwgg

wf

dpRB

BRR

BRRR

mP ( )sgwpwopgo RRRB =

Using Eq.37 well test data is analyzed for water phase effective permeability

=*

..

g

P

Ppgw

ww

rw

wf

dpRB

kkmP

1

10

100

1000

0.01 0.1 1 10 100 1000

Time [hrs]

mP

& t*

(dm

P/dt

)

Fig. 24.Pseudopressure and its derivative with new

pseudopressure.

Fig.25. Water phase effective permeability integral, Eq.49.

Fig.26. Water phase effective permeability, derivative Eq.49.


0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5 6 7 8 9

Gas Flow Rate [MM SCF/D]

Pres

sure

[psi

]

Fig.27. Gas Phase IPR against pressure.

0

5

10

15

20

25

30

0 1 2 3 4 5 6 7 8 9

Gas Flow Rate [MMSCF/D]

mP

[MM

psi

2 /cp]

Fig.28. Gas Phase IPR against pseudopressure.

0

1000

2000

3000

4000

5000

6000

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850

Water Rate [STB/D]

Pres

sure

[psi

]

Fig. 29. Water Phase IPR against pressure.

Appendix-A Pseudopressure Curves (Region-1) [Eq.38a] Region-1: Gas Phase Effect of Temperature

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

500 900 1300 1700 2100 2500 2900 3300 3700 4100 4500 4900 5300 5700Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]/M

g1

Gas GravityFrom Top-

Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rp = 5000 SCF/STB

Rpwg = 8000 SCF/STBAPI = 45

Pb = 1000 psid = 0.5 cp

Water Salinity 15%

T = 150 F

Fig.A-1 Gas phase pseudopressure Region-1[Eq.38a]

[T = 150]

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

500 900 1300 1700 2100 2500 2900 3300 3700 4100 4500 4900 5300 5700Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]/M

g1


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rp = 5000 SCF/STB


Pb = 1000 psid = 0.5 cp

Water Salinity 15%

T = 200 F


[T = 200]


0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

500 900 1300 1700 2100 2500 2900 3300 3700 4100 4500 4900 5300 5700Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]/M

g1


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rp = 5000 SCF/STB


Pb = 1000 psid = 0.5 cp

Water Salinity 15%

T = 250 F


[T = 250]

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

525

550

575

600

625

650

675

700

500 900 1300 1700 2100 2500 2900 3300 3700 4100 4500 4900 5300 5700Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]/M

g1


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rp = 5000 SCF/STB


Pb = 1000 psid = 0.5 cp

Water Salinity 15%

T = 300 F


[T = 300]

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

525

550

575

600

500 900 1300 1700 2100 2500 2900 3300 3700 4100 4500 4900 5300 5700Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]/M

g1


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rp = 5000 SCF/STB


Pb = 1000 psid = 0.5 cp

Water Salinity 15%

T = 350 F


[T = 350] Region-2 and Region-3 [Eq. 40 and 41]

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

460

470

480

490

500

6000 6400 6800 7200 7600 8000 8400 8800 9200 9600 10000Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rpgo = 5000 SFC/STB

Rpgw =5000 SCF/STB

Rpow = 0.5T = 150 FAPI = 45

d = 0.5 cp

Fig.A-6 Gas phase pseudopressure Region-2 and 3[Eq.43] [T = 150]


200

210

220

230

240

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

460

470

480

490

500

6000 6400 6800 7200 7600 8000 8400 8800 9200 9600 10000Pressure [ps i]

Pseu

dopr

essu

re [M

Mps

i2 /c

p]


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rpgo = 5000 SFC/STB

Rpgw =5000 SCF/STB

Rpow = 0.5T = 200 FAPI = 45

d = 0.5 cp

Fig.A-7. Gas phase pseudopressure Region-2 and 3[Eq.43] [T = 200]

200

210

220

230

240

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

6000 6400 6800 7200 7600 8000 8400 8800 9200 9600 10000Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rpgo = 5000 SFC/STB

Rpgw =5000 SCF/STB

Rpow = 0.5T = 250 FAPI = 45

d = 0.5 cp

Fig.A-8 Gas phase pseudopressure Region-2 and 3[Eq.43]

[T = 250 ]

200

210

220

230

240

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

6000 6400 6800 7200 7600 8000 8400 8800 9200 9600 10000Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rpgo = 5000 SFC/STB

Rpgw =5000 SCF/STB

Rpow = 0.5T = 300 FAPI = 45

d = 0.5 cp


[T = 300]

150

160

170

180

190

200

210

220

230

240

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

6000 6400 6800 7200 7600 8000 8400 8800 9200 9600 10000Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rpgo = 5000 SFC/STB

Rpgw =5000 SCF/STB

Rpow = 0.5T = 350 FAPI = 45

d = 0.5 cp


[T = 350 ] Effect of Rp


250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

460

470

480

490

500

6000 6400 6800 7200 7600 8000 8400 8800 9200 9600 10000Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rpgo = 6000 SFC/STB

Rpgw =5000 SCF/STB

Rpow = 0.5T = 350 FAPI = 45

d = 0.5 cp


[Rp= 6,000]

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

460

470

480

490

500

6000 6400 6800 7200 7600 8000 8400 8800 9200 9600 10000Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rpgo = 7000 SFC/STB

Rpgw =5000 SCF/STB

Rpow = 0.5T = 350 FAPI = 45

d = 0.5 cp


[Rp = 7,000] Effect of Rpgw

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

460

470

480

490

500

6000 6400 6800 7200 7600 8000 8400 8800 9200 9600 10000Pressure [psi]

Pseu

dopr

essu

re [M

Mps

i2/c

p]


Bottom

0.600.650.700.750.800.850.900.951.001.051.10

Rpgo = 5000 SFC/STB

Rpgw =8000 SCF/STB

Rpow = 0.5T = 350 FAPI = 45

d = 0.5 cp


[Rpgw = 8,000]

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

460

470

480

490

500

6000 6400 6800 7200 7600 8000 8400 8800 9200 9600 10000

Pressure [psi]

Pseu

dopr

essu

re[M

Mps

i2 /cp

]

Gas Gravity

From Top-Bottom

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

Rpgo = 5000

SFC/STB

Rpgw =9000

SCF/STB

Rpow = 0.5

T = 150 F

API = 45

d = 0.5 cp


[Rpgw = 9,000]


8090

100110120130140150160170180190200210220230240250260270280290300310320330340350360370380390400410420430440

6000 6400 6800 7200 7600 8000 8400 8800 9200 9600 10000

Pressure [psi]

Pseu

dopr

essu

re[M

Mps

i2 /cp

]/Mw

2

Temp.[F]

From Top-

Bottom

400

350

300

250

200

150

SG = 0.6

Rpgo = 5000

SFC/STB

Rpgw =7500

SCF/STB

T = 150 F

API =45

d = 0.5 cp

Fig.A-15 Gas phase pseudopressure Region-2 and 3[Rpgw =

7.500 Eq.43]

Documents

spe76752 Establishing Gas Phase Well Performance for Gas Condensate Wells Producing.pdf