20724-An Improved Method to Predict Future Ipr Curves

7/24/2019 20724-An Improved Method to Predict Future Ipr Curves

1/8

An improved Method To Predict

Future IPR Curves

M.A. Klins,

SPE, Chevrm U.S.A. Production CO. Inc., and J.w. Clark III, spEt

Chevron Petroleum Technology Co. Inc.

5P6

Q 07a9

Summaw This

paper presents a si~lcantly improved yet simple method to prdct future oilwelf deliverability and inflow per-

formance relationship (IPR) curves. For the 21 reservoirs studied, current empirical techniques overpredlcted future performance by

117%, while the new approach reduced the average error to only 9%. This new method, when coupled with nodal analysis, could

affect equipment stilng, ifr@iii6i-plarming, and properly sales economics significantly because it provides more realistic predictions.

Introduction.

An

important engineering td for

mzddziug future fmancid return

through design optimization is the abtity to develop a family of

future fPR curves for a given well or field. These curves maybe

able to provide answers to such questions as tubing and choke size,

timing of atitkikd lift, future revenue streams, and abandonment

time with some certainty.

Currently, three simple hand-held metfmds 1-3 are used to esd-

mati future absobme-open-f low (AOF) rates for wells producing

from solution-gasdrive reservoirs. After several maxiumm-ratel

mservok-pressure pairs have been established, these values nor-

mally are coupled with Vogels4 dimensionless fPR equation to

create a family of future LPR curves. However, the e methods appear

to introduce significant error into the estimation process.

First, we will describe the current methods to predict future max-

imum flow rates. Fetkovich 1 presented a relationship between oil

flow rate, average reservoir pressure, and flowing bottomhole pres-

sure (BHP) by

q. J P? Pn/)n,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(1)

where tbe flow exponent, n, is assumed to be cons~t orrOughOut

the life of the reservoir and the flow constant, J2, varies accord-

ing to

.J2=J1(P2/Pr,).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(2)

J1 =flow constant at current reservoir pressure,

P,I,

and Jz =flow

constant at a future reservoiz pressure,

pa.

Therefore, with a

three- or four-point flow test, n and J can be estimated for that test

rind that reservoir pressure, and any future maximum flow rate cwi

be projected by

dm=Jz prz2)~ . . . . . . . . . . . . . . . . . . . . . . . . . . ...(3)

fn a second approach, Eickmeier2 coupkd Feikovichs 1 work

with Vogels4 equation and set the flow exponent to a freed value

of 1..0 to arrive at

(40)m@=(qo)m1(Pfi/P,1 )3. . . . . . . . . . . . . . . . . . . . ..(4)

Instead of a multipoirx test liie that needed to implement Fet-

koviclr)s

Eqs. 1, 2, and 3, a one-point test can be coup]ed With

Vogels equation to estimate (qo)m=i. Then, for any selected

future reservoir pressure, the corresponding maximum open-flow

petentiaI, (qo)mm, can be predicted with Eq. 4.

The tbhd method is Uhri and Blounts3 pivot-point approach,

which requires two separate flow-rate tests at two different average

reservoir pressures. Their numerical solution requires that two flow

constants be determined from tie two flow-rate tests such that

(Pr, Pd

a=

[

P,l 2 _

Pr2=

. . . . . . . . . . . . . . . . . . . . . . ..(5)

(%?)mwl (%Jmm2

[

P,l

and b=j+

1.0. . . . . . . . . . . . . . . . . . . . . . . . . ..(6)

(Qlaxl

The maximum flow rate for any given resemok pressure is then

determined from

(qo)mrx=(ap?)/@ r+b). . . . . . . . . . . ... . . . . . ...0)

These three simple methods are available to esdmate timrre max-

imum open-flow rates for wells under solution-gasdrive. These

AOF values, coupled witi Vogels4 equation, can be used to esti-

mate future IPRW The Eickmeier2 approach requires a single-

point flow test to implement, the Fetkovich L method uses a muki-

point test, and the pivot-point procedure needs two single-point tests

taken at different times.

IPR Data Development

Before describing M papers new method of estimating future

AOFS and hence future IPR performance, discussion of the de-

velopment of the pressureltlow database used is appropriate. Kim

and Majcher5 give a more complete description.

Intlow performance of 21 theoretical solution-gasdrive reser-

voirs was simulated with the WeUer6 method. Table 1 shows that

these reservoirs contain a wide range ,of rock and tluid properdes,

relative permeability characteristics, and skin effects. .To constmct

the >19,000 flow-ratelpressure-point data set, WeUer describes

the pressure gradient as

ap

()

w%% r? rz

; =141.2

. . . .

(8)

rkkmh rj +,

The d saturation at any time and location can be estimated from

;=SL(,-9).,2.6_~. . . ...(9)

The fractional recovery, NP/N, is calculated with tie Muskat7

method.

Eqs. 8 and 9 allow stepwise calculation of pressure and satura-

tion profiles for a specitied flow rate from the outer boundary to

the weUbore. To conserve computer time, and because pressure

gradients get gradually steeper approaching the weUbore, a vti-

able stepping procedure was incorporate l. At any point >200 ft

from the weUbore; a 1.O-ft step was ustxl between 100 and 200

ft, a 0.5-ft stew between 10 and 100 ft, a 0.05-ft stew and within

10 ft of the wellbore, a O.01-ft step. The variable stepping proce-

dure was checked by compming its results WM those obtained with

a constant radius step of 0.01 ft results were v@ualIy identical.

Tb& prccedure produces an accurate solution wbife mark.dy reduc-

ing computation time.

Because V/eUer6 did not account for skin in his formulation, tie

method had to be adjusted to simulate the performance of damaged

or improved weUs. Hawkins8 viewed the skin effect as a zone of

ilnite widti with ~tered permeability and defined it as

(k. ) (rw)

= 11 h~ . . . . . . . . . . . . . . . . . . . . . . . . . . ....(10)


2/8

TABLE 1RESERVOIR DATA VARIABLES FROM

21 THEORETICAL RESERVOIRS

Base-Case

Range

100 to 4,000

25 to 45

1,052.2 (2o to 80)

wpyia

2,000 1 ,0(

r., ft (acres)

7447(40) 526.6 to 1

sgc Yo 5

Otolo

so,, % 30 20

to 40

k,

md 100

10 to 1.000

&

oh

15 10

to

20

I

.

s

..s %

30

A 2

s

o

20 to 40

4 and co

-4 to +6

I

Eq. IO

was solved fork.

to

include the skio effect in the model.

A vaiue of altered perme&ility can be calctiated by specifying a

skin value aud damage radius when k and IWare known. For con-

v&ience, a

4-ft damage radius was used in the

model.

To include the desired range of PVT data, it was necessay to

use general correlations to estimate those values. The following

correlations were used to develop the rock and fluid propeties of

the reservoirs mcdeled Dranchuk et al. s9 correlation was used

for gas @repressibility; ke et al.s 10 correladon for gas viscosi~,

Vazquti and Beggs11 correlations for solution-gasloil ratio, oil

compressibility, and oil ~ and Burdines 12 correction for mla-

twe penno@ili ty.

Model Verification

Data from Vogels4 origimd work w,ere used with the model, and

the results were compared with his inflow performance curves to

verify the developed models accuracy. IPR cwves for three. stages

of mservok depletion were generated with Vogels Case A data.

The curves from the two works were virtuauY identical. ~y minor

differences in results were probably tbe&sult of commting Vogels

graphical data to workable, tabular form.

Data Generation

To develop a general equation that could b.e used to predict future

inflow performance for my solution-gas reservoir, IPR curves were

generated for wells producing from 21 theoretical reservoirs. Mid

reservoir pressure (lwbblepoint pressure), reservoir depletion, oil

API gravity, resid@ oil smuwion, critical gas saturation, rela-

tive and absolute permeabfbies, and skin effec~ on AOF were in-

vestigated. Table 1 lists each va able, the base+ase value, and the

rauze used in the study. For each case. runs were made for eieht

diff&nt skin values: 6, 4,2,0, 1, -2, 3, .&d 4. Also, ~or

each data case and sk@, curves were genemted foreight depletion

stages. These combinations of conditions resolted in the generation

of 1,344 12R curves with 19,492 total data points.

10s

EEl\

-.

10?

n

=0.Y70

,3

lO6-

~ n

7X1 *~@~

:: ::: -

,.5

.&

,,,,, .,,CJ

M.lm psis

10

%=1750@

A F+=15C4 @a

103

1 10

100 103) 10COO

% @OPD)

Fi9. IFIow constants

J

and n calculated with base-case

reservoir data.

Development of a Simplified Approach

To Estimate Future AOF

Fetkovich-type I isochronal plots were generated for each of the

J =0 cases to estimate the flow exponent, n, aod PI coefficient, J.

J and n parameters for each case were calculated with regression

techniques. Fig. 1 is an example of basecase resolts for three reser:

voir pressures. Although it is not readily apparent from the plot

that n cbaoges considerably with reservoh pressure, as pressure

declines furthe~, the values for n and J do vary significantly. Fig.

2 shows that the values for n increase with depleting reservok pres-

sure, whiIe the values for J

decrease (Fig.

3). Investigations of n

and J behavior for the ~emaiiiing 20 reservoir cases showed simi-

lar trends for a wide vaiiety of cases.

Because the absolute values for n

and

J varied greatly ftom case

to case, these relatiombips had to be comerted to a dimensionless

form before a statistically mea@r@l relationship could be d.svel-

oped. After several differeni format attempts, we decided dmt the

n and J values at any pressure could be related to the values at the

bubblepoint pressure and that a reIationsbip between dimemion-

less n/nb, dimensionless

J/Jb,

and dimensiodess pressure,

p~b,

could be made. Note that, with the 156 cases investigated, n/rab

increases with decreasing pressures @ii. 4) while Jflb (Fig. .5)

decreases. These same trends also were obserfed for cases witl

varying skin values. We determined that skin had almost no effect

when these dimensior@s relationships (F&. 6 and T) were used

to esdmate futme AOF rates.

A third-order polynomi~ fit was generated with the dimmsio@ess

tz lnb and

J/Jb vabms,

~d the quations that descnie the trends are

.

I.m

I

o

1.05

i

1,C4 j

i

iLO

500 IWO 1S00 2W4

R w)

603

484

1

200

0

a

.

o

0 500 limo 1504 Zmo

Fig. 2Base-case n with resewoir prassure decline.

Fig. 3-Base-case J with reservoir pressure decline.


3/8

4:

1,4

1

0

1.3

4

1.

:L

.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fig. 4-Dimensionless flow exponent, nhb, a3 a function of

dimensionless pressure.

1,0-

0.9-

0.8-

0.7-

0,6-

.

0.5-

~o

LdAiilL

.0 0.1 0;2 0.3 0.4 0.5 3.6 0.7 0.8 0.9 1.0

(:) (:Y

nd 1=13.5718 1 +4.7981 l

Jb

3

2.3065 1 3

, . . . . . . . . . . . . . . . . . . . . . . . ..(12)

Fig. 5Dlm.enslordess flow constant, .VJb, as a function of

dimensionless pressure.

120-

1.15-

1.10-

1.05-

:

2

%.=0

- Skin= 6

.

w=.

k

k

ml

a,

0.0 0.1 0,2 0,3 0.4 0.5 0,6 0.7- 0.8 0.9 1.0

Fig. 6Skin effect on nhb.

( ~b) ( J

=1+0.0577 l~ 0.2459 l~

b

3

+0.5030 l~

, . . . . . . . . . . . . . . . . . . . . . . . . . ..(11)

12-

~

skin= o

1.0- 9 Skin= 6

m

A skin=4

0.8

.k ~,6-

0,4-

0,2-

.

*

k

0.0.

,

&0 0.1 0.2 02 0.4 ?5 0,6 0:7 0.8 0:9 .1.0

g

Fig. 7Skin effect on J/J~.

1CCLC4

o

marl

..*P 0

mm

d

.;.O

.%O 0

103

.;?&@

10

~o o

80

~ .

1 0

Avera~ Akdte Error 130.70%

o

Maximm Awl. . Em, 21635%

Awrw Enm

-17839?4

0.,

0.1 1 10 100 1030 Iomo Iwo

Actual (qJ,w @OPD)

Fig. 8Error analysis using the Fetkovlch t approach.

Im

.@

10333

. ..OOO .

. . .90%0

H

.oom 0

Km:

0 0.

0 00

0 0?0 ., ~

103 ?

o .s

.o@

10

~oo.. o

o

.0

1

Avaa@ Ah dute Era 189.08%

Maximum Absolute Em 297.41%

o

+vcrw Em,

-1785s%

0.1

0.1 1 10

iwl ICal Icmo Icaoo

Add (W., (?OPD1

Fig. 9Error analysis using the Eickmeier2 approach.


4/8

Im

o

moo

s

~

Km

8

%F +P

.3

~ ~w

g

0 d%

E

&o&

10

.0

~

.OO

0

1

0

Avcra@ .4bsdu,c En., 124 5%

o

Maximum AWW Emw 176,27%

AvePw Em, 44.36%

0.1

0.1 1 10 1C4 1000 1r3m

Icmoo

AmJd (q.)= @OPD)

Fig. 10Error analysis

using the

pivot-points approach.

Im

o

Im

~

Icm

g

~ @@O

%

Q 1~

.3

3

g h

10

:&

..O.

1:

.

Average Absolute Error 30.70%

a Maxim. &dute Error 37,35%

.

AWW Em, .9.29%

0.1.

.

0.1 1 10 100 lam 10W4 lCQCOJI

Ati


5/8

I

TABLE 3CALCULATION RESULTS FROM BASE-CASE DATA

E

(P%)

1,990

i ,750

1,500

1,250

1,000

750

500

nln ~ n

J/Jb

1.00030,8507 0.9823

1,0044 0.8542 0.6240

1.0069 0,8564 0.3709

1.0136 0.8621 0.2137

1.0303 0.8762 0,1253

1.0628 0.9039 0,0786

1.1172 0.9502 0,0470

(STS/~-psia2)

0.0048

0.0031

0.0018

0.0010

0.0006

0.0004

0.0002

Calculated

(qO)mU

(STBID)

1,974

1,061

500

229

111

61

31

Actual

(q.)mw

(STBID)

2,001

i , 082

449

215

117

63

31

Step 3. Using the known flow point, the AOF, and Fetkovichs 1

equation, solve for n and J.

l?=J(P; -PwJ+,

where n= O.8508 and J= O.0048.

Step 4. Use Eqs. 11 and 12 to solve for nlnb and J/Jb:

2=+0(--)-+--7

b

()

1,990 3

+0.5030 l

=1

.CO03

2,000

J

( :;) ( ;gY

and =1-3.5718 1 +4.7981 l

Jb

()

1,990 3

2.3066 1 =0.9823.

2,000

Step 5. From Steps 3 and 4, solve for constants nb and Jb:

0.8508

~b=L=

=0.8505

nhtb

1.0003

J 0.0048

and Jb=-= =0.0049.

J/Jb 0.9823

Step 6. Use l+?+. 11 and 12 to solve for n

andJ at future

pressures.

The deliverability at reservoir pressures below bubblepoint can

be estimated with the nb and Jb constants and an estimate of the

IIJnb and J/Jb ratios for any pressure. At a 1,750-psi reservoir

pressure, estimates for n and J aIe derived fmm

n=nb(n/nb)

=0.8505 X 1.0044=0;8542,

and J=Jb (J/Jb)

=0.0049x0.6240=0.0031.

Stsp 7. Use Eq. 1 to solve for the new (qo)m .

With these values and assuming pWf=O pm, the maximum

deliverability

at the new reservoir

pressure can be calculated by

( j)max 0.0031 (1,702)08542 =1,061 BOPD.

Steps 6 and 7 can be repeated to estimate deliverability at other

pressures. Table 3 shows results of calculations with the base-case

dat6.

Conclusions

Inflow performance curves were generated for 21 ihwretical

solution-gasdrive reservoirs. These reservoirs encompassed a wide

rage of depletion, reservoir, PVT, and relative penmability char-

acteristics

The data then were evdwiied to examine tie ibtluence of 10 prop

erties on future AOF potential. Of these variables, only pressore.

depletion was found to 6ffect future flow rates significantly and

measurable.

Empiric~ equations were developed tlzt related Fetiovichs I PI

to be auo icable to the wide range of solution-gas-drive reserioits

.,

imfesti~ated.

Comparison of the new approach with three tmditiond approaches

of estimating future maximum flow rates showed that eiisting em-

pirical procedures for predicting future performance were in sub-

stantial error (> 110%) and tie new approach introduced average

errors of < 10%.

These analyses verify the increased accuracy of predicting fu-

ture AOFs and LPR curves with the procedures in this study. More

accurate esdmatm of foture well perfonnqm for recove~ timing,

ardtlcial-lii selection, and production-equipment sizing should

resuk.

STB/D-psia,

b = Ubri and BIounts3 flow constant, m/Lt2, psia

B. = oil FVF, dimensionless, bbl/STB

B; = initial o~ FVF, dimen~onkss, bb fSTB

Coi = 01 compressibility at initial conditions, Lt2/m,

psil

d = polynomial exponent, dimensionless

h = reservoir thickness, L, ft

J = Fetkovich PI coefficient, LZ3fm2, STBID-psia2

J~ =

Fetkovich PI cceffkient at bubblepoint, L5t3/m2,

sTB/D-psia2

k = absolute reservoir permeability, L2, md

koi = permeability to oil at initial conditions, L2, md

km = relative permeabili~ to oil, dimensionless

k, = altered permeabfity tlom skin effwt, L2, md

n = Fetkovich flow exponent, dimensionless

nb = Fetkovich flow exponent at bubblepoint,

dimemionkss

N = original oil in place, L3, STB

NP = cuumfative oil production, L3, STB

Np, = cumulative oil producdon during transient period,

L3 s~

p = pressure, mlLt2, psia

Pb = bubblepoint pressure, m/Lt2, psia

p. = reservoir pressure, mJLt2 psia

pwf = flowing BHP, ro/L.t2, psia

q. = oil flow rate, L3/t, STB/D

(qJ_ = ofl flOW mte at

P~j=o, AOR L3k STBD

r = radial distance Ilom qenter of well, L, h

rd = external

drainage radim, L, II

r, = d~age Iafis, L, fl

rW = we~bOre radi~, L, H

s = sh .q=&t

S8, = criticzl gaz saturation, dimensionless, fraction

SO = Oil saturation, dimerisioidess, fraction

SOi = oil saturation at initial conditions, dimemionk.ss,

fmction

SW =

connat+water saturation, dimensionless, IYaction

h = pore size distribution iodex, diroeosionkzs

P. = 03 viscosity, m/Lt, cp

Y.i = ofi Viscosiv at initial conditions, m/Lt, cp


6/8

Mark A. Kilns is a

district engineer for

Chevron U.S.A.

Production Co. In

Lost Hills, .CA,

whers his responsl-

bllitles include d8-

slgn and lmplemen-

tat[on of a Lost Hills

dlatomite water-

flood and direction

Kilns

Clark of the new district

well-development

program. He previously was a petroleum engineering profes-

sor at Penn8ylv8nia St8te U. and a consultant, and he worked

in drilling, produ.zfion, and reservoir engineering for chevron

on the U.S. gulf cdast and In the Permian Sash and San Joa-

quin valley. Kilns holds MS and PhD degrees in petroleum

and n8tural gas engineering from Pennsylvania State U. He

was 1983-S4 Pittsburgh Petroleum Section chairman, Hobbs

Section 1989-90 membership chairman, a 7984-88 Technical

Editor, a 19s4-67 Career Guidance Committee member, 1988-

91 member and 1991-92 chairman of the Distinguished Leo-

turer Committee, and the 1982-83 chairman of the Education

and Professionalism Technical Committee. Klins received the

19S6 SPE Outstanding Young Member Award.

Jame8 W.

Clark Ill is a ga8- and

waterdrive engineer for Chevron Pe-

troleum Techtiology Co. Inc. in L8 Habr8, CA. His responsi-

bilities include ressrvoir consulting and simulation of U.S. and

international fields for Chevron affiliates. He previously held

various reservoir and production engineering assignments

in Louisiana, Arkansas, New Mexico, and Texas. Clark holds

SS and MS degrees in petroleum engineering from Texas A&L

U. He was the Permian Basin Sstion 1980-91 continuing edu-

cation director and 1636-90 Hobbs Section publicily chalnqan.

Acknowledgments

We thank Chevron 7J.S .A. Produ&on Co. hc. for permission

publish this paper. Special thanks go to Phoebe Frisbie for typing

the manuscript md to Becky Davis for figure preparation.

References

1. Fetkovich, M.K.: The Isochronal Testing of Oil Wells, paper SPE

4529 presented at tie 1973 SPE Annual Meeting, Las Vegas, Sept. 30

Ott. 3.

2. Eickmeier,

J.R.: HOW to Accurately Predict

Fume Well Prcdnctivi-

ties, World Oil (l&y 1968) 99,

3. U&i, D.C. and Blount, E. M.: Pivot Point Method Quickly Predicts

Well Pecfmmance,s,

Wo,fd Oil (My

S982) 153.

4. Vogel, J. V.: gInOow Performance Relatiombips for 2cduti0n-GasDive

Wells,,> JPT.(Jan. 1968) 83; Trans., AOvfE, 243.

5. Klim, MA. and M+ichm, M. W.: Tntlow Performance Relationships

for Dammd or Immoved Wells Frcducine Under Si.tion-Gas Dtie.

JPT (Dc: 1992) i357.

6. Weller, W.T.: Reservok Performance Dining IW@Phase Flow, JPT

(Feb. 19661 2Q Trans., A3ME, 237.

7. hkkat. M.: The Prodcdm Histories of Oil Pm&wing Gas-Drive

Reservoirs,, J.

Applied Physics (1943) 16, 147.

8.

Haw dns. M. F.: A Note on the Skin Effect.,, Trans.. A3ME (1956)

207, 356.

9.

Dranchuk, P.M., Fmrvis, R.A., and Robinson, D.B.:

Computer Cd-

cul.ati.ms of Natural Gas Compressibility Factors Using the N@ing

and Katz Correlation, Jam of Petroleum Technical Series, No. f

74-0C08, Edmonton (1974) 1.

10. k. A.L.. Gonzalez. M. H.. and E&in. B. E.: The Viscosifv of Na

& Gases, JPT

(April 1966) 9n Trans., AIME, 237. .

11. Vazquez, M. and Beggs, H.D.: Correlation for Fluid PhysicaI PmP

erty pmdicdon,

JPT

(June 1980) 968.

12. Bmdim. N.T.: Relative Permeabiiiw Calculations From Pore Size

DNrib&n Data,,, Tram., - (i953) 196, 71

S1

Metric Conversion Factors

acre X 4.046 S73

E01 = ha

API 141.5/(131.5+ API) = gk?ms

bbl X 1.5S9 S73 E01 = ms

Cp x 1.0*

E03 = Pas

II X 3.048* E01 = m

ma

x 9.S69 233 E04 = pmz

psi x 6.S94 757 E+OO = Wa

.Covwsron Wt., is ,=. . SP33R33

original SPE manuwlpt mewed for review Sm. 2,1990. Revised manuscript mcdved

Jan. 22, 1993. Paper accepled (0, pubbcatim March 4, 1993, Pwer (SPE 20724] IIrs

w-em at the 1990 SPE Am.a Tech.rca C.nfe~.@ a.d ~fib[fi.. held i. N.w

Orleans sem 23-26.


7/8

SP

1.0

0.9

0.8

a)

1.20 T

1.15-

&

c

l.lo -

Z

Sk

Sk

A Sk

0

0

0.7

0.6

1

0.5

1

o

0.4

ii

A

-1

0 ti

0.2 +

0.1-

R, .,.,.,.,.,.,,,

Oo

.

m

II

i o

0.0

A

i

1.00 1 1 1 1 I t 1

I

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Pr/Pb

PrlPb

PIGIJRE 6

EffectONSkmon IhcDnncmmnk.x Fh>wExpnmnt, nlnr,,

FJGIJRE 5

Dimcmimfss F lmvCon.want.CfCP~ m aFuntxrnnof ~mnlm Fnmnc.

1.2

~n

Skin = O

1.0

= Sxjn = 6

A Skin=-4

0.8

8

4

0.6

0.4

1

i-sL---

0

Average Absolute Error

1

o

Maximum Absolute Error 2

Average Error

-12

.1 i 10

100

1000 IOooo

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Actual Qomax (BOPD)

Pr/Pb

FIGURE 7

EfkuofSkinon hc~

Jmticmslam,acpb

FIGIJRE 8

&rnr Adyss UsingIJKFdkovich Appmxh,


8/8

I

(~dOEl) Wd loA~

XWUO~

o

o

.

-7

o

t-

9

I-

o

o

adofi WWJ IX Xew)

Documents

20724-An Improved Method to Predict Future Ipr Curves