USMS01!3454 Material Balance Application to Water-Drive Gas

Reservoirs To Predict Gas in Place and Future ForecastsM. Ahal Abbasi, Mari Gas Co. Ltd.

‘9,

-M 198SSOOWY of Petroleum~neeraThismanuacriptwaapvidadtotheSccietyofPetroleumEngineerafcrdiatributionandpoasiblepublicationinanSPEjoumal. Thematerial issubjecttocorrectionbythe ●uthor(s).Perrnkeiontocopyis reatrbd to an abetractof notmorethan~~-n WmtoSPE SookOrderOept.,LibratyTechnician,P.O.Sox833SSS,

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“~~,yl-J TOW3RF%WKPREDICT GAS /l’h/ PLACE ~ND FUTURE FORECASTS

J~Pj ~ 7 15!$I M, AJMAL ABBASl, MS (P.E) TULSA OKLAHOMA - FtTARIGAS FIELD-PAKIS-~AN

C?E

puELiC/{~lONs SUMMARY:-This paper presents a description at Material (3alance and app!LCatiOn to evaluation

of Gas Reserves of the ivlari Gas Field located in Pakistan. This method is

applied precisely and accurately to predict Gas in place and future performance,of Gas Reservoir producing under partially or active water drive conditions.

lNl”RODUCTION:-

CiENERAL:-

The Mari Gas Field is located about 270 mi Ies North East of Karachi, Pakistan

and was discovered by the drilling and testing of Mari X-1 in August, 1957,

.

The principal Gas producing formation is the Lower Kirthar Zone ’13t Lime stone

which occurs at a depth of about 2300 ft. Thus far this reservoir has been

developed in four phases:-

One in 1966, another in late 1977, a third in 1981 and a fourth in 1985. After

each phase of Development Dr’iIIing, Reserves evaluation has been done the Gas

are as under:-

RecoveryFactor

75*3O

75,00

67,50-

65.00

in place, and recoverable reserves evaluated each time

Gas in Place RecoverableYEAR Bill ion SCF Proved Reserves

July - 1967 2854 2149

March u 1979 4013 3010

March - 1982 4970 3355

March - 1988 ’7914 !5144

*.Conventional Volumetric and Simulation models were used

Gas in place’ and future forecasts. Duriny the first phase of

in 1966, five wells were drilled for an off take rate of 40

,!e

~for estimating the

C)evelopment drilling

MMEX2FD from the

field. In 1977 another ei$ht wells were drilled and one well was recompleted

to incr%ase the of ftake from 40 m 120 MIMSCFD. Then in 1981, seven more

WQIIS were drilled and completed inordt?r to increase the off take rate from 120

to 200 MMSCFO* The fourth phase was carried out in 1985, during which 27

contd..,p/2,.,,

SPE l$Ht:- 2 -:

.

Development wel Is were dril led and completed and thus the of ftake rate

from 200 to 300 MivlSCFD. The current- maximum commitment for

is 300 MMSCFD. As a result of the drilling compaign in 1985 t

Seismic Surveys, the productive limits of the lower kirthar Zone ‘B

were extended. The main purpose of this study is to redetermine the I

gas reserves and the production potential of the field. As of OC

616.724 Billion SCF of gas has been produced out of a total of 7

SCF of recoverable gas the material balance application wi II not giv

results. In order to apply the gas material balance at early times,

wi II present the methods used for predicting the gas in place i

performance of the reservoir as accurately as possible for a partially \

reservoir.

GEOLOGICAL AND PET’ROPHYSICAL DETAILS STRUCTURE:-

A structure map drawn on top of the principal producing zone in the

the lower kirthar zone %’ Iimestone, is presented on Fig-1. The

is approxi inatel y 285 ft thick. The map was prepared using wel I dril I i

open hole logs, and seismic interpretations. The structure is a f

dipping (the average dip is approximately 1 de~ree) anticline. Litt

has been noted. Some uncertain it y sti II exists as to the exact

attitude on the flanks of the structure.

PETROPt-tYSICAL PROPERTIES: -

All available well logs and core analysis information were quantitative

to determine porosity, permeability, and water sturation. Average

these petrophysical properties are as follows:-

Porosity 22.6

Permeability, md 10-50 *1

,Water saturation, percent 26 I

Detailed mappiny and analysis indicate that, although the reservoir is

consistent in thickness and Iithology, iJOroslty tends to decrease fro

nlat,ely 23 percent in the Nofth West portion of the fiel(’ .to about

in the South. Fwr(lleabi Iity tends to flow the same trend..

-,

.

.

,,,,

~,,!:, I :- ‘3 .“ :-*:’!!

:, *E 1“94.54“,

GAS WATER CONTACT:.

As indicated on” Fig-1 the lower kirthar zone 18) is completely underlain by

an original gas water contact at an average depth of 2250 ft S.S. Some

variation in the depth of the~ Gas Water (Mntact has been observed due to either

changes. in reservoir rock ctiaractetistics~ localised water invasion, or a gently,,North to South slope of the contact. For practical reasons an average contact

of 2,250 ft. S.S has been used’ in the ~Material Balance calcu Iat ions...;

GAS PROPE#.TIES:-

The produced gas has a gross calorif ic value of 739 BTU/SCF and is composed,.of Methane (73 percent), Carbon-di-Oxide (7 percent) and Nitrogen (20 Percent]

on the average. The composition of the gas varies areally. The Carbon-

di-Oxide content $rades ~f rom less than 3 “~rcent in the North West portion

of the field to appro+i~ately 15 ~rcent in ~the Sbuth East, Average” initial1/

reservoir” gas ,properfi@s at a datum level of 2135 ft S.S “are ~ follow;-,,~ !,

i ‘“ :

Initial Preqwre

Initial Te~per?+”ve

Gas Deviation t ..$tor (Z)

Gas Volume Factor (1/Bgi)

Specific Gravity (Aiv 21.0)

Gas Viscosity

1184 PSIA

’133 ‘F

0.9250

75.11 SCF/ft=

0.705

.0137 CP

Gas Gradient .028 PS1/ft.

WATER INFLUX:,..

In response to a pressure drop in the reservoir the acquifer reacts to Offset

or retard pressure decline by providing a source of water influx or encroachment

by (a) expansion of the water (b) expansion of other known o.r unknown Hydro-.,.carbon accumulations in the acqui fer rock (c) cornpressibilit~ of the acquifer

rock and or (d) artesion flow where the acquifer ‘rises to a level above the

reservoir! whether it out crops or not and whethkr or not ttie out crop is. .replenished by surface water, From an, analytical point of view the acquifer

may be considered an independent unit which supplies water to a ,reservoir in

response only to the time variations in the boundary ~pressure, i.e., the average

pressure at the GaMNater contact’. The boundary pressure’ wil,l general Iy be

,

,,

contd ....~/4 . ...::

b,

:- 4 -:

higher than the average reservoir pressure, however, in

tion is made between the two, the average reservoir

the average boundary pressure, Water encroachment,

encroachment, d We/dt have been expressed with good

as functions of the boundary pressure p and time t

equations:-

(a) Schilthuis steady state:-

We = K ft (Pi-P) dt]-------l.O

d We = K% (Pi - P) ---------

dt,,

SEE19454

some studies no distinc-

pressure being used for

We and rate of water

precision in many cases

by one of the fOllOwfl!J

1.1

Where K is the water Influx constant in barrels per day per pounds per square

inch and (Pi-P) is the boundary pressure droP in pounds Per s~.--re inch”

(b) Hurst Modified Steady State:-

k

We=Ct (Pi - P) dt

Log at

dWe ‘= C (Pi - P) ------- 1.1

dt Log at

Where C is the water inf Iux constant in barrels per day per pounds per squ:.re.

inch (Pi - P) is the boundary pressure drop in pounds $er square inch, and ‘a’

is a time conversion constant which depends upon the units of, t~e time ‘tl.

(c) Van Everdingen and Hurst Unsteady state:-

We = B DP X Q (t) ---- 1.2

Where ‘~’13is the water Influx constant in barrels per poufl~s per square inch,

DP is the pressure decre[nent in pounds per square inch, and Q(t) is the

dimensionless water influx, which is a function of dimensionless time.

Dimensionless water Influx which enters the reservoit

drop for any valut? of ctilnensionless time, tll, which,

“3tl-) = 6.323 X 10 ~ Kt

9UCe rwz

in response to unit pressure

is related to real tinle bv:-

--”-- (1*3)

ccmcd,,.,p/5. *,,

.

I

I

i

i

I

ii

Where K= Millidarcys

t= Days

0= Porosity, factor

u= Viscosity, centipoise

Ce . Volume per pore volume per pound pa. square inch

rw = Reservoir radius, feet.l>-.-;.,—----

Dimensionless time is used so that separate calcul~tions wiII not be necessary.for each ~ &uifer. The conversion to real volume i.”.-barrels is made using the

constant

B= 1.119 x O Ce x rw2 x Q ---— 1.4

360

B ‘is the water lnf Iux constant in barrels per pounds per square inch and Q is

the angle subtended by the reservoir circumference, e.g., for a full circle

Q = 360° and for a semi circular reservoir against a fau!t. Q = 160° Ce is .ir

volume per pore volume per sound per square inoh~ rw and h are in feet. Tha

Q (t) values are found from Fig-1 ffom the dimensionless time. The water InfIu>

is t~ found using equation (2).

GAS MATERIAL” BALANCE:-

The Material Balance method may be used to calculate the initial gas in placx

only to the reservoir as a whole, because of the migration of gas from Om

portion of the reservoir to another in both volumetric and water drive reservoirs

The conservation of mass may be applied to gas reservoirs to give the follow in!

material balanc&.-

Weight of Gas = Weight initially

Produced. in the reservoir;$*.

The balance may also be made on

Weight remaining

the reservoir ..k“

any definabie component,

in

ie I

e.g., “Methane.

Where the composition of the production is constant, the standardcubic feet

both produced and remaining in the reservoir are directly proportional to the

masses, and a materiai balance may be made in terms of standard cubic feet,

as.. .

contd...6,6,., .

1

i

:- 6 -: WE 19454 -

SCF Produced = SCF initially - SCF remaining in

from the reservoir in the reservoir the reservoir

Finally, a material balance may be made in terms of moles of

np = ni - nf ---------- 1.5

gas as

The subscripts p, i and f stand for produced, initial and final respectively.

The term final means at some later stage of production rather than necessarily

at abandonment. If Vi is the initial gas pore volume in cubic feet and if at

the final pressure Pf, We cubic feet of water has encroached into the reservoir

and Wp cubic feet of water has been produced from the reservoir, then the

final volume Vf after producing Gp standard cubic feet of gas is

Vf = Vi - We + Rw Wp ------- 1.6

6W is the volume factor for the water in

Vi and Vf are gas pore volumes, i.e., they

terms in equation 1.1 may be replaced by

Eqn. iO Pi Vi = P2 V2 and

Ti 12

as-

units of barrels per surface tt.rrelm

do not include connate water. The

their equivalents using the gas /aw

equation 1.2

. .

Pi Vi --=— Pf (Vi-We + Bw WD) ------ 1.7

Tsc ZiT . ZfT

Gp is the standard cubic feet of produced gas at siandar~ pressure and

temperature, Psc and Tsc.

Equation 1.3 may be written in terms of gas volume factors Bgi and Bgf by

solving it for Gp as

Gp = Pi Tsc x Vi - Pf Tsc (Vi-We+Bw Wp)

Psc ZiT Psc Zft

But Byi = Pi Tsc SCF/CUFT—.PscZiT

,:,;! 13gf = Pf Tsc SCF/CUFT

Psc Zft

Then Gp = Bgi Vi - Bgf (Vi - We + Bw Wp)

Dividing through by Ryf and expanding

Gp=G(l- 1 )+ We- E3wWp.— —13gf 13gf Bgi

contd..ip/7..

. :- 7 -:

If the gas volume factor are

feet instead of standard cubic

expressed in units of cubic feet per standard cubic

feet per cubi,c feet, they will be in the numurator,

and the equation reduces to the simpler form,

Gp Bgf = G (Bgf- Bgi) + We - Bw Wp ------ 1.9

It is recalled that the gas volume factOr is commonly expressed in fOur sets

of units as tuft/scf, bbl/scf, scf/tuft and scf/bbl. Equations containing the gas

volume factor must therefore be checked caref uIIy to see that the proper units

ate used. Also in equation 1.5 G and Gp must be expressed at the same base

temperature and pressure as the gas volume factOr. GP Bgf is the volume of

the produced gas at the pressure pff G (B9f - Bgi) is the change in volume of

the initial gas when expanded from Pi to Pfs

of water ● Influx and production respectively,

conceptual forrn as-

. .. . . . . . . . ., .. —-.ana we and 5W wp are me volumes,

equation 1.5 may be expressed in

[ Production ] = [ Expansion ] + [ Water Influx ] - (

CASE H;STORY:-

Water Influx calculations were performed on Mari

Water Production ]

Reservoir to evaluate We and

Gas in place from material balance for Gas reservoir. Future predictions were

made with the Water Influx and material balance calculations. Hurst modified

steady state equation 1.1 and Van everding@n and Hurst unsteady state equation

.1.2 were used for water Inf Iux CalCUlatiOfISi

The Reservoir parameters used for water Influx calculations are given in Table-

I. The fluid flux Q(t) at different times were calculated from Fig-1 (a). The

estimated f Iuid flux Q(t) is plotted versus tD in Fig-1 [b) Fig-1 (c) is’ a semi log

plot of Q(t) versus tD. The water Influx calculated by Van everdingen and Hurst

equation, 1.2 are given in Table-2. The period covered for water Influx.

calculati&s shows 1967 til I 1987 for actual measured field ‘Jdata. After year

1987 ti II year 2000 the predicted values were used for, calculations. For future

projections of cunwiative gas and cumulative water, actual figures were plotted

versus time ti II year 1987 and extrapolated to year 2000, Fig-2 and Fi&3 are

plots of cumulative gas and water production- This study presents a 300

MivlSCFD with drawal rate from the field, Calculated cumulative water Inflbx.were piotted a@inst reservoir pressure, a constant drop of 15 psi per yesr

I

Contd..i.pik..

.,

:- 8, -* SW 19454

was calculated for a 300 [viIMSCFD with drawal rate with the existing production

wells. This plot is given in Fi@3, it is noted that one million tuft of water

encroached the reservoir for one psi drop in reservoir pressure. To test the

accuracy of the steady state equation 1.0 in describing the water InfIux, the

Influx rate is fOund at each time period, either numerically as shown in

Table-2, or ,by taking the slopes fronl a plot of We versus t. It’ is noted values

of ‘K’ decline till year 1977 when the gas off take was 40 MMSCFD, increased

to 236 cft/day/psi when the was off take increased to 120 MMSCFD in year 1987

and followed a declining trend till year 1985. The value of ‘K’ increased to

297 in year 19%6 and to 322 tuft/day/ixi in year 1987 when the field off take

rate increased to 300 MMSCFD. There after it followed a declining trend, titl

year 2000 using the predicted reservoir performance data. This indicates that

steady state equation 1.0 does not adequately describe the water Inf Iux. For

some studies, however reliable reservoir predictions may be based on values of

‘K’ obtained from extrapolating a graph of ‘K’ plotted versus cumulativO

production or time as shown in Fig-S. If the value of ‘K’ had declined in Mari

Field instead of remaining substant;ally constant at 200 tuft/0/psi the calcu-

lations of future pressures would be the same, except for usinu a declining value

of ‘K’. For example, if a plot of()

%’ versus time Fig-5 showed that’ ‘K’ was

200 tuft/day/psi when the pressure was 1012 psi Fi@. in year 1991

)

( Fig-5

& 6 @after year 1991 it is decreasing at the rate of 5 tuft/D/p$ia mr year.

The water Inf Iux data of Table-2 may next be tested for adequate representation

by equation 1.1

d We = C (Pi-P)/log at . The values

dt

have already been determined in Table-2 so

K Ioga + Klogt =

K is not a constant, however, but is now

may be weighted by time to give

Ktloga+Ktlogt=ct

Roth equation 2,0 and 2,1 may be written

following summation equations obtained.

of (d We/at)/Pi J P) = K

equation 1,1 may be written oas’

c -------- 2.0 ‘“

replaced by C a;d A. Equation 2.(

----------- 2.1

for each of n time periods and th~

Logax EKi+EKixlogti= nc

:. 9 -: SEE‘19454

Lcaga x E KI x ti + E Ki x ti x log ti = C E t! -------2.3

Table Ill shows the steps used to obtain the summation values to place i(

equation 2.3 the primary data having been obtained from Table Ill. Then:-

7!506 log a + 26126 = 32 C

36516060 log a + 139540026 = 192720 C

Wowing these equations simultaneously a = .0088 and C = 334.5.

Then equation 1.1 representing the wat@r Influx may be written

d We = 334.5 (Pi -P) or We=

~

334.5 t jPi - P) dt

dt log .0088 t o log 0.0088 t

Using a = 0,0088 and c = 334.5 the values of the water Influx rates have bee

calculated in column 10 of Table Ill. Column 11 shows the Influx rate

calculated from equation 1J? Van Everdingin and Hurst, The good agreemen

between the two is shown in Fig-7. The cumulative water Inlfux is plotte

versus “ cumulative gas produced shown in Fig=8. The r?te of increase c

cumulative water Influx is estimated as 74000 tuft/BSCF. This is also plotte

versus time itrr Fig=9, it is seen from Fig-9 that We increases at 14 x 106 Cu1

per year, These calculated rates would be helpful in estimating the total L%

in place and proved reserves and future pt?rf~rmance of gas reservoir

producing under partially water drive ccmditons, Fify10 is a structural ma

. of Iowdr kirtnar Zcme ‘B1 lime stone, rnari , reservoir on which the study

performed.

.

*.

,,.

1,

2*

3,

4,

5.

&

7.

8.

9.

10.

11,

120

13.

:- 10 -:

~ABLE - I

RESERVOIR DATA

Initial Reservoir Pressure

Area Inside GWC Eastern

Area Inside (3WC Western

Area Inside Southern

Area Inside - 2150 Ft *

Area Outside - 2150 Ft *

Porosity @Average

Effective Compressibi lit y Average Ce

Permeabi Iit y Formation Average K

Wel I Bore Radius

Formation Thickness h

Water Influx Constant ‘B’ in Van

Everdingen Equation

Water Saturation Sw Average

= 1164 PSIA

= 62,307 ACRES

= 42,007 ACRES

,% 77,103 ACRES

= 93,310 ACRES

= 92,107 ACRES

= ?26

= .000776 PSI-l

= 12.1 md

= 0.29 Ft

= 170 Ft

= ,00281 Bf3LS/DAY

PER LBS PER

= 0s261 FRACTION

* Area Inside 2150 Ft Contour is evaluated as Proved area and Outsi

2150 Ft. is evaluated as probable reserves.

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:- 15 -: ‘SPE 19454.

~STIMATION GF GAS IN PLACE (PF.OVED):-.

Gas in place proved is estimated by equation (1,9)

Which is :-

Gp”f3gf = G (Bgf - Bgi) + We - BW WP.

Bg = 0.02829 ZTT

Bgi = 0.02829 .849 X 592 = ,0122151164

At the end of year 2000

42x106 MM US GALS = 5,62 X 10b CUFT FROM FIG.(3)

1.03 APPROX BBL/SURFACE BBL.

2.059 x 10’2 SCF FROM FIG (2).

191.6 x 106 CUFT FROM FIG (9)

883 FROM FIG (6) E3gf = .02829 X .876x592 = ,016649~

(3P 9gf - We + Bw Wp(13gi - Bgi)

2.059 x 1012(.0166149) - 191.6x106 + (1.03) (5.62x106~

(.0166149 - .012215)

3.421 x 1010- 1.9739x 108

.0043999

7.73 x 1012 SCF Proved Gas in place as the deplet

taken place in the proved area and the wells are

in the proved area. Therefore this Gas in place

regarded as proved Gas in place.

ESTIMATION OF GAS IN PLACE RECOVERABLE AND TC)TAI- GASz~

FROM FIG. 8 d We= .000108 CUFT/SCF

d GP ,FROM’”FIG. 4 dP = 1 PSF/MMCUFT

d We

d We x dP=’ ,000108 CUFT/SCF X lPS!/’MMCUFTa= TKwe

dP 5 .000IWJ PS1/SCF

d G? 106

9 SPE 19454. :- 16 -:

The economical analysis recommended the following assumptions.

1, At abandonment conditions 1 MMSCFD per well would be economic

2* At this rate well head pressure of 300 psi would be required.

3. A reservoir pressure of 376 psi would be maintained,

Therefore at these conditions.

dP = 1164 - 376 = 788 Psi

. d GP = 106 SCF x 788 psi——.000108 psi

“ b+GP = 7.30 x 10’2 SCF Recoverable Gas.

This also shows that proved reserves is equivalent to recov~rable Gas.

For estimating Total Gas in vlrace dp = 1164 - 0 = 1164 psi

d GP = 106SCF X 1164 = 10.78 x 10‘2 SCF = G (Total Gas in vlace)——,000108 psi

ESTIMATION OF RECGVERY FACTOR ,--

Recovery factor can be estimated by the following relation:-

Recovery factor = (3R X 100T

= 7.3 x 1012x 100 = 67.7 APPROX 68%

\ 10.78 x ‘1012

CONCLUDING REMARKS

The Gas/Water production data and reservoir pressures from we! I testinkl \

#rejected to future tii,,es for estii,latin~ the Gas in place by material bala..It is seen that lnaterial balance cannot be applied Successfully” during early, t

to accurately @’edict the Gas in place and recovery factor froil) existing I

and equiprnellts. Froln this study we also conclude that fnaterial balance

be successful Iy a~pl ied when 20°~ of the Gas in place is @roducedt Resw

pressures and water oroductmn is very iiflportant for a field producing u

Vartially or active vikitw drive conditions!accurate mkmurtiliwnt of t..

paralnetersisthereforerecoinmended.

ccmtds..P/l

*

:- 17 -:

The Gas in place determined by material balance in this paper c;omes to.,2

10.78 X 10 SCF compares wel I with the Gas in place calculated by Geological

mapping which is 9.71 x 1012 SCF. Also the Gas in place calculated by

volumetric methods during the model initial isation phase is estirfiated as

9.65 x 1012 SCF. The three values matches wel 1, hence. this method can be

regarded as a reliable method to predicting Gas in place and future performan-

ce of a reservoir producing under partially or active water drive conditions.

In Mari, a weak water drive is present and

are “very important to monitor the future

NOMENCLATURE

a

8

Bg

Bw

c

Ce

G

GR

GP

h

k

k

P

Q(t) “.:

rw

t

tD

we

Wp

. z

G

Time conversion constant

Water Influx contant in(Vaneverdingin Equation)

future accurate pressure measurements

performance presented in this paper.

bbls/day per pounds per square incf

Gas volume factor, tuft/scf

Formation vol. factor water, bbi/surface bbl

Water InfnJx constant in bbls/day Wr Pounds @r square i~l(Hurst Modified Equation)

Effective compressibility evaluated at Pav, PSIA

Total Gas in place, SCF

Recoverable Gas, SCF

produced Gas, SCF

Formation thickness, feet f

Water Influx constant in bbls/day per pnllflds per square incl(Schilthuis Equation)

Permeability (red)

Reservoir pressure (PSIA)

Dimensionless water Influx, a function of dimensionless ti~e.

WelI bore radius, feet

Producing time, days

Dimensionless time

Cumulative water Influx, bbls

Cumulative water produced, cubic feet

Gas deviation factor, dimensionless

Porosity, dimensionless

contd...,p/ 18.,

.

u

Q.. d GP/dt

d Wp/dt

d We/alp

dk/dt

dP/dt

D We/D t

d We/dGp

d We/dt

SUBSCRIPTS

i =

f =

SPE 19454:- 18 -:

Viscosity, CP

Angle subtended by the reservoir circumference, degrees

Change in gas produced with respect to time, bscf/year

Change in currmlative water produced with respect to timeMMGALS/YEAR

Change in cumulative water inf Iux wit’, respect to pressureMivlCUFT/PSl

Change in water Influx constant with respect to time, CUFTDAY/PSIA/YEAR

Change irr reservoir pressure with respect to time

Chnage in water Influx rate with respect to time, CUFT’DAY/YEAR

Change in cumulative water Influx with respect to Gaproduced, CUFT/SCF

Change in cumulative water influx with respect to timfCUFT/YEAR

InitialFuture

Gas

Standard conditions

Recoverable

Produced

Water

ACKNOWLEDGEMENT

I acknowledge the support of Mari Gas Co. Ltd., Pakistan which sponsored wor

to utilise Reservoir and Testing Data of well leading to this paper, an

perrnjssion granted for publication of this paPer by Mari,, Gas COD is al:

appreciated.

REFERENCES—.—1, R.J,Schilthui& “Active (Ii I and Reservoir Energy” Trans. AIM

(1936),118,376

.2* S.J.Pirscm, Elelnents of oil Reservoir Engineering, 2nd EC

(New York: McGraw Hill Book CQWJanY ln~~t 195~h P* 60

contd,,.p/1%

3.

4.

w

:- 19 -:

A.F. Van Everdingen and ‘N. Hurst, “The Application of the Laplace

Transformation to flow problems in Reservoirs,” Trans, AIME (1949),

186, 305.

B.C. Craft and M.F. Hawkins, “ Apll ied Petroleum Reservoir

Engineering, Prentice Hall, Inc., Englewood Cliffs, N.J”.

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LEGEND

+2 GAS WELLM GAS WELL PLUGGED+ DRY ANO AEANOONEO ml* OELINEATON WELL

—