SPE-14359-MS

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SPE 14359

Evaluation of Naturally Fractured Gas Reservoirs Through

Pressure Transient Testing

by F. Samani ego-V. * and H. Ci nco- Ley*, PEMEX and UNAM, and D. Monti el - H. ,PEMEX

SPE Members

SPE

Copyright19S5, Societyof Petroleum Engineers

This paper was prepared for presentationat the S43thAnnualTechnicsl Conference and Exhibitionof the Society of Petroleum Engineers held in Lss

Vegas, NV September 22-25, 19S5.

This paper waa eelscted for presentation by an SPE Program Committeefollowingreview of informationcontained in an abstractsubmittedby the

author(s).Contentsof the paper, aa presented, have not bean reviewed by the Society of PetroleumEngineers and are subject to correctionby the

author(s).The material, as presented, doas notnecessarily raflsctany positionof tha Seciety of Petroleum Enginaers, itsofficers,or membsra. Papsra

presented at SPE meetingsare subjectto pubfiiation review by Editorial Committees of the Society of Petroleum Engineera. Permission to copy is

rastrictarlto an nhewm-1nf n -t nmra thsn %lr l w.-t rr ls I lh ,.ztmti rm . m-w nnt ha r?nnied Tha ahetrae t shnt, ld crmta in mmnnictmti ,n acknnwldnment o fwham

----- ----- ---- . —-..”---- . .. . . ... . . . ... . ---- . .. . . . . .... . . . ... . .- . ... . .- . ----r----

-------------------- . ..-.. .--. .-r ----------- .- . . .--=...-. ..-, . .-----

and by whom the paper is presantsd. Write PublicationsManager, SPE, P.O. Box SS38S6, Richardson,TX 75083-S6S6. Telex, 7309S9 SPEDAL.

LBSTRACT

w thin a 1i mestone formati on, contai ni ng numerous

Fi el d cases are presented of natural l y fractured

hai rl i ne fr actures.

The mai n assumpti on i mpl i ct i n

thei r model i s that the fractures present i n the dol o-

as reservoi rs where the mai n storage capaci ty i s i n

;hef ractures, since the matri x permeabi l i ty i s

mte cause an overal l i ncrease i n apparent permeabi l -

I egl i gi bl ef or practi cal purposes. Wel l s i n these

i ty, averaged over a l arge vol ume of reservoi r. Thi s

‘ eservoi rs i ni ti al l y exhi bi t hi gh producti vi ty. These

model fal l s i nto the category of composit e reservoi r

‘ i ei fi sare l ocated i n the north of Mexi co. Upon compi e-

p~~b~ern~due to the acci mnt+nn ~,$~~ +ha wall emrurn,n+–

ue.?u,,,p u ,“,,

IJIG w.=, 1 Lull.ltull 1-

; i onof the expl oratory wel l s a set of mul t i pl e rate

cates w th the fracture systemonl y vi a the adj acent

j estswere carri ed out i n open hol e condi ti ons. Al l

rel ati vel y ti ght matri x.

Through the use of thi s

- r -—* : - _

. . ..-41-L1- <.-44----- *L-L *L- . . . . . . . . . . . ..- ----

rllurwmc]uri ctvdl Idule lrlulcdLes crksL me reservulrs dre

model they were abl e to obtai n re~erv~i r i nf~rmat~~n

ocated i n strati graphi c traps i n uni formy fractured

that was reasonabl e i n l i ght of known geol ogi c and

I ackstonef ormati ons of Cretaceous age. Pecul i ar to

core data.

; hesecases i s the fact that pseudosteady-state fl ow

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Strobel , Gul ati and Ramey20 have reported resul ts

2

“EVALUATION OF NATURALLY FRACTURED GAS RESERVOI RS THROUGH PRESSURE TRANSIENT TESTING”

SPE 14359

cases i s the fact that pseudosteady-state fl ow condi -

t ions are reached i n a very shor t t ime (about 2 to 4

hours) .

GENERAL CHARACTERI STI CS OF THESE RESERVOI RS

The reservoi rs A and B di scussed i n thi s paper

are natural l y fractured. Al l i nformati on avai l abl e

i ndi cates that the fractured zone i s very l ocal i zed

and i s the resul t of the tectoni c stresses caused by

the Laramdi c orogeny. Wel l s A-1 and

B-1

are l ocated

a di stance of 32 ml es apart and produce froma pack-

stone of Lower Cretaceous age. wel l l oggi ng and petro-

physical i nformati on cl earl y show the presence of fr ac-

tures and a ti ght matri x.

These reservoi rs are geographi cal l y l ocated i n the

North of Mexi co. Producti on i n both expl oratory wel l s

A-1

and

B-1

i s mai nl y due to the presence of these

fractures, si nce the matr ix as stated has a very l ow

permeabi l i ty,

COMMENTS ON DI AGNOSIS OF FLOWREGI ME

Vari abl e fl ow rate condi ti ons are frequentl y pres-

ent when testi ng gas wel l s. These are someti mes i nher-

ent t o t he natur e of t he r eser voi r i t sel f , i . e. l ow

permeabi l i ty, or i n other cases due to the desi gn of

the test i n accordance to specif i c purposes. Regardi ng

thi s l ast case, a typi cal exampl e i s that of a conven-

t i onal back pressure test i n whi ch the wel l f l ows at

several di ff erent fl ow rates. Pressure data regi stered

under these condi ti ons can be normal i zed di vi di ng the

pressure drop or real gas potenti al drop by the speci f-

~~ ~Q~~~~~~ f~~w p~~~,

Pesul ti r i gi i ia graph as that

shown i n Fi g. 1. The funct i on f(t) on the hor izontal

axi s i s str ict ly rel ated to the fl ow condi t i ons prevai l

i ng dur i ng t he t est , Of i nt er est t o us i n t hi s st udy i s

the pressure behavi or for pseudosteady state fl ow whi t

i n terms of di mensionl ess vari abl es may be wri tten as

fol l ows:

mwD=

2ntDA+$l n(~2)+$l n(-

2 ~; 58)+S+Dq

w

1)

Thus, mul ti pl e rate pseudosteady- state test h“ta

shoul d appear as a strai ght l i ne when pl otted as

mPi )- mPwf )

N ( qj - qj - l ) (t -t j - l )

qN

Vs ~

J=l

qN

The shi f t i ng of t he st rai ght l i nes of Fi g. 1 i s

due to the presence of hi gh vel oci ty fl ow aff ecti ng

the test . Thi s bei ng the case, the i ntercepts can be

~~ed to e~t~mate P. a~~ the h+ h wnl e++I, fim-=r:-:-~+

,,~11 TGlouley GUCIIIVI=IIL

D, provided a val ; g for the skin factor s i s avai l able

t hr ough a gr aph of [Mp) / qI . nt vs q as w l l be fur thel

di scussed i n

the next sectioa. This procedure is in-

deed si ml ar to that used, i n the seml ogari thmc anal -

ysi s of hi gh vel oci ty f l ow test23.

A powerful tool that has greatl y advanced our

abi l i ty to i nterpret t ransi ent test data i s the pres-

sure deri vati ve approach, that when used together w th

the cl assi cal Pressure data anal (si sresul ts i n a bet=

ter i nterpretati on of test data2t’ 25’ 26’ 27.

One maj or

advantage of the pressure deri vati ve response i s i ts

hi gher sensi ti vi ty to smal l eff ects of i nterest whi ch

are di mni shed by the i ntegrated pressure versus ti me

sol uti ons cotnnonl yused i n wel l test anal ysi s. Fi g. 2

shows a doubl e l ogari thmc graph of the pressure deri v.

ati ve functi on tdp/ dt versus t for the si x more conmon

fl ow regi mes present duri ng a test. Of di rect i nterest

t o us i n t hi s st udy i s t he case of t est dat a f ol l ow ng

a strai ght l i ne of sl ope uni ty, correspondi ng to wel l -

bore storage or pseudosteady- state f l ow condi ti ons.

Li near, bi i i ne~r ~nd radi al fl ow pressure data show

the sl opes ofz,

and zero, respectivel y. Last, spher.

i cal fl ow data fo~l ows a strai ght 1i ne of sl ope equal

to - ~.

PRESSURE ANALYSI S FOR WELL

A-1

Tabl e 1 shows the reservoi r and fl ui d data perti -

nent to wel l A-1. The fl ui d produced i s of gas conden-

sate nature of speci f i c gravi ty of 0.902, a dew poi nt

pressure of 3015 psi g and contai ns a smal l porti on of

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SPE 14359 FERNANDO SAMANI EGO V. ,

HEBER CI NCO- LEY AND DAVI D MONTIEL H.

3.

ti me i nterval s correspondi ng to the di ff erent fl ow

rates. I t i sobvi ous fromthe resul ts of thi s f i gure

that no st rai ght l i ne i s shown by the data. Thi s of

course i s expected i n l i ght of our previ ous comnents

. -- ”-- . -1<. . ”<-

reyaruilly rly. 2.

In ~CC~~~anFa tft IWIt- CJ~SCUSSjQn regardi na the

s, , - - ““ ““.

possi bi l i ty of pseudosteady- state f l ow condi ti ons

affect i ng the test , Fi gs. 5 and 6 present graphs of

the pressure deri vati ve functi on tdmpwf) / dt versus

t for the pressure data regi stered dur i ng the fi rst

and thi rd f l ow rates. The resul ts of Fi g. 5 and spe-

ci al ?y those of Fi g. 6 i ndi cate the presence of pseu-

dasteady-state fl ow aff ecting the test, starti ng at

a t ime of about 2-4 hours. Fi g. 5 gi ves us the pos-

si bi l i ty to obtai n a val ue for the formati on conduc-

ti vi ty kh, si nce an approxi mate hori zontal porti on i s

shown by the pressure curve. Based on thi s i nforma-

ti on, the defi ni t i on of tDdmD/ dtDand usi ng a 0. 5 val

ue for the di mensionl ess pressure deri vati ve functi on

correspondi ng to radi al i nfi ni te-acti ng fl ow25, a

kh of 657 md-f t i s cal cul ated. The data of the second

fl ow per iod w l l be di scussed l ater due to operat i ng

probl ems expi erenced duri ng the test that resul ted i n

i mportant vari ati on of fl ow rate.

A poi nt that deserves to be stressed i s that

even a hi gh sensi ti vi ty pressure gauge was used i n

the test , the data of Fi g. 5 showed such a scat ter

that an anal ysi s was practi cal l y i mpossi bl e. To i m

prove thi s sit uati on a smoothi ng data routi ne was

progranrned,whi chcoul d take a vari abl e number of data

poi nts i n i ts smoothi ng process. Thi s i s further di s-

cussed byCi nco et al ~a.

Wthout the use of thi s rou-”

t i ne the rawdata for the f i r st f l ow rate di d not

showany cl ear i ndi cati on of the fl ow regi me aff ect-

i ng the test .

+ad j n ~~j ~ f j g~p~ ~~~

The data presen~=.

cal cul ated usi ng

11 points 5 forward and 5 backward

of the center poi nt) i n the smoothi ng process. On the

other hand, the data of the thi rd f l ow per i cd coul d

be anal yzed w thout needi ng previ ousl y bei ng smoothed

Fi g. 7 exhi bi t s t he r esul t s of t hi s t est f or t he

It

has been di scussed regardi ng Fi gs. 3 and 7

that data for the thi rd f l ow rate show the best l i -

near rel ati onshi p between pressure and ti me. An al -

ternati ve method for presenti ng these data can be

through the use of the pri nci pl e of superposi ti on

consi deri ng that pseudosteady- state f l ow condi ti ons

appi i es. Ti nen, the resul ti ng expressi oi i i s essen-

t i al l y Eq. 2 i f mul t i pl i ed by q , Fi g. 9 present s

the data regi stered for thi s fl ~w peri od i n accordanc

to thi s method, and as expected, the al i gnment of th~

data i s excel l ent . I t shoul d be cl ear that the sl ope

of thi s graph and that of Fi g. 7 have to be the same;

thi s i s approxi matel y the case si nce the two val ues

of 150 and 146. 86 psi 2/ cp/ MSCF/ D hr compare wel l .

Usi ng thi s l ast f i gure we can est i mate a val ue for

the ori gi nal gas vol ume G“of 915 MMSCF.

Our previ ous di scussi on has adressed the i mpor-

tant poi nt of smoothi ng the pressure data to obtai n

a better anal ysi s of the test . Fi g. 10 shows a car -

tesi an raph of the pressure deri vati ve function

7

dmp f /dt , usi ng the raw data versus t i n accordanc

to th~ method presented by Ci nco et al .28 for the

anal ysi s of pressure data taken under the i nfl uence

of an unknown trend. As commented w th regard to Fi g.

5, an anal ysi s of the non-smoothed (raw) data i s

practi cal l y i mpossi bl e. Through our smoothi ng process

We cl earl y see the i mprovement shown by the smoothed

data; better resul ts are obtai ned when

11

poi nts

(Fi g. 12) instead of 5 (Fig.

11)

are used. Accordi ng

to the method of these authors we expect the data

when graphed i n thi s manner to fol l ow a strai gh l i ne

porti on of i ntercept.m2. 303; thi s i s not evi dentl y

the case due, among other factors, to the fl ow rate

var i at i on effect i ve dur ing thi s port ion of the test .

For compl eteness purposes, the smoothed data for

the ~e~~nd f~~w peri od of Fi g, ~~ i q qh~wn i n a doubl

. - - . ..

l ogar i thmc scale in Fig. 13. As i t i s expected, we

can not i denti fy the fl ow regi me prevai l i ng duri ng

the test . Thi s graph i s based on part ial data regi s-

tered duri ng the test and i t coul d be concl uded that

a short radi al i nfi ni te acti ng peri od, represented

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4 “EVALUATIONOF NATURALLY FRACTURED GAS RESERVOI RS THROUGH pRESSURE TRANSIENT TESTINGI I

SPE 14359 ~

B-1

w th the mai n purpose of estimati ng the reser-

voi r parameters and gas reserves. A conventi onal

(Amerada- type) gauge was used i n thi s test. The

wel l was open to the atmosphere through a 3/ 16”

( hnke-

Tahla ~ nwacnntc ~~~ data PaI.nwkId

in .+nwmc-------- ,“” ,-

1“, ---,,”-

“-”u r ..””. “b” ,.. “s ,,,.7

of fl ow rate and bottomhol e fl ow ng potenti al

mp f ).

Fi gure 16 exhi bi ts the smoothed fl ow rate

dat (regi stered duri ng the test. I t i s i mportant

to not i ce that f low rate data for t<36 hr i s con-

si dered non- rel i abl e.

In the same way as di scussed for wel l A-1, l et’

thi nk we approach the anal ysi s of thi s test i n a

conventi onal way, and a mul ti pl e rate test i nterpre-

tat ion techni que i s used, as shown i n Fi g. 17. I t

i s clear f romthe resul t s of thi s f igure that no

easy detectabl e strai ght l i ne i s shown by the data.

I n t hi s t est , as i n any ot her t est i n a gas

wel l , there i s a strong possi bi l i ty of hi gh vel oc-

i ty fl ow affecti ng the test. Currentl y avai l abl e

techni ques of anal ysi s assume that the hi gh vel oc-

i ty fl ow effects are negl i gi bl e 29’ 30’ 31. Thus we

choose the approxi mated i nf l uence functi on or

nor-

mal i zat i on met hod Am(o)/o. Fia. ]~ nrP~mt~ ~ aranh

—— .

.. . . . - — . , 1- , J 7- . . a -

. r. - -- . .- -

of the normal i zed pressure deri vati ve functi on

=. -r. .

td[Amp)/ q]/ dt versus t for the data regi stered dur-

i ng the test . Af ter an osci l l at ion per iod, the re-

sul ts i ndi cate the presence of pseudosteady- state

f l ow affecti ng the test. Thi s f i ndi ng readi l y ex-

pl ai ns the i nterpretati on probl ems poi nted out re-

l ated to the seml ogari thmc anal ysi s of Fi g. 17.

Based on thi s concl usi on, we next present the nor-

mal i zed data of thi s test i n the car tesian graph -

of Fi g. 19. I t can be not iced that the al i gnment

of these l ow sensit i vi ty recorded data i s remark-

abl e. Consi deri ng a conti nuousl yvaryi ng f l ow rate,

an i nterpretati on equati on may be wri tten starti ng

w th Eq. 1 and fol l ow ng a sim l ar reasoning to

that i nvol ved i n the theory of Wnestock and Cul pi t~

resul ti ng i n the fol l ow ng expressi on:

that the bottomhol e pressure was stabi l i zed for the

l ast 20 hours.

Our di scussi on regardi ng Fi g. 20may be empha-

si zed i f we further anal yze the possi bi l i ty of pseu-

dosteady- state pressure condi ti ons aff ecti ng the

pressure bui l dup test.

For pseudosteady- state f l ow condi ti ons before

shut-i n the pressure behavi or i n terms of the real

gas potenti al may be expressed as fol l ows:

AT=

$p$cTq (tpa+&J

mpws)=mpi ) -

.

Ah@Tsc

[

1

~q.

n(~)+l n(- )

+q~l Ata

khTsc

r; CA

(6)

.,

wnere Am(At ) i s the i nf l uence functi on, si ml ar

to the pfcN tt) def i ned by Bost ic et al f i ”and 4ta

i s the Agarwal ’ s pseudo- ti me functi on. 33

Deri vi ng Eq. 6 and consi deri ng vari abl e fl ow

rate condi ti ons before shut- i n;

1 dAmpws)

d~

ta)A ta

-A~a ~~+mj) = dAt~

(7)

where m* i s the sl ope of the pseudosteady- state

st rai gh~ l ine on a l i near graph of Amp) /q vs ta.

We can concl ude fromEq. 7 that a doubl e

l ogar i thmc graph of i ts l ef t hand si de vs At f or

pseudosteady- state bui l dup pressure data shou?d show

a strai ght l i ne of uni ty sl ope. Fi g. 21 presents the

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SPE 14359 FERNANDO SAMANI EGO V. ,

HEBER CI NCO-LEY AND DAVI Q M~NTIEL He

~.

ervoi rs were expl oi tedonl y through these expl oratory

Wnllc

..* +.

The pressure behavi or i n wel l A-1 was practi cal -

l y enti rely domnated by pseudosteady- state f l ow con-

di ti ons. Thi s was checked mai nl y through the classi ca

l i near rel ati onshi p between pressure deri vati ve func-

t i on graphs for the f i rst and thi rd f l ow rates that

cl earl y show the characteri sti c uni ty sl ope. The val u

for the ori gi nal gas vol ume G estimated fromt he pseu

dosteady- state anal ysi s fo 896 MMSCF and that comng

f rom the graphi cal materi al bal ance study of 692MMSC

di ft er, perhaps due to the measurement of the “stati c

reservoi r (wel l ) pressures.

The anal ysi s of the vari abl e fl ow rate drawdown

test i n wel l B-1 was l i mted by the uncer tai nty of th

ear ly f l ow rate data. Thi s, i n addi t ion to the l i mts

~j ~~~ ~f ma. - am+l , ,=, , 3; 1mhl a +.- . -h. . ; ”, , , . . .. s

a...sl.,.-:.-

pr=acllkty avuIiauic r,cbillllquca ul almly>l>

that negl ect the ef fect of hi gh vel oci ty f l ow on the

i nf l uence functi onmcertai nl y l i mt the qual i ty of th

resul ts of the anal ysis. Neverthel ess, the anal ysis

based on the fi rst approxi mati on to the i nfl uence fun:

ti on Amp)/ q appears to render reasonabl e resul ts, i n

di cati ng the presence of pseudosteady-state fl ow af-

fect ing the test . The val ue of the or igi nal gas vol um

c ae++nl.+m,-l 4....”. *L.... r..a,,.4.-.-4,...4.. .4..4- . ...1..”.- -s

u == I. Inia r,cu I I UIII LIIC p>cuuu> r,cauy-> La Le aiia Iy> 1> ul

89. 5 MMSCF compares wel l w th that cal cul ated fr om th

graphi cal materi al bal ance study of 94. 5 MMSCF.

As regard to the esti mati on of formati on conduc-

ti vi ty kh, onl y approxi mated cal cul ati ons were carri e(

out si nce for practi cal purposes the radi al i nf i ni te-

acti ng fl ow peri od does not show i n these tests.

Based on the anal ysi s of three f i el d tests car-

ri ed out i n two natural l y fractured gas condensate

reservoi rs, whose mai n storage capaci ty i s i n the

fractures, the maj or concl usi on of thi s study i s that

i n smal l reservoi rs of thi s type pseudosteady-state

fl ow condi ti ons may enti rel y domnate the tests. Em

phasis on thi s work has been ori ented toward the prop.

er i denti f i cati on of the f l ow regi me affecti ng the

ta

Y 7--

real gas pseudo-t i me, f~fi ~ ~ c1 ~)dp

‘ u ““””c”””

‘ pa

= produced ti me converted to pseudo- ti me

‘D =

di mensi onl ess ti me based on wel l bore

radi us,

~kt

twtrwz

At

= shut- i n time

Ata

= pseudo- ti me el apsed si nce shut- i n

T

= temperature

z = r eal gas devi ati on factor

P

= vi scosi ty

4 = porosi ty .

Subscri pts

9

= gas

i nt

= i ntercept

Sc

= standard or reference condi ti ons

ACKNOWLEDGMENTS

The authors w sh to thank PEMEX for permssi on

to present thi s paper. we are gratefui to many peopl e

that~rked’ ~nthe gatheri ng of the data anal i zed i n

thi s paper.

REFERENCES

1.

2.

3.

Barenbl att , G. I . and Zhel tov, I . P. : “on the

Basi c

FIOW

Equati ons of Homogeneous Liqui ds i n

Fi ssured Rocks”,

Docl . Akal . Ntl uk. SSSR (1960)

132, N3, 545-548.

Warren, J.E. and Root, P.J.: “The Behavi or of

Natural l y Fractured Reservoi rs”, Sot. Pet. Eng.

J . (Sept. , 1963) 245-255; Trans. , AI ME, 228.

Odeh, A. S. : “Unsteady- State Behavi or of Natural -

l y Fractured Reservoi rs”, Sot. Pet. Eng. J .

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6 “EVALUATI ON OF NATURALLY FRACTURED GAS RESERVOI RS THROUGH PRESSURE TRANSI ENT TESTI NG” SPE 1435

11.

12.

13.

14.

15.

16.

17.

18.

Natural l y Fractured Reservoi rs and i ts Appl i cati on

to Devoni an Gas Shal es”, paper SPE 9327 presented

at the SPE 55th Annual Fal l Conference and Exhi bi .

t i on, Dal l as, Tex. Sept. 21-24, 1980.

Bourdet, D. , and Gri ngarten, A. C. : “Determnati on

of Fi ssure Vol ume and Bl ock Si ze i n Fractured

Reservoi rs by Type Curve Anal ysis”, paper SPE

9293 presented at the SPE 55th Annual Fal l Tech-

ni cal Conference and Exhi bi ti on, Dal l as, Tex. ,

Sept. 21- 24, 1980.

Serra, K. V. , Reynol ds, A. C. , and Raghavan, R. :

-. 7. . -: . M+h . . 4nw ~&. ~=

‘ : NewPressure Transi ef i t

Arialy>l> l.leLIK)ua J.v,

ural l y Fractured Reservoi rs”, paper SPE 10780

presented at the SPE 1982 Cal i forni a Regi onal Mee;

i ng, San Francisco, Ca. , March 24- 26, 1982.

Strel tsova-Adams, T. D. :

“Wel l Pressure Behavi or

of a Natural l y Fractured Reservoi r”, paper SPE

10782 presented at the >Ft l YUZ Cal i f orni a i ?egfow

-m a- a-

1 Meeti ng, San Francisco, Ca. , March. 24-26, 198;

Ci nco- Ley, H. and Samani ego V. , F. : “Pressure

Transient Anal ysis for Natural l y Fractured Reser-

voi rs”, paper SPE 11026 presented at the SPE 1982

Annual Fal l Techni cal Conference and Exhi bi ti on,

New Orl eans, La. , Sept. 26-29, 1982.

Moench, A. F. :

“Doubl e Porosi ty Model s for a Fi s-

sured Groundwater Reservoi r w th Fracture Ski n”,

Water Resour. Res. ,

Vol . 20, No. 7 ( Jul y, 1984’)

831-846.

Reynol ds, A. C. , Chang, WL. , Yeh, N. and Raghavan

R

. :

“Wel l bore Pressure Response i n Natural l y Frac

y~ed Reservoi rs”,

J . Pet . Tech. (May, 1985) 908-

.

Braester , C. : “Inf l uence of Bl ock Si ze on the

Transi ti on Curve for a Drawdown Test i n a Natural

l y Fractured Reservoi r”, Sot. Pet. Eng. J . (Oct .

1984) 498- 504

Ci nco-Ley, H. , Samani ego V. F. and Kucuk, F. : “The

Pressure Transient Behavi or for Natural l y Fract-

25.

26.

27.

28.

29.

30.

31.

32.

33.

Bourdet, D. ,

Whi ttl e, T. M,

Dougl as, A. A. and

Pi rard, Y.M :

“A New Set of Type-Curves Si mpl i -

fi es Wel l Test Anal ysi s”, Worl d Oi l (May 1983)

95-103.

Bourdet, D. , Ayoub, J . A. and Pi rard, ”Y. M: “Use

of Pressure Deri vati ve i n Wel l Test I nterpreta-

ti on”, paper SPE 12777 presented of the SPE 1984

Cal i forni a Regi onal Meeti ng, Long Beach, Ca. ,

Apri l 11-13, 1984.

Cl ark, G. and van Gol f- Racht, T. D. : “Pressure

Deri vati ve Approach to Transi ent Test Anal ysi s:

A Hi gh-Permeabi l i ty NQrt h Sea Exampl e”$ paper

SPE 12959 presented at the 1984 European Petrol e~

Conference, London, Oct. 25- 28, 1984.

Ci nco- Ley, H. , Saman{ego V. F. , Vi turat, D. and

Morales, C. :

“Pressure Transi ent Anal ysi s for

Hi gh Permeabi l i ty Reservoi rs”, paper SPE 14314

presented at 60th p, nnua Fal l CQ~fePe~Ce and

Exhi bi t i on of SPE of AI ME, Las Vegas, Nev. , Sept.

22- 25, 1985.

Odeh, A. S. and J ones, L. G. : “Pressure Drawdown

Anal ysis, Vari abl e-Rate Case”, J . Pet. Tech.

(Aug. 1965) 960- 964; Trans., AI ME, 234.

Bost i c, J . N. , Agarwal , R. G. , and Carter , R.D.:

“Combi ned Anal ysi s of Post Fracturi ng Perf ormance

Bui l dup Data for Eval uati ng an MHF Gas Wel l ”,

paper SPE 82-80 presented at 54th Annual Fal l

Conference and Exhi bi ti on of SPE of AI ME Las Vega

Nev. ,

Sept. 23- 26, 1979.

Fetkovi ch, MJ . and Vi enot, M E. : “Rate Normal i -

zati on of Bui l dup Pressure By Usi ng Afterfl ow

Data”,

J . Pet. Tech. (Dec. 1984) 2211-2224.

Wnestock, A. G. and Col pi tts, G. P. : “Advances i n

Esti mati ng Gas Wel l Del i verabi l i ty”, J . Can. Pet.

Tech. (J ul y- Sept. 1965) 111- 119.

Agarwal , R. G. :

“Real Gas Pseudo- Ti me - A New

Functi on for Pressure 8ui l dup Anal ysis of MHF Gas

Wel l s”s Paper SPE 8279 presented at 54th Annual

8/18/2019 SPE-14359-MS


TABLE 1 - RESERVOIR ANO FLUID DATA - U’ELL A-1

TABLE 2 THREE RATE FLOW TEsT-WELL A- I

Formation temperature, “F

= 138° F

Porosity, fraction

=

0.07

Specific gravity

= 0.902

Type

of

completion: open hole

Gas Composition

Component

Carbon dioxide

N trogen

Methane

Ethane

Propane

i sO - Butane

n-Butane

i so- i entane

n- Pentane

Hexane

Hept ane pl us

Hole Percent

0. 0013

0.0061

0.6932

0. 0900

0. 0519

0.0192

0. 0282

0.0199

0,0108

0.0192

0.0602

mpw )

mpw )

(h:)

(FIS:F/0)

(psi 2/ cp)x10- y (h: ) (MS I F/ 0) (PSi 2/ CP)X10- 9

o

0.083

0.10

0.42

0.67

0.92

1.17

1.42

1.67

1.92

2.17

2.42

2.67

2.92

3.17

3.42

3.6?

3.92

~. ~y

4.42

4.67

4.92

5.17

5.42

5.67

5.92

6.17

6.42

6.67

7.17

7.67

8.17

8.67

9.17

9.67

10. 17

10. 67

11. 17

11. 67

12. 00

12. 25

ql=l 158

1.08288

1.08161

1.08146

1.08144

1.0

1.0

1.0

1.0

1.0

?. 0

1.0

1.0

1.0

1.0

1.0

1,0

1.0

1.0

; . 0

1137

1118

1101

1061

1074

1060

1049

1044

1027

1016

006

’ 005

’ 995

‘ ~g

3>1

1.07953

1 .079s8

1.07955

1.07951

1.07935

1.07930

1,07921

1.07918

1.07894

1.07888

1.07877

1.07864

1.07862

1.07851

1. 07844

1.07832

1.0782

1 .07C07

1.07799

a. El~l@

1 n7Lc9

/.

. . -, ”,.

13.17

13.67

14.17

14.67

15.17

15.67

16.17

16.67

1.7.17

1;.6;

18.17

18.67

19.17

19.67

20.17

20.67

21.17

21.67

22. i7

22. 67

22. s2

23. 67

24, 17

24. 67

25.17

25.67

26.17

26.67

27.17

27.67

28.17

28.67

29.17

29.67

30. 17

30. 67

j l . l j

31.67

32.17

32.67

33.%7

1. 07611

1. 07606

1.07584

1.07572

1.07565

1.07550

1. 07528

1. 01525

1.07514

1.07503

1.07485

1.07471

1. 0;457

1. 07442

1. 07427

1. 07413

1. 07390

1. 07373

1. 07355

I . 07341

q,=312G

1.07336

f I l knse

, . . ”- ,

1.06710

1 . 0667C

1. 06658

1. 06643

1.06615

1.06596

1.06575

1. 06553

1. 06530

1. 06509

1. 06486

1. 06458

1. 06435

1. 06412

1. 06388

1. 06364

1. 06340

8/18/2019 SPE-14359-MS


TABLE 3. -

S1 PREFERRED UNI TS, CUSTOMARY UNI TS AND UNI T

CONVERSION CDNSTANTS USED IN THESE SYSTEMS

TABLE 4. -

VARI ABLE FLDW RATE TEST-WELL B- 1

Parameter or

Variable

S1 preferred units Customary units

Tiempo, t

nl (Pw )

Tiempo, t

Hr (H$: }D)

dpti )

(psi ’ / cp)xl o- ’ ‘ r

(M% j o) pSj2,cp)x~o-6

k

h

q9

P

B

‘$

%

P

m(p)

t

~

T

W12

m

m9/ d

Pas

m3/ ms

fracti on

Pa- l

kPa

kPa2/ Pa. s

hr

1293

3.6 X 10- g

“K

d

f:

t4SCF/D

CP

RB/STB

fraction

psi-l

psi

psi*/ cp

hr

1424

2.637x10-*

“R

o

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.25

2.75

3.75

4.75

5.75

6.75

7.75

B.75

13. 75

17. 75

21. 75

25. 75

29. 75

33. 75

41. 75

49. 75

57. 75

65. 75

73. 50

El .50

89. 50

97. 50

105. 50

TABLE 5

BUI LOUP TEST-WELL B- 1

3333. 8

3331.6

3329. 4

3327. 2

3325.0

3372.B

3321

3316

3312

3303

3294

3285

3276

326B

3259

3211

3168

3124

3091

3044

3008

2932

2855

2784

2714

2648

2582

2521

2465

2415

1500

1452

i 372

1264

1252

1244

1240

1230

1216

1211

1211

1201

1198

1195

1191

1182

1157

1139

1115

1095

1070

1043

1007

972

940

906

899

862

B38

812

799

113. 50

121. 50

i Z. 5Ci

137.5

149.5

277. 50

281. 50

2B5. 50

293. 50

301. 50

309. 50

317. 50

325. 50

333. 50

2365

2318

2?77

2234

2177

2140

2102

2069

2032

2000

1966

1934

1905

1875

1851

1819

1790

1776

1738

1721

1709

1630

1669

1657

1630

1605

1580

1556

1530

1510

760

732

. . . . ,

I Uo

684

671

650

631

610

590

576

560

502

485

480

464

451

450

428

417

402

391

378

367

361

357

342

341

329

308

300

8/18/2019 SPE-14359-MS


000

%0

%

000

0

>

‘$3

o

0

°

0

0

o

u-)

o

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o

~-o[ X a/~~sw -df)

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‘ ‘ b/ [ (~md)u@d)w]

—.—.——.—.—.—

0

0

0

8/18/2019 SPE-14359-MS


>

\

o

\

0

0

0

0

0

“0

w

c

1P

.

d3 / ~l Sd ‘ (d)wVp 1

\

\

\

\

\

\

*

m

N

1?

o

0

0

0

, ~1~CI \ 49SWd9/ ZI Sd ‘

*N’ [( l )b\ (d)~v]

0

8/18/2019 SPE-14359-MS


T

0

0

0

0

c

+-

0

0

0

0

0

0

0

0

0

t

0

0

0

0

—

—

—

—

—

—

I

--l

In

*

u

ox

~

.

4

0

0

0

IQ

0

.x

0

0

:

0

0

0

0

0

0

0

+

In

r=

J---L--

L

0°

0

0

0

0

c

0°

1

J-

0

0

0

0

0

0

0

0

0

0

0

0

I

0

u m-l 04

0

0

0

e

0

0

0

8/18/2019 SPE-14359-MS


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8/18/2019 SPE-14359-MS


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0

‘0

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0

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0

00

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0

‘0

0

0

I I

0

0

0

0

0

0

0

0

0

1

o

0

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0

0

0

0

0

0

0

0

8/18/2019 SPE-14359-MS


8

6

4

2

0

106

105

MSCP/ D. HR

1

~—LJ_—J

100

200

300

400

t

, HR

Fb.WNornuti zwdmpht~hol e PI . SM I .

or2h. varlabh-rm. drwdown WS2In W.11Z1

1

1

0

0

0

0

0

0

0

0

. .

°

,.7

,.8

flto

Fig.21-PIUWIC dulvatlw tm Ztuhttu.nm fu.czbmfortlmbuildup2981nW.116.1,

In

1

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x

Q

v

\

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ii

n

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w

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100

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400C

3000

2000

1000

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\

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20

40

60

80

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Documents

SPE-14359-MS