spe14237-case study of a low-permeability volatile oil field using individual-well advanced decline...

8/9/2019 SPE14237-Case Study of a Low-Permeability Volatile Oil Field Using Individual-Well Advanced Decline Curve Analysis

1/20

SPE

SPE 14237

Case Study of a Low-Permeability Volatile Oil Field Using

Individual-Well Advanced Decline Curve Analysis

by M J . Fetkovi ch,Phillips Petroleum Co.; ME. Vi enot, Phillips Petroleum Co. Europe-Africa;

and R. D. J ohnson and B. A. Bowman,

Phill ips Oil Co.

.CPE Marnha ..

“. - . ..”..,””.”

Copyright1985, .%xiety of PetroletFrn-Engineers

This paper waa prepsred for presentationat the 60th AnnualTechnical Conferenceand Exhibitionof the Society of PetroleumEngineera held in Las

Vegaa, NV September 22-25, 1985.

This paper was selected for presentationby an SPE Program Committee followingreview of informationcontained in an abstract aubmiwedby the

author(s).Contents of the paper, as presented, have notbeen reviewed by the Society of Petroleum Engineers and are subject to correctionbythe

author(a).Tha material, as presented, does not necessarily reflect any positionof the Societyof PetroleumEngineera, itaofficers,or members. Papers

presented at SPE meetings are subject to publicationreview by EditorialCommitfaesof the Sodety of Petroleum Engineers. Permiaaicmto copy is

restrictedtoan abetractof notmore than300 words.Illustration maynotbe copied.The abatractshouldcontainmnapicuouaacknowledgmentofwhere

and by whom the paper iapresented.Write PublicationsManager, SPE, P.O. Sox 833836, Richardson,TX 750S34S36. Telex, 730389 SPEDAL,

Am.7. .*T

AD> I KIW I

rMTnnnlm*TTn.t

111 I uuub I lull

Thi s paper presents a detai l ed case hi story study

I n sol uti on gas dri ve reservoi rs, decl i ne curve

of a l ow permeabi l i ty vol at i l e oi l f i el d l ocated

anal ysi s of rate-ti me data for predi cti ng future

i n Campbel l County, Wyomng. The fi el d was anal -

- producti on and determni ng recoverabl e reserves for

yzed on an i ndi vi dual wel l basis usi ng advanced

a fai rl y l arge number of wel l s i s conwnonl ydone

decl i ne curve anal ysi s for 40 i ndi vi dual wel l com

using the Arpsl empi ri cal equati ons and a compu-

pl eti ons. Wel l permeabi l i t i es, ski ns and ori gi nal

teri zed stati sti cal approach to arri ve at answers

oi l i n pl ace are cal cul ated for each wel l f romrate-

fai r ly qui ckl y. For wel l s i n hi gh permeabi l i ty

ti me anal ysis usi ng constant wel l bore pressure type

reservoi rs produci ng essenti al l y w de- open$ wf thout

curve anal ysi s techni ques.

future backpressure changes and w thout future

sti mul ati on treatments, the resul ts obtai ned shoul d

Origi nal oi l i n pl ace val ues cal cul ated fromrate-

be reasonabl y good provi di ng the l i mts of thede-

t i me anal ysi s for i ndi vi dual wel l s are used w th

cli ne exponent b of between O and 1. 0 are honored.

recoverabl e reserve proj ecti ons fr omthe decl i ne

anal ysi s to obtai n fracti onal recoveri es for each

At the other extreme i n anal yzing rate-t i me data

wel l .

Gas-oi l rati os versus fracti onal recovery

for predi cti ng future producti on and recoverabl e

curves are al so made for each wel l usi ng hi stori cal

reserves, a reservoi r si mul ati on study coul d be

cumul ati ve production and the cal cul ated oi l i n

undertaken.

However, thi s approach coul d take as

pl ace val ues. Ul ti mate fr acti onal recovery numbers

much as a year to accompl i sh and normal l y woul d not

and GOR vs fracti onal recovery curves, pl otted for

be considered acceptabl e, parti cul arl y f or ti me-

each wel l , are shown to suggest di ff erent rock types

constrai ned property acqui sit i on or sal es sit uati ons

and reservoi r fl ui ds.

Mul ti -wel l decl l ne curve

where f ew of the detai l ed reservoi r parameters

anal ysi s shows the val i di ty of the varfabl es s

necessary for a si mul ati on study are avai l abl e.

(ski n), k, OOI P, ul t i mate fracti onal recovery and

GOR vs fr acti onal recovery eval uated fr omeach

Many of the newer oi l and gas fi el ds bei ng di scov-

wel l ’ s type curve eval uati on.

These vari abl es must

ered and produced are i n the l ow permeabi l i ty class-

al l gi ve consi stent and reasonabl e numbers when

i fi cati on, where transi ent behavi or can l ast for

compared w th each other. A si ngl e wel l anal ysi s

years, and therefore are not amenabl e to anal ysi s

can easi l y gi ve resul ts that are not recogni zed as

using the Arps equati on al one.

Al so, a model study

bei ng i nval i d unl ess compared w th other wel l s i n

of such l ow permeabi l i ty reservoi rs woul d requi re a

the f i el d.

very fi ne gri d systemto correctl y si mul ate and

match the earl y transi ent rate-t i me decli ne data.

The study al so i l l ustrates fl ow ng and pumpi ng wel l

backpressure changes i n a wel l ’ s decl i ne, the method

An approach to the probl emof anal yzi ng l ow petme-

of handl i ng such changes, and thei r effect on ul t i -

abi l i ty wel l s and total f i el d rate-t i me decl i ne has

mate recoverabl e reserves predi cti ons. Conventi onal

been given in papersz 3 q 5 6 that i l l ust rate

decl i ne curve anal ysi s can not handl e backpressure

methods of handl i ng both the transi ent and depl eti on

chant-m. haeaii.n of ~~~ .-nq.+o..+n+ +k.+ A..* ---+--I-

,.-,.=-- “-----=

stages Of ‘ atQ- tj me decl i ne.

*v, =bI 91111,briat. WIIaI. Lurlbrui>

.ah414A.-..

K l? ~t?rmcautl Ibles,

t he decl i ne i n t he past w l l al so cont i nue i n t he

ski ns fr omsti mul ati on treatments and ori gi nal oi l

future.

i n pl ace or ori gi nal gas-i n-pl ace can be cal cul ated

for each wel l from rate-t i me data using constant

wel l bore pressure type curve anal ysi s techni ques.

References and 111ustratl ons at end of paper.


2/20

CASE STUDY OF A LOWPERMEABI LITY VOLATI LE OI L FIELD

USi?K

iNDIViWAIL-klELL ADVA

Wth a f ield case study of the School Creek Fi el d i n

Campbel l County, Wyomng, a l ow permeabi l i ty vol a-

t i l e oi l f i eld, we w l l present a stepw se procedure

for doi ng a total f i el d study usi ng i ndi vi dual wel l

advanced decl i ne curve anal ysi s techni ques.

Ori g-

i nal oi l i n pl ace val ues cal cul ated fromrate-ti me

anal ysi s for i ndi vi dual wel l s are used w th recover-

abl e reserve proj ecti ons fr omthe decl i ne anal ysi s

to obtai n fracti onal recoveri es for each wel l .

Gas-o~l rati o versus fr acti onal recovery curves are

al so made for each wel l usi ng hi stori cal cumul ati ve

producti on and the cal cul ated oi l i n pl ace val ues.

Ul ti mate f racti onal recovery val ues and GOR versus

fracti onal recovery curves, pl otted for each wel l ,

are shown to suggest di ff erent rock types and reser-

voi r f l ui ds. Mul t i -wel l decl i ne curve anal ysi s

shows the val i di ty of the var iabl es s (ski n) , k,

OOIP, ul ti mate fr acti onal recovery and GOR versus

fr acti onal recovery eval uated fr omeach wel l ’ s type

curve match poi nt. –- These vari abl es must al l gi ve

consi stent and reasonabl e numbers when compared w th

each other . A si ngl e wel l anal ysi s can of ten gi ve

resul ts that are not recogni zed as bei ng i nval i d

unl ess compared w th several other wel l s i n the

fi el d.

The study al so i ncludes and i l l ustrates

f l ow ng and pumpi ng

well

backpressure changes i n a

wel l ’ s decl i ne, the method of handl i ng such changes

and thei r eff ect on ul ti mate recoverabl e reserves

predi cti ons. Conventi onal decl i ne curve anal ysi s

approaches do not consi der backpressure changes and

thei r eff ect on proj ected recoverabl e reserves.

School Creek Fi el d - Wyomng

- .

The School Creek Fi el d i s l ocated on the eastern

fl ank of the south central porti on of the Powder

Ri ver Basi n i n Campbel l and Converse Counti es,

Wyomng. Fol l ow ng deposi ti on of the underl yi ng

Skul l Creek Shal e, the l ower Cretaceous sea receded

fromthe area of the Powder Ri ver Basi n. Subse-

quentl y, a w de- spread drai nage systemdevel oped and

carved i ts pattern i nto the Skul l Creek Shal e. As

the l ower Cretaceous sea tr ansgressed east, Muddy

del tai c sedi ments buri ed the previ ousl y deposi ted

channel sedi ments as the sea conti nued to i nundate

the basi n. Conti nuous basi n f i l l by deposi t i on of

+k- - . , f i - l . . i - -“”, . Ck. l a m.ae,,7+aA ;“

the ~W,~~~

Gil= UVCI IJ ITIY IW.IWIJ .I - C C=UtbCU b

reservoi r sands bei ng i deal l y “sandw ched” between

two mari ne hydrocarbon source shal es.

In

the School Creek Area, a north- south pal eodrai n-

age patt ern

was

devel oped upon the underl yi ng Skul l

Creek Shal e and control l ed the di stri buti on of the

producti ve ti dal channel and poi nt- bar sands of the

l ower Muddy formati on. Younger upper Muddy mari ne

faci es uni ts were then deposi ted as the Cretaceous

sea transgressed east resul ti ng i n some wel l devel -

QPQd Producti ve rnarj neof f shore b? ’ Se l ( s

it n t

fi el d area.

In the School Creek Fi el d, the Lower Muddy channel

sands have 35 wel l compl eti ons w th an average of 11

net feet of pay per wel l and an average porosi ty and

water saturati on of 13. 6%and 39% respecti vel y.

Upper Wddy bar sands have 5 wel l compl eti ons w th

an average of 12 net feet of pay per wel l and an

average porosi ty and water saturati on of 22%and

14% respecti vel y. Producti on has al so been estab-

l i shed i n secondary obj ecti ves, whi ch i ncl ude the

Sussex, Turner, and Dakota formati ons. These wel l s

- - -

are i i Oti ncl uded i i ithi s Study.

rn llrn lNC @ lDllE ANhl vCTC

L

IJLJLL lIIL bUnVL _lllAL1.lAti

CDF 1A9

4, b .T*

Fi gure 1 i s a pl at show ng the wel l l ocat ions, thei

rel ati onshi p to the Channel Sand and Bar Sand and

the three wel l s fr omwhi ch PVT sampl es were taken.

Fi gure 2 is a type l og for a School Creek Fi el d

Muddy formati on compl eti on.

The School Creek Fi el d was di scovered i n 1980 when

the Matheson

E-1

wel l was dri l l ed to 10,000 feet an

compl eted i n the Muddy formati on.

The i ni t ial res-

ervoi r pressure was approxi matel y 3700 - 3600 psi.

Basi c fl ui d properti es are gi ven fromthree di ffer-

ent PVT studi es i n Tabl e 2 and Fi gure 3. Two qui te

di ff erent fl ui d sampl es were obtai ned i n the Channe

Sand:

the Federal EE-1 sampl e w th a bubbl e poi nt

pressure of 3400 psi , GOR of 1557 SCF/ BBL and the

Matheson E-1 sampl e w th a bubbl e poi nt pressure of

2705 psi , GOR of 736 SCF/ 8BL. Based on reported

i ni ti al produci ng gas-oi l rati os, the Federal EE-1

sampl e was used to represent wel l s i n the southern

porti on of the fi el d whi l e the Matheson E-1 sampl e

was used for wel l s i n the northern portion of the

fi el d.

The Federal

J-1

sampl e was onl y usedl ~~ rep

resent the fi ve Bar Sand wel l compl eti ons.

bubbl e poi nt pressure was 2838 psi w th a gas-oi l

rati o of 1189 SCF/ BBL.

Basi c Decl i ne Anal ysi s Equati ons

The Arpsl empi ri cal decl i ne equati ons that can be

used for anal ysi s and forecasti ng future producti on

when depl eti on i s cl earl y i ndi cated are, for

b>O

qi

q(t) =

. . . . . . . . . . ..o... lj

[1 + b~it]l/b

and f or b =

O (exponenti al )

q t .

_l I-

eDi t

where the l i m ts of b

For type curve ai i al ys’

q(t)

qDd = —

qi

and

tod = Dj t

. . . . . . . . . . . . . 0. . ( 2)

are between O and 1.

s

. . . . . . . . . . ...0..(3)

. ..0............(4)

~p~fi

1,-.-1-”+,,-

-,,”..a

“1=+,.h;m”

+hc. ,n.+.h a+ ~~e

I“Y-,WJ

t J @ L“ .C WZkb ty L C 11.b “

rate- t ime data yields b, t -

tDd$ and q(t) - qDd.

Fromthese val ues qi and Di are eval uated and can

then be used i n the predi ct i ve equati orrs1 or 2

above to forecast future producti on and to obtai n

ul ti mate recoverabl e reserves.

As gi ven i n reference 3, we can al so eval uate the

producti vi ty factor fromq(t) - qod match poi nt, the

same match poi nt as woul d be used w th the above

~ equat i ons.


3/20

~E 14237

M J . FETKOVICH M E. VI ENOT, I

kn

‘ “’

S.ah’i,.h +ha” SIlm.,e ,..” —

la \p* j, WIIILI1 Lllclt al tuna Lall-

el l at i on of the vi scos ty terms i n equati on 10.

For cases where pwf < pb and~R > pb, as i s the case

for most of the School Creek Fi el d wel l s i n thi s

study, the producti vi ty factor i s eval uated from

kh

141. 2 (P6)1

q(t)

. - . .

(11)

.()]f

‘e

i n — -~

~R -

1

b) pb2pwf2) qDd

rw

2 2pb

and

(B)E

t

q(t)

~ .—.—

.~

(12)

‘ P

1

(et) - (TR -

1

pb)+(pb2 - pwf2)

‘ Dd

ql )d

P

“R L

Equat~ons

11

when pR < pb

Appendi x~.

To cal cul ate

we have

and 12 reduce to a si mpl e APZ form

(see for exampl e equati on A-9 i n the

a drai nage radi us fr omthe pore vol ume,

d

p x5. 615

re =

nh$

and oi l i n pl ace at

ysi s i s

Vp(1 - Sw)

OIP =

. . . . . . . . . . . . . . . . . . . ( 13)

the start of the decl i ’ neanal -

. . . . . . . . . . 00. . . . . . . ( 14)

R

Fi nal l y, the or igi nal oi l i n pl ace i s determned

from

~~ p = ~~p + $ f l K\

P

. . . . . . . * . . . . . . . . . . . . 4- .

where Np i s the cumul ati ve producti on to the start

of the decl i ne anal ysi s.

Changes i n Backpressure

Si nce many of the wel l s i n the School Creek Fi el d

were eval uated under fl ow ng condi ti ons w th more

than one change i n backpressure occurri ng, we have

extended the si ngl e backpressure change superpo-

sit i on equati on gi ven i n reference 20

Expressed i n

terms of mp)oi l , for si mpl i ci ty, we have

—


4/20

.’.

CASE STUDY OF A LOWPERMEABI LI TY VOLATILE

OIL

FI ELD

}

USING INDIVIDUAL-WELLADVA

(71 ~

.m i.. .

~-l

kh

cm{p/

R

111~wt

]J

q( t) =

1

[ () ]

1

141. 2 I n 3 - —

t-w

2

qDd

tD~

mpwf l ) -mPwf2) mpwf2)- mpwf3)

qDd(tD@odl ) +

+ m~R)-mp~l )

mFR)- mpwfl )

mPwfn- l ) -mPwfn)

“ q~(t~ -

tDd2) + . . . +

mFR)- (pwf l )

qf)d(tod tDdn ~)

-1

. . . . . . . . . . . . . . .(16)

The rate change Aq for any backpressure change i s

a constant fract ion of the i ni t ial rate at the same

i ni ti al transi ent tfme peri od, as the rate change

r et races t he or i gi nal q~ - t~ cur ve. The same

value of the decl i ne exponent b i s used for al l r ate

change superposi ti on cal cul ati ons.

[

m

(Ptil) -

m (pwf2)

Aql = q2 = ql

1

. . . . . . (17)

m (FP) - m (Pwf l )

—

..

.

[

m (pwf2)

1

mpwf3)

and Aq2 = q3 = ql . . ..00.(18)

m (TR) - m (pwf l )

Not e t hat t he ql / [m ( TR) - m (pwf l ) ] i s t he i ni t i al

producti vi ty i ndex i n BOPD/ psi or BOPD/ psi2, whi ch-

ever i s appropr i ate, t i mes a Ap or A(p2) termfor

successi ve f l ow ng pressure changes.

For the more general expressi on used i n thi s study

for pressure above and bel ow the bubbl e poi nt pres-

sure-

Aql “ qz s

and

Aq2 =q?J =

AI

[Pti$::l

““”””””(19)

P~2*”Pq2

1

..... . (20)

ZPb

J

ED DECLINE CURVE ANALYSI S

SPE 14237

I f nd when~R < pb the expressi on reduces to the

9

A(p ) fOr’M.

Si i i i i l ar l ywhen p f > pb the Ap form

i s obtai ned.

Y

he Ap formwou d be appropri ate for

use w th decl i ne exponent val ues of b =

O and AP2

~orm for b val ues greater than zero.

For A(P2),

PRSPbt the fi rst backpressure change rel ati onshi p

becomes

q (PM12 - Pwf22)

Aql= qz =

. . . (22)

(~R2

- Pwf12)

For Ap, pwf > pb, the fi rst backpressure change

rel ati onshi p becomes

q

(Pwfl - Pwf2)

Aql

.

. . . ..(23)

= ‘2 = (FR -

Pwf )

Successi ve rate changes woul d be handl ed as shown i n

the previ ousl y gi ven equati ons.

One shoul d note that i f (n) were correct l y eval u-

ated frommp)oi l using the i nfl ow performance rel a-

ti onshi p di scussed i n the Appendi x, al l the decl i ne

cl i ne curve anal ysi s coul d be done di rect l y i n

pressure terms i . e.

(IF) =

FR - Pwf

. . . . . . . . . . . . . . . ( 24)

m (FR)

- m (pwf)

A detai l ed exampl e i l l ustrati ng two backpressure

changes i s gi ven for the Federal

A-1

wel l , Fi gures 9

and 10 and Tabl es 9 and 9A. The exampl e i s carr ied

out usi ng the type curve match poi nt and the basfc

Arps formof the decli ne equati on. The procedure i s

qui te simpl e usi ng the concept of superposi ti on

gi ven by equati on 16.

A conveni ent equati on8 that can be used for cal cu-

l ati ng the total Aq as a resul t of n pressure

changes i s,~a

Ap

case,

I

R

- Pwfl

P~n

= P@ -

I

[Aql + Aq2 +. . . +

Aqn] (25)

ql

..,.,


5/20

SPE 14237

M J . FETKOVI CH, M E. VI ENOT,

for l l l (p)~i l

/

i

(2~R Pb-Pb

2- Pwf 12) (Aq1 z

Aq +. . .

Aqn)

Pwfn= Pwf12-

ql

. . . . . . (26)

The Aq val ues are al l speci f i cal l y def i ned at a

common poi nt i n ti me w th respect to the i ni t i al

rate ql ; 1 day or 1 month, for exampl e. A one month

t ime per iod i s used i n thi s study. The Federal

A-1

exampl e i l l ustrates thi s poi nt.

(See Fi gure 9).

One can al so back cal cul ate i ntermedi ate fl ow ng

pressures and rate changes

Aq

whi l e performance

matchi ng know ng the i ni ti al fl ow ng pressure and

rate, and the f inal f l ow ng pressure. Thi s al so

w l l be di scussed w th the Federal A-1 exampl e.

METHOD OF DECLI NE ANALYSI S

Log- Log Data Pl ots

The fi rst step i n approachi ng the rate-ti me l og-l og

anal ysi s i n the study of the School Creek Fi el d was

to make a l og- l og pl ot of al l the rate- t i me data

for each wel l . We next ex~ned each wel l ’ s pl ot to

f i nd when i t actual l y started on decl i ne. The rate-

t i me data was then rei ni t i al i zed at the poi nt of

decl i ne to t = O and a new l og- l og pl ot for each

wel l was prepared.

We have thus el i mnated the

constant rate or excess capaci ty ti me peri od whi ch

actual l y represents the constant rate sol uti on i n-

stead of the constant wel l bore Dressure sol uti on.

For l og-l og type curve anal ysis: we can’ t- do-decii ne

anal ysi s unti l the wel l

i s actual l y on decl i ne.

Based on the assumpti on that each wel l was drai ni ng

i ts 160 acre spaci ng and that al l wel l s had been

equal l y st imul ated - i .e. re/ rw woul d then be the

same for each wel l , a School Creek Fi el d Type Curve

was constructed by ~v~rl~vino @ach we~~ls ~q-lnn

. . .= -----

curve, w th the axi s al l kept paral l el , unt i l a-=

singl e curve was obtai ned. Fi gure 5 represents thi s

attempt to obtai n a total f i el d type curve usi ng

data from19 wel l s that exhi bi ted a cl ear decl i ne i n

thei r data.

Wote the “apparent” l ong tr ansi ent

peri od demonstrated by wel l s D-1, RA-1, and K-3. I f

thi s f i el d type curve were val i d, we woul d have a

simpl e and qui ck method of prepari ng an oi l produc-

ti on forecast and of determni ng ul ti mate recover-

abl e reserves for these wel l s and the remai ni ng

compl eti ons. I &woul d take the rei ni ti al i zed l og-

l og pl ot for each wel l , f i nd the best match on the

fi el d +. . l . . a. , - - - - -.. . A4. . - , . . 1

4 . . 4.L.-.. *L- J.*. J----

k~pe QUI v=, aIIU ur aw a I

Irle brrr-u brws

udcd sown

the depl et ion stemof b = 0.30. Future

rates would

be read di rect ly f romthe real t ime pl ot . Ul t imate

recovery woul d then be a summati on of forecasted

rates pl us the cumul ati ve producti on to the start of

decl i ne, pl us any addi ti onal producti on as a resul t

of pl acing the wel l on pump, where appl i cabl e.

Ta Aa+.s-.lms 46 +h,. .-,..-.-..+ . . ...-4--- ---- . ..- -.-I

Iv Ucbcrllllllc 1 I LIIC appaf CIIL LI arl>lerlb >Lem was real ,

wel l s D-1, BA-1, and K-3 were al l eval uated for k

and ski n (s) froma l og- l og type curve match on the

c@stant w~~~h~r~ nraccllr~ cnl tinn /FimIr.nc ~ A- ~

-“,-”,”,, {,

,Yul=- w,

The eval uati on of the match-poi nts

of reference 3)0 “-”- - ’

l ead to unreasonabl e val ues of permeabi l i ty and,

more speci f i cal l y ski ns for al l three wel l s,

None

of the wel l s were massi vel y hydraul i cal l y fr actured.

.

D. J OHNSON, and B. A. BOWMAN

Wel 1 k- red s

D-1 0.017 -7.6

BA-1

0.040 -8.2

K-3 0.024

-8.0

It was therefore concluded that the data for these

three wel l s was not real l y transi ent and shoul d be

pl aced i n the earl y depl eti on peri od of the total

f i eld type curve. Fi gure 6 i s our f inal School

Creek Fi el d Type Curve that does not exhi bi t a l ong

t ransi ent stem The f i el d type curve i s pr imar i l y a

depl et i on type curve w th a b = 0.30. (We w l l

l ater di scuss the b =

0. 30 sel ected for thi s study. )

Bl i nd matchi ng of l og-l og data to a type curve and

extrapol ati on can someti mes l ead to erroneous pro-

ducti on forecasts.

An eval uati on of the match

poi nts to obtai n reservoi r vari abl es for al l wel l s

bei ng studi ed shoul d gi ve consi stent and reasonabl e

numbers when compared w th each other thus conf i rm

i ng the val i di ty of the forecast and the ul t i mate

reserves numbers devel oped.

The el i mnati on of the

apparent transi ent stemi n thi s case i s a good exam

pl e of such a checki ng procedure. The composi te

type curve, Fi gure 4 of reference 2, was used for

al l match poi nt eval uati ons performed i n thi s study.

Basi c Wel l and Reservoi r Data

Tabl e 1 l i sts basi c i ndi vi dual wel l i nformati on and

the match poi nts obtai ned froma l og-l og type curve

eval uati on for 40 wel l compl eti ons.

Three of the

wel l s are commngl ed. The tabl e l i sts f i rst produc-

ti on, the start of decl i ne anal ysi s and the cumul a-

t i ve producti on to the start of the decl i ne anal ysi s.

Ini t i al l y, vi r tual l y al l wel l s came on f low ng w th

several on curtai l ed or restri cted producti on before

starti ng on decl i ne.

Many wel l s, because of earl y

hi gh gas-oi l - rati os and gas di sposi ti on probl ems,

were shut i n for as much as a year before bei ng

returned to producti on. Thi s accounts for the

di ff erence i n ti me of as much as one year between

fi rst ~f’ ndl l ~ti ~nnd start of rl nel +na with li++la

. ----

. . . . . -, “ , “o, , , ““ , =

cumul ati ve producti on for some wel l s duri ng thi s

i nterval .

Reservoi r shut- i n pressures, TR, were general l y

assumed to be cl ose to the ori gi nal pressure of

approxi matel y 3600 psi except i n a fewcases where

bott omhol e pressure surveys were avai l abl e to i ndi -

cate otherw se. Fl ow ng pressures were esti mated

f romgeneral pressure surveys conducted on 10 wel l s

i n l ate 1982 and ear ly 1983. Fl ui d l evel s shot on

pumpi ng wel l s i ndi cated a mnimum bottomhol e f l ow ng

pressure of approxi matel y 100 psi .

Porosi ty, thi ckness and water saturati on for each

wel l were furni shed by a l og anal yst.

Fi gure 4 i s a

permeabi l i ty-porosi ty pl ot devel oped f rom43 pl ug

sampl es taken on four wel l s i n the f i el d. The core

porosi t i es, i n general , are si gni f i cantl y l ess than

the average val ues determned froml og anal ysi s.

Thi s w l l be di scussed further under cal cul ated re

. . - 7, - -

vamue>.

The f i nal four col umns of the tabl e l i st the match

nninte nhtstnad frm ~~e Ifi–-I,w. +..-,. -.,---- .-.I...:-

r“.,,-.. -“-=,,,=-

IVS-IUy I,ypc LUI ve aflalysl>

f or each of the wel l compl et ions i n terms of t - tDd

and q(t )

- q~ obtai ned using the composi te type

curve (Fi gure 4 of r~f~r~n~~ ~) and a ~ecl i ne ~xPo-

nent b

= 0.30.


6/20

CASE STUDY OF A LOWPERMEABI LITY VOLATI LE OI L FI ELO

I

USING I NDI VI DUAL-WELL ADVA

PVT Data

PVT properti es requi red for eval uati on of reservoi r

vari abl es fromthe type curve match poi nts are pre-

sented i n Tabl e 2 and al so Fi gure 3.

These are U,

B and~t, al l eval uated at reservoi r shut- i n- pres-

sure, pR. The total compressi bi l i ty term et, was

3 ~ ,O- l i P5, - {

cal cul a ed us”ng a water compressi bi l i ty, Cw of

and pore vol ume compressi bi l i ty, Cf ,

obtai ned fr omHal l ’ s13 correl ati on. The product

(~) was “mechani cal l y” eval uated at the average

pressure (pR + p~)/ 2.

I ni ti al l y onl y two PVT sampl es were avafl abl e for

thi s study, the Federal EE- 1 bottomhol e sampl e to

represent Channel Sand compl eti ons and the Federal

J-1

bott omhol e sampl e to represent Bar Sand compl e-

ti ons. The Matheson E-1 PVT surface recombi ned

sampl e became avai l abl e onl y aft er our i nft i al

studi es were vi rtual l y compl ete.

Thi s sampl e, be-

cause of the vastl y di fferent gas-oi l -rati o (763

SCF/ B versus 1557 SCF/ B for the Federal EE-1 wel l )

and because of bei ng a surf ace recombi ned sampl e,

had been l abel ed an unrepresentati ve sampl e.

I nspecti on of i ni ti al GORS pl otted for each wel l

and a gas-oi l -rati o versus fracti onal recovery

curve, based on ori gi nal oi l i n pl ace devel oped from

the match poi nt eval uati ons, cl earl y suggested that

the Matheson

E-1

sampl e was val i d. The f i nal sum

mary of the eval uati on of reservofr vari abl es from

type curve anal ysi s was made using the Federal EE-1

PVT data for al l wel l s south of and i ncl udi ng wel l s

LL-1, H-1 and R-3.

See Fi gure 1 and Tabl es 3 and 4.

For wei i s to the north of these wel l s we used the

PVT data f romthe Matheson E-1 wel l sampl e.

Because the study had been vfrtual l y compl eted when

the Matheson

E-1

sampl e resul ts became avai l abl e, we

have I ncl uded the resul ts of al l channel sand wel l s

eval uated usfng both f l ui d sampl es.

Basfc patt erns

of eval uati on resul ts remai ned essenti al l y the same

between the northern and southern wel l s, i . e. ,

hi gher percentage recoveri es for the sc t hernwel l s

than the northern wel l s si nce thei r actual rate-ti me

perf ormance was based on the real fl ui d present, not

what we sel ected to use for the ffnal eval uati on

summary. The more undersaturated a wel l was, the

l ess recovery woul d be obtai ned as compared wft h a

wel l w th a f l ui d saturated at i t s f ni t f al shut - i n

pressure, al l el se being equal . Tabl es 5, 6, 7, and

8 summari ze the~esul ts of the match poi nt eval ua-

tiOtIS

based on (pR -

pwf) / (~) and mp)oi l

eval uati on.

Cal cul ated Resul ts FromDecl i ne Curve Anal ysi s

The f i nal resul ts of the type curve eval uati on fn

terms of cal cul ated reservoi r varfabl es are pre-

sented i n Tabl es 3 and 4; the wel l s have been

arranged on the basis of PVT areas.

~ mP)oi l

eval uati ofl was used for al l resul ts gfven i n Tabl e

3 and a (pR -

pwf) / (ZK) eval uat ion for al l

val ues fn Tabl e 4.

Pore Vol ume (Vn)

The pore vol ume cal cul ati ons are based on equatf ons

6 and 12, where

ED DECLI NE CURVE ANALYSI S SPE 1423

,— .

[Y8)

t ‘ “’

Vp=

q(t)

.—* —

. . ...(6)

( l l ct )_ ( FR - Pwf l )

tDd

qDd

PR

and

t3)F t

q(t)

.~. .

‘ P

[

1

—

12)

(ct)F

(TR-Pwf )+(Pb

*- Pq2)

tDd

qDd

R

2p

b

Equati on 6 woul d most certai nl y appl y to reservoi rs

where the si ngl e phase l i qui d sol uti on i s appl i ca-

bl e, i .e. , where the decl i ne curve exponent b = O.

The i ntroducti on of the (~) termeval uated at

~R + Pwf ) / 2 w th the Ap form i s simpl y an attempt

to account for sol uti on-gas drfve or two phase fl ow

behavfor. A ri gorousl y deri ved (~) frommp)

concepts, as di scussed previ ousl y, woul d be the

approach to make equati on 6 and 12 equi val ent.

For sol utfon gas dri ve reservoi rs, reference 2

demonstr ates that the

A(p2)

formof IPR (of l wel l

backpressure curve w th n = 1. 0) used w th a non-

l i near~R versus Np materi al bal ance rel ati onshi p

produces a decli ne exponent b = 0. 33. Levi ne and

Prats~, fn thefr simul ati on study of a sol uti on

gas dri ve reservoi r produci ng under a constant wel l -

bore pressure condi ti on, presented a l og qD - l og tD

type curve. (See thei r Ffgure

11. )

The depl etfon

stemof thefr type curve basi cal l y f fts a decl i ne

exponent b s 0.33. Fi gure 7 i l l ustrates one of

several wel l s i n the School Creek Fi el d that ex-

hi bi ted rate-tf me data fn a suffi ci ent stage of

decl fne to hel p us establ i sh a si ngl e decl fne expon-

ent h . tl ‘M

~~~ ~~~ Anel+na -II-M- .ma~y~j~ ~fi~

-..” - - “.””.

“.=.-n ,81.= GUI v= all

rate predi cti ons were based on matchfng and fore-

cast i ng on b = 0.30 f or al l wel l s. Al l f or ecast s

for thi s study were done~ graphi cal nrntoc+:nn-

. -u-””. ”. , .

Fi gure 8 fs a pl ot of percent recovery versus

bottomhol e f l ow ng pressure for the Federal A-1

wel l . Usfng equati ons 6 and 12, the bottomhol e

fl ow ng pressure was vari ed between 1600 psi to 100

psi and the pore vol ume Vp and

OOIP

cal cul ated.

Ul tfmate recovery was fi xed at 36, 000 60 for both

Ap/(fi) and Alll(p)ojl cases to arr ive at a percent

recovery. Note the l ack of sensftfvfty i n percent-

age recovery for the

Alll(p)ojl

case w th the vari a-

ti on of bottomhol e fl ow ng pressure. Sfnce the

Amp)oi l case i s effecti vel y a di f ference i n pres-

sures squared eff ect, we do not see a propO@onal

i ncrease i n rate w th drawdown as i n the (UB) case

even though (~) was eval uated at each fl ow ng-

pressure.

Thf s i s vi r tual l y fdent i cal w th the

effect found for gas wel l s. The precfse determn-

ati on of f l ow ng pressure, p~, may not then greatl y

affect our f i nal resul ts.

Oi l in Pl ace

Oi l i n place fs cal cul ated di rectl y fromVp usi ng

equatf on 14


7/20

SPE 14237

M J . FETKOVI CH, M E. VI ENOT, R. O. J OHNSON, and B. A. BOWMAN

Vp

(1-SW)

OIP =

. . . . . . . . . . . . ..(14)

(B)T

R

The cal cul ated oi l i n pl ace i s at the star t of

decl i ne whi ch, when added to the cumul ~ produc-

t ion up to the start of the decl i ne anal ysi s, yi el ds

the or iginal oi l i n place, OOIP, equati on 15. The

or igi nal oi l i n pl ace i s l ater used to cal culate

fracti onal oi l recoveri es, Tabl e 10, and GOR versus

fracti onal recovery, i n an attempt to hel p i denti fy

or confi rmdi ff erent fl ui d properti es used i n the

f i el d anal ysi s and al so to possi bl y i denti fy di f fer-

ent rock types.

Cal cul ated Drai nage Radi us (rP)

A “cal cul ated” drai nage radi us i s determned fromVp

w th equati on 13

II

Vp X 5. 615

re =

. . . . . . . . . . . . . . . . ( 13)

nh$

The cal cul ated val ue of re i s not onl y a funct ion of

pore vol ume Vp determned fromthe type curve anal -

ysi s match poi nt but al so of porosi ty $ and thi ck-

ness h. In thi s type of reservoi r , w th i ndi cated

thi n “di rty” sands and possi bl e l i mted areal

extent, the val ue of average h used as determned

fromthe l ogs may be too hi gh. Thi s woul d resul t

i n a cal cul ated re val ue i n some cases much l ess

than re = 1490 feet for 160 acres.

Al so, very few

of the core sampl e pl ugs obtai ned fromwel l s i n the

fi el d (see Fi gure 4) appear to approach the average

porosit y val ues reported fromthe l og anal ysi s

l i sted on Tabl e 1.

If

one were to bui l d a si mul a-

t i on model of the School Creek Fi el d, outl i ned i n

Fi gure 1, based on the l og deri ved val ues of +, h,

and 160 acre spacing for each wel l , we woul d have

to cut the pore vol ume to match the type curve

anal ysis deri ved reservoi r vari abl es, specif i cal l y

oi l i n pl ace, that have al ready been hi story matched

to the rate-t i me decli ne data.

To come up w th cal cul ated val ues of re approachi ng

on average the 160 acre fi el d spaci ng, the $h pro-

duct woul d have to be decreased. Otherw se, the

rather tenuous concl usi on that many wel l s are not

drai ni ng the exi sti ng spaci ng coul d l ead to a con-

si derat i on of i nf i l l dr i l l i ng.

Producti vi ty Factor (P. F. )

The producti vi ty factors for each wel l are cal cu-

l ated fr omequati ons 5 and

11,

where (m i s eval uated at average pressure

(PR + Pwf) / 2

and

141. 2 (Pf3)5

. . . . . . .

.. 11

........,--,

Si nce there i s a l ack of ear ly t ime transi ent rate

data to suf f i ci ent ly def i ne an re/ rw stem uni que

val ues of permeabi l i ty and ski n cannot be cal cul ated

for each wel l .

We know that al l compl eti ons were

i ni ti al l y stimul ated.

The core data i ndi cates an

ari thmeti c average permeabi l i ty of 0. 650 md and a

geometri c average of 0. 195 md, w th a range of 0. 2

md to 7 md.

We al so had one bui l dup test conducted

on the KK-1 wel l where the fi nal f l ow ng pressure

pri or to shut- i n was above the bubbl e poi nt pressure.

The anal ysi s yi el ded a val ue of k = 2.5 md and s =

- 3. 4.

A range of val ues of ski n f romO to -4 was sel ected

to eval uate permeabi l i ti es for each wel l . When we

f i x rw

on the basi s of ski n, rw = r e- s, and

havi ng previ ously cal cul ated re from

he pore vol ume

cal cul ati on we can then cal cul ate kh and k fromequa-

t ions 5 and 11.

The ranges of values of k l i sted on tabl es 3 and 4

for vari ous val ues of ski n are surpri si ngl y narrow

w thi n a gi ven tabl e and even between the two meth-

ods of cal cul ati on used. I t shoul d be poi nted out

that the val ues of permeabi l i ty and ski n cal cul ated

fromthe decl i ne curve anal ysi s are those at the

start of the decl i ne anal ysi s.

If a good correl ati on fromthe core deri ved $ - k

pl ot had been obtai ned and i f l og deri ved average

porosi ti es were consi dered reasonabl y rel i abl e, we

coul d have used i t to determne k and then i ts cor -

respondi ng ski n fromthe tabl es for each wel l .

Based sol el y on the KK-1 bui l d-up anal ysis resul ts

and the fact that al l wel l s were sti mul ated, one

coul d al so sel ect the -3 ski n col umns on Tabl e 3 or

4 to arr ive at speci f i c val ues of permeabi l i ty at

the star t of decl ine for each wel l . There are no

unreasonabl e val ues of permeabi l i ti es l i sted on

ei ther tabl e.

Near ly al l l i e w thin the range of

the core permeabi l i ti es shown on Fi gure 4. Val ues

of permeabi l i ti es i n the 10s or 100s md on any wel l

woul d, of course, be suspect.

Exampl e of Ef fect of Backpressure Change on Recovery

and Decl i ne

The equati ons to cal cul ate the change i n produci ng

rates w th backpressure changes have been gi ven

previ ousl y as equati ons 16 - 26. The Federal A-1


8/20

CASE STUDY OF A LOWPERMEABI LI TY VOLATILE OIL FI ELD

USING I NDI VI DI J AL-WELLADVA

wel l produced agai nst three di ff erent fl ow ng pres-

sures that resul ted i n two rate changes.

Fi gure 9

i s a l og- l og pl ot of the rate- t ime data w th the

sol i d l i ne through the poi nts cal cul ated fromthe

type curve match poi nts used w th the Arps hyper-

bol i c decl i ne equat i on. Onl y the f i rst and l ast

fl ow ng pressures of 1400 psi and 100 psi , respec-

ti vel y, were known. Equati on 26, sol ved i n terms

of Aq total w th pwf3 = 100 psi yi elded a total

Aq = 747 BOPM A tri al and error cal cul ati on was

then made varyi ng Aql unt i l a best f i t of both

rate changes was obtai ned. Thi s resul ted i n a pwf2

= 1069 psi.

Tabl es 9 and 9-A i l l ustrate i n detai l the method of

devel opi ng a forecast w th two backpressure changes

usi ng the mp)oi ~ approach.

Note speci fi cal l y that

si nce the rate-t i me decl i ne i s undergoi ng depl eti on,

the Arps equati on i s used for al l the cal cul ati ons.

One does not have to deal w th the reservoi r vari -

abl es, kh, s, re/ rw , obtai ned fromthe match eval u-

at i ons. Thi s, however , woul d not be the case for a

transi ent si tuati on.

Theoreti cal l y, the rates for

the fi rst fewmonths shoul d be cal cul ated at the

md-poi nt of the t ime i ntervai , i . e. , 0.5, 1.5,

2. 5, to represent average monthl y producti on rates.

For simpl i cit y of presentati on of the superposi ti on

exampl e, the rates have been eval uated at ful l month

ti me i nterval s.

Tabl e 9-A col umn 2 l i sts the rates for the i ni t i al

f~ow ngpressure, pwfl , cal cul ated fr om~rps’ equa-

t i on w t t l b = 0. 3, qi = 4545. 5 t+l J t JMna LJ i = O.Zi Z

- - - - - -

me- l . The rate change as a resul t of a choke change

t o pwf z = 1069 psi i s l i st ed i n col umn 3. I t i s

si mpl y a constant fracti on of the i ni t i al decl i ne

rates. The second backpressure change, when the

wel l was pl aced on pump to pwf3 = 100 psi , i s

treated si ml arl y. For superposi ti on, col umns 3

and 4 are retabul ated at a ti me 1 month past the

actual ti me of the pressure change.

Total rate i s

then the sums of col umns

2, 5,

and 6. Addi ng the

cumul ati ve producti on to the start of decli ne

anal ysi s (2633 go), we have

Nn Ul ti mate, BO

Ah(p)njl A(p)

No backpressure change

30, 347

30, 347

Fi rst backpressure change

32, 667 34, 668

Second backpressure change

35, 858 47, 226

The Ap numbers i n the above tabl e were generated

for compari son by recal cul ati ng

Aql

and

Aq2

on

the basi s of a

Ap

superposi ti on usi ng equati on 23.

Fromthi s approach, a procedure usi ng actual produc-

t i on data (and i ts proj ected rates for a known

i ni ti al f l ow ng pressure) coul d be devel oped to

determne the eff ect of a backpressure change on

ui ti mate recovery, as foi i ows.

Determne Np at pwf l to t = T, where T = total t ime

of rate- ti me forecast,

T- ~ (a pwf

Aql

E

2

then

ANP1 = — “

q actual

ql

t l

.

FIl llFCi TNF CIIRVF ANAIYSIS

SPE 142

------- ... . . . . . .. ... Q---

T- t@ pwf3

Aq2

and

ANP2 = — “

L

q actual

ql

t=l

where q actual may al so be actual producti on pl us

that proj ected for the i ni t i al f l ow ng pressure,

Pwf l

Ul ti mate Recoverabl e = Np + ANpl + ANP

2

Si ml arl y, actual earl y ti me producti on rates i n-

stead of cal cul ated val ues can be used to generate

the rate-ti me superposi ti on as i l l ustrated i n Tabl e

9-A. Thi s i n essence woul d have the ef fect of i n-

cl udi ng a downti me i f any earl y ti me rate vari ati ons

were due to downti me.

Fi gure 10 i l l ustrates one more poi nt about backpres-

sure changes w th regard to the decl i ne exponent.

As has been previ ousl y poi nted out i n references 2

and 3, the sumof two forecasts, both havi ng the

same vai ue of deci i ne exponent b, w l l rarel y

resul t i n a total forecast havi ng the same decl i ne

exponent. I n general , the total forecast decl i ne

exponent w l l be l arger . Rei ni t ial i zi ng the rate-

ti me data af ter the second backpressure change

whi ch al so has b =

0.3 resul ted i n a decl i ne

exponent b = 0. 40.

Fi nai i y, uni ess ai i wei i s are pi aced on pump at the

same ti me, a backpressure change can cause a wel l ’ s

drai nage radi us to i ncrease w th respect to offset

wel l s. The gi ven superposit i on exampl e i mpl i ci tl y

assumes that re remai ns constant.

Commngl ed Wel l s

There are three wel l s i n the School Creek Fi el d

where Bar Sand producti on and Channel Sand produc-

ti on are presentl y commngl ed. Fi gures 11 and 12

- . LL. P. , . , , .

~or tne teaeral K-1 wei i i l l ustrate the method of

anal ysi s used to eval uate these wel l s. A di ff erence

curve was devel oped between the forecast rates of

the Channel Sand producti on onl y and the connni ngl ed

producti on whi ch came on producti on l ater. Separate

forecasts were then made and added together.

Surmnaryof School Creek Fi el d OOIP and Ul t i mate

Recoverv

Tabl e 10 summari zes the resul ts of the cal cul ated

ori gi nal oi l i n pl ace and ul ti mate recovery forecast

for each wel l based on anmp)oi l and a

AP/(ti)

eval uati on. The superposi t i on of rates as a resul t

of backpressure changes usi ng equati ons 19 and 23

have al so been i ncl uded where appropri ate.

Channel Sand compl eti on resul ts are di vi ded i nto the

northern and southern areas of the fi el d based on

the two PVT sampl es di scussed previ ousl y. Both

eval uati on methods i ndi cate a much l ower percentage

recovery for wel l s i n the northern porti on of the

fia ld dC r ~ ndP a d With wane +. th~ =~,ith~m~ ~er~fefi-

. . . . . . “., u“.,,~”, -“

“,”., “=, ta ,,, .am= a“ubtac, ,,

Wel l s i n the southern porti on have percentage recov-

er ies near twce those of wel l s to the nor th. Thi s

woul d be consi stent sol el y on the basi s of the

di ff erences i n bubbl e poi nt pressures between the


9/20

‘ 3PE14237

M J. FETKOVI CH, M E. VI ENOT\

two fl ui d sampl es. Val ues of percentage recoveri es

are al ways l ower for the mp)oi l eval uati on method.

Wth regard to the addi ti onal recoverabl e reserves

that coul d possi bl y be obtai ned by pl aci ng al l wel l s

on pump to a fi nal bottomhol e fl ow ng pressure of

100 psi, the fol l ow ng tabl e summari zes those re-

sul t s. (Near l y hal f of t he wel l s were i ni t i al l y at

or near 100 psi bottomhol e fl ow ng pressure at the

start of decl i ne.)

Reserves Increase of

I ncrease of

for mo}. . +l hoi (ZJ

I ni ti al R&&~~&

- r , \ l - w

Reserves

Fl ow ng

to pwf to pwf

Pressure

of 100 psi

of 100 psi

%

%

STB

STB I ncrease STB I ncr ease

Northern

Wel 1s 223,900

15, 594 7% 51, 361 23%

Southern

Wel 1s

312, 105 19, 220 6% 67, 605

22%

Total

Fi el d 819, 484 68, 354 8% 230,346 28%

I f , i n fact the i nf l ow performance rel ati onshi p

based on

Ap~

appl i es, the percentage i ncrease as

a resul t of placing al l wel l s on pump to a f i nal

fl ow ng pressure of 100 psi woul d be approxi matel y

8%or 68, 000 BO.

If

the i nf l ow perf ormance rel a-

ti onshi p were to fol l ows Ap (PI) behavi or, the

anti ci pated i ncrease i n reserves woul d be 28%or

230, 000 BO. Perhaps the real i ncrease i n reserves

due to l oweri ng the fi nal bottomhol e fl ow ng pres-

sure l i es somewhere between these two l i mt s.

I ndi vi dual Wel l Gas-Oi l -Rati o Perf ormance

Fi gures 13 thru 16 refl ect gas-oi l -rati o performance

of i ndi vi dual wel l s i n the f i el d based on expressi ng

~~~ Pa?- l ”a. ”

.t-+tl. +“ +ame m+ a..h I.m.11 Is ~c~,da~

, -“ ” .=,J ,“GI,” , ,,, l.=,,,,= “ , cat.,, “ c, ,

cumul ati ve producti on di vi ded by the

OOIP

cal cul ated

fromthe mp)oi l eval uati on. Ei ther method of cal -

cul ati ng OOIP shoul d show siml ar trends.

Gas and

oi l rates are metered separatel y for each wel l and

are not based on al l ocati on fromtests.

Fi gures 13 and 14 are on an expanded gas-oi l -rati o

scal e i n an attempt to hel p i dent i f y rock types fn

each area of the f i el d.

If

one assumes the fl ui ds

are the same for each area, three di ff erent rock

types and/ or i ni ti al water saturati ons are possi bl y

i ndi cated i n the southern porti on of the f i el d.

Fi gures 15 and 16, prepared on a scal e where the

enti re gas-oi l -r ati o performance of each wel l can

be shown cl earl y, i ndi cate two di fferent fl ui ds,

based mai nl y on the wel l s’ peak gas-oi l -rati o al one

whi ch i s not a functi on of the method of cal cul ati ng

an OOI P number.

Note that the gas-oi l -rati o has

turned over on several wel l s.

The peak gas-oi l -

rati os for the northern wel l s i s general l y much

l ower than those of the southern wel l s. These gas-

oi l -rati o curves coul d be used i n devel opi ng a gas

forecast to go w th the oi l rate forecast devel oped

fr omthe decl i ne curve anal ysi s.

.

D. J OHNSON, and B. A. BOWMAN

CONCLUSIONS

Or igi nal oi l i n pl ace val ues can be cal cul ated f rom

rate-ti me anal ysi s for i ndi vi dual wel l s and can

al so be used w th reserves proj ecti ons devel oped

fromthe decl i ne anal ysis to obtai n fracti onal

recover ies for each wel l i n a f iel d. These f rac-

ti onal recovery numbers shoul d be reasonabl e,

consideri ng the fl ui d type and the permeabi l i ty of

the reservoi r.

Each wel l ’ s eval uati on of the r~s~rv~i r Vari ab~eS

k, s ( ski n) ,

OOIP

and fr acti onal recovery, obtai ned

from i ndi vi dual wel l rate-t i me decli ne anal ysis,

shoul d gi ve consi stent and reasonabl e numbers when

compared w th other wel l s i n the f ield. A si ngl e

wel l anal ysi s can gi ve resul ts that are not recog-

ni zed as bei ng i nval i d unl ess compared w th other

wel l s i n the f iel d.

Fai l ure to consi der a future l oweri ng of a wel l ’s

fl ow ng bottomhol e pressure fr omthat causi ng a

wel l ’s i ni t i al rate- t i me decl i ne can resul t i n

underesti mati ng ul ti mate recoverabl e reserves.

A method of tr eati ng future backpressure changes

based on the superposit i on pri ncipl e and an oi l

Nel l i nfl ow performance rel ati onshi p i s easil y

appl i ed to decli ne curve anal ysis.

An oi l wel l

i nfl owperf ormance rel ati onshi p can be uti l i zed

Over an enti re producti on forecast, not onl y at

an i nstant i n ti me.

NOMENCLATURE

b=

8

=

Cf =

-Ct .

Cw =

Di =

~.

h

.

k

=

kro =

( p)oi l =

n

.

oh’ :

OOI P =

M=

PR =

Pwf =

.

J : .

re =

rw =

rw =

=

s: =

t

=

tod =

T=

“~ ;

‘ $=

reci proca’

fo~: ; ; : n

of decl i ne curve exponent

vol ume factor,

res vol / surf ace vol

effecti ve rock compressi bi l ty, psi - l

total compressi bi l i ty, psi-

1

water compressi bi l i ty, p i - l

i ni t i al decl ine rate, t -

nat lral lrmarithm haca 9 71Q9Q

,,..””, “,

,“~”, , “,,,,, ““== G., S“CU

thi ckness, ft

ef f ecti ve permeabi l i ty, md

rel ati ve permeabi l i ty to oi l , f racti on

oi l pseudo pressure, psi/ cp

exponent of backpressure curve

cumul ati ve oi l producti on, STB

oi l i n pl ace at st ar t of decl i ne

anal ysi s, STB

or iginal oi l i n pl ace, STB

bubbl e poi nt pressure, psi a

reservoi r shut- i n pressure, at start

of decl i ne, psi a

bottomhol e f l ow ng pressure, psi a

decl i ne curve di mensi onl ess rate

sur face rate of f l owat t ime t

external boundary radi us, ft

wel l bore radi us, ft

effecti ve wel l bore radi us, ft

ski n factor, di mensi onl ess

water saturati on

ti me, mo.

decl i ne curve di mensi onl ess ti me

total t ime of forecast , m

reservoi r pore vol ume, ft

”

vi scosi ty, Cp

porosit y, fracti on of bul k vol ume


10/20

CASE STUDY OF A LOWPERMEABI LITY VOLATILE OI L FIELD

o

USI NG I NDI VI DUAL-WELL AOVANCED DECLI NE CURVE ANALYSIS

SPE 142:

ACKNOWLEDGEMENTS

We w sh to thank Phi l l i ps Petrol eumCompany for

permssi on to publ i sh thi s paper . We al so w sh to

thank U. G. Ki esow M D.

Bradl ey, and S. D. Dunstal

for thei r t i mel y assi stance i n parts of thi s study.

REFERENCES

1.

2.

3.

40

5.

6.

7.

8.

9.

10.

11.

12.

13.

Arps, J . J . : “Anal ysi s of Decl i ne Curves,”

TRANS, AIME (1945) 160, 228- 247.

Fetkovi ch, M J. : “Decl i ne Curve Anal ysi s

Using Type Curves,” J . Pet. Tech (J une 1980)

1065- 1077.

Fetkovi ch, M J . , Vi enot , M E. ,

Bradl ey, M D., and Ki esow U. G. : “Decl i ne

Curve Anal ysi s Usi ng Type Curves: Case

Hi stori es,”

paper SPE 13169 presented at the

59th Annual Fal l Meeti ng of SPE of AI ME,

Houston, Texas, September 1984.

Carter, R. D. : “Characteri sti c Behavi or of

Fi ni te Radi al and Li near Gas Fl ow Systems -

Constant Termnal Pressure Case, ” SPE/ DOE 9887

presented at the 1981 SPE/ DOE Low Permeabi l i ty

Symposi um Denver, CO, May 27- 29, 1981.

Carter, R, D. :

“Type Curves for Fi ni te Radi al

and Li near Gas-Fl ow Systems:

Constant Term nal

Pressure Case, ” SPE 12917 presented at the 1984

Rocky Mountai n Regi onal Meeti ng, Casper, WY,

May 1984.

Da Prat, Gi ovanni , Ci nco- Ley, Heber and

Ramey, H.

J., Jr.:

“Decl i ne Curve Anal ysi s

Usi ng Type Curves for Two-Porosi ty Systems,”

Sot. Pet. Eng. J ( J une 1981) 354-362.

Fetkovi ch, M J . and Vienot , M E. : “Shape

Factor, CA, Expressed as a Ski n, SCA,” J . Pet.

Tech. (February 1985) 321- 322.

Bradl ey, M D. : Personal communi cati on.

Levi ne, J . S. and Prats, M: “The Cal cul ated

Perf ormance of Sol uti on Gas Dri ve Reservoi rs, ”

Sot. Pet. Eng. J . (Sept. 1961) 145-152.

Fetkovi ch, M J . :

“The I sochronal Testi ng of

Oi l Wel l s, ” paper SPE 4529 presented at the

48th Annual Fal l Meeti ng, Las Vegas, Nev. ,

Sept . 30 -

October 3, 1973. (SPE Repri nt

Seri es No. 14, 265. )

Vogel , J . V. :

“Inf l ow Perf ormance Rel ati on-

shi ps for Sol uti on Gas Dri ve Wel l s, ” J . Pet.

Tech. (J an. 1968), 83.

Whi tson, C. H. :

“Reservoi r Wel l Performance

and Predi cti ng Del i verabi l i ty, ” Unsol i ci ted

paper SPE 12518, U. of Trondhei m

Craf t, B. C. and Hawki ns, M F. , J r . :

“& &

Petrol eumReservoi r En i neeri n

I nc.

kngl ewood

cl i f f *i J rf i i : ce ‘ a’ ”

S1 METRI C CONVERSION FACTORS

acre x 4. 046873

bbl X 1.589873

bbl / D X 1.589873

Cp x

1.0*

f t X 3.048*

ft3/ D X 2.831685

md x 9. 869233

psi x 6. 894757

E+I )3=

M2

E-01 =

m3

E-01 =

m3/ D

E-03 = Pa*3

E-01 = m

E-02 = M3/ D

E- 04 = pm2

E- 03 = MPa

*conversion factor i s exact

APPENDI X

Oi l Pseudo Pressure, mp)oi l For Decl i ne Curve

Anal vsi s

Reference 10) i ntroduced the concept of a pseudo-

pressure mp) for oi l wel l drawdown tests si ml ar to

that now commonl y used for gas wel l s. I t was pre-

sented al ong w th a general i nfl ow perf ormance

rel ati onshi p devel oped frommul ti - poi nt test data of

some 40 oi l wel l tests.

A general i nf l ow perf ormance equati on for decl i ne

anal ysis that treats fl ow both above and bel ow the

bubbl e poi nt pressure for an undersaturated oi l wel l

assumng no non-Darcy f l ow component i s

qo

=

J* (FR - pb) + J “ ( pb2 - pwf 2) . . . . . . ..(A-l)

where J* =

()

141. 2 i ~~~ - I I

“‘ °F-“ ”

and J * =

J *

R

a2

l @o)_ “ ;

. . . . . . . . (A-3)

PRs p.

b

Assumng (UOBO) i s a constant val ue above the

bubbl e poi nt pressure equal to (BOB )b (the basis

for the constant

PI

assumpti on for

?1OWabove the

bubbl e poi nt pressure, pb) then (See al so Appendi x

of reference 10)

1

%2 = . . . . . . . . . . . . . . . ( A- 4)

pb( l @o)

P

b

‘or l / @ to go through a zero i ntercept on draw-

i own, we are real l y l ooki ng at a (kro)

/ (B0130),

Pwf

i pseudo (poB ). Thi s then woul d reproduce f i el d

i at a 10 - l og PR curves w th n =

1.DO and also

i

I ogel ’ s 1 Fi gure 7, a computer generated I PR.

{Fi gure 17 i n thi s paper. )

I


11/20

.,.

------- .. . .. ..-

.... ....-

m -

. -. . .--. -— . r

“

ma, ,., ”,,

PE

14237

M J . FklKUVICH, M t . Vl tNUl , K. u WINXJN, ana D. H. UUWI’IMII

1

Thus

J* (@o)p

Jir

Vogel form 12

:(;);[+:)

Ill(p) oil = -

J“ =

b ._

. . . . . . . . .

(A-5)

2Pb(l@ )

2p

R

P

b

b . . ...**.... .

(A-n)

Substi tuti ng equati on (A-5) i nto (A-1) we obtai n the

f i nal formof the si ngl e phase and two phase I PR

equati on

[

TR- Pb)

(Pbz - Pwf2)

q~

. J*

+

1

. 0. . . . . (A-6)

2pk

u

or i n terms of reservoi r var iables, w th kro = 1

at start of decl i ne anal ysi s

kh

1

[

1

~R-pb)+(pb2-pwf2)

qo =

[( ) ]

1 “ =). 2pb

141. 2 i n ~ - —

pR

rw

2

. . . . . . . . . . . . ( 7) 7)

or i n terms of I l l ( p) oi l

For t he case of~ SP

Rb

we have f romequati on (A- 7)

kh

1

(~R2-pwf2,

q. =

.— .

[ ]

1 l@30 _

2~

141.2

i n ~ -—

R

‘ R

‘ w‘

2

. . . . . . . (A-9)

Wth pR < p we can compare the Vogel and the AP2

?”

nf l ow r=l a l onshi p i n terms of mp)oi ~. We have

The Vogel formwoul d be extr emel y cumbersome i f

entered i nto the constant wel l bore pressure s l u-

ti ons as an mp)oi l expression whereas the

AP

?

formresul ts i n a si mpl e expressi on i denti cal i n

formto the l ow pressure gas wel l backpressure

equat ion. Oi l wel l IPR curves, j ust as gas wel l

backpressure curves are most appl i cabl e to the

-. . . -- +. -+. 61kfi -- ~-- . . , evecnlii++nn rnnfi$tinnc

GullaLallti w=, Iuul c pt Gaaul = ou~uv~”,s .-”, . . . . . ..”~.a. .A

compari son of the AP 2 formof IPR and Vogel ’s IPR

equati on (both these forms assume a non-Darcy f l ow

component of zero) can be seen i n f i gure 17. The

resul ts shown on Vogel ’ s fi gure 7 are the onl y com

pl ete set of curves gi ven i n hi s paper w th whi ch

we coul d make a compari son of the two methods when

usi ng the same match poi nt. Vogel ’ s poi nts of match

A thru H were used to devel op the compari son. Note

fr omthe fi gure 17 compari son that the

Ap2

form

of the equati on better fi ts hi s computer cal cul ated

I PR over the enti re range of depl eti on than hi s own

di mensi onl ess formof the

R equat ion. At very l ow

fl ow ng pressures approachi ng O fl ow ng pressure, a

regi on we sel domdeal w th, the Ap2 formis sl i ght ly

l ess than the si mul ati on run resul t but sti l l cl oser

than usi ng Vogel ’ s di mensi onl ess equati on.

Reference 2 i l l ustrates that when the

Ap~

formof

the I PR equati on i s combi ned w th a non-l i near p

versus N rel ati onshi p for sol uti on gas dri ve reser-

E

oi rs, t e expected decl i ne curve exponent b =

0.333. Thi s i s practi cal l y the same val ue as that

found and used i n thi s study.

1

()

k

P2

Ap2 fOf’ M

ro

: mp)oi l = ~ —

..(A-1O)

‘“R \

@“/~

R


12/20

TA 8L E I

S 25 P3 0L C RE EK F IE LD , c P 6E LL - C ON 2E RS E C O. , U fE U1 f fi

f lA 21 c R CS ER VO IR O AT A N KI 0 2C LI II E C mV 2 W AT CH P Wf ~

T18LE 2 SC1030 2REEK FIELD, CNQBELL - COWERSE CO,, W3511m

Channe sand PvT Data Bar Sand PVT Data

Federa M- Pw--(ph . 340+3] Hat h

m E-

P VT [ Ph

.

2705] Fed

ra J-1

(Pb

53]

P

FA

@ .9P

@&

@p P

.

u

~ R$B cjii& “ ,O~?St- $ RII;%8 CP,$ ji x ,0- P _

&R, - & &;B .p,~;B x 10-:

UCI1

Oate

(m . VP)

F4rst

‘ r

0

M 1

Oecliin

Pm du ct f c dl m ly sf s

A-1

c-

D-2

00-1

EE-1

F-1

FF-1

G.]

G&1

6G-2

74-1

1-1

J-1 (B)

JJ-1

K-1

K-1 (B )

F.-4

m-

KK-2

LL-1

L::: (B]

0-1

R-1

R-2

R-3

R-3 (B )

k-4

s-1

S -1 ( 0)

T-1

T-2

T-3

r-d

0.150

0.1S3

0.150

D.224

0.200

0.154

0.180

0.1342

0.150

0.15D

0.150

O.m

1.90

1.9D

1.9D

1.70

1.70

1.9D

1.70

1.90

1.9D

1.90

1.9D

1.?0

D.366

D.420

0.40D

0.431

0.405

0.4.3U

0.41317

0.366

0.37.s

0.405

0.420

0.425

27.4

24.6

22.1

24.5

21.6

15.9

21.4

24.5

24.5

24.5

24.5

?7.5

0.46

0.46

0.46

0.43

0.44

0.46

0.45

0.46

0.46

0.46

0.46

0.43

1.47

1.47

1.41

;::

1.47

1.47

1.47

1.47

1.47

1.47

1.48

0.647

0.6%

0.677

0.707

0.682

0.6%

0.677

0.638

0.658

0.68?

D.696

0.702

15.7

14.5

13.2

15.0

13.4

11.6

15.6

14.2

14.7

14.7

14.1

15.5

9-61

10-81

1-22

2-83

3-ss3

10-63

1~-~

9-82

6-82

10-81

9-62

5-63

2-63

6-82

3-83

12-82

5-63

7-83

5-.93

6-83

4-02

6-E33

8-83

8-83

12-82

5-83

5-83

5-.92

3-83

6-83

8-83

7-83

5-83

4-83

7-22

2-83

10-81

5-02

12-81

12-62

6-81

3-93

6-83

11-63

11-83

10-81

9-83

12-82

7-83

3-83

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3-83

7-83

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11-53

lD-80

3-82

12-82

2633

6226

7821

13839

764;

3?2

:

3839

1761

4287

501

74;

R:

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21473

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24533

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m-1

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FF-1

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so-1

62-2

H-

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K -1 ( 8)

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n-3 (B )

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6-62

6-22

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8-82

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3-83

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8-92

8-82

8-62

11-81

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S-83

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5-m

5-W

7-82

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9-82

10-80

5-23

7-81

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.132

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0.212 1030 0.220

0.0s9

l lk 30 0 .6 80

0.156

10 0.110

0.334 lCQD 0.ss0

0.313 lDOO 0.432

0.21D 10 0.076

0.510 100 0.086

0.100

lm 0.270

0.130 IDm 0.430

0.098

l GW 0.914

0.083 1~ 0.670

0.29D

low 0.19D

0.146

l oD Ll 0 .2 Q5

0.115

I rm 0.1 3D

D.07$

l DI M 0.580

0.185

1000 0. 7B

0.210 i

0S4 0. 17

0.229 IDOD 0.527

0.190

100 0. 098

0.079

10 0.550

0.250

l DD 0. 092

0.178 1003 0.231

0.144

100 0.310

0.130 1233 0.380

0.092

100 0. 670

0.063

l fX l 0.2.95

0.115

1 0D 0 .0 67

0.118

1 L1 3 0 .0 70

0.115

l DD O 0 .2 64

0.203

100D 0. 2W

0.220

100 0. 069

0.270

]m 0.25D

D.20D

l DO 0 .2 2J 3

0.239

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Om

l DD 0.028

0.165

1C430 0.33D

0.018

l @J 0 ,1 70

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1 Y 3 0 .1 31

0:111 I& ::74

0.20

1.70

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0. 20 1.70 0.368 26

0.180

0.150

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1.73

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1.88

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28.9

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0.44

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24.5 0.45 1.47 0.712

21.6 0.45

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0.46 1.47 D.640

16.2

0.46 1.47 0.696

13.2

0.46

1.47

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14.7

0.46 1.41 0.6% 14.7

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1.47

0.668

14.3

14.3

13.3

20.8

15.2

0.20 1.70

D.368 22

0.355

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28,9

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24.5

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1.70 o.36a 25

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24.3

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1.47

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0.670

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0.696

0.672

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1.70

1.72

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0.391

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28.9

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