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E L S E V I E R

Journal of Petroleum Science and Engineering 17 (1997) 237 246

J O U ~ I M O F

~ ~ I G I N E E R I N G

dent i f icat ion of f low units in shaly sand reservoirs

Kittiphong Jongkittinarukorn l , jebbar Tiab

Unit~ersity of Oklahoma Norman OK 73019-0628 USA

Receiv ed 17 July 1995; accepted 21 June 1996

A b s t r a c t

T he key to improv ing re s e rvo i r des c r ip t ion and exp lo i t a t ion i s to des c r ibe complex va r i a t ions in pore geome t ry wi th in

d i f fe ren t l i t ho fac ie s . Va r ia t ions in s ha le p ro pe r t i e s , s ha le d i s t r ibu t ion and pore geom e t r i ca l a t tr ibu te s de f ine the ex i s t ence o f

d i s t inc t hydrau l i c ( f low) un i t s w i th s im i la r f lu id - f low cha rac te r i s t i c s in s ha ly s and re s e rvo i r s .

T h i s s tudy p ropos es a new me tho d fo r iden t i fy ing hydra u l i c f low un i t s in s ha ly s and re s e rvo i r s . T he p ro pos ed m e thod i s

b a s e d o n t h e a p p l i c a t i o n o f s e v e r a l s h a l y s an d m o d e l s , in c l u d i n g th e C o a t e s - D u m a n o i r , a n d W a x m a n a n d S m i t s m o d e l s , th e

Coa te s and Denoo , and Morr i s and B iggs cor re la t ions , and the S imandoux mode l .

T h e d e v e l o p e d eq u a t i o n s i n d i c at e t h a t f o r an y f l o w u n it , a l o g - l o g p l o t o f a r e s e r v o i r q u a l i ty i n d e x ( R Q I ) v s . p o r o s i t y

s hou ld y ie ld a s t ra igh t l ine wi th a cha rac te r i s t i c s lope ; 1 .5 fo r s and re s e rvo i r s , 2. 5 fo r l am ina ted s ha le and s t ruc tu ra l s ha le ,

and 3 . 5 fo r d i s pe rs ed s ha le . T he in te rcep t o f the s t ra igh t line wi th 05 = 1 , de s igne d a s the s ha le zone in d ica to r (SZ I) , i s a

un ique pa rame te r fo r each f low un i t .

T he p ro pos ed t echn ique has been s ucces s fu l ly t e s t ed in s ha ly and ve ry s ha ly s and re s e rvo i r s f rom T exas . T he exam ples

s how tha t the re a re s t rong re l a t ions h ips be tween ca t ion-excha nge capac i ty , fo rma t ion re s i s t iv i ty fac to r , pe rmeab i l i ty , and

res e rvo i r qua l i ty index and s ha le zone ind ica to r . T h i s pap e r inc ludes the theore t i ca l deve lopm ent , va l ida te s and ch a rac te r i ze s

the f low un i t s to demons t ra t e the e f f i c i ency o f the p ropos ed t echn ique .

Keywords:

flow units: shaly san d reservoirs

1 I n t r o d u c t i o n

I t i s w e l l r e c o g n i z e d t h a t i m p r o v e m e n t s i n r e s e r -

v o i r d e s c r i p t i o n w i l l r e d u c e t h e a m o u n t o i l a n d g a s

l e f t b e h i n d w e l l s . T h e c e n t r a l e l e m e n t i n i m p r o v e d

r e s e r v o i r d e s c r i p t i o n i s a c c u r a t e d e t e r m i n a t i o n o f

p o r e - b o d y / t h r o a t a t tr i b ut e s a n d f l u i d d i s tr i b u ti o n

( A m a e f u l e e t a l . , 1 9 9 3 ) .

T h e r e l a t i o n s h i p s b e t w e e n s a t u r a t i o n o r p o r o s i t y

Corresponding author.

i SPE member.

a n d m e a s u r e d p h y s i c a l q u a n t it i e s a re w e l l k n o w n f o r

c l e a n s a n d s . T h e p r e s e n c e o f c l a y o r s h a l e m i n e r a l s

g r e a t l y c o m p l i c a t e s l o g i n t e r p r e t a t i o n a n d c o n s i d e r -

a b l y a f f e c t s c h a r a c t e r i z a t i o n o f h y d r o c a r b o n - b e a r i n g

f o r m a t i o n s . T h e e f f e c t s i n c l u d e :

r e d u c t i o n i n t h e e f f e c t i v e p o r o s i t y ;

r e d u c t i o n i n t h e p e r m e a b i l i t y ;

a l t e r a t i o n i n t h e r e s i s t i v i t y .

T h e r e a r e t h r e e b r o a d c a t e g o r i e s o f s h a l e d i s t r i b u t i o n

i n a s a n d :

1. L a m i n a t e d l a y e r s o f s h a l e w i t h i n t h e s a n d ;

2 . D i s p e r s e d s h a l e o n t h e s a n d g r a i n s , o r p o r e f i l l -

i n g ;

0920-4105/97/$17.00 Copyright 1997 Elsevier Science B.V. All rights reserved.

PH

S 0 9 2 0 - 4 1 0 5 ( 9 6 ) 0 0 0 4 6 - 0

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238 K. Jongkitt inarukorn. D. Tiab / Journal of Petroleum Science and Engineering 17 1997) 237-24 6

3 . S t ruc tu ra l sand-s i ze d sha le pa r t i c l es in load-

bear ing pos i t ions wi th in the rock .

W a x m a n a n d S m i t s ( 1 9 6 8 ) a n d H i l l a n d M i l b u m

( 1 9 7 7 ) h a v e s h o w n t h a t e l e c t r o c h e mi c a l b e h a v i o r o f

s h a l y s a n d s i s re l a t e d t o th e c a t i o n - e x c h a n g e c a p a c i t y

( CE C) o f t h e s e d i me n t a n d t o t h e c a t i o n - e x c h a n g e

c a p a c i t y p e r u n i t p o r e v o l u me o f t h e r o c k , Q v . T h e

s u c c e s s f u l u s e o f t h i s p a r a me t e r g u i d e s t o p r e d i c t i n g

p o s s i b l e r e l a t i o n s b e t w e e n t h i s p a r a me t e r a n d o t h e r

p e t r o p h y s i c a l p r o p e r t i e s o f s h a l y s a n ds .

A m a e f u l e e t a l . (1 9 9 3 ) d e f i n e d t h e r e s e r v o i r q u a l -

i ty index (RQI) as :

v / K ( 1 )

Q I ( t ~m ) = 1 0 2 w ~

a n d p r o p o s e d t h e n e w me t h o d f o r i d e n t i f i c a t i o n a n d

c h a r a c t e r i z a t i o n o f h y d r a u l i c u n i t s w i t h ma p p a b l e

geo log ica l un i t s ( fac ies ) in sands tone reservo i rs .

T h i s s t u d y e x t e n d s t h e w o r k o f A ma e f u l e e t a l .

( 1 9 9 3 ) a n d T i a b ( 1 9 9 3 ) t o c o v e r d i f f e r e n t t y p e s o f

sha le d i s t r ibu t ion - - l amina ted sha le , d i spersed sha le

a n d s t r u c t u r a l s h a l e - - a n d p r o p o s e s a n e w me t h o d

for charac te r i z ing and iden t i fy ing f low un i t s in sha ly

s a n d r e s e r v o i r s . T h e p r o p o s e d me t h o d i s b a s e d o n

the app l i ca t ion o f severa l sha ly sand model s , i nc lud-

i n g t h e Co a t e s a n d D u ma n o i r ( 1 9 7 3 ) mo d e l , t h e

W a x ma n a n d Smi t s ( 1 9 6 8 ) mo d e l , t h e Co a t e s a n d

D e n o o ( 1 9 8 1 ) c o r r e l a t i o n , t h e Mo r r i s a n d B i g g s

( 1 9 6 7 ) c o r r e l a t i o n , a n d t h e S i ma n d o u x ( 1 9 6 3 ) mo d e l .

Mo r r i s a n d B i g g s ( 1 9 6 7 ) p r o p o s e d t h e f o l l o w i n g

corre la t ion :

k

( 2 c )

where B V W = ~S,~ .Both Eqs . 2 and 3 show tha t

permeab i l i ty (k ) i s a func t ion o f ~b4 f o r c l e a n s a n d

reservo i rs .

Th i s s tudy inc ludes f ive d i f fe ren t sha le model s

w h i c h a r e L a mi n a t e d Sh a l e , D i s p e r s e d Sh a l e , S t r u c -

tu ra l Sha le and To ta l Sha le , and the sha le model

b a s e d o n t h e Co a t e s - D u ma n o i r c o r r e l a t i o n . A l l s h a l y

s a n d mo d e l s c a n b e r e p r e s e n t e d b y :

l o g ( R Q I ) = m l o g (q S ) + l o g ( S Z I ) ( 3 )

Th i s equa t ion ind ica tes tha t fo r any f low un i t , a

l o g - l o g p l o t o f RQ I v s . p o r o s it y y i e l d s a s tr a i g h t l i ne

w i t h s l o p e m . Sa m p l e s w i t h d i f f e r e n t SZ I v a l u e s w i l l

l i e on d i f fe ren t para l l e l l i nes . The va lue o f the con-

s t an t SZ I c a n b e d e t e r mi n e d f r o m t h e i n t e r c e p t o f t h e

s t ra igh t l ine a t po ro s i ty (~b) = 1 . Sam ples tha t l ie on

the same s t ra igh t l ine have s imi la r res i s t iv i t i es , water

sa tu ra t ion , sha le d i s t r ibu t ion , sha le p roper t i es , po re

shape fac to r , and cons t i tu t e a f low un i t .

2 . 1 . L a m i n a t e d S h a l e M o d e l

2 . M e t h o d d e v e l o p m e n t

Co a t e s a n d D e n o o ( 1 9 8 1 ) p r o p o s e d t h e f o l l o w i n g

corre la t ion :

4 4 [ 1 S w i ] 2

w h e r e ~ i s t h e e f f e c t i v e p o r o s i t y . A p p l y l o g - l o g o n

bo th s ides o f Eq . (2a) and rear range as :

l O , 0

= 1 .51o g( ) + log[ ' r r{(1 -

S w i ) / S w i } ]

= l o g ( R Q I ) ( 2 b )

T h i n s h a le l a m i n a t i o n s a r e i n t e r s p e r s e d w i th c l e a n

s a n d . T h e o v e r a l l p o r o s i t y a n d p e r me a b i l i t y o f t h e

a v e r a g e d i n t e r v a l i s r e d u c e d i n p r o p o r t i o n t o t h e

f r a c t i o n a l v o l u me o f s h a l e s i n c e t h e e f f e c t i v e p o r o s -

i ty and the permeab i l i ty o f the sha le a re es sen t i a l ly

zero . The equat ion , which i s der ived in de ta i l i n

A p p e n d i x A , p r o p o s e d b y t h i s s t u d y f o r l a mi n a t e d

shale is:

RQ I = ~ 5SZ1, (4 )

Apply log on bo th s ides o f Eq . (4 ) as :

l o g ( R Q I ) = 2 . 5 l og + l o g ( S Z I , )

5 )

This equa t ion ind ica tes tha t fo r any f low un i t , a

l o g - l o g p l o t o f RQ I v s . p o r o s i ty y i e l d s a s t r a ig h t l in e

w i t h s l o p e o f 2 . 5 f o r t h e L a mi n a t e d Sh a l e Mo d e l .

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2 3 9

2 . 2 . D i s p e r s e d S h a l e M o d e l

C l ay r ep l aces po re f l u i d and d i s s em i na t es i n t he

po re s pace o f t he s and . A re l a t i ve l y s m a l l am oun t o f

c l ay can p l ug po res and r educe e f f ec t i ve po ros i t y and

par t i cu l a r l y pe rm eab i l i t y t o nonp roduc i b l e va l ues .

The re fo re , th i s t ype o f d i s t r ibu t i on can caus e s eve re

f o r m a t i o n d a m a g e .

Neas ham (1977 ) has p ropos ed t h ree d i f f e ren t ca t -

ego r i e s o f d i s pe r s ed c l ays :

( 1 D i s c r e t e p a r t i c l e c l a y s

r e f l ec t t he t yp i ca l m od e

o f occu r rence o f kao l i n i t e in s ands t ones . K ao l i n i te

c ry s t a l s t ha t ex t ens i ve l y f i l l po res have a r andom

ar rangem en t wi t h r e s pec t t o one ano t he r and a f f ec t

rock pe t rophys i ca l p roper t i e s p r i m ar i l y by r educ i ng

t he i n t e rg ranu l a r po re vo l um e and behav i ng as m i -

g ra t i ng f i nes i n t he po re s y s t em .

(2)

P o r e l i n i n g c l a y s

a re a t t ached t o t he po re

wa l l s , o f t en fo rm i ng a r a t he r con t i nuous and t h i n

c l ay m i ne ra l coa t i ng . I l l i t e , ch l o r i t e , and m on t m or i l -

l on i t e s have been obs e rved wi t h po re l i n i ng m or -

pho l og i es .

(3)

P o r e b r i d g i n g c l a y s

also include i l l i t e , ch lo-

r i t e , and m on t m or i l l on i t e s . The ex t ens i ve deve l op -

m en t o f i n t e rg rown c l ay c ry s t a l s w i t h i n po re s y s t em

crea t es bo t h m i c ropo ros i t y and t o r t uous f l u i d f l ow

pa t hways .

W a x m a n a n d S m i t s ( 1 9 6 8 ) c o n s id e r e d t he c o n d u c -

t i v i t y o f c l ay t o be due t o ca t i on exchange and

deve l oped t he m ode l t o ca l cu l a t e r e l i ab l e wa t e r s a t u -

ra t i on ca l cu l a t i ons fo r r e s e rvo i r s w i t h d i f f e ren t c l ay

c o n t e n t s a n d o v e r a w i d e r a n g e o f f o r m a t i o n - w a t e r

sal in i t i es . They assumed that :

(1 ) A pa ra l l e l conduc t ance m echan i s m fo r f r ee

e l ec t ro l y t e and c l ay -exchange ca t i on com ponen t s .

(2 ) An exchange ca t i on m ob i l i t y t ha t i nc reas es t o

a m ax i m um and cons t an t va l ue wi t h i nc reas i ng equ i -

l i b ra t ing e l ec t ro l y t e concen t ra t i on .

(3 ) Iden t i ca l geom et r i c conduc t i v i t y cons t an t s ap -

p l i cab l e fo r t he con t r i bu t i ons o f bo t h t he f r ee e l ec -

t ro l y t e and t he c l ay -exchange ca t i on conduc t ance t o

t he s and conduc t i v i t y . Th e i r we l l -known m ode l i s

g i ven by :

R,~ F ~

S ~ , = ( R , 1 +

R ~ B QS ~

( 6 )

The equa t i on , wh i ch was de r i ved i n de t a i l s i n Ap-

pend i x B , p ropos ed by t h i s s t udy fo r d i s pe r s ed s ha l e

i s :

RQ I = ~b~ 5SZId (7 )

Tak i ng t he l oga r i t hm on bo t h s i des o f Eq . (7 ) g i ves :

l og (R QI) = 3 .5 l og (~ he) + l og (S ZId ) (8 )

Th i s equa t i on i nd i ca t e s t ha t fo r any f l ow un i t , a

l og - l o g p l o t o f R QI v s . po ros i t y y i e l d s a st r a igh t li ne

wi t h s l ope o f 3 . 5 fo r t he Di s pe r s ed S ha l e Mode l .

2 .3 . S t r u c t u r a l S h a l e Mo d e l

In t h i s fo rm c l ay g ra i n s t ake t he p l ace o f s and

g ra i n s . P o ros i t y and pe rm eab i l i t y o f t he s and a re

affected very l i t t l e . S ince i t s proper t ies are s imi lar to

t hos e o f l am i na r s ha l e , one can u s e t he s am e equa-

t i on a s t ha t fo r t he Lam i na t ed S ha l e Mode l .

2 .4 . T o t a l S h a l e Mo d e l

S i m andoux (1963 ) p ropos ed t he genera l s ha l e r e -

l a t i ons h i p s wh i ch i s i ndependen t o f s ha l e d i s t r i bu -

t ion . This model i s a l so appl icable to d i spersed or

laminated shale . The re la t ion i s :

, b ' E h 1

, m - - S ? , ~ S , , - - = 0 ( 9 )

R~h RI

The equa t i on , wh i ch was de r i ved i n de t a i l s i n Ap-

pend i x C , p ropos ed by t h i s s t udy fo r t he To t a l S ha l e

Model i s :

R Q l = ~ h ) S S Z I t 1 0 )

A p p l y l o g o n b o t h s i d e s o f E q . 1 0 ) a s:

l o g ( R Q l ) = 3 .5 l o g @ + I o g ( S Z l , ) ( 1 1 )

Th i s equa t i on i nd i ca t e s t ha t t o t any f l ow un i t , a

l og - l o g p l o t o f R QI v s . po ros i t y y i e ld s a s t r a igh t l ine

wi t h s l ope o f 3 . 5 fo r t he To t a l S ha l e Mode l .

2 . 5 . S h a l e m o d e l b a s e d o n C o a t e s a n d D u m a n o i r

co r r e l a t i o n

C oat es and Dum ano i r (1973 ) p ropos ed t he fo l l ow-

i ng co r re l a t i on fo r s ha l y s and r e s e rvo i r s :

300 ~w

V k - R , , ( 1 2 )

W 4 - -

R t i u . ) a d j

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K. Jongkittinarukorn, D. Tiab / Journal o f Petroleum Science and Engineering 17 1997) 237 -246

wh ere W = 2 .0 . Subs t i tu t ing Eq . (1 ) in to Eq . (12)

and rear rang ing as :

0.58 9R tirr 1 - Vsh )

l o g ( R Q I ) = 3 . 5 l o g ( ~b ) + l o g Rw

( 1 3 )

Let us def ine the sha le zone ind ica to r (SZI) as :

R t i r r

SZ l c a D = 0 . 5 8 9 ( 1 - Vsh ) ( 1 4 )

Rw

Subs t i tu t e Eqs . (1 ) and (14) in to Eq . (13) and app ly

l o g - l o g o n b o t h s i d e s g i v e s :

I o g ( R Q I ) = 3 . 5 l o g ( b ) + l o g (SZ l c e D ) ( 1 5 )

The equat ion ind ica tes tha t fo r any f low un i t , a

l o g - l o g p l o t o f RQ I v s . p o r o s i t y y i e ld s a s t r a i g h t li n e

wi th s lope o f 3 .5 .

T a b l e 1 s u m ma r i z e s SZ I s f o r d if f e r e n t r e s e r v o i r

mo d e l s . D i f f e r e n t mo d e l s y i e l d d i f f e r e n t v a l u e s o f

SZ I a n d d i f f e r e n t s l o p e s . C l e a n s a n d r e s e r v o i r s h a v e

the lowes t s lope o f 1 .5 . Al l o f the sha le m ode l s have

h i g h e r s l o p e s . T h e L a mi n a t e d Sh a l e Mo d e l h a s t h e

l o w e s t s l o p e o f 2 . 5 a mo n g s h a l e mo d e l s . T h e D i s -

p e r s e d Sh a l e , Co a t e s a n d D u ma n o i r , a n d T o t a l Sh a l e

Mo d e l s y i e l d t h e s a me s l o p e o f 3 . 5 . T h u s t h e Co a t e s

a n d D u ma n o i r a n d T o t a l Sh a l e Mo d e l s a r e n o t a p p l i -

c a b l e f o r l a m i n a t e d s h a l e r e s e r v o i r s .

3 . G e o log ic a l s ign i f i c an t o f S Z I

SZ I i s a u n i q u e p a r a me t e r t h a t i n c o r p o r a t e s t h e

geo log ica l a t t r ibu tes o f t ex tu re and sha le in the d i s -

c r imina t ion o f d i f fe ren t hydrau l i c un i t s . In genera l ,

rocks con ta in ing c l ays o r sha le as wel l as f ine-

g ra ined , poor ly so r t ed sands t end to exh ib i t h igh

s u r f a c e a r e a a n d h i g h t o r t u o s i t y , h e n c e l o w SZ I . I n

con t ras t , l es s sha le , coarse-g ra ined and wel l - so r t ed

s a n d s e x h i b i t l o w e r s u r f a c e a r e a s , l o w e r s h a p e f a c t o r ,

l o w e r t o r t u o s it y , a n d h i g h e r SZ I v a l u e s . D e p o s i t i o n a l

e n v i r o n me n t s a n d d i a g e n e t i c p r o c e s s e s c o n t r o l p o r e

g e o me t r y a n d SZ I i n s h a l y s a n d r e s e r v o i r s .

4 . H y d r a u l i c ( f l o w ) u n i t z o n a t i o n p r o c e s s

T h i s p r o c e s s i s d i s c u s s e d i n d e t a i l s b y A ma e f u l e

e t a l . ( 1 9 9 3 ) , T i a b ( 1 9 9 3 ) a n d T i a b a n d D o n a l d s o n

( 1 9 9 6 ) . T h e p r o c e d u r e f o r t h i s n e w me t h o d i s :

T a b l e 1

S u m m a r y o f r e s e r v o ir m o d e l s

Mo del S lope SZI in t e r cep t )

(1 - S,~i)

Clean Sand 1.5 zr

S w ~

1(1 - i )

L a m i n a t e d S h a l e 2 . 5

- t - - R s h j i r r

Iv (1 i )

Dis p er s ed Sha le 3 .5

Tota l Sha le 3 . 5

C o a t e s a n d D u m a n o i r 1 9 7 3 )

3.5

( l - Swi )

- -

F* RwR t

R t i r r

0.5 89 1 - V~h)

R ~

- -

F* Rw R t

i r r

l r

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2 4 1

(1 ) For each da ta po in t , ca l cu la t e :

I QI m) =

R Q I

SZ1 -

( 2 ) Co n s t r u c t t h e l o g - l o g p l o t o f RQ I v s . p o r o s -

ity.

(3 ) Draw a s t ra igh t l ine pass ing th rough a g roup

o f d a t a p o i n ts w i t h t h e s l o p e s u m ma r i z e d i n T a b l e 1.

(4 ) Determ ine SZ I fo r each s t ra igh t l ine @ q5 = I .

( 5 ) D e t e r mi n e t h e n u mb e r o f u n i t s b y e mp l o y i n g

s ta t i s t i ca l methods .

h i s t o g r a m

t es t fo r norm al i ty

c lus t e r ana lys i s

e r ro r ana lys i s

(6 ) Es tab l i sh the re l a t ionsh ips be tween SZI and

the above var i ab les .

( 7 ) D e v e l o p t h e e q u a t i o n f o r p e r me a b i l i t y :

k = 1 0 1 4 ( S Z I 2 ) @ ~

(8) Replot k vs. qS,

T h i s p r o c e s s p r o v i d e s a u n i q u e p a r a me t e r , SZ I ,

f o r d e l in e a t i n g t h e n u m b e r o f h y d r a u l i c ( f l o w ) u n i t s

r e q u i r e d a s g e o l o g i c a l a n d p e t r o p h y s i c a l p a r a me t e r s

in reservo i r s imula t ion .

5 F i e l d e x a m p l e s o f s h a l y s a n d r e s e r v o i r s

T w o f i e l d e x a m p l e s f r o m t h e T a y l o r a n d W i l c o x

f i e l d s , T e x a s , U . S . A . . a r e p r e s e n t e d t o d e mo n s t r a t e

t h e a p p l i c a b i l i t y o f t h e p r o p o s e d me t h o d .

5.1. Taylor Sand, Big Foot, Texas cerv shalv sand-

stone)

A l o g - l o g p l o t o f RQ I v s. c f o r t h is d a ta s et

(Fig . 1 ; W ax m an and Sm i t s , 1968) shows the ex i s -

t ence o f th ree d i s t inc t hydrau l i c un i t s (HU) wi th in

the co red in te rva l . Diagenes i s has modi f i ed the o r ig i -

na l depos i t iona l parameters to g ive these mul t ip le

f low un i t s . F ig . 2 i l l u s t ra t es the exce l l en t co r re l a t ion

b e t w e e n Q ~ a n d SZ I . A s e x p e c t e d Q v d e c r e a s e d

0 . 1

C ~ 0 0 1

0 . 0 0 1

. . . . . . . . . . . . . . . . . . . o o i : i : . . .

0.1

P o r o s i l y f r a c t i o n

F i g . 1 . P l o t o f R Q I v s . p o r o s i t y .

w i t h i n c r e a s i n g SZ I . T h e r e l a t i o n s h i p b e t w e e n Q v

a n d SZ I

is:

A

Q , - S Z IB ( 1 6 )

whe re A = 0 .994 and B = 0 .272 . S ince the d i f fe r -

e n c e b e t w e e n t o t a l p o r o s i t y a n d e f f e c t i v e p o r o s i t y i s

a l i n e a r f u n c t i o n o f CE C. T h e r e f o r e t h e l o w e r CE C,

the h igher the ab i l i ty o f fo rmat ion to t ransmi t f lu ids

a n d t h e h i g h e r th e v a l u e o f SZ L T h e e x i s t e n c e o f SZ I

w a s f u r t h e r v e r i f i e d b y p l o t t i n g f o r ma t i o n r e s i s t i v i t y

f a c t o r a n d p e r me a b i l i t y v s . SZ I ( F i g s . 3 a n d 4 ) . T h e

r e l a t io n s h i p b e t w e e n F* a n d SZ I i s:

C

F ~ - ( 1 7 )

SZ I ~

w h e r e C = 21 .1 4 a n d D = 0 .2 4 4. T h e l o w e r t h e

v a l u e o f f o r ma t i o n r e s i s t i v i t y f a c t o r f o r s h a l y s a n d ,

the l es s the to r tuos i ty o f the fo rmat ion and the h igher

10

c3 1

0.1

0 1

1

SZI

F i g . 2 . C a t i o n e x c h a n g e c a p a c i t y v s. S Z I .

10

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2 4 2 K. Jongkininarukorn, D. Tiab /

Journal

of Petroleum Science

and ngineering

17 1997) 237-246

100

10

0 1

SZb

Fig. 3. Fo r m a t i o n r e s i s t i v i ty fa c to r vs . SZ1.

1

0.1

0.01

m ~ l H L 1 S Z I 1 6

l o l l

0 1

P o r o s i t y f r a c t i o n

Fig. 6. Pl o t o f R Q I v s . p o r o s ity .

1 0 0

10

1

~ 0 .1

i

0 . 0 1

0 . 0 0 1

0 . 0 0 0 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

m,

o 1

SZl

Fig 4 P ermeabi l i ty vs SZI

10

t h e v a l u e o f S Z I . T h e r e l a t io n s h i p b e t w e e n k a n d

S Z I c a n b e r e p r e s e n t e d m a t h e m a t i c a l l y b y t h e fo l -

l o w i n g e x p r e s si o n :

k = E * S Z I F 1 8 )

w h e r e E = 0 . 0 4 a n d F = 2 . 4 8 6 . F ig . 5 s h o w s t h e

l o g - l o g p l o t o f R Q I a n d S Z1 w h i c h c a n b e e x p r e s s e d

a s :

R Q I = G * S Z I ( 1 9 )

w h e r e G = 0 . 0 1 2 a n d H = 1 .2 13 . T h e h ig h e r t he

p e r m e a b i l i t y a n d t h e h i g h e r t h e r e s e r v o i r q u a l i t y

i n d e x , t h e h i g h e r t h e v a l u e o f S Z I .

5 . 2 . Wilcox Sand Sheridan Texas

F ig . 6 s h o w s a l o g - l o g p l o t o f R Q I a n d ~b w h i c h

h a s t w o d i s ti n c t h y d r a u l ic u n i t s ( H U ) . T h e p l o t s o f

Q , F ~ k a n d R Q I v s . S Z I a r e s h o w n i n F i g s . 7 , 8 ,

9 a n d 1 0 , r e s p e c t i v e l y . T h e y h a v e t h e s a m e t r e n d s o f

r e l a t i o n s h i p a s t h o s e i n t h e p r e v i o u s e x a m p l e b u t

d i f f e r e n t s t r a i g h t l i n e s . T h e c o n s t a n t s i n E q s . ( 1 6 ) -

0.1

0 0 1

0 0 0 1

0 0 0 0 1

0 1 1

S Z l

Fig . 5 . Re s e r v o i r q u a l i ty i n d e x vs . SZ I .

10

+o.1

0 . 0 1

10 1 0 0

S Z I

Fig. 7. Ca t i o n -e x c h a n g e c a p a c i ty vs . SZ1.

1 0 0 0

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K . J o n g k i t t in a r u k o r n , D . T i a b / J o u r n a l o f P e t r o l e u m S c i e n c e a n d E n g i n e e r i n g 1 7 1 9 9 7 ) 2 3 7 2 4 6 2 4 3

1 0 0 -

5_

1 0

10

1E5

1 0 0

S Z l

F i g . 8 . F o r m a t i o n r e s i s t iv i t y v s . S Z I .

1 O0 0

1E4

1E3

1E2

1E1

lEO

1E-1

1E-2

1E-3

lO loo lOO,O

SZI

Fig . 9 . Pe rm e a b i l i ty vs . SZ I .

( 1 9 ) f o r th i s s e t ( W a x m a n a n d Sm i t s, 1 9 6 8) o f d a t a

are:

A = 2 . 2 0 , B = 0 . 6 0

C = 7 7 . 4 , D = 0 . 2 3

E = 3 . 3 10 6 F = 3 . 2 4

G = 1.86 1 0 - 4 H = 1.55

10-

~ 0 .1

0 . 0 1

0 . 0 0 1

1

m m . m r

1 0 0

S Z I

F i g . 1 0 . R e s e r v o i r q u a l i ty i n d e x v s . S Z I .

1 0 0 0

Fi g s . 7 - l 0 s h o w t h e s t r o n g r e l a t i o n s h i p b e t w e e n Q v ,

F* , k , RQ I , r e s p e c ti v e l y , a n d th e p r o p o s e d p a r a me -

te r (SZI) . I t i s ev iden t f rom Fig . 7 tha t Qv decreases

w i t h i n c r e a s i n g SZ I , t h u s ma n i f e s t i n g t h e e f f e c t o f

c l a y m i n e r a l s o n t h e r e s e r v o i r s f l o w q u a l it y .

6 C o n c l u s i o n s

A n e w p r a c t i c a l t e c h n i q u e h a s b e e n d e v e l o p e d t o

iden t i fy hydrau l i c ( f low) un i t s in sha ly sand reser -

vo i rs . The t echn ique i s success fu l ly app l i ed to two

shaly sand reservo i rs in Texas . Th i s s tudy in t roduces

a new un ique parameter , t he sha le zone ind ica to r

( SZ I ) f o r o u t l i n i n g t h e n u mb e r o f l a y e r s r e q u i r e d f o r

r e s e r v o i r d e v e l o p me n t . T w o e x a mp l e s s h o w t h e r e a r e

s t r o n g r e l a t i o n s h i p s b e t w e e n c a t i o n - e x c h a n g e c a p a c -

i ty , fo rmat ion res i s t iv i ty fac to r , permeab i l i ty , reser -

vo i r qua l i ty index and sha le zone ind ica to r .

7 N o t a t i o n

/

B V W

F *

Fr~

hsh

h~

k

m

t/

Q

R ~d

Rsh

g t i r r

R Q I

S~

SZ I o

SZI~

SZI t

V,h

W

e q u a t i o n c o e f f i c i e n t a s s o c ia t e d w i t h m

b u l k v o l u m e o f w a t e r

f o r ma t i o n r e s i s ti v i t y f a c t o r f o r s h a l y s a n d

f o r ma t i o n r e s i s ti v i t y f a c t o r f o r c l e a n s a n d

sha le th i ckness , f t

reservo i r th i ckness , f t

p e r m e a b i l it y , m D

c e m e n t a t i o n e x p o n e n t

s a t u r a t i o n e x p o n e n t

c a t i o n - e x c h a n g e c a p a c i t y

res i s t iv i ty o f sand , f~

res i s t iv i ty o f sha le , ~~

f o r ma t i o n r e s i s t i v i t y a t i r r e d u c i b l e w a t e r

saturat ion, f~

reservo i r qua l i ty index

water sa tu ra t ion

s h a l e z o n e i n d i c a t o r l b r D i s p e r s e d Sh a l e

M o d e l

s h a l e z o n e i n d i c a t o r f o r L a mi n a t e d Sh a l e

Mo d e l

s h a l e z o n e i n d i c a t o r f o r T o t a l Sh a l e Mo d e l

sha le vo lume, f rac t ion

s ing le t ex tu ra l exponen t

ef fec t ive poros i ty in sha ly sand , f rac t ion

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244 K. Jongkittinarukorn, D. Tiab / Journal of Petroleum Science and Engineering 17 1997) 237-246

A p p e n d i x A . D e v e l o p m e n t o f L a m i n a t e d S h a l e

M o d e l

The t o t a l r e s i s t i v i t y o f a r e s e rvo i r w i t h l am i na t ed

shale

is:

1 1 - V,h V~h

- - - + - - A - l )

R t R s d R s h

where t he l am i na t ed s ha l e vo l um e as a f r ac t i on i s

V~h = ~ h ~ h ) / h ~ ( A - 2 )

The r e s i s t iv i t y o f t he c l ean s and l aye r i s:

Frd Rw

R s d - - - - ( A - 3 )

S nw

The fo rm a t i on r e s i s ti v i t y f ac t o r o f c l ean s and i s:

a

Frd - - (A -4 )

s d

and m = 2, n = 2, and a = 1C om bi n i ng Eqs . A - l -

A-4 and r ea r rang i ng g i ves :

s~ = R, R~. 1 - E h ) A-5)

In t he i r r educ i b l e wa t e r s a t u ra t i on zone , Eq . (A-5 )

b e c o m e s :

, { [ , } A 6 ,

S~ i = ~ Rt R s h i r r

S ubs t i t u t e Eq . (A-6 ) i n t o Eq . (2a ) and r ea r range as :

1 4 ( 1 - - S w i ) 2

k = d ) { [ lR t

R s h V S h ]

w ( 1 - ~ s h ) ir r ( A - 7 )

S ubs t i t u t e Eq . ( l ) i n t o Eq . (A-7 ) and r ea r range as :

{ [

] , 2

R Q I = ~b 25 9. 86 ( 1 - Swi

e 1 V ~ h R w ( 1 _ V s h ) /

R~ R~h J irr

( A - S )

Le t u s de f i ne t he s ha l e zone i nd i ca t o r fo r l am i na t ed

shale as:

{ [ s w ,2 )

s z l : 1 ~ i

/ ~ t ~ ] R w l - V s h ) ir r

( A - 9 )

Subs t i tu te Eq. (A-9) in to Eq. (A-8) as :

R QI =

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K. Jongkitt inarukorn, D. Tiab Journa l of Petroleum &'ience and Engineering 17 (1997) 237 246 245

S u b s t i t u t e E q . ( B - 4 ) i n t o E q . ( 2 a ) a s : S o l v i n g f o r w a t e r s a t u r a t i o n :

10acbs(1 _ S,,i)2 S,, 2,:b ' R ,h V [ R h ] R ~ R ~

_ _ + _ _ +

F * F * F * R , , R t I n t h e i r re d u c i b l e w a t e r s a t u r a t i o n z o n e , E q . ( C - l )

r

( B - 5 ) b e c o m e s :

I a R v

S u b s t i t u t e E q . ( l ) i n t o E q . ( B - 5 ) a n d r e a r r a n g e a s :

R Q I = @ ~ 5 ~ ( 1 - S wi )

{ aR ~

- - + +

F F R w R t

i r r

( B - 6 )

L e t u s d e f i n e t h e s h a l e z o n e i n d i c a t o r f o r d i s p e r s e d

sha l e a s :

SZ l d = w (1 - S ,~ i )

- - + +

F * ~ 2 - F ~ R w R t

i r r

( B - 7 )

S u b s t i t u t e E q . ( B - 7 ) i n t o E q . ( B - 6 ) a s :

~ Z I

Q I = S

d

( 7 ' )

T a k i n g t h e l o g a r i th m o n b o t h s i d e s o f E q . ( 7 ) g i v e s :

l o g ( R Q I ) = 3 .5 l o g ( b ) + l o g ( S Z I d )

( s )

1

S , , i - 4 ~ _ ~

j f - 4 1 }

- - _ _

F R , , R t

ir -

( C - Z )

S u b s t i t u t e E q . ( C - 2 ) i n t o E q . ( 2 a ) a s :

k _

1 0 4 l - S w ~ ) : C

9

t w - 7 + ~ + F = w= ~ r

c-3)

S u b s t i t u t e E q . ( 1 ) i n t o E q . ( C - 3 ) a n d r e a r r a n g e a s :

R Q I -

x

T r ( 1 - S ,,i ) 4 ~ 5

7 Z ~ F ~ = w = ,

i r r

C-4)

L e t u s d e f i n e t h e s h a l e z o n e i n d i c a t o r f o r t h e T o t a l

S h a l e M o d e l a s :

A p p e n d i x C . D e v e l o p m e n t o f T o t a l S h a l e M o d e l

S i m a n d o u x ( 1 9 6 3 ) p r o p o s e d t h e f o l l o w i n g r e l a -

t i o n s h i p :

& ' ~ V~h 1

a R ~~ S ; ' ~ S ' ~ h R t - 0 ( 9 ' )

SZI~ =

X

. : [ + 4 1 1

,,h , R ,,h ] F * R w R t

i r r

c-5)

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246

K. Jongkittinarukorn, D. Tiab / Journal of Petroleum Science and Engineering 17 1997) 237-246

S u b s t i t u t e Eq. C-5 ) into Eq. C-4) a s :

R Q I = ~ b) 5 S Z I t ( 1 0 )

A p p l y l o g o n b o t h s i d e s o f E q . ( 1 0 ) a s :

l o g ( R Q I ) = 3 . 5 l o g 0 , . + l o g ( S Z I t ) ( 1 1 )

R e f e r e n c e s

Amaefu le , J .O . . Ahunbay , M . , T iab , D . , Ke rsey . D .G. and Kee lan ,

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ab i l i ty in unco red in te rva l s /we l l s . 68 th Annu . Tech . Con f .

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Pe t . Eng . , Denve r , CO, SPE Pap . 6858 .

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and app l ica t ion to sha ly fo rma t ions . Rev . In s t . Fr . Pr t . , Supp l .

I s s . , pp . 193 -21 5 .

Tiab , D . , 1993 . M ode rn Core Ana ly s i s , Vo l . 1 . Theo ry . Co re

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Tiab , D . and Don a ld son , E .C. , 1996. Pe t rophy s ic s . Gu l f Pub l . Co . ,

Hous ton , TX, 706 pp .

Waxman , M .H. and Smi t s , L . J .M . , 1968 . E lec t r ica l conduc t iv i t i e s

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(Am. In s t . M in . M e ta l l . Eng . ) , 243 : 107 -122 .