Permeability Controls

7/27/2019 Permeability Controls

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Clay Minerals(1994) 29, 491-501

A N A LY S I S OF P E R M E A B I L I T Y C O N T R O L S :

A P P R O A C H

A N E W

C . A . C A D E , I . J . E VA N S A N D S . L . B R Y A N T *

BP Exploration Operating Com pany Limited, Uxbridge, Middlesex, and* B P Chemicals, Grangemouth, UK

(Received 23 June 1993; revised 25 M arch 1994)

A B S T R A C T : By model ling a range of rock-forming processes such as compact ion and var ious s ty les o fcem entat ion, a new unde rstand ing of how they affect pore-system geom etry, and henc e permeabil i ty, hasbeen gained. For ex ample, alm ost identical p ermeab il i ty-porosi ty trends result from progressive comp actionor gra in overgrowth cem enta t ion in a c lean sandstone , and these t rends are curv i l inear on the t rad i tionallog-l inear plot . The steep ening which defines the curve ma rks the onset of pore-th roat blocking. O the rcem ent styles, su ch as pore-fil ling ca rbona tes or grain-rim ming clays, show different porosi ty-pe rmeab il i tytrends. T his new un derstan ding can be used predict ively (predict ing perm eabil i ty from pred ict ions ofgrain size and diagenetic style), or as a tool fo r identifying the im por tant perme abil i ty controls in a set offield data. This lat ter applicat ion is presented and i l lustrated using data from a variety of sandstonetypes. This approach has important advantages over commonly used mult ivariate stat ist ical analysisapproaches . I t can qu ick ly provide a good u nders tanding of what a re (and are no t ) the importan t cont ro ls onperm eabil i ty. It also provides a basis for more focused and m eaningful stat ist ical analysis to quan tify thesecontrols.

T h e r a t e a t w h i c h f lu i d s c a n b e p r o d u c e d f r o m ap o r o u s s u b - s u r f ac e r e s e r v o i r r o c k is f u n d a m e n -t al ly d e p e n d e n t o n t h r e e p a r a m e t e r s : t h e t h ic k -n e s s o f r e s e r v o i r p r e s e n t , t h e p r e s s u r e d r a w d o w nw h i c h c a n b e a p p l i e d t o t h e r e s e r v o i r a t t h ew e l l b o r e , a n d t h e p e r m e a b i l i t y o f t h e r e s e r v o i r .A s f l ow r a t e s a r e a n i m p o r t a n t c o n t r i b u t o r t o t h ee c o n o m i c v i a b i l i ty o f a n o il o r g a s f i el d , t h e n t h ea c c u r a t e p r e d i c t i o n o f p e r m e a b i l i t y a h e a d o fd r i ll i n g c a n h a v e a m a j o r i m p a c t o n b u s i n e s sd e c i s i o n s s u c h a s p r o s p e c t r a n k i n g o r a p p r a i s a lw e l l l o c a t i o n .

F o r e x a m p l e , i f a w e l l i n p r o s p e c t X ( F i g . 1 ) ,p e n e t r a t e s m e d i u m g r a i n e d s a n d s t o n e s w i th p er -m e a b i l i t i e s in t h e r a n g e 1 00 m D t o 50 0 m D , c a nw e p r e d i c t p e r m e a b i l i t y o ~ t h e r e s e r v o i r i n p r o -s p e c t Y, w h i c h f r o m g e o l o g i c a l m o d e l s w e b e l i e v et o b e s i m i l a r b u t f i n e r - g r a i n e d ? W h a t i f t h e f i n e r-g r a i n e d s a n d s t o n e i n p r o s p e c t Y h a s m o r e q u a r t zc e m e n t , o r c o n t a i n s l es s c l ay , o r i s b e t t e r s o r t e d ?C a n w e p r e d i c t p e r m e a b i l i ty i n p ro s p e c t Y, b a s e do n m e a s u r e d p e r m e a b i l i t y d a t a f r o m p r o s p e c t Xa n d o u r g e o l o g i c al m o d e l ?

To a n s w e r t h e s e q u e s t i o n s , t h e r e la t iv e i m p o r -t a n c e o f d i f f e r e n t p o t e n t i a l c o n t r o l s o n p e r m e a b i -l it y (s u c h a s g r a i n s iz e , s o r t in g , c o m p a c t i o n a n d

d i f f e r e n t s ty l e s o f c e m e n t a t i o n ) m u s t b e e s t a b -l i s h ed . T h e e f f e c t o f t h e m a j o r c o n t r o l s o np e r m e a b i l i t y m u s t t h e n b e q u a n t if i e d . I d e n t i f y i n gt h e i m p a c t o f t h e s e c o n t r o l s , b o t h i n d i v i d u a l l ya n d i n c o m b i n a t i o n , i s t h e k e y t o p e r m e a b i l i t yp r e d i c t i o n . I f v a r i a t i o n i n t h e v o l u m e o f c a r b o -n a t e c e m e n t i n a r es e r v o i r r o c k h a s a m u c h g r e a t e ri m p a c t o n p e r m e a b i l i t y t h a n v a r i a t i o n in g r a ins i ze , b u t o u r a b i li ty t o p r e d i c t c e m e n t v a r i a t i o n i sl i m i t e d , t h e n o u r a b i l i ty t o p r e d i c t p e r m e a b i l i t y iss i m i l a r l y l i m i t e d , H o w e v e r , i f g r a i n s i z e i s t h ed o m i n a n t c o n t r o l , a n d t h e g eo l o gi c al m o d e l

M e d ~ n s a n d ~ From ~i o~ ca l model\ a s X g bt ~ t f o r e ~ ( a m p l c :\ ~ner S r a L n e d o r

t mzre ~ c e m e n t o rle~ clay o rb e l i e r s o r t e d

FIG. 1. Il lustrat ion of perme abil i ty si tuat ion (see text).

9 1994 Th e Mineralogical Society


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492 C . A . C a d e et al.

allows predicti on of this parameter , t hen perm ea-bility predicti on may be feasible.

R E V I E W O F P R E V I O U S W O R K

In numerous previous studies using statisticaltechniques, a strong correlation between permea-bility and porosity has been shown. An exam ple isa study on the Cretaceous Travis Peak Formatio nin East Texas, USA (Dutton & Diggs, 1992).Using a data set of over 600 samples, thecorrelatio n coefficient of permeab ility on porosityis 0.79, higher than any other textural or diagene-tic parameters included in multiple regression.

With this high correlation coefficient, it might beexpected that predictions of porosity could beused to predict permeability. A cross-plot of thedata from this study (Fig. 2), however, showsthat, for a given porosity, permeability varies byc. three orders of magnitude. Porosity alonecannot, therefore, be used to predictpermeability.

In a recent review, Bloch (1991) described twogeneral approaches to predicting reservoir qualityin sub-surface sandstones: empirical techniques

and 'process-oriented' techniques. The work onthe Travis Peak Formation is an example of theempirical approach to the quant ification of per-meabilit y controls for predictive purposes.

Empirical techniq ues use a calibration data set(e.g. data from core samples from a well inprospect X) and multiple regression analysis to

1 0 0 0 i i

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1 " . . 1 7 . , : : . {, 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . 9 . . . . . . . . . . . . . . . . . . . . . . . . .

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0 ,001 _ _~J9 , ~ '~t~-';I. . . . . . . . . . . . . . . . . . . . . . + . . . . . . . . . .. . . . . . . .. . . . . . . . ~ l . . . . . . . . . . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

lO 'S z : : : - ~ ~ . . ~ : : I

0 5 1 0 1 5 2 0 2 5

Po~ros~, ( . )FIG. 2 . Cross-plot of porosity v s . permeability for TravisPeak Sandstone samples. Linear regression of porosity onpermeability gives a correlation coefficient of 0.79 (Dutton

& Diggs, 1992).

determine the relationship between rock propertyvariables and reservoir quality. Dutton & Diggs(1992) and Bloch (1991) described the mostfrequently used application of this approach, inwhich relationships between measured porosityand permeability (usually ambient helium poro-sity and single phase gas permeability), andtextural and mi neralogical variables (usually mea-sured on thin-sections) were investigated. Com-monly -used variables are grain size, sorting, theratio o f rigid to plast ically-deformable grains,matrix clay content, volume of individualcements, total cement volume, and point -countedinterparticle porosity. Bloch (1991) stated thatmultivar iate statistical techniques will not work asa predictive tool in some situations (because thekey permeability controls cannot themselves bepredicted). However, he suggested that "despiteits limitations, the empirical technique providesthe only feasible approach to reservoir qualityprediction". Dutton & Diggs (1992) concludedthat predicting porosity using statistical analysisof a calibration data set may be feasible, but thatprediction of permeability will have much lowersuccess.

We suggest that this lack of success is largely aconsequence of the interplay and overprintin g ofthe various permeability controls. If all possiblepermeability controls are considered together,the statistical processing may show that bothgrain-size and quartz cementation are of moder-ate importance as permeability controls, as thereis no strong relationship between either para-meter and permeability. However, within coarseor m edium sa nd grain-size classes, the volu me ofquartz cement may be the dominant control onpermeability. If the textural controls are firstremoved, t hen the important diagenetic overprintcontrols should become clearer.

A variation on the empirical approach isdescribed by Ehrlich e t a l . (1991). Using theobservation that, even in a single formation,permeability commonly varies by several ordersof magnitude, they concluded that the configur-ation of porosity, rather t han the absolute poro-sity value, is the control on permeability. Tocharacterize the pore system configuration, Ehr-lich e t a l . (1991), made measuremen ts of pores intwo dimensions (on polished thin-sections) andcombined these with pore-throat size distributiondata (from mercury porosimetry) to develop asimple pore-system model. Fo r selected data sets


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An alys is o f permeability controls

a good degree of fit between the simple pore-system model and measured permeability hasbeen established.

While the method presented by Ehrlich et a l .(1991) has merit in its focus on pore type andconnectivity, it has limitations as a predictivetool. For predictic, n of permeability ahead ofdrilling, the criteria for success of any methodmust be that it establishes a quantitative linkbetween meast:red permeability and other rockparameters, and that those correlative para-meters can themselves be predicted from ageological model. With the current level ofunderstanding, it is very unlikely that we wouldbe able to predict with confidence the pore-typeand pore-throat size distribution parameters in anundrilled sandstone from a geological model.

The 'process-oriented' approach described byBloch (1991) focuses on modellin g diageneticprocesses in an undri lled area, based on chemicaland math ematica l models, and the effects of thoseprocesses on reservoir quality. There are twoimp orta nt limitations to this approach. First,there is the uncer tain ty associated with the sub-surface geological model, and how that impactson the thermodynamics and kinetics of thediagenetic model. Second, there is the lack of adetailed quantitati ve understandi ng of how diage-netic processes control permeability . To date, thequantification of the impact of specific controls,particularly diagenetic controls, has been eitherformation specific (and therefore not generallyapplicable) or very general. Ethi er & King (1991)illustrated a general un ders tand ing of a variety ofcontrols (Fig. 3), b ut with little or no quanti tativ edetail, the value of such trends is limited.

To summarize, previous work on permeabilitycontrols has been limited by the lack of a i~quantitative understanding of how textural, and /in particular, diage~aetic, permeability controlsoperate, and has been hampered by statisticalapproaches which consider all possible controlstogether. In this paper we present researchfindings which address the quantitative under-standing of permeability controls, and propose amodified approach to reservoir quality analysiswhich can improve predictive capability.

A N A LT E R N AT I V E A P P R O A C H

Our approach is based on a simple model of asandstone, a sphere pack. Using a numerical

493

model of this sphere pack, we simulate diageneticprocesses, such as compaction and various stylesof cementation. Their progressive impact onporosity, and more importantly permeability, ismeasured. The result of these sim ulations is animproved un derstandi ng of the ways in whichpermeabi lity is influenced by different di ageneticmodifications. The controls are considered bothin isolation and in combina tion . Over a full rangeof porosities (


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494 C.A. Cadeet al.

p o r o s i t y w a s 3 6 . 2 %. T h e p a c k w a s t h e n i m p r e g -n a t e d w i t h w a x a n d d i s m a n t l e d , o n e b e a r i n g a t at ime , and the re la t ive pos i t ions o f a l l o f theb e a r i n g s m e a s u r e d . Wi t h t h e p o s i t i o n s o f a ll th eg r a i n s k n o w n , a n d b e c a u s e a l l t h e s p h e r e s w e r ethe same s ize , the in te rpa r t i c le po re space i s , apriori , c o m p l e t e l y c h a r a c t e r i z e d . W e b e l i e v e t h ist o b e t h e o n l y r ea l p o r e - s y s t e m w h i c h h a s b e e n s oc o m p l e t e l y c h a r a c t e r i z e d , a n d i t i s t h i s f e a t u r ewh ich a l lows the ca lcu la t ion o f po ros i ty andp e r m e a b i l i t y. P e r m e a b i l i t y i s c a l c u l a t e d b y ar i g o r o u s g e o m e t r i c a l c o n v e r s i o n o f t h e F i n n e yp o r e - s y s t e m i n t o a n e t w o r k c o m p r i s i n g p o r e s a n dc o n n e c t i n g t h r o a t s ( B r y a n t et al., 1993a ) . Thesep o r e - t h r o a t s , a n d m o r e s p e c i f ic a l ly t h e i r d i a m e t e ra n d ' i n t e r c o n n e c t e d n e s s ' , a r e t h e k e y t o s a n d -s t o n e p e r m e a b i l i t y.

U s i n g d a t a f r o m t h i s p o r e - s y s t e m , a r a n g e o fd i f f e r e n t d i a g e n e t i c p r o c e s s e s h a s b e e n m o d e l l e d(Fig. 4).

C o m p ac t io n

d u e t o g r a v i t a t i o n a l l o a d i n g d u r i n g b u r i a l . Wes i m u l a t e t h i s b y r e - sc a l i n g o n e o f t h e c o - o r d i n a t ea x e s in F i n n e y ' s p a c k i n g a c c o r d i n g t o t h e f o r m u l az' = zo + )v(z-zo) where zo i s an a rb i t r a ryr e f e r e n c e v a l u e a n d ~. r e f e r s t o t h e d e g r e e o fcom pac t ion (F ig 4b ) . A phys ica l ly r ea l i s t i c r ang efor )v is 1 .0 > )v > 0 .7 , c orr es po nd ing to a 0-3 0%c h a n g e i n b u l k v o l u m e . O u r s i m u l a t i o n o f c o m -p a c t i o n c a u s e s g r a i n s t o i n t e r p e n e t r a t e , a n d t h i s i sana logous to p re ssu re so lu t ion a t g ra in con tac t s inrocks .

S o l id o v e rg ro w th cem en ta t io n

O n e o f th e m o s t c o m m o n s ty l es o f c e m e n t a t i o nin sands tones i s the p rec ip i ta t i on o f so l id ove r-g rowths on de t r i t a l g ra in s ( e .g . qua r tz and fe ld s -p a r s) . O v e rg r o w t h c e m e n t s a r e s i m u l a t e d a sc o n c e n t r i c r i m s o n e x p o s e d s p h e r e s u r f a c e s in th esphe re pack (F ig . 4c ) .

C o m p a c t i o n is o n e o f t h e m o s t i m p o r t a n tp r o c e s s e s o f p o r o s i ty r e d u c t i o n d u r i n g s a n d s t o n ed iagenes i s . I t c an be de f ined a s r educ t ion inp o r o s i t y a s a c o n s e q u e n c e o f t h e r e d u c t i o n i n b u l kr o c k v o l u m e . T h e v o l u m e r e d u c t i o n i s u s u a ll y th ere su l t o f ve r t i ca l sho r ten ing , and tha t in tu rn i s

a b

eliFIG. 4. Numerical simulation of geological processes.

(a) 2D slice through a dense packing of equal spheresrepresenting sediment of clean, well-sorted sand. (b)Compaction forces spheres closer together and interpenet-ration occurs. (c) Quartz overgrowths cement the com-

pacted packing together. (d) Pore-filling cement.

Micro p o ro u s g ra in - r im m in g cem en t s '

S e v e r a l m i n e r a l s f o r m c e m e n t s i n s a n d s t o n e sw h i c h c a n b e d e s c r i b e d a s m i c r o p o r o u s g r a i nr i m s . E x a m p l e s a r e c h l o r i t e a n d i l l i t e . T h e s etyp ica l ly fo rm as b locky, f ib rous o r p la ty c ry s ta l swh ich g row rad ia l ly a round de t r i t a l g ra in s . Inb e t w e e n t h e c r y st a l s t h e r e i s e n c l o s e d m i c r o p o r o -s i ty, and the s ize s o f these po res a re typ ica l ly oneo r t w o o r d e r s o f m a g n i t u d e s m a l l e r t h a n t h ei n t e rg r a n u l a r p o r e s . T h e p e r m e a b i l i t y o f t h e v o i ds p a c e w i t h i n t h e m i c r o p o r o s i t y i s n e g l i g i b le c o m -p a r e d t o t ha t f o r th e i n t e r p a r t i c l e p o r e - s p a c e .T h u s , w h e n f lu i d m o v i n g t h r o u g h a p o r e - s y s t e me n c o u n t e r s a gr a i n r i m m e d b y c e m e n t o f t h is t y p e ,the e ffec t i s s imi la r to tha t o f a so l id ove rg rowthw h o s e v o l u m e e q u a t e s t o t h a t o f cl ay a n dm i c r o p o r o s i t y c o m b i n e d . We t h e r e f o r e m o d e lg r a i n - r i m m i n g c l a y c e m e n t s a s m i c r o p o r o u s , b u ti m p e r m e a b l e , o v e r g r o w t h c e m e n t s .

Pore-fi l l ing cements"

S e v e r a l m i n e r a l s p r e c i p i t a t e a s p o r e - f i l l i n g ,r a t h e r t h a n g r a i n - r i m m i n g , c e m e n t s . C a r b o n a t e s(e .g . ca lc i t e and s ide r i t e ) , and some c lays (e .g .k a o l i n i t e ) o f t e n o c c u r i n th i s f o r m . W e m o d e l t h iss t y l e o f c e m e n t b y c o m p l e t e l y f i l l i n g r a n d o m l y


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Analysis o f permea bility controls

s e l e c t e d p o r e s w i t h i n t h e p a c k i n g ( F i g . 4 d ) . T h e s ep o r e s a n d t h e i r c o n n e c t i n g t h r o a t s a r e t h e nu n a v a i l a b l e f o r f lo w. A m i c r o p o r o u s p o r e - f il l in gc e m e n t , s u c h a s k a o l i n i t e , is m o d e l l e d i n am a n n e r a n a l o g o u s t o t h e m i c r o p o r o u s g r a in r im .

C o m b i n e d c a s e s "

W e h a v e m o d e l l e d c o m b i n e d c a se s , e. g . ap h a s e o f c o m p a c t i o n , f o l l o w e d by e i t h e r a p h a s eo f o v e r g r o w t h o r p o r e -f i ll i n g c e m e n t a t i o n , a n dp r o g r e s s i v e c o m p a c t i o n w i t h p r e s s u r e d i s s o l v e dg r a i n m a t e r i a l ( g r a i n i n t e r p e n e t r a t i o n ) r e p r e c i p i -t a t e d o n t h e g r a i n s u r f a c e s .

M o d e l r e s u l t s

I t is w e l l k n o w n t h a t , f o r a g i v e n p o r o s i t y,p e r m e a b i l i t y w i l l b e l o w e r i n a f in e r g r a i n e ds a n d s t o n e t h a n i n o n e t h a t i s c o a r s e r g r a i n e d ( a lle l s e b e i n g e q u a l ) , a n d t h a t a p o r e - b r i d g i n g c l a ys u c h a s i l l it e is v e r y e f f e c t i v e i n r e d u c i n g p e r m e a -b il it y . T h e s p h e r e p a c k m o d e l l i n g p r o v i d e s p h y s i-c a l c o n f i r m a t i o n , e x p l a n a t i o n , a n d q u a n t i f ic a t i o no f t h e s e c o n t r o l s , a n d p r o v i d e s s i m i l a r in s i g h t in t oh o w o t h e r , p r e v i o u s l y l es s w e l l u n d e r s t o o d ,c o n t r o l s o p e r a t e .

I n e a c h c a s e , p o r o s i t y is r e d u c e d i n c r e m e n t a l l ya c c o r d i n g t o t h e s t yl e o f c e m e n t a t i o n a n d t h er e s u l t a n t p e r m e a b i l i t y i s c a l c u l a t e d ( d e t a i l s o f t h ec a l c u l a ti o n a r e l e n g t h y a n d a r e g i v e n i n B r y a n tetal . , 1 9 93 b ). W e p r e s e n t t h e p e r m e a b i l i t y - p o r o s i t yt r e n d s w h i c h r e s u l t f r o m t h e s i m u l a t i o n s a s l O g l 0p e r m e a b i l i t y vs . p o r o s i t y c r o s s - p l o t s. I n F i g . 5 ,p e r m e a b i l i t y i s p r e s e n t e d i n t h e d i m e n s i o n l e s sf o r m K/Ko w h e r e K o i s t h e i n i ti a l p e r m e a b i l i t y o ft h e p a c k in g b e f o r e c o m p a c t i o n a n d / o r c e m e n t a -t i o n . T h i s i n it i a l p e r m e a b i l i t y ( i n D a r c i e s )d e p e n d s o n t h e s i z e o f t h e s p h e r e s i n t h e p a c k i n gs u c h t h a t K o = 3 x 1 0 - 3 r 2 , w h e r e r is t h e s p h e r er a d i u s m e a s u r e d i n m i c r o n s. T h i s e x p r e s s i o n i so b t a i n e d f r o m n e t w o r k m o d e l c a lc u l a t io n s a n da g r e e s w i th m a n y m e a s u r e m e n t s a n d s e m i - e m p i r -i ca l e x p r e s s i o n s s u c h a s t h e K o z e n y - C a r m a nr e l a t i o n s h i p ( C a r m a n , 1 9 37 ) . I n o t h e r f i g u r e s ,p a r t i c u l a r g r a i n - s i z e c a s e s a r e p r e s e n t e d a n dp e r m e a b i l i t y i s n o t n o r m a l i z e d t o t h e i n it ia l v a lu e .

C o m p a c ~ o n

T h e t r e n d o f d e c l in i n g p o r o s i t y a n d p e r m e a b i l -i ty f o r a p r o g r e s s i v e l y c o m p a c t e d s a n d s t o n e is

49 5

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0 , . . . . . . . . . . . o k

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.0001 J Co m pac t ionnlyCementation onlyCompacUon and cemen tation

. 0 0 0 0 1 ~ . - - . ~. - Pore hroats l o c k , e, d .

o . o o . 1 0 . 2 o . 3 0 . 4

l ~ , o ~ i t y ( v / v )

F[c. 5. Model-derived porosity-permeability trends forcompaction, c ementation, and a combination o f theseprocesses. Note that in this cross-plot, permeability isexpressed as a ratio of original uncompacted/uncementedpermeability. T his removes any grain-size dependence. Th edashed line shows the percentage of pore-throats blocked as

porosity decreases.

c u r v e d , w i th a m a x i m u m r a t e o f c h a n g e o f s lo p e a t- - 1 2 % p o r o s i t y ( F i g . 5) . T h i s s t e e p e n i n g c o i n -c i d e s w i t h t h e p o r o s i t y a t w h i c h t h e b l o c k i n g o fp o r e - t h r o a t s b e g i n s .

O v e r g r o w t h c e m e n t a t i o n

P r o g r e s s i v e q u a r t z s ty l e o v e r g r o w t h c e m e n -t a t i o n p r o d u c e s a n a l m o s t i d e n t i c a l p o r o s i t y -p e r m e a b i l i t y t r e n d t o t h e c o m p a c t i o n t r e n d( F ig . 5) . D i v e r g e n c e o f t h e c o m p a c t i o n a n do v e r g r o w t h t r e n d s o n ly o c c u r s b e l o w 5 % p o r o -s i ty, a n d t h is d i v e r g e n c e is s m a l l . C o m b i n a t i o n s o fc o m p a c t i o n a n d o v e r g r o w t h c e m e n t a t i o np r o d u c e t h e s a m e c u r v e d t r e n d . T h e s i g n if i ca n c eo f t h is t r e n d c o i n c i d e n c e i s t h a t a n y d i v e r g e n c ef r o m t h e c u r v e , f o r a g i v e n g r a i n s iz e a n d s o r t i n gc l as s , m u s t b e d u e t o c o n t r o l s o t h e r t h a n c o m p a c -t i o n o r q u a r t z c e m e n t a t i o n .

P o r e - fi ll in g c e m e n t

P r o g r e s s i v e c e m e n t a t i o n b y a p o r e - f i l l i n gc e m e n t p r o d u c e s a s t e e p e r d e c l i n e in p e r m e a b i l i t yw i t h p o r o s i t y ( F i g . 6 a ) . T h e r e a s o n f o r t h is is t h a tb l o c k i n g o f p o r e - t h r o a t s o c c u r s a s s o o n a s t h e f i rs tp o r e i s c e m e n t e d , r a t h e r t h a n w h e n p o r o s i t y h as


6/11

496

b e e n r e d u c e d t o - - 1 2 %o v e r g ro w t h c e m e n t .

C.A. Cadeet al.

Grain-rimming clays

i n th e case o f an

G r a i n - r i m m i n g c l a y s a l s o r e s u l t i n a s t e e p e rp e r m e a b i l i t y d e c l i n e t h a n o v e rg r o w t h c e m e n -t a t io n (F ig . 6 b ) b u t fo r a d i f f e ren t r easo n to p o re -f il li n g c e m e n t : T h e m i c r o p o r o u s g r a i n r i mb e h a v e s l i k e a s o l i d o v e rg r o w t h , b u t t h e i n e ff e c -t i v e p o r o s i t y, w h i l e n o t c o n t r i b u t i n g t o p e r m e a b i l -i t y, n e v e r t h e l e s s f o r m s p a r t o f t h e t o t a l p o r o s i t y.T h u s f o r a gi v e n p e r m e a b i l i t y, a s a n d s t o n e w i t hc l a y g r a i n r i m s w i ll h a v e h i g h e r p o r o s i t y t h a n o n e

w i t h s o l i d g r a in o v e rg r o w t h s .

The effect o f grain size

G r a i n - s i z e f u n d a m e n t a l l y c o n t r o l s t h e s i z e o fp o r e s , a n d , m o r e i m p o r t a n t l y, fo r p e r m e a b i l i t y,t h e s i z e o f t h e p o r e - t h r o a t s w h i c h c o n n e c t a d j a c -en t p o re s . T h e e f f ec t o f g ra in s i ze o n p o ro s i ty an dp e r m e a b i l i t y r e d u c t i o n i s i n v e s t i g a t e d i n o u rs im u la t io n s . A ran g e o f san d g ra in - s i zes h as b eens e l e c t e d t o p r o v i d e t h e s c a l in g fo r t h e n e t w o r km o d e l . P e r m e a b i l i t y is c a l c u la t e d f r o m t h i sn e t w o r k r e p r e s e n t a t i o n o f t h e p o r e - s y s t e m . P e r -m e a b i l i t y ( in D a r c i e s ) i s d e p e n d e n t o n t h e s iz e o fth e sp h e res in th e p ack su ch th a t K o = 3 x 1 0 -3 r2,w h e r e r i s t h e s p h e r e r a d i u s m e a s u r e d i n m i c ro n s .N o t e t h a t i n a l l o f o u r s i m u l a t i o n s , t h e s o r t i n g o fth e p ack i s p e r fec t ( a l l g ra in s o f t h e sam e s i ze ) .

T h e p o r o s i t y - p e r m e a b i l i t y d e c l i n e t r e n d s w h i c h

IOOOOOlooo a C o m ~

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P o r o s i t y ( % )

r e s u l t f r o m t h e s i m u l a t i o n o f c o m p a c t i o n , f o r t h ese l ec t ed r an g e o f g ra in s i zes , a r e i l l u s t r a t ed inF ig . 7 a .

The effect of sorting

P e r m e a b i l i t y a l s o d e p e n d s o n t h e g r a i n s i z ed i s t r i b u t i o n ( s o r t i n g ) . S i n c e o u r m o d e l l i n ga p p r o a c h i s b a s e d o n a p a c k o f i d e n t i c a l ly - s i z e dsp h ere s , t h e e f f ec t o f so r t in g i s n o t a cco u n te d fo r.M o d e l l i n g s y s t e m s w i t h a r a n g e o f g r a i n s i ze s isn u m e r i c a l l y c o m p l e x , a n d r e q u i r e s f u r t h e rr e s e a r c h . A t p r e s e n t a n e m p i r i c a l c o r r e c t i o nb a s e d o n e x p e r i m e n t a l d a t a ( B e a r d & We y l ,

1 97 3) i s u sed (F ig . 7 b ) . T h i s so r t in g co r rec t io nd o e s n o t a f f ec t th e s h a p e o f th e p r e d i c t e d t r e n d s ,b u t c h a n g e s t h e s t a r ti n g p e r m e a b i l i t y v a l u e a t3 6 % p o r o s i t y.

Plastically-deformable grains

M a n y s a n d s t o n e s c o n t a i n g r a i n s s u c h a s m u d -s t o n e c l a s t s o r m e t a m o r p h i c g r a i n s w h ic h w i lld e f o r m i n a p la s t i c m a n n e r d u r i n g b u r i a l.A l t h o u g h w e h a v e n o t m o d e l l e d a p a c k c o n t a i n -in g su ch g ra in s , w e b e l i ev e th a t t h e p o ro s i ty -p e r m e a b i l i t y tr e n d w o u l d b e s i m i l a r t o t h a t f o rp r o g r e s s i v e p o r e -f i ll i n g c e m e n t a t i o n . T h e r e a s o nfo r th i s su g g es t io n i s t h a t a s th e p l a s t i c g ra in sd e f o r m , t h e y f i l l a d j a c e n t i n t e r p a r t i c l e p o r e -s p a c e . T h i s p r o c e s s w i l l c a u s e p o r e - t h r o a t b l o c k -i n g e a r l ie r th a n w i t h t h e q u a r t z g r a i n c o m p a c t i o nc a s e d i s c u s s e d e a r l i e r.

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10 20 30 40P o r o s i t y (% )

FIG. 6. M odel-derived porosity-permeability trends for simulations of (a) pore-fillingcementation and (b) grain-rimmingclay.


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Analysis of permeabilitycontrolsA N A LY S I S O F P E R M E A B I L I T Y

C O N T R O L S

The approach

T h e g e o m e t r y a n d s c a l e o f t h e p r i m a r yi n t e r p a r t ic l e p o r e - s y s t e m i s f u n d a m e n t a l l yc o n t r o l l e d b y t h e s i z e o f t h e s a n d g r a i n s w h i c hd e f i n e it . D i a g e n e t i c m o d i f i c a ti o n s a r e t h e n o v e r -l a i d o n , o r r e s u l t in th e d e f o r m a t i o n o f , th i sp r i m a r y p o r e - sy s t e m t e m p l a t e . R a t h e r t h a n c a r r yo u t a n o v e r a l l , m u l t i v a r i a t e , s t a t is t i c a l an a l y s is o na l l p o s s i b l e p e r m e a b i l i t y c o n t r o l s i n a s e t o f d a t a ,w e p r o p o s e t h a t a b e t t e r r e s u l t is a c h i e v e d i f t h ep r i m a r y t e x t u r a l c o n t r o l s a r e r e m o v e d f r o m t h ea n a l y s is a t t h e o u t s e t . T h u s t h e f i r st s t e p i n t hi sa p p r o a c h i s t o s p li t t h e s a m p l e d a t a s e t i n t o g r a i ns i z e ( a n d , i f p o s s i b l e s o r t i n g ) c l a s s e s . F o r e a c ht e x t u r a l g r o u p , t h e p o r o s i t y - p e r m e a b i l i t y t r e n d i ss o l e l y t h e r e s u l t o f d i a g e n e t i c m o d i f i c a t i o n . B yd i s p l a y i n g e a c h g r a i n s iz e d a t a g r o u p s e p a r a t e l y,w i t h t h e m o d e l d e r i v e d c u r v e s f o r t h e c o r r e s p o n d -i n g t e x t u r e , a q u a l i t a t i v e a s s e s s m e n t o f t h ep e r m e a b i l i t y c o n t r o l s c a n b e m a d e . F o r a w i d er a n g e o f d a t a s e t s, w e h a v e f o u n d t h a t , w i t h ju s tt h i s in i t ia l s t a g e , a g o o d i n s i g h t i s g a i n e d i n t o w h a tt h e i m p o r t a n t p e r m e a b i l i t y c o n t ro l s a re . T h i si n s i g h t is t h e r e s u l t o f t w o s i m p l e s t e p s , s p l i t ti n gt h e d a t a b y p r i m a r y t e x t u r e , a n d c o m p a r i s o n w i t hr e s u lt s o f s p h e r e p a c k m o d e l l i n g .

A t t h e i n i t i a l d i s p l a y s t a g e , a f t e r t e x t u r a ls p l i t t i n g , s e v e r a l c o n c l u s i o n s c a n b e m a d e a b o u t

49 7

t h e d a t a s e t. A n y d a t a p o i n t s f a i l in g w e l l a b o v et h e c o m p a c t i o n / o v e r g r o w t h c e m e n t c u r v e ( i . e .h i g h e r p e r m e a b i l i t y f o r a g i v e n p o r o s i t y ) , s h o u l db e c a r e f u l l y i n v e s t i g a t e d f o r d a t a q u a l i t y. Ac o m m o n e x p l a n a t i o n f o r s u c h p o i n t s ( lo w p o r o -s it y b u t h i g h p e r m e a b i l i t y ) i s t h e e x i s t e n c e o f a no p e n f r a c t u r e i n t h e p l u g u s e d f o r p e r m e a b i l i t ym e a s u r e m e n t . T h i s m a y b e a n a t u r a l f r a c t u r e , o rm o r e l ik e l y i t w i ll h a v e b e e n i n d u c e d d u r i n g p l u g -c u t t i n g , b u t i n e i t h e r c a s e , s u c h d a t a s h o u l d b er e m o v e d f r o m t h e d a t a s e t b e f o r e f u r t h e r a n a l y -s is . T h e p e r m e a b i l i t y o f s u c h p l u g s is d o m i n a t e db y t h e p e r m e a b i l i t y o f t h e f r a c t u r e a n d n o t t h es u r r o u n d i n g m a t r i x r o c k . F o r d a t a p o i n t s w h i c hf a ll j u s t a b o v e t h e m o d e l c u r v e , t h e q u a l i t y o f t h eg r a i n s iz e d a t a s h o u l d b e c h e c k e d . A s i t i s b a s e do n a p e r fe c t l y s o r t e d s p h e r e p a c k , t h e m o d e lc u r v e p r o v i d e s a n u p p e r l im i t o n p o r o s i t y - p e r -m e a b i l i t y v a l u e s f o r a sa n d w i t h t h a t t e x t u r e .

T h e g e n e r a l t r e n d o f th e d a t a w i t h i n e a c h g r a i ns i ze c l a ss s h o u l d p o i n t t o t h e i m p o r t a n t c o n t r o l so n p e r m e a b i l i t y. I f t h e d a t a l ie s o n o r j u s t b e l o wt h e m o d e l t r e n d , a n d p a r a l l e ls t h a t tr e n d , t h e nc o m p a c t i o n a n d / o r o v e r g r o w t h c e m e n t a t i o n a r ep r o b a b l y t h e d o m i n a n t c o n t r o l s. I f t h e t r e n d i ss t e e p e r , t h e n t h e r e m u s t b e s o m e c o n t r i b u t i o nf r o m a p o r e - f il l in g o r m i c r o p o r o u s c e m e n t . I ts h o u l d b e n o t e d h e r e t h a t a s t e e p e r t r e n d d o e s n o tp r e c l u d e a c o n tr i b u ti o n f r o m o v e r g r o w t h c e m e n -t a t io n o r c o m p a c t i o n .

A f t e r r e m o v i n g t h e i n f l u e n c e o f p r i m a r y t e x -t u r al c o n t r o l s , t h e d i a g e n e t i c o v e r p r i n t c a n b e

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FIG. 7. The effect of grain-size and sorting variation on the m odel-derived porosity-permeability trends: (a) calculatedtrends for different grain sizes; (b) empirically-derived trends for different sorting classes.


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FJ6.8. Fontainebleau Sand stone--po rosityvs. permeabilitycross-plot showing the close correspondence betweenmodel predictions based on grain size and cem ent style, and

measured porosity-permeability data.

e v a l u a t e d . T h i s c an b e d o n e b y u s i n g m u l t i v a r i a t es t a ti s ti c a l a n a l y si s , o r b y p e r f o r m i n g f u r t h e r d a t as p li ts , e . g . b y v a r i a t i o n i n t h e v o l u m e o f c a r b o n a t ec e m e n t . B y u s i n g s t a t i s t i c a l a n a l y s i s a f t e r t h et e x t u r a l c o n tr o l s a r e r e m o v e d , t h e r e i s a m u c hr e d u c e d p o s s ib i li ty o f a n i m p o r t a n t d i a g e n e t i cc o n t r o l o n p e r m e a b i l i t y b e i n g m a s k e d b y at e x t u r a l p a r a m e t e r , a n d v i c e v e r s a . T h is a p p r o a c ht o r e s e r v o i r q u a l i t y a n a l y s i s i s i l l u s t r a t e d i n t h ef o l l o w i n g c as e e x a m p l e s .

Case example 1--Fontainebleau Sandstone

T h e O l i g o c e n e F o n t a i n e b l e a u S a n d s t o ne ,w h i c h o u t c r o p s i n t h e I l e d e F r a n c e a r e a , n e a rP a r i s , i s t h e r o c k o n w h i c h t h e s p h e r e p a c km o d e l l i n g r e s u l t s w e r e f i r s t v a l i d a t e d . I t i s at e x t u r a l l y a n d d i a g e n e t i c a l l y s i m p l e q u a r t z s a n d -s t o n e , w h i c h i s f i n e g r a i n e d a n d w e l l s o r t e d . I t isc e m e n t e d a l m o s t e x c lu s i v e ly b y q u a rt z . S a m p l e ss h o w a w i d e r a n g e o f p o r o s it y a n d p e r m e a b i l i t y .U s i n g c a t h o d o l u m i n e s c e n c e t o d is t in g u i sh g r a i n sf r o m o v e r g r o w t h s , t h e a v e r a g e g r a i n s i z e is1 9 0 ~ tm , c l o s e t o t h e v a l u e o f 2 0 0 p .m r e p o r t e d b yC a y e u x ( 1 9 2 9 ) .

A s t h e g r a i n - s i z e i n t h i s d a t a s e t v a r i e s s o l i t t l eb e t w e e n s a m p l e s , t h e r e i s n o n e e d t o c a r r y o u ta n y s pl it b y t e x tu r e . W h e n t h e p o r o s i t y - p e r m e a b i -l it y d a t a a r e d i s p l a y e d w i t h t h e m o d e l - d e r i v e dt r e n d f o r t h e c o m p a c t i o n / o v e r g r o w t h c e m e n -t a t i o n c a se , a n a l m o s t e x a c t c o i n c i d e n c e b e t w e e n

t h e d a t a a n d t h e t r e n d c a n b e s e e n ( F i g . 8 ) . A s t h es a m p l e s h a v e a ll b e e n s u b j e c t to a c o m p a r a b l eb u r i a l h i st o r y , a n d h a v e b e e n b u r i e d t o a m a x i -m u m d e p t h o f o n l y a f e w h u n d r e d m e t r e s , i t isc o n c l u d e d t h a t t h e p o r o s i t y - p e r m e a b i l i t y v a r i a -t i on i s p r e d o m i n a n t l y d u e t o v a r i a t i o n i n th ev o l u m e o f q u a rt z o v e r g r o w t h c e m e n t ( c. 5 - 3 0 %o f th e r o c k v o l u m e ) .

T h e c l o se m a t c h b e t w e e n m e a s u r e d d a t a f r o mt h i s r e a l , a l b e i t t e x t u r a l l y a n d d i a g e n e t i c a l l ys i m p le , s a n d s to n e a n d o u r m o d e l - d e r i v e d t r e n dp r o v i d e s c o n f i d e n c e t h a t t h e s p h e r e p a c k m o d e l i ss u c c e s s f u ll y s i m u l a t i n g r e s u l t s o f r e a l d i a g e n e t i cp r o c e s s e s .

Case example 2-- Gar n Formation,Haltenbanken, Norway

T h e M i d d l e J u r a s s ic G a r n F o r m a t i o n o c c u r s inw e l ls fr o m o f f s h o r e w e s t e rn N o r w a y , a n d c o m -p r i s e s s a n d s t o n e s d e p o s i t e d i n a f l u v ia l t o s h a l l o wm a r i n e e n v i r o n m e n t . I t is o n e o f t h e p r i n ci p a lh y d r o c a r b o n r e s e r v o i r un i ts in t h e H a l t e n b a n k e na r e a ( E h r e n b e r g , 1 99 0 ). M e d i a n g r a i n -s i z e ist y p ic a l ly in th e r a n g e 0 . 3 ~ 0. 5 m m ( u p p e r m e d i u ms a n d ) , a n d m o s t s a m p l e s a r e w e l l t o v e r y w e l ls o r t e d . E h r e n b e r g ( 19 9 0) p r e s e n t e d a d e t a i l e da n a ly s is o f th e p e t r o g r a p h y a n d r e s e r v o i r q u a l it yo f s a n d s to n e s f r o m 1 6 w e l l s. T h e b u r i a l d e p t h o ft h e G a r n F o r m a t i o n i n t h e s e w e l ls r a n g e sb e t w e e n 1 40 0 a n d 4 0 00 m , a n d i n th e d e e p e rw e l l s, w h e r e t e m p e r a t u r e s h a v e e x c e e d e d 1 4 0~a u t h i g e n i c i l li t e i s a n i m p o r t a n t d i a g e n e t i c p h a s e .E h r e n b e r g ( 19 9 0) s t a t e d t h a t th e p r i m a r y c o n t r o l so n p o r o s it y v a r i a t io n a r e c o m p a c t i o n a n d q u a r t zc e m e n t a t i o n , a n d t h a t p e r m e a b i l i t y is a f u n c t i o no f t h e r e m a i n i n g v o l u m e o f i n t e r g r a n u l a rm a c r o p o r o s i t y .

T h e t e x t u r a l a n d m i n e r a l o g i c a l d a t a p r e s e n t e db y E h r e n b e r g ( 19 9 0) h a v e b e e n u s e d t o a n a l y s ea v e r a g e p o r o s i t y - p e r m e a b i l i t y v a l u e s f o r e a c hw e l l u si n g t h e t r e n d c u r v e s f r o m t h e s p h e r e p a c km o d e l l i n g . T h i s a n a l y s is is s u m m a r i z e d i n F i g . 9.T h e s t a r t p o i n t is a si m p l e c o m p a c t i o n / q u a r t zo v e r g r o w t h c e m e n t a t i o n m o d e l t r e n d f o r t h ea p p r o p r i a t e g r a i n si z e , i n t h is e x a m p l e , m e d i u ms a n d . N o t e t h a t i n th i s c a s e , a s w i t h t h e F o n t a i n e -b l e a u S a n d s t o n e , t h e r e i s a r e l a t i v e l y sm a l l s p r e a do f g r a i n - s i z e , s o t h e t e x t u r a l s p l it h a s n o t b e e ne s s e n ti a l. T h e s a n d s t o n e s f r o m w e l ls i n w h i c ht h e r e a r e l o w a b u n d a n c e s o f a u t h i g e n i c i ll it e s h o wa v e r a g e p o r o s i t y - p e r m e a b i l i t y v a l u e s w h i c h fa l l


9/11

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0 1 0 2 0 3 0 , 0

Porosity (%)Fro. 9. Porosity vs. permeability cross-plot for GarnFor m ation sandstones. Porosity-permeability values areaverages f or wells with different geographical locations andburial histories (data from E hren berg , 1989). Th e curvesare model-derived and match the measured textural anddiagenetic characteristics of the Garn Formation

sandstones.

o n , o r c l o s e t o , t h is m o d e l t r e n d . T h i s s u p p o r t st h e c o n c l u s io n s o f E h r e n b e r g ( 19 9 0) a n d p r o v i d e sf u r t h e r c o n f i r m a t i o n t h a t o u r m o d e l s a r e r e a l i s t i cr e p r e s e n t a t i o n s o f r e a l s a n d s t o n e s . A l s o s h o w no n F i g . 9 a r e t w o m o d e l t r e n d s f o r c o m b i n e d c a s e so f c o m p a c t i o n / q u a r tz c e m e n t a t i o n , f o l lo w e d b yg r a i n - r i m m i n g c la y c e m e n t a t i o n . T h e t w o c a s e sd i f f e r in t h e d e g r e e t o w h i c h p o r o s i t y i s fi rs tr e d u c e d b y c o m p a c t i o n / q u a r t z c e m e n t a t i o n ( to2 5 % i n o n e c a s e , a n d t o 1 5 % i n t h e o t h e r ) .

A s i s t h e c a s e in e x a m p l e 1 , t h e m o d e l t r e n d s ,c o n s t r u c t e d u s i ng t e x t u ra l d a t a f r o m t h in -s e c t i o n s , a n d a u t h i g e n i c m i n e r a l o g y d a t a f r o m X -r a y d i f f r a c t i o n a n a l y s i s , p r o v i d e a fu l l e x p l a n a t i o no f t h e m e a s u r e d p o r o s i t y - p e r m e a b i l i t y d a t a a v e -r a g e s. T h e a v e r a g e s f r o m t h e d e e p e r w e l l s w i t hm o r e i l l it e a r e e n c l o s e d b y t h e t w o c o m b i n e dm e c h a n i s m m o d e l tr e n d s , i n m o r e d e t a i l , i n c r e a s-i n g il l it e c o n t e n t i s r e f l e c t e d i n p r o g r e s s i v e l y l o w e rp e r m e a b i l i t i e s .

H a v i n g e x p l a i n e d t h e o b s e r v e d t r e n d s i n t h ep o r o s i t y - p e r m e a b i l i t y d a t a u s in g th e m o d e lr e s u l t s, t h i s u n d e r s t a n d i n g c a n b e u s e d p r e d i c t i -v e ly . F o r e x a m p l e , i f a G a r n F o r m a t i o n p r o s p e c ti s s i m i l a r t o t h e d r i l l e d o c c u r r e n c e s , b u t w i t h f i n e -s a n d g r a i n s iz e , t h e n t h e m o d e l - d e r i v e d t r e n d s f o rt h a t f i n e r g r a in s i z e , i n c o m b i n a t i o n w i t h b u r i a lh i s to r y i n f o r m a t i o n , c o u l d b e u s e d to m a k e a p r e -d r i l l r e s e r v o i r q u a l i t y p r e d i c t i o n .

A l a r g e d a t a s e t f r o m M i s s i s s ip p i a n a g e s a n d -s t o n e s i n a w e l l i n t h e E n d i c o t t F i e l d h a s b e e na n a l y s e d u s i n g th e m o d e l r e s u l ts . T h e s e s a n d -s t o n e s h a v e a m o r e c o m p l e x s u i te o f t e x t u r a l a n dd i a g e n e t i c c o n t r o l s o n r e s e r v o i r q u a l i t y t h a n t h ep r e c e d i n g c a s e s , a n d t h i s is a ' b l i n d ' a n a l y s is , w i t hn o p r i o r s t a t i s t i c a l w o r k o n p e r m e a b i l i t y c o n t r o l s .

S a m p l e s f r o m t hi s w e l l s h o w w i d e l y v a ry i n gg r a i n s i z e s, w i t h a v e r a g e g r a i n s iz e r a n g i n g f r o mf i n e -s a n d t o v e r y c o a r s e s an d o r g r e a t e r . T h e d a t as e t i s f i rs t s p li t b y g r a i n - s i z e c l a s s ( F i g . 1 0 a ) . O n em o d e l tr e n d , f o r a m o d e r a t e l y s o r t e d , m e d i u ms a n d s to n e u n d e r g o i n g c o m p a c t i o n / q u a r tz c e m e n -t a t io n is s h o w n o n t h e p l o t f o r g u id a n c e . F r o m t h isi n i t i a l p l o t s e v e r a l c o n c l u s i o n s c a n b e d r a w n .F i r s t l y, w i t h i n e a c h g r a i n - s i z e c la s s , t h e p o r o s i t y -p e r m e a b i l i t y t r e n d i s s t e e p e r t h a n t h e s i m p l em o d e l t r e n d , i n d i c a t in g t h a t th e d o m i n a n t r e s e r-v o i r q u a l i ty c o n t r o l ( s ) a r e p o r e - f i l l in g c e m e n -t a t i o n a n d / o r p o r e - l i n i n g / f i l l in g c l a y. S e c o n d l y ,t h e r e i s c o n s i d e r a b l e o v e r l a p b e t w e e n t h e g r a in -s i ze c la s s e s , w h i c h i n d i c a t e s t h a t t h e d i a g e n e t i cc o n t r o l s o n p o r o s i t y a n d p e r m e a b i l i t y h a v er e a c h e d t h e s t a ge o f d e v e l o p m e n t w h e r e t h e ym a s k t h e p r i m a r y t e x t u r a l c o n t r o l . H o w e v e r ,s o m e r e m n a n t t e x t u r a l c o n t r o l i s s ti ll e v i d e n t : e . g .t h e v e r y c o a r se s a n d s a m p l e s h a v e a h ig h e rp e r m e a b i l i t y f o r a g i v e n p o r o s i t y t h a n t h em e d i u m s a n d s a m p l e s , w h e r e a s f i ne t o m e d i u ms a n d g r a d e s a m p l e s h a v e l o w e r p e r m e a b i l i t y .

H a v i n g e s t a b l i s h e d t h a t t h e t e x t u r a l e f f e c t h asb e e n l a r g e ly , b u t n o t c o m p l e t e l y , s w a m p e d b y t h ed i a g e n e t i c o v e r p r i n t , e a c h t e x t u r a l g r o u p i n t h ed a t a s e t is t h e n a n a l y s e d o n i t s o w n , t o e s t a b l i s hw h a t t h e i m p o r t a n t d i a g e n e t i c c o n t ro l s o n r e s e r -v o i r q u a l i ty a r e . T h e a n a ly s is o f t h e m e d i u m s a n dg r a d e s a m p l e s e t is i l l u s t r a te d i n F ig . 1 0 b .

T h e m e d i u m s a n d d a t a p o i n t s a r e c o d e d b y c la yc o n t e n t ( p o i n t - c o u n t d a t a ) , a n d a c l e a r r e l a t i o n -s h ip o f d e c r e a s i n g p e r m e a b i l i t y w i t h i n c r e a s in gc l ay c o n t e n t c a n b e s e e n . S e v e r a l o f t h e m e d i u ms a n d g r a d e s a m p l e s h a v e p o r o s i t y - p e r m e a b i l i t yv a l u e s w h i c h f a l l o n o r c l o s e t o t h e m o d e lc o m p a c t i o n / q u a r tz c e m e n t a t i o n t r en d . A s w ew o u l d p r e d i c t , t h e s e s a m p l e s a l l h a v e a l o w c l a yc o n t e n t , a n d t h e r e i s a tr e n d f o r l o w e r p o r o s i tyc o r r e s p o n d i n g w i t h h i g h e r v o l u m e s o f q u a r t zc e m e n t . I t c a n b e c o n c l u d e d , t h e r e f o r e , t h a t t h em a j o r c a u s e s o f r e s e r v o i r q u a l i t y v a r i a t io n i n


10/11

5O0

t h e s e s a n d s t o n e s a r e v a r i a t io n i n t h e v o l u m e s o fq u a r t z c e m e n t a n d p o r e - f i l li n g cl a y, w h i c h l a r g e lyo b s c u r e t h e p r i m a r y t e x t u r a l c o n t r o l .

D I S C U S S I O N

T h e t h r e e c a s e s t u d i e s d e s c r i b e d i l l u s t r a t e , f o rs a n d s t o n e s o f v a ry i n g t e x t u r a l a n d d i a g e n e t i cc o m p l e x i t y , h o w t h e sp h e r e p a c k m o d e l s r e p l i c a t et h e r e s u l t s o f d i a g e n e t i c p r o c e s s e s i n r e a l sa n d -s t o n es . T h i s h a s i m p o r t a n t c o n s e q u e n c e s . T h em o d e l l i n g ha s p r o v i d e d a q u a n t i f i e d u n d e r -s t a n d i n g o f h o w d i f f e r e n t s ty l es o f c e m e n t o rc o m p a c t i o n i n f lu e n c e p o r e s a n d p o r e - t h r o a t s .T h i s u n d e r s t a n d i n g p e r m i t s t h e i d e n t if i c a ti o n o fi m p o r t a n t r e s e r v o i r q u a l it y c o n t r o ls f r o m p o r o -s i t y - p e r m e a b i l i ty t r e n d s . I n s i m p l e s a n d s t o n es y s t e m s , i t m a y b e p o s s i b l e t o d r a w c o n c l u s i o n sa b o u t c o n t r o l s u s i ng j u s t th e p o r o s i t y - p e r m e a b i -l it y d a t a a n d t e x t u r a l i n f o r m a t i o n f r o m c u t ti n g s ,s i d e w a l l c o r e o r c o r e d e s c r i p t i o n . C l e a r l y, t h e r e i sl es s u n c e r t a i n t y i f m o r e d e t a i l e d p e t r o g r a p h i cd a t a o n t e x t u r e a n d c e m e n t s a r e a v a i l a b l e .

I n n u m e r o u s c a s e s, w i t h a w i d e r a n g e o fs a n d s t o n e t y p e s , t h e m o d e l t r e n d s h a v e g i v e n aq u i c k a n d a c c u r a t e i n s i g h t i n t o t h e p e r m e a b i l i t yc o n t r o l s . T a k i n g t h e r e s u l t s a s t e p f u r t h e r , s e n s it i -v i ti e s c a n b e i n v e s t i g a t e d , a n d p r e d i c t i o n s m a d e .F o r e x a m p l e , f o r a g iv e n s a n d s to n e t y p e , i n v e s ti -

C . A . C a d e et a l .

g a t e t h e g r a i n s iz e o r c e m e n t v o l u m e a t w h i c hp e r m e a b i l i t ie s a r e r e d u c e d b e l o w t h e t h r e s h o l df o r e c o n o m i c f l ow r a t e s c a n b e i n v e s t ig a t e d .

I t sh o u l d b e e m p h a s i z e d t h a t o n l y s in g l e p h a s ep e r m e a b i l i t y h as b e e n m o d e l l e d t o da t e . P o t e n t i a le x t e n s i o n s o f t hi s w o r k i n c l u d e m o d e l l i n g o fp a c k s w i t h a r a n g e o f g r a i n s i z es a n d t w o p h a s ep e r m e a b i l i t y .

C O N C L U S I O N S

( 1) B y m o d e l l i n g t h e r e s u lt s o f c o m p a c t i o n a n dv a r i o u s s t yl e s o f c e m e n t a t i o n i n a n u m e r i c a ls p h e r e p a c k a n d c a l c u la t i n g p o r o s i t y - p e r m e a b i -l it y t r e n d s f o r t h e s e d i a g e n e t i c m o d e l s , a g o o dm a t c h b e t w e e n p o r o s i t y - p e r m e a b i l i t y d a t a f o rr e a l a n d m o d e l s a n d s t o n e s h a s b e e n a c h i e v e d .

( 2) T h e s p h e r e p a c k m o d e l s g iv e a n i m p r o v e da n d q u a n t i f i e d u n d e r s t a n d i n g o f h o w a r a n g e o ft e x t u r a l a n d d i a g e n e t i c r e s e r v o i r q u a l i t y c o n t r o lso p e r a t e .

( 3 ) P r o g r e s s i v e c o m p a c t i o n a n d q u a r t z o v e r -g r o w t h c e m e n t a t i o n p r o d u c e a l m o s t i d e n t ic a lp o r o s i t y - p e r m e a b i l i t y d e c l i n e t r e n d s .

( 4) P o r e - f i l l in g c e m e n t s ( s u c h a s c a r b o n a t e s ) ,a n d g r a i n - r i m m i n g c l a y s c a u s e a s t e e p e r p e r m e a -b i li ty d e c l in e t r e n d w i t h p o r o s i ty t h a n c o m p a c t i o no r q u a r t z c e m e n t a t i o n .

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FIe. 10. Porosityv s . permeability cross-plots for Mississippian age sandstones from a well in the Endicott field, Alaska,U SA ; (a) plot illustrating the diagenetic overprint o f the primary textural control on reservoir quality; (b) p lot showing the

diagenetic controls operating within one grain-size class.


11/11

An a ly s i s o f p e r m e a b i l i ty c o n t r o ls

( 5) T h e s p h e r e p a c k m o d e l l i n g h a s u n d e r l i n e dt h e i m p o r t a n c e o f c o n s i d e r i n g t h e p r i m a r y ( t e x-t u r a l ) , a n d s e c o n d a r y ( d i a g e n e t i c ) c o n t r o ls o nr e s e r v o i r q u a l it y s e p a r a te l y . B y r e m o v i n g t h et e x t u r a l c o n t r o l f i rs t , a n a l y s i s o f t h e d i a g e n e t i cc o n t r o l s i s f a c i li t a t e d .

( 6 ) I n o r d e r t o a n a l y s e a s e t o f d a t a t o e s t a b l is ht h e r e s e r v o i r q u a l i t y c o n t r o l s w e s u g g e s t t h e f i r s ts t a g e s h o u l d b e t o s p l i t t h e d a t a s e t b y g r a i n - s i z ec l a ss ( a n d i f a p p r o p r i a t e , s o r t i n g c l a s s) . I f t e x t u r a lc o n t r o l i s s t il l i m p o r t a n t , i t w i l l b e e v i d e n t a f t e rt h i s s p l i t . Wi t h i n e a c h g r a i n - s i z e c l a s s , t h e d i a g e -n e t i c c o n t r o l s c a n t h e n b e e v a l u a t e d , b o t h q u a l i t a -t i v e ly u s in g c o m p a r i s o n w i t h th e m o d e l - d e r i v e dt r e n d s , a n d q u a n t i t a t i v e l y u s i n g s t a t is t i c a l a n a l y -s is , i n d e p e n d e n t o f te x t u r e .

( 7) I n o r d e r t o p r e d i c t p e r m e a b i l i t y a h e a d o fd r i l l i n g , i t i s n e c e s s a r y t o b e a b l e t o p r e d i c t t h ec o n t r o l l in g p a r a m e t e r s . B y c o m b i n i n g t h e s p h e r ep a c k m o d e l r e su l ts w i th a n a p p r o a c h w h i c hs e p a r a t e s t e x t u r a l a n d d i a g e n e t i c p a r a m e t e r s , t h ep o t e n t i a l f o r d e f i n in g t h e i m p o r t a n t c o n t r o l l i n gp a r a m e t e r s is m a x i m i z e d .

A C K N O W L E D G M E N T S

The perm ission of BP Exploration to publish the results andapplication of this research is acknowledged. In addition,permission has been granted by the Endicott partner,group: Exxon, Unocal, Amoco, BP, Arco, Cook Inlet,Nana and Doyon, to utilize data from this field.

R E F E R E N C E S

501

BEARD D.C . & W EYL P.K. (1973) Influence o f texture onporosity and permeability of unconsolidated sand.

A A P G B u l l .57, 349-369.BLOCH S. (19 91) Empirical prediction of porosity and

permeability in sandstones.A A P G B ull.75, 1145-1160.BOURBIET. & ZINZSNERB. (1985) Hydraulic and acoustic

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