Dr. Hilmi S. Salem Archie Cementation Factor (JPES-Elsevier).Pdf20130812-30876-Vyubwx-libre-libre

Ž .Journal of Petroleum Science and Engineering 23 1999 83–93www.elsevier.comrlocaterjpetscieng

The cementation factor of Archie’s equation for shaly sandstonereservoirs

Hilmi S. Salem a,), George V. Chilingarian b

a Atlantic Geo-Technology, Suite 307, 26 Alton DriÕe, Halifax, NoÕa Scotia, Canada, B3N 1L9b Department of Engineering, UniÕersity of Southern California, Los Angeles, CA 90089-1211, USA

Received 7 May 1998; accepted 18 March 1999

Abstract

The cementation factor, m, of Archie’s equation has specific effects on electric conduction processes in porous media. Itdepends on the shape, type, and size of grains; the shape and size of pores and pore throats; and the size and number ofdead-end pores. The dependence of m on the degree of cementation is not as strong as its dependence on the shape of grainsand pores. Therefore, it is suggested that it is more accurate to call m ‘‘shape factor’’ instead of ‘‘cementation factor’’. Inthis study, m was derived from well-log data for the Hibernia and Terra Nova reservoirs in the Jeanne d’Arc Basin, offshoreof the eastern Canadian coast. Empirical equations, linking m, tortuosity, pore-water resistivity, and electric and hydraulic

Ž .anisotropy coefficients, were obtained. The cementation factor shape factor is not a constant, but is a variable depending onmany physical parameters and lithological attributes of porous media. An average value of 2.28 was obtained for m, whichcan be used for similar reservoirs. q 1999 Elsevier Science B.V. All rights reserved.

Ž .Keywords: Electric conductivity; Cementation factor shape factor ; Tortuosity; Hibernia; Terra Nova; Jeanne d’Arc Basin

1. Introduction

( )1.1. Jeanne d’arc Basin JDB

Marine geophysical and geological investigationsof the eastern margin of North America were firstcarried out in the 1950s by Canadian and Americangovernments and university research agencies. Ex-ploration by oil companies outlined the principalsedimentary basins, offshore eastern Canada, and

) Corresponding author. Tel.: q1-902-477-4396; E-mail:[email protected]

eventually established the presence of hydrocarbonsŽ .in the Jeanne d’Arc Basin JDB . Some wells, pene-

trating the JDB, can produce up to 2=103 barrelsrŽ .day Benteau and Sheppard, 1982 . Nine wells,

Ž .drilled in the Hibernia reservoir JDB , have oilŽreserves of 500 to 800 million barrels Grant and

. ŽMcAlpine, 1990 . The Grand Bank basins including.JDB have a sedimentary cover of more than 20 km

in thickness. These basins began to develop betweenearly Jurassic and late Cretaceous due to riftingbetween North America and Africa from sea-floorspreading.

Ž .The Hibernia and Terra Nova reservoirs JDB aremosaic systems made of complex, heterogeneous,anisotropic, and compacted rocks saturated with oil,

0920-4105r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0920-4105 99 00009-1

( )H.S. Salem, G.V. ChilingarianrJournal of Petroleum Science and Engineering 23 1999 83–9384

gas, and brine. The rocks of these reservoirs areŽcomposed of various lithological components shale,

sandstone, siltstone, limestone, marlstone, and con-.glomerate , which have various sizes and shapes of

grains and pores and, generally, high specific surfaceŽ .area Salem and Chilingarian, 1999 .

( )1.2. Cementation factor m

The cementation factor, m, indicates reduction inthe number and size of pore openings or reduction in

Ž .the closed-off dead-end channels. It has been widelyused in hydrocarbon and groundwater exploration,

Žand in porous-media engineering studies e.g.,Archie, 1942; Winsauer et al., 1952; Wyllie andGregory, 1953; Hill and Milburn, 1956; Towle, 1962;Helander and Campbell, 1966; Waxman and Thomas,1974; Windle and Worth, 1975; Jackson et al., 1978;Biella and Tabbacco, 1981; Sen et al., 1981; Wonget al., 1984; Givens, 1987; Brown, 1988; Donaldsonand Siddiqui, 1989; Ruhovets, 1990; Salem, 1992;

.Tiab and Donaldson, 1996 .The cementation factor exhibits wide variations

from sample to sample, formation to formation, in-terval to interval in the same medium, and from

Ž .medium to medium. Wyllie and Rose 1950 statedthat m can vary in the mathematical sense betweenone and infinity, but practically, it lies within thelimits of 1.3 and 3.0, as originally observed by

Ž . Ž .Archie 1942 . Keller 1982 summarized differentvalues for m, showing that m is affected by lithol-ogy, porosity, degrees of compaction and cementa-

Ž .tion, and age. Ehrlich et al. 1991 showed that mvaries widely and changes continuously in the bore-hole due to variations in depositional subfacies. Thegeneral range of m, given in the literature, is be-tween slightly less than one for fractured rocksŽ .Aguilera, 1976; Jorgensen, 1988 and 5.12 for well

Žconsolidated and highly compacted rocks Wyble,.1958 .

(2. Factors affecting cementation factor Archie)shape factor, m

Because of the dependence of m on various prop-erties, it has been given different names, includingfor instance, cementation factor, shape factor, con-

ductivity factor, resistivity factor, porosity exponent,Ž .and cementation exponent. Atkins and Smith 1961

pointed out that m is strongly dependent on theshape of grains and pores, and is analogous to the

Ž .shape factor S of the Kozeny–Carman equationhfŽ .Kozeny, 1927; Carman, 1937 . The dependence ofm on the degree of cementation is not as strong as its

Ždependence on the grain and pore properties shapeand type of grains, and shape and size of pores and

.pore throats . Therefore, it is suggested that m shouldbe called the ‘‘shape factor’’ instead of ‘‘cementa-

Žtion factor’’. The term ‘‘Archie shape factor’’ or.shape factor is used for m, unless otherwise indi-

cated. Some of the factors that cause considerablevariations of m are discussed below in more detail.

2.1. Shape of grains and pores

The shape of grains and pores in porous media isone of the most significant properties affecting m.Many researchers focused their attention on thisproperty as the major contributor to the wide varia-tions of m. Increase in the degrees of diagenesis,

Žcatagenesis, and epigenesis consolidation, com-.paction, cementation, etc. causes an increase in the

degree of irregularity of grains. Higher angularityŽ .less sphericity results in higher values of m. Theshape of grains and pores also contributes to otherfactors affecting m, and it has a particular impor-tance in defining the magnitudes of various parame-

w Ž . Ž .ters e.g., porosity f , permeability k , tortuosityŽ . Ž .t , formation resistivity factor F , specific surface

Ž . Ž .xarea s , and Kozeny–Carman coefficient K .s cc

2.2. Type of grains

ŽThe type of grains lithological and mineralogical.composition affects m greatly. Increase of shaliness

Ž .clay content , presence of specific clay mineralswith different grain shapes, and presence of hetero-geneous mixtures of sediments or rocks can lead toan increase in m. Increase in the contents of sands,sandstones, porous dolomites, and fractured lime-stones generally results in lower values of m. Pres-ence of diatomites lowers the value of m to generallyless than 1.3. The Archie shape factor exhibits awide range of values for different sediments androcks. It is, for example, 1.09 for porous dolomites;

( )H.S. Salem, G.V. ChilingarianrJournal of Petroleum Science and Engineering 23 1999 83–93 85

1.2 to 1.3 for fractured limestones; 1.3 for glassspheres and unconsolidated-poorly cemented rocks;2 to 2.3 for clean sands; and 1.8 to 3.0 for com-pacted sandstones and limestones. The variations ofm for clays depend on the type of clay minerals,because of their differences in the chemical composi-tion and internal structure, and thus, their ability toconduct electric current. It is, for example, 1.87 forkaolinite; 2.11 for illite; 2.46 for attapulgite andmuscovite; 2.70 for calcium montmorillonite; and3.28 for sodium montmorillonite. The size of grainsappears to affect m less than the shape and type ofgrains and pores.

2.3. Type of pores

Based on petrographical analysis, m can be de-fined as the logarithm of throat area divided by the

Ž .logarithm of pore area Ehrlich et al., 1991 . Thisdefinition of m is the inverse of the nonlogarithmic

Ž .definition of aspect ratio pore arearthroat area .This indicates that the closer the value of throatradius to pore radius, the closer is the value of m tounity. The shape factor is affected by the pore sys-

Žtem intergranular, intercrystalline, fractured, or. Žvuggy , and can indicate the type of porosity total

‘‘absolute f ’’, open ‘‘saturation f ’’, or effective.‘‘dynamic f ’’ . For example, the increase of fractur-

Ž .ing decreases the value of m Aguilera, 1976 , andthe increase of vugginess increases the value of mŽ . ŽLucia, 1983 . In micro-porous media where fF

.5% , m increases because the grains are pressedcloser to each other and the pores become smaller.

2.4. Specific surface area

Ž .The specific surface area s is variously defineds

as the interstitial surface area of the pores and poreŽ .channels per unit of bulk volume s , grain volumeb

Ž . Ž . Ž .s , pore volume s , or per unit of weight s .g p wt

This parameter becomes a minimum for any specificgrain size when the shapes of grains are spherical.Abundance of grains with a high degree of irregular-ity causes an increase in s , with consequent increases

in m. Also, because s is inversely related to k, ans

inverse relationship between k and m can be ex-Ž .pected Aguilera, 1976; Jorgensen, 1988 .

2.5. Tortuosity

Tortuosity is defined as the ratio of the actual oreffective length of a flow path to the length of aporous medium, parallel to the over-all direction offlow. It has a considerable effect on various parame-

Ž .ters e.g., f, k, s , F , and thus, its effect on m iss

significant. Higher values of t correspond to highervalues of m. The type of f is an important factorcontributing to the variations of t . In micro-poroussystems, with many dead-end pores, the current can-

Ž .not be easily conducted through the pores higher t .Porous materials with grains of irregular shape exert

Ž .more resistance to electric current higher t . Inrocks characterized by complexity of electrolyticpaths, the current encounters more resistance in pass-

Ž .ing through the pores higher t .

2.6. Anisotropy

Anisotropy is a measure of the variations of phys-ical properties in the horizontal and vertical direc-tions, which contributes to the variations of m. It isexpressed in terms of the electric anisotropy coeffi-

w Ž .1r2 xcient l s R rR , where R and R are,e v h v h

respectively, the vertical and horizontal electric resis-tivities, normal and parallel to the bedding planes. Itis also expressed in terms of the hydraulic anisotropy

w Ž .1r2 xcoefficient l s k rk , where k and k are,h h v h v

respectively, the horizontal and vertical permeabili-ties, parallel and normal to the bedding planes. Both

Žcoefficients increase with increasing R and k in-v h

creasing the horizontal conductivities along the bed-.ding planes . The horizontal conductivities are al-

ways greater than the vertical ones, unless themedium is completely isotropic. Anisotropy is at-tributed to many reasons, including, e.g., orientationof grains, variations in the grain and pore properties,

Ž . Ž .and tortuosity Salem, 1994 . Kunetz 1966 , SalemŽ . Ž .1992 , and Tiab and Donaldson 1996 pointed outthat l and l normally range from 1 to 2 and frome h

1 to 5, respectively. For shaly sandstones, SalemŽ . Ž .1994 obtained values ranging from 1 to 1.7 le

Ž .and from 1 to 6.2 l .h

( )2.7. OÕerburden pressure compaction

The effect of overburden pressure on m is notclearly known. Variations in m, f and F, due to


compaction, were experimentally demonstrated byŽ . Ž .Fatt 1957 and Wyble 1958 . Compression of rocks

results in radical changes in pore structure and shapeof grains. As the degree of compaction increases,

Ž .grains are flattened become more deformed , whichresults in higher degrees of angularity, pore constric-tion, cementation, and thermal expansion, as well as

Ž .higher resistivity higher m .

3. Theory

3.1. Mechanisms of electric-current conduction inporous media

Electric-current conduction in porous media isaffected by various mechanisms. Conductance ofelectric current in saturated systems can be repre-

w Ž .sented by a two-phase model grain-matrix relativeconductance, known as dispersed phase, and pore-

xfluid conductance, known as continuous phase . Thus,electric current is conducted in porous media by

Ž .means of the solid and ionic or electrolytic con-stituents in the pore fluid. The two-phase model canbe developed into a five-phase model, consisting ofŽ .in addition to the above surface conductance occur-ring at the charged fluid–solid interface, ion-ex-change conductance, and the Maxwellian-effectsconductance. The Maxwellian-effects conductanceŽ .Maxwell, 1881 is that of both solid particles in thematrix and those suspended in the pore fluid.

Ž .The observed conductivity C for the five-phaseobŽ .model is the sum of: pore-fluid conductivity C ,pf

Ž . Ž .fluid–solid interface surface conductivity C ,fsŽ .grain-matrix conductivity C , ion-exchange con-gm

Ž .ductivity C , and the Maxwellian-effects conduc-exŽ . Žtivity C Patnode and Wyllie, 1950; McKelveymax

et al., 1955; McEuan et al., 1959; Pfannkuch, 1969;.Salem, 1992 , i.e.:

C sC qC qC qC qC . 1Ž .ob pf fs gm ex max

Ž .The observed resistivity R for the same modelob

is:

R sR qR qR qR qR . 2Ž .ob pf fs gm ex max

Ž .The pore-fluid ionic conductivity and theŽ .fluid–solid surface conductivity are the most im-

portant mechanisms in the process of electric-currentconduction. The C -mechanism depends on the fluidpf

conductivity, which is affected by the ionic composi-Ž .tion salinity , ionic-exchange capacity of the solid

matrix, and acidity-alkalinity of the pore fluid. TheC -mechanism depends on the clay conductivity,fs

which is affected by the content and type of clay,and the charged ions concentrating at the grain

Ž .boundaries double-layer theory . When the pore fluidŽ .has a low concentration of ions fresh water , Cfs

becomes predominant in the process of electric-cur-rent conduction. When the pores are saturated withsaline water, C becomes predominant, because thepf

conduction of electric current takes place through theŽsaline water Pfannkuch, 1969; Ransom, 1984; Alger

.and Harrison, 1989; Salem, 1992 . Patnode and Wyl-Ž .lie 1950 developed a parallel-resistor model and

showed that C increases at the expense of C , orpf fsŽ .vice versa. Hill and Milburn 1956 experimentally

showed that the current is totally conducted throughthe pore water when it is saline, and thus, no conduc-tion takes place via the clays. Waxman and SmitsŽ .1968 developed a model that consists of conduc-tance of pore-fluid electrolyte and conductance re-sulting from exchange cations associated with theclays. The Waxman and Smits model is essentiallyvalid for oven-dried cores, where no formation water

Žis left on the clay surfaces Waxman and Smits,.1968; Tiab and Donaldson, 1996 . Hoyer and Spann

Ž .1975 used the Waxman and Smits model andŽ .showed that the effect of shales clays on the forma-

tion-electric conductivity is negligible when thepore-water conductivity is high.

( )3.2. Archie shape factor m

For a two-phase model, consisting of uniformsolid spheres imbedded in a fluid continuum,

Ž .Maxwell 1881 observed that the resistivity ratioŽ .bulk resistivity to pore-fluid resistivity; R rRb pf

depends on the resistivity of the pore fluid and thesize of the spheres, as long as the pore fluid and the

Žspheres are nonconductive as in the case of highly. Ž .dilute fluid . Maxwell 1881 also observed that

R rR slowly decreases with increasing f:b pf

R rR s 3yf r2f . 3Ž . Ž .b pf


Ž .Based on Maxwell’s observations, Fricke 1931showed that R rR increases with increasing irreg-b pf

ularity of grains. Accordingly, he developed thefollowing equation by introducing the variable x thatequals 2 for spheres and less than 2 for spheroids:

R rR s xq1 yf rxf . 4� 4Ž . Ž .b pf

Ž .Eq. 4 shows that at any f, the resistivity ratiowill be minimized by increasing sphericity of grains,and maximized by increasing irregularity of grains.This indicates that the shape of grains has a specificinfluence on R rR for spherical and nonsphericalb pf

Ž .aggregates of grains. Sundberg 1932 demonstratedŽthat R resistivity of a formation 100% saturatedo

.with formation water is directly proportional to RwŽ . Ž .resistivity of the pore water . Archie 1942 modi-fied Sundberg’s proportionality by introducing F:

FsR rR . 5Ž .o w

The formation resistivity factor, F, is a functionof f, k, t , and s , as well as the formation resistiv-s

ity, lithology, and texture; pore-water resistivity,salinity, viscosity, density, and saturation; clay con-tent; degrees of compaction and cementation;cation-exchange capacity; and uniformity coefficientŽ .Salem, 1992 . The uniformity coefficient embodiesthe effects of size, shape, distribution, packing, and

Žsorting of grains Chilingar et al., 1963; Salem,. Ž .1992; Tiab and Donaldson, 1996 . Archie 1942

recognized that F and f are inversely related; hegeneralized his observations as:

Fs1rf m . 6Ž .

Ž .Winsauer et al. 1952 modified Archie’s equationŽby adding the pore-geometry factor or tortuosity

. Ž Ž ..factor, a, which is different from t Eq. 7 , knownas Archie–Winsauer equation:

Fsarf m , 7Ž .

leads to:

msy log Fy log a rlog f . 8� 4Ž . Ž .

The value of m can be obtained from the slope ofthe line representing the inverse F–f relationship on

Ž .log–log paper, or according to Eq. 8 by using FŽ .and f Wyllie, 1957; Donaldson and Siddiqui, 1989 .

The value of a can be assumed or obtained as theintersection of the best fitting line of the F–f rela-

Ž .tionship at 100% porosity Wyllie, 1957 . Winsauer

Ž .et al. 1952 generalized values of 0.62 for a andŽ .2.15 for m for sandstones Humble equation :

Fs0.62rf 2.15 . 9Ž .

Researchers gave or used various values of a fordifferent lithologies. For example, ParkhomentoŽ .1967 obtained a value of 0.40 for a, representingdifferent consolidated sandstones.

4. Methodology

Ž .Different digital electronic stored data and ana-Ž .logue hard-copy form logs for 14 wells, penetrating

the Hibernia and Terra Nova reservoirs, were ana-Ž .lyzed at sampling-depth intervals DZ of 0.2 m. For

this purpose, various computer programs were devel-oped and others used.

Ž .To derive m, Eq. 8 was used, which requires f,F, and a. The porosity, along with the lithology, wasdetermined from a combination of various logs; F

Ž .was obtained using Eq. 5 ; and a was obtained fromthe F–f relationship for each well investigated,resulting in an average value of 0.44. Tortuosity was

wŽ .1r2 xobtained as fF , and R was obtained fromw

the spontaneous potential log.The electric and hydraulic anisotropy coefficients

for the 200 m depth interval of the Hibernia C-96well were obtained by dividing the interval into 22

Žzones each of them is composed of one layer ormore, depending on the lithological and physical

.properties . For each zone, independently, l ande

l , as well as the average value of m, were obtained.h

A statistical technique was used for dividing thethicknesses of both reservoirs into different zones toidentify the porous and permeable zones that arelikely continuous between the wells. The zones wereidentified such that the variations of the variousproperties are minimized within the zones and maxi-mized between the zones. The zonation techniquecan be successfully applied not only to permeabilityand porosity, but also to other reservoir propertiesŽ .Testerman, 1962; Salem, 1994 .

wExamples of the results lithological components:Ž . Ž . Ž .shale SH , sandstone SS , siltstone SI , and lime-Ž . Ž . Ž .stone LS ; as well as porosity f ; tortuosity t ;

Ž .Archie shape factor m ; and pore-water resistivityŽ .xR are given in Table 1. The Archie shape factorw


Table 1w Ž . Ž . Ž . Ž .x Ž . Ž .Lithological components shale SH , sandstone SS , siltstone SI , and limestone LS , in %; porosity f , in %; tortuosity t ,

Ž . Ž . Ž .dimensionless; Archie shape factor m , dimensionless; and pore-water resistivity R , V.m, at sampling-depth intervals DZ of 10 m forwŽ . Ž .the Terra Nova H-99 well 3072–3452 m; 380 m and the Hibernia C-96 well 4203–4403 m; 200 m

Ž . Ž . Ž . Ž . Ž . Ž . Ž .Z m SH % SS % SI % LS % f % t m R V.mw

( )Terra NoÕa H-99 well 3072–3452 m; 380 m3072 30.3 22.9 21.7 16.7 8.4 3.05 2.24 0.0113082 34.8 17.2 17.6 8.9 21.5 1.90 2.37 0.0983092 37.6 17.1 17.4 7.2 20.7 1.95 2.36 0.0863102 33.7 17.1 17.6 9.5 22.1 1.81 2.33 0.0723112 32.1 21.8 20.9 14.7 10.5 2.72 2.25 0.0173122 37.9 16.5 17.0 6.5 22.1 1.76 2.29 0.0833132 27.7 23.1 21.9 18.4 8.9 2.98 2.25 0.0123142 26.6 19.7 19.6 15.9 18.2 2.03 2.31 0.0573152 42.1 9.3 25.0 14.5 9.1 2.97 2.26 0.0133162 28.9 20.0 26.4 22.4 2.3 5.64 2.14 0.0043172 44.6 3.6 21.0 9.0 21.8 1.71 2.25 0.2323182 23.4 24.0 26.6 25.2 0.8 6.80 1.95 0.0013192 46.3 0.0 10.5 0.0 43.2 1.35 2.70 0.6223202 48.8 0.0 12.8 0.0 38.4 1.35 2.49 0.5243212 48.0 0.0 16.7 2.5 32.8 1.06 1.83 0.7463222 27.5 16.5 21.9 18.3 15.8 2.06 2.23 0.1163232 6.0 30.2 20.3 27.2 16.3 3.87 2.94 0.3883242 6.6 29.9 20.4 27.0 16.1 6.27 3.46 0.2253252 9.4 29.0 15.4 25.2 21.0 1.91 2.36 9.2783262 14.2 29.5 19.6 27.1 9.6 4.59 2.65 0.1033272 14.7 26.5 18.6 24.4 15.8 2.01 2.21 0.7283282 22.5 23.9 23.8 24.4 5.4 6.54 2.57 0.0193292 35.2 8.7 27.2 14.0 14.9 2.53 2.40 0.0683302 30.3 19.2 27.9 22.3 0.3 2.97 1.51 0.0013312 34.4 14.3 29.1 19.0 3.2 6.07 2.29 0.0023322 37.0 9.5 29.1 15.3 9.1 3.42 2.37 0.0243332 29.0 20.4 27.5 23.0 0.1 1.80 1.30 0.0013342 31.4 18.2 28.5 21.8 0.1 4.73 1.81 0.0013352 14.3 32.4 20.9 29.8 2.6 10.8 2.54 0.0033362 11.7 30.1 17.8 26.9 13.5 1.90 2.04 0.4703372 0.0 46.8 13.3 38.0 1.9 10.3 2.40 0.0103382 36.8 0.0 24.5 6.1 32.6 1.49 2.45 0.3583392 22.4 24.4 23.9 24.8 4.5 4.50 2.24 0.0133402 30.1 0.0 32.3 33.3 4.3 4.52 2.22 0.0073412 33.0 0.0 33.8 31.6 1.6 6.66 2.13 0.0013422 37.4 0.0 32.4 20.5 9.7 3.13 2.34 0.0223432 34.0 0.0 32.7 27.2 6.1 4.39 2.34 0.0093442 25.8 0.0 32.1 40.4 1.7 8.44 2.27 0.0013452 29.8 0.0 31.6 32.2 6.4 4.38 2.38 0.015

( )Hibernia C-96 well 4203–4403 m; 200 m4203 24.5 16.0 23.0 16.9 19.6 1.57 2.06 0.1264213 19.6 21.2 20.1 21.2 17.9 1.75 2.13 0.1654223 16.8 25.0 18.8 24.5 14.9 1.89 2.10 0.1024233 20.4 23.1 21.6 23.2 11.7 1.89 1.97 0.1304243 17.1 25.3 19.2 24.8 13.6 1.51 1.83 0.2424253 43.5 0.0 36.0 4.2 16.3 2.03 2.23 0.0644263 32.3 11.4 29.1 13.7 13.5 1.77 1.98 0.1174273 30.6 12.0 27.6 14.0 15.8 1.85 2.12 0.0844283 33.2 11.6 30.1 14.0 11.1 2.69 2.28 0.074


Ž .Table 1 continued

Ž . Ž . Ž . Ž . Ž . Ž . Ž .Z m SH % SS % SI % LS % f % t m R V.mw

( )Hibernia C-96 well 4203–4403 m; 200 m4293 0.1 39.1 7.3 35.4 18.1 1.72 2.11 0.0374303 7.4 31.2 11.6 28.8 21.0 1.65 2.17 0.1364313 38.5 5.2 33.0 8.6 14.7 1.85 2.07 0.0764323 23.6 17.5 22.7 18.2 18.0 9.90 4.15 0.1554333 17.6 24.7 19.4 24.3 14.0 2.01 2.12 0.0784343 28.3 14.4 26.2 15.9 15.2 1.73 2.02 0.0974353 28.8 13.6 26.4 15.2 16.0 1.81 2.09 0.1034363 15.8 26.5 18.3 25.7 13.7 1.99 2.11 0.1684373 29.4 14.1 27.2 15.8 13.5 1.97 2.09 0.0694383 4.4 37.3 10.9 34.4 13.0 2.14 2.15 0.0824393 31.8 10.8 28.4 13.0 16.0 1.77 2.07 0.1034403 10.5 30.9 14.6 29.1 14.9 1.84 2.07 0.198

Ž . Ž . Žis plotted against: t Fig. 1 , R Fig. 2 , l Fig.w e. Ž .3 , and l Fig. 4 . The results presented in Table 1h

were obtained at DZs10 m and those plotted inFigs. 1–4 were obtained at DZs1 m for the Terra

Ž .Nova H-99 well 3072–3452 m; 380 m and theŽ .Hibernia C-96 well 4203–4403 m; 200 m . Empiri-

Ž .cal equations, with coefficients of correlation RcŽranging from 0.83 to 0.97, were obtained given in

.the plots .

5. Results and discussion

The values of m for both reservoirs show consid-erable variations from well to well and reservoir to

Ž . Ž .Fig. 1. Tortuosity t vs. Archie shape factor m for the HiberniaŽ .C-96 well 4203–4403 m; 200 m at sampling-depth intervals

Ž .DZ of 1 m.

reservoir due to variations in depth, lithology, andvarious petrophysical properties. Table 1 shows that

Ž .the values of m for the Hibernia reservoir 1.83–4.15are greater than those for the Terra Nova reservoirŽ .1.30–3.46 . This can be attributed to the greater

Ždepth of the Hibernia reservoir increase in overbur-den pressure; more compaction and change in miner-

.alogy and texture of the rocks . From the analyses atDZ of 0.2 m for the fourteen Hibernia and TerraNova wells, an average value of 2.28 was obtainedfor m. Generally, both reservoirs exhibit high values

Ž .of m larger than 2.25 , which may suggest highdegree of heterogeneity and presence of microporouszones and large amounts of plate-like clays, with ahigh degree of angularity.

Ž . Ž .Fig. 2. Pore-water resistivity R vs. Archie shape factor m forwŽ .the Terra Nova H-99 well 3072–3452 m; 380 m at sampling-de-

Ž .pth intervals DZ of 1 m.


Ž .Fig. 1 for the Hibernia C-96 well; 200 readingsŽshows an increasing relationship between m 1.5–

. Ž .4.2 and t 1–10 . This relationship suggests that,with greater degrees of compaction and cementation,a significant decrease in f occurs, which forces thecurrent to pass through longer and more tortuous

Ž .passages higher t and m . The relatively high val-ues of t and m may indicate abundance of clays,presence of complicated porosity types, andror highdegree of irregularity of grains. The relatively lowvalues of t and m may indicate higher f and k, andpresence of spherical grains and micro-fracturesŽlength of flow path through fractures is much shorter

.than that through interconnected pores .ŽFig. 2 for the Terra Nova H-99 well; 380 read-

.ings shows an increasing relationship between mŽ . Ž1.4–3.7 and R 0.001–2 V.m; pore-water con-w

.ductivity ranges from 0.5 to 1000 mho . The lowresistivities of the pore water, which generally corre-spond to high values of m, indicate that the electric-current conduction is electrolytic due to the mobilityof ions present in the brine. Apparently, R alonewŽwithout considering the influence of other parame-

.ters on m, such as porosity, bulk resistivity, etc.has, relatively, a low influence on m.

ŽFigs. 3 and 4 each of 22 readings for the Hiber-.nia C-96 well show the relationships between m

Ž . Ž . Ž .1.93–2.2 , l 1–1.16 , and l 1–1.5 . The m–le h eŽ .relationship Fig. 3 shows a direct correlation,

Ž .whereas the m–l relationship Fig. 4 shows ah

Ž .Fig. 3. Electric anisotropy coefficient l vs. Archie shape factoreŽ .m for the Hibernia C-96 well; 22 readings representing a total

Ž . Ž .depth of 200 m 4203–4403 m at sampling-depth intervals DZof 1 m.

Ž .Fig. 4. Hydraulic anisotropy coefficient l vs. Archie shapehŽ .factor m for the Hibernia C-96 well; 22 readings representing a

Ž .total depth of 200 m 4203–4403 m at sampling-depth intervalsŽ .DZ of 1 m.

Žreverse correlation the lower values of l corre-e.spond to the higher values of l . In terms ofh

electric and hydraulic conductivities, both l and le h

increase when most of the electric current and hy-draulic flow occur along the bedding planes, as a

Ž .result of lower resistance easier flow paths . Whenflow is parallel to the bedding planes, lower valuesof t and m are obtained. When flow is normal to thebedding planes, higher values of t and m are ob-tained. These results may suggest that m is a mea-sure of the efficiency of electric-current conductionand fluid flow in porous media.

6. Conclusions

ŽThe cementation factor m, in the Archie–. ŽWinsauer equation and the shape factor S , in thehf

.Kozeny–Carman equation have received consider-able attention from many researchers working onporous media. Because of the dependence of m onthe shape of grains and pores more than its depen-dence on the degree of cementation, it is suggestedthat m should be the ‘‘shape factor’’. Both factorsŽ .m and S are affected by the same influenceshfŽlithology, mineralogy, grain and pore properties,

.and various petrophysical parameters . They are, ge-ometrically and physically, similar to each other, andcan mutually replace each other in both equations.


For the Hibernia and Terra Nova heterogeneousand compacted reservoirs, saturated with oil, gas,and brine, and primarily consisting of shalestone,

Žsandstone, siltstone, and limestone with varieties of.grain and pore sizes and shapes , m generally ranges

from 2 to 3, with an average value of 2.28. Thisvalue can be used in application to similar reservoirsŽ .if other data on m were not available . The varia-tions of m are attributed to several reasons, includ-ing, e.g., heterogeneity and compaction of rocks,clay content, irregularity of grains, type of porosity,tortuosity, formation and pore-water resistivities, andanisotropy. Correlations between m and variousphysical parameters were obtained, with coefficientsof correlation ranging from 0.83 to 0.97.

7. Nomenclature

Ž . Ž .y1C Ion-exchange conductivity mho s V.mexŽ .C Fluid–solid interface surface conductivityfs

Ž .mhoŽ .C Grain-matrix conductivity mhogm

Ž .C Maxwellian-effects conductivity mhomaxŽ .C Observed conductivity mhoobŽ .C Pore-fluid conductivity mhopf

Ž .F Formation resistivity factor dimensionlessŽ .K Kozeny–Carman coefficient dimensionlesscc

Ž .R Bulk resistivity V.mbŽ .R Correlation coefficient dimensionlesscŽ .R Ion-exchange resistivity V.mexŽ .R Fluid–solid interface surface resistivityfs

Ž .V.mŽ .R Grain-matrix resistivity V.mgm

R Horizontal resistivity parallel to the beddinghŽ .planes V.m

Ž .R Maxwellian-effects resistivity V.mmaxŽ .R Observed resistivity V.mobŽ .R Pore-fluid resistivity V.mpf

R Vertical resistivity normal to the beddingvŽ .planes V.m

Ž .R Pore-water resistivity V.mw

R Resistivity of a formation 100% saturated withoŽ .formation water V.m

Ž .S Shape factor dimensionless analogous to ce-hfŽ .mentation factor m , dimensionless

Ž .Z Depth mŽ .DZ Sampling-depth interval m

Ža Pore-geometry factor or tortuosity factor di-.mensionlessŽ 2 .k Permeability mD or cm

k Horizontal permeability parallel to the beddinghŽ 2 .planes mD or cm

k Vertical permeability normal to the beddingvŽ 2 .planes mD or cm

Ž .m Cementation factor dimensionless analogousŽ .to shape factor S , dimensionlesshf

Ž .s Specific surface area in general ; per unit of:sŽ y1 .bulk volume, s cm ; grain volume, sb g

Ž y1 . Ž y1 .cm ; pore volume, s cm ; or per unitpŽ 2 .of weight, s cm rgmwt

Žx Variable for spheres and spheroids dimension-.less

Ž .l Electric anisotropy coefficient dimensionlesseŽl Hydraulic anisotropy coefficient dimension-h

.lessŽ .f Porosity fraction or percentageŽ .t Tortuosity dimensionless

JDB Jeanne d’Arc BasinŽ .LS Limestone component %

Ž .SI Siltstone component %Ž .SH Shale component %

Ž .SS Sandstone component %

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