147Journal of Petroleum Geology, Vol. 30(2), April 2007, pp 147-158

2007 The Authors. Journal compilation 2007 Scientific Press Ltd

PERMEABILITY ANISOTROPY DISTRIBUTIONSIN AN UPPER JURASSIC CARBONATE RESERVOIR,EASTERN SAUDI ARABIA

A. Sahin1, 2, A. Z. Ali1, S. Saner1 and H. Menouar 1

Most classical reservoir engineering concepts are based on homogeneous reservoirs despitethe fact that homogeneous reservoirs are the exception rather than the rule. This is especially trueof carbonate reservoirs in the Middle East which are known to be highly heterogeneous. Therealistic petrophysical characterization of these kinds of reservoirs is not an easy task and mustinclude the study of directional variations of permeability. Such variation can be incorporated intoengineering calculations as the square root of the ratio of horizontal to vertical permeability, aparameter known as the anisotropy ratio.

This paper addresses the distribution of anisotropy ratio values in an Upper Jurassic carbonatereservoir in the Eastern Province of Saudi Arabia. Based on whole core data from a number ofvertical wells, statistical distributions of horizontal and vertical permeability measurements as wellas anisotropy ratios were determined. The distributions of both permeability measurements andanisotropy ratios have similar patterns characterized by considerable positive skewness. Thecoefficients of variation for these distributions are relatively high, indicating their very heterogeneousnature.

Comparison of plots of anisotropy ratios against depth for the wells and the correspondingcore permeability values indicate that reservoir intervals with lower vertical permeability yieldconsistently higher ratios with considerable fluctuations. These intervals are represented by lowerporosity mud-rich and/or mud-rich/granular facies. Granular facies, on the other hand, yieldedconsiderably lower ratios without significant fluctuations.

1King Fahd University of Petroleum and Minerals,Dhahran, Saudi Arabia.

2KFUPM Box 661, Dhahran 31261, Saudi Arabia.email: asahin@kfupm.edu.sa

Key words: permeability, permeability anisotropy,anisotropy ratio, carbonate reservoir, Arab-D, SaudiArabia.

INTRODUCTION

Permeability values in most reservoir rocks aredependent on the direction in which the measurementsare made. Very often, measurements made in thehorizontal plane are not significantly different fromone another, but considerable differences may existbetween measurements made in horizontal and verticaldirections. These differences in permeabilitydistributions may significantly affect the reservoirduring depletion, and should be taken into account inreservoir engineering calculations, including wellproductivity, formation of water and gas coning,secondary recovery methods and well test analyses.

Therefore, it is essential to determine permeabilityvariations in different directions, particularly invertical and horizontal directions within the reservoir.Such variation can be incorporated into engineeringapplications as the square root of the ratio of thehorizontal to vertical permeability (Muskat, 1937;Henley et al., 1961; Forrest, 1971; Wilhite, 1986;Farouq et al., 1988; Joshi and Ding, 1996; Menouarand Hakim, 1995). This ratio is commonly referredto as the anisotropy ratio.

Due to zonation and layering in a reservoir, theanisotropy ratio may vary from one zone to anotherand even from one layer to another. Significantvariations in this ratio within a particular zone or layercan also be observed. The pattern of variation of thisratio provides valuable information about flow

148 Permeability anisotropy distributions in an Upper Jurassic carbonate reservoir, E. Saudi Arabia

behavior within the reservoir, and should bedetermined prior to any engineering calculations. Ifsignificant variations do not exist within a particularzone, it is logical to use a single anisotropy ratio torepresent this zone.

Because of the dependence of permeabilityanisotropy on lithology, it is also important toinvestigate variations in anisotropy ratio within eachlithofacies in the reservoir. This will help to identifyany facies which is prone to major variations in thisratio. General information related to these topics mayalready be available in geological reports in adescriptive format. However, results based onnumerical data will greatly enhance our understandingand, at the same time, facilitate the transfer ofinformation to reservoir engineers.

This study outlines patterns of distribution of thepermeability anisotropy within the Upper JurassicArab-D carbonate reservoir in an active oilfieldlocated in the Eastern Province of Saudi Arabia. Briefreviews of reservoir geology and of data sets availablefor the study are given in the following two sections.Then we present and discuss the distributions ofhorizontal and vertical permeability as well aspermeability anisotropy. The final part of the paper is

devoted to an analysis of anisotropy ratio - porosityrelationships, and to specific conclusions which canbe drawn from the study.

RESERVOIR GEOLOGY

The stratigraphic section through the Upper Jurassic-Lower Cretaceous succession in Eastern Saudi Arabiais illustrated in Fig. 1. The Upper Jurassic in the areaconsists mainly of shallow-marine carbonates andintervening evaporite units. Four carbonate cycleseach having an evaporite seal have been distinguishedin the final stages of the Upper Jurassic. The Arab-Dreservoir, which is the subject of this study, representsthe oldest of these cycles. It comprises anapproximately 300 ft (91.5m) thick carbonatesuccession exhibiting an overall decrease in porosityand an increase in dolomite content with depth.Grainstones dominate the upper intervals, whereaswackestones and fine-crystalline dolomitic rocksdominate the lower units. Lithological andpalaeontological evidence suggests that the reservoirrocks represents a shallowing-upward depositionalsequence (Hughes, 1996).

Based on porosity-log characteristics, it is possibleto distinguish six zones in the reservoir, referred to asZones 1 to 6 (from top to bottom) in our study. Zones2 and 3 are the most prolific hydrocarbon producingzones. The data used in this study originated fromZones 2 to 4, which are briefly described in thefollowing paragraphs.

Zone 2 is a 54 ft (16.4 m) thick interval consistingmainly of grainstones which overlies Zone 3 with asharp contact. Grains are mainly bioclasts, peloids andooids. The most common bioclasts are miliolid andtextulariid foraminifera and echinoid fragments. Theaverage grain size is 0.5 mm, but some grains reachup to 1 cm in diameter. The average core-derivedporosity for this zone is approximately 26%.

Zone 3 is an 82 ft (25 m) thick heterogeneouscarbonate unit consisting of alternating bioclastic-intraclastic grainstones, packstones, wackestones,dolomite and dolomitic lime-mudstones. This is atransitional zone between the mud-rich Zone 4 belowand the almost mud-free Zone 2 above. Therefore,mud-bearing rock types such as packstones,wackestones and mudstones are common in Zone 3.Grains are moderately to poorly sorted and range indiameter from 0.15 to 1 mm. Stromatoporoids, 1 to 7cm across, were observed in the lower portion of thezone. The most common bioclasts are miliolid andtextulariid foraminifera, and echinoids. Zone 3 hasan average core-derived porosity of about 21%.

Zone 4 is a 53 ft (16.1 m) thick interval consistingmainly of fine-crystalline dolomite and dolomiticmudstones with thin bioclastic packstone/grainstone

Fig. 1. Stratigraphic column for the Upper Jurassic-Lower Cretaceous succession in Eastern SaudiArabia.

149A. Sahin et al.

)%( Y TIS

OR

OP LAT

OT

CORE PERMEABILITY

1.0 1 01

001

0001

00001

)'02 = "1( HTPE

D

SEN

OZ 35 0

ANISOTROPY RATIO (mD)

04080120160

GAMMA RAY0 GAPI 40

RHOB2 G/C3 3

CALIPER5.5 IN 6.5

NPHI

45 V/V -15

kv

kh1

kh2

R1

R2

R3

WELL: A5

920

940

960

980

1000

1020

1040

3 enoZ4 en oZ

Fig. 2. Plot of open-hole log quantities, core permeability measurements, and anisotropy ratios for Well A5.Horizontal and vertical permeability values almost overlap in higher-porosity intervals, and deviatesignificantly from eachother elsewhere.

150 Permeability anisotropy distributions in an Upper Jurassic carbonate reservoir, E. Saudi Arabia

laminations. A 6ft (1.8 m) grainstone horizon marksthe basal contact with Zone 5. The allochems in thegranular horizons are mainly peloids, intraclasts andbioclasts. Bioclasts include brachiopods, echinoderms,benthonic foraminifera, stromatoporoids and sponges.Dolomitization is widespread in fine-grained rocks, anddolomites appear to have originated from the diagenesis(Powers, 1962; Cantrell et al., 2001). This zone hasthe lowest porosity with an average value of 8.7%.

DATA SETS

The data used for this study include whole-core andopen-hole log data from six vertical wells intersectingthe reservoir. Code letters have been used to representthe wells, and the actual depth values are not reportedin this paper. However, the relative positions of datapoints have been preserved by subtracting a constantfrom each depth value. Considering the number ofmeasurements, results from only two wells (Well A5and Well A3) are presented to show the generalapproach adopted in our study. The data for Well A5are based on cores from reservoir zones 3 and 4,whereas the data for Well A3 is from Zone 3 only. Bothof these wells were represented by a significant numberof whole core measurements: a total of 108 core

measurements were available from Well A5, and 81measurements from Well A3.

The whole-core permeability measurementsprovided an ideal data set for this study because theyincluded one vertical and two horizontalmeasurements at each sampling point. The horizontalmeasurements were recorded in two perpendiculardirections. Using these permeability measurements,it was possible to determine three anisotropy ratiosas outlined later.

Complete open-hole log data for each well werealso available. These data consisted of a number ofwell-log derived variables, including, gamma-ray,neutron porosity, total porosity, density, resistivity,water saturation and caliper measurements. Most ofthese variables and the whole-core permeabilitymeasurements were plotted together with calculatedanisotropy ratio values to aid interpretation (Fig. 2).

PERMEABILITY DISTRIBUTIONS

To determine the pattern of permeability distribution,statistical analyses of two horizontal permeabilitymeasurements (kh1 and kh2), the average horizontalpermeability (kh), and the vertical permeability (kv)were conducted. Analyses included the construction

Fig. 3. (a) Histogram of average horizontal permeability measurements (n=108) from Well A5. The highlyskewed nature of the histogram is apparent.(b) Histogram of log-transformed average horizontal permeability measurements from the same well,showing a more symmetrical pattern.(c) Probability plot showing the observed and expected normal values for the histogram in (b).The symmetrical nature of the distribution is indicated by the approximately straight-line fit.

151A. Sahin et al.

of histograms, determination of statistical parameters,and the study of correlations between permeabilitymeasurements.

Histograms of the average horizontal permeabilityand the vertical permeability for Well A5 are illustratedin Figs. 3 and 4, respectively. Both of these histogramsdisplay positively skewed patterns with only a fewoutlier values. Most permeability values are below500 mD. The histograms of the log-transformedpermeability values and the corresponding probabilityplots showing the observed values versus expectednormal values are also included in Figs. 3 and 4. Thesediagrams indicate the lognormal nature of thepermeability distributions.

Statistical parameters representing each set ofmeasurements are listed in Table 1, and include valuesfor the arithmetic, geometric and harmonic mean, thestandard deviation, the coefficient of variation togetherwith skewness, and kurtosis. The results indicate thatthe means of vertical permeability are much smallerthan the corresponding means of horizontalpermeability measurements. Similar observations havebeen reported from the Arab-D reservoir in the Abqaiqoilfield (Sahin and Saner, 2001).

The coefficient of variation is defined as the ratioof the standard deviation to the mean. This parameterhas commonly been used to define various classes ofheterogeneity (Corbett and Jensen, 1992; Jensen et

Fig. 4. (a) Histogram of vertical permeability measurements (n=108) from Well A5. The pattern is similar tothe corresponding histogram of horizontal permeability in Fig. 3a.(b) Histogram of log-transformed vertical permeability measurements from the same well, showinga bimodal distribution.(c) Probability plot showing the observed and expected normal values for the histogram in (b). Thesymmetrical nature of the distribution is indicated by the approximately straight-line fit.

Parameters k v k h1 k h2 k h Samples 108 108 108 108

Arithmetic mean 152.57 405.38 318.95 362.17Geometric mean 2.69 207.22 150.42 182.41Harmonic mean 0.07 111.83 76.96 96.95

Standard deviation 586.88 569.98 467.75 499.72Coefficient of variation 3.85 1.41 1.47 1.38

Skewness 7.36 2.58 2.5 2.3Kurtosis 61.71 6.96 6.1 4.81

Table 1. Statisticalparameters of thewhole-core permeabilitymeasurements (WellA5).

152 Permeability anisotropy distributions in an Upper Jurassic carbonate reservoir, E. Saudi Arabia

al., 1997). If the coefficient of variation is greater than1.0, permeability distributions are considered to bevery heterogeneous and this is the case for ourdistributions. The coefficient of variation also providesa basis for comparisons of the variability of thedifferent distributions. As shown in Table 1, thiscoefficient for vertical permeability is much greaterthan corresponding values for horizontalpermeabilities, reflecting greater heterogeneity in thevertical permeability distribution. It should also benoted that the variability of two horizontal permeabilitymeasurements are very similar with values ofcoefficient of variation ranging between 1.41 and 1.47(see Table 1).

Skewness is a measure of the deviation of adistribution from symmetry. The skewness of a normaldistribution is zero, so that a positive value for thisparameter indicates a distribution with a positive skew,and vice versa. As shown in Table 1, skewness valuesfor our case are greater than zero, indicating thepositively skewed nature of the distributions. Kurtosisis used to measure the flatness or peakedness of adistribution, relative to a normal distribution. Acommon measure of kurtosis is defined as the fourthmoment about the mean expressed in dimensionlessform (Spiegel, 1972). Although this measure is equalto three for a normal distribution, it is commonly takenas zero, so that a distribution more peaked than thenormal results in a positive value (leptokurtic), andmore flat than the normal results in a negative one(platykurtic). Most of our permeability distributionswere characterized by positive kurtosis and hence wereleptokurtic. This indicates that there are more thanexpected permeability values around the meanpermeability value.

PERMEABILITY CORRELATIONS

To determine the pattern of correlation between variouspermeability measurements, Pearsons linear

correlation coefficients between pairs ofmeasurements were determined. For Well A5, thecorrelation diagram for the pair kh1-kh2 is illustratedin Fig. 5, and the correlation diagram for the pair kv-kh in Fig. 6. Similar correlation patterns were recordedfor Well A3. The overall distribution of points and avery high positive correlation between the twohorizontal measurements in Fig. 5 indicate the closesimilarities of corresponding horizontal permeabilityvalues, and hence the isotropic distribution ofpermeability in the horizontal plane. The correlationcoefficient between the two horizontal permeabilitymeasurements is equal to 0.84. On the other hand,the correlation between the vertical and horizontalmeasurements is generally poor, as illustrated in Fig.6. Scrutiny of points in Fig. 6 indicates that there aretwo clusters of points. One cluster represents pointshaving very small kv values with a full range of khvalues. This cluster represents the muddy facies. Thesecond cluster is characterized by equally variable kvand kh values and represents granular facies. Thesetwo facies are also distinguished from the anisotropyratio-porosity relationship presented later.

The poor correlation between the kv-kh pair ispossibly a reflection of the fact that geological factorscontrolling the horizontal and vertical permeabilityvalues are generally independent in nature. It is well-known that bedding planes and laminations aredominant controls enhancing horizontal permeability,but that these same features act as barriers to flow ina vertical direction (Lake, 1988). However, thisgeneral pattern may be disturbed by the presence ofvertical and/or inclined fractures or bioturbation,which may enhance flow in the vertical direction.

PERMEABILITY ANISOTROPY

Permeability anisotropy can be incorporated intoengineering calculations as the square root of the ratioof the horizontal to the vertical permeability. This

Fig. 5. Correlation plot forhorizontal permeability (kh1 andkh2) measurements. Therelatively high positivecorrelation coefficient (0.84)indicates the isotropicdistribution of permeability inthe horizontal plane.

153A. Sahin et al.

parameter is referred to as the anisotropy ratio. Basedon the whole-core permeability measurements describedearlier, it was possible to determine the followinganisotropy ratios:

............................................ (1)

............................................ (2) and

where kh= (kh1+kh2)/2 .... (3)

Because of the similarity of the horizontalpermeability values at each measurement point asreflected by the correlation patterns, plots against depthof the above-mentioned three ratios (R1, R2, and R3)showed almost identical patterns as illustrated in Fig. 2.These plots are characterized by three thin (eachapproximately 20 ft thick) intervals with relatively highanisotropy ratios between which are quite uniformdistributions of very low values. High ratio intervals arelocated at approximately 920 ft, 990 ft and 1,040 ft.Overall fluctuations in ratios are considerable with amaximum value reaching approximately 160 andminimum at 0.

A comparison of the corresponding open-hole logplots with the anisotropy ratios in Fig. 2 indicates thathigh anisotropy ratios are generally correlated withlithological changes. At 920 ft, the high ratios areprobably due to the presence of thin beds of dolomiteand limestone as identified on the neutron and densitylogs. At 990 ft, they are related to alternating low andhigh porosity stringers. Finally, at 1,040 ft, a very lowporosity interval with oblique hairline fractures and/ora very thinly bedded interval with a variable lithologymay have given rise to the fluctuations. The latter

generally provides parallel neutron and density logsdue to the averaging effect, yet the vertical andhorizontal permeability measurements differconsiderably resulting in higher anisotropy ratios.

From the anisotropy ratio equations, it is obviousthat higher ratio values could either be due to veryhigh horizontal permeability relative to vertical orto very low vertical permeability relative tohorizontal. A comparison of individual higheranisotropy ratio values with correspondingpermeability measurements showed that themajority of these ratios were due to unusually lowvertical permeability values.

The histogram for the anisotropy ratio (R3),illustrated in Fig. 7, shows a strong positive skewwith highly fluctuating behaviour. A significantproportion of the data are clustered at the lower endof the distributions with values below 10, and amuch smaller proportion of data with frequent gapsare displayed in the tails of the distribution. Thelog-normal nature of this distribution is clear fromboth the probability plot and the histogram of thelog-transformed values displayed in the same figure.

Statistical parameters for the three anisotropyratios are listed in Table 2. As in the case of thepermeability distributions, these parameters includethree types of mean, standard deviation, coefficientof variation, skewness, and kurtosis. Skewness andkurtosis values are positive in all cases, indicatingthat the distributions are positively skewed andleptokurtic. Due to close similarities in the valuesof three ratios, the corresponding statisticalparameters are very similar. A comparison of thevalues of three types of means for each ratioindicates that the arithmetic mean is the largest andthe harmonic mean the smallest, consistent with thetheoretical expectations (Spiegel, 1972).

Fig. 6. Correlation plot forthe average horizontalpermeability (kh) and thevertical permeability (kv)measurements. Thecorrelation in this case ispoor with the correlationcoefficient being only 0.48.

R k kh v1 1= /

R k kh v2 2= /

R k kh v3 = /

154 Permeability anisotropy distributions in an Upper Jurassic carbonate reservoir, E. Saudi Arabia

ANISOTROPY RATIO - POROSITYRELATIONSHIP

The general pattern of permeability anisotropy in thereservoir indicates that there is a possible relationshipbetween the anisotropy ratios and lithology, withmuddy facies generally possessing higher anisotropyratios. But it was not possible to quantify such arelationship because of the lack of completelithological information. However, we had sufficientporosity data to look at the relationship from anotherperspective. The statistical parameters of the porositydata for Well A5 are listed in Table 3, and the samedata are summarized in the form of a histogram in

Fig. 8. This histogram illustrates the bimodal natureof the porosity distribution and indicates the co-existence of two populations, one representing muddyfacies and the other granular facies. The cut-offporosity value separating these two populationsappears to be located at approximately 11%.

A plot of the anisotropy ratio (R3) against porosityfor Well A5 is illustrated in Fig. 9. This plot displaysan obvious negative correlation between theanisotropy ratio and porosity, with a correlationcoefficient of approximately 0.65. However, thisrelationship is not a simple one and the scatter diagramreveals two main clusters of points. One ischaracterized by higher porosities and considerably

Fig. 7. (a) Frequency histogram of the anisotropy ratio (R3) for Well A5. The pattern of the distribution issimilar to those observed for permeability measurements (see Figs 3 and 4).(b) Frequency histogram of log-transformed anisotropy ratios from the same well, showing the bi-modalcharacter of the data.(c) Probability plot showing the observed and expected normal values for the histogram illustrated in (b). The bi-modal character of the distribution is reflected by the alignment of points along lines with differentslopes.

Parameters R 1 R 2 R 3 Samples 108 108 108

Arithmetic mean 25.37 20.87 23.38Geometric mean 8.77 7.47 8.23Harmonic mean 3.54 3.03 3.35

Standard deviation 37.26 30.46 33.92Coefficient of variation 1.47 1.46 1.45

Skewness 1.9 2 1.89Kurtosis 2.81 3.59 2.9

Table 2. Statistical parameters ofanisotropy ratios (Well A5).

155A. Sahin et al.

lower ratios without any significant fluctuations. Thesecond cluster of points is characterized by lowerporosities and higher anisotropy ratios withconsiderable variation. This relationship is alsoobvious from the open-hole log plots illustrated in Fig.2. A dominant pattern observed in these plots is thatthe horizontal and vertical permeability values arecloser to each other in higher-porosity intervals, anddeviate significantly in lower-porosity intervals.Therefore, higher porosity areas are expected to yieldlower anisotropy ratios, and lower porosity areashigher ones, as shown in Fig. 9. It should be notedthat the porosity cut-off value separating the twoclusters in Fig. 9 is about 11%. This value matches

closely with the porosity cut-off separating the twopopulations in Fig. 8.

To assess whether the anisotropy ratio versusporosity relationship observed in Well A5 is laterallypersistent, we constructed the same plot for Well A3.The plot for this well, illustrated in Fig. 10, indicatesthat its pattern is very similar to that for Well A5. Theonly difference appears to be in the size of theanisotropy ratio fluctuations representing lower-porosity facies. The fluctuations for these facies arerelatively small in the case of Well A3. This is due tothe fact that Well A3 intersects Zone 3 which consistsmainly of grain-dominated facies with only a smallproportion of mud-rich intervals. On the other hand,Well A5 intersects both Zone 3 and Zone 4. The latterzone includes considerable proportion of mud-richfacies. Consequently, a reasonable number ofmeasurements from both granular and muddy faciesis represented in Well A5 data, resulting in a widerspectrum of anisotropy ratios values.

DISCUSSION

Based on the results from both wells, it can beconcluded that for the reservoir under consideration,there is a close relationship between the anisotropyratio and porosity. Thus, for a good quality reservoirwith relatively high porosities, anisotropy ratios canbe expected to be relatively low without significant

Fig. 8. Frequency histogram of porosity measurements for Well A5, displaying two populations separated byapproximately 11% porosity.

Parameters Porosity (%)Samples 108

Arithmetic mean 13.25Geometric mean 11.13Harmonic mean 8.51

Standard deviation 6.46Coefficient of variation 0.49

Skewness -0.17Kurtosis -1.11

Table 3. Statistical parameters of core porositymeasurements (Well A5).

156 Permeability anisotropy distributions in an Upper Jurassic carbonate reservoir, E. Saudi Arabia

Fig. 9. Plot of anisotropy ratio(R3) versus porosity for WellA5, displaying two distinctclusters of points: one ischaracterized by higherporosities and considerablylower ratios without anysignificant fluctuations. Thesecond is characterized bylower porosities and higheranisotropy ratios withconsiderable fluctuations.

Fig. 10. Plot of anisotropyratio (R3) versus porosity forWell A3, displaying a similarpattern to the correspondingplot for Well A5 (Fig. 9).

fluctuations. On the other hand, poor quality reservoirrocks are associated with highly fluctuating ratios. Inother words, the distribution of permeabilityanisotropy in the reservoir is dependent on the faciesdistribution. Granular facies with higher porosities aremore homogeneous reservoir rocks, and hence yieldconsiderably lower and more uniform ratio values.Muddy and mixed granular-muddy facies representgreater heterogeneity in terms of permeabilitydistributions. Therefore, the anisotropy ratios in thesefacies will show considerable fluctuations.

Considering the rock-fabric, Lucia et al. (2001)proposed a more complex model for the Arab-D faciesand recognized three classes each having a widespectrum of porosity and permeability values.Considering their model, it is apparent that to producethe plot illustrated in Fig. 9, we must have differentkh and kv relationships above and below the 11%porosity cut-off. For any facies with porosity greaterthan 11%, kh and kv values are very similar, resultingin anisotropy ratios close to one. On the other hand,

below 11% porosity, kh and kv values are highlyvariable giving rise to greater fluctuations inanisotropy ratios: the grain-dominated facies showprobably very similar values of kh and kv and henceanisotropy values closer to one, in contrast to mud-dominated facies with greater anisotropy ratio values.Investigation of the correlation patterns of kh and kvmeasurements below and above the 11% porosity cut-off revealed that there is almost no correlation betweenthese measurements below the cut-off. However, asignificant correlation was observed between the samemeasurements above the cut-off.

As pointed out above, results provided in this studyare based on the whole core measurements. Todetermine zonal anisotropy parameters, up-scaling ofanisotropy ratios would be required. Depending onthe direction of flow with respect to the stratification,different mean values have been used to represent thepermeability of a stratified sequence (Richardson etal., 1987; Jensen et al., 1987). Thus, if the flow isparallel to the strata, the arithmetic mean is used. If

157A. Sahin et al.

the flow is perpendicular to the strata, the harmonicmean is considered to be more appropriate. However,in other cases, where the flow is neither strictly parallelnor perpendicular, or where different facies are notclearly stratified, the geometric mean is used (Isaaksand Srivastava, 1989).

Assuming a relatively uniform stratified sequencewith horizontal flow in our case, the horizontalpermeability values can be averaged using thearithmetic mean and the vertical permeability usingthe harmonic mean as discussed above. Combiningthe permeability measurements based on sampleswithin a uniform zone in this manner, it is possible toderive the horizontal and the vertical permeabilityvalues, and hence to determine the anisotropy ratiofor the entire zone.

CONCLUSIONS

The main conclusions drawn from this study of acarbonate reservoir in Eastern Saudi Arabia aresummarized as follows:1. Statistical distributions representing permeabilityand anisotropy ratios display similar patterns with adominant positive skew. Mean values for the verticalpermeability are considerably lower than thecorresponding parameters for the horizontalpermeability distributions.2.Values of the coefficient of variation for thehorizontal permeability and anisotropy ratio aresimilar with values close to 1.5, indicating the veryheterogeneous nature of these distributions. Thiscoefficient for vertical permeability is greater than thecorresponding values for the horizontal permeability,reflecting greater heterogeneity in the verticalpermeability distribution.3. Higher fluctuations in anisotropy ratios along wellscan be correlated with low-porosity muddy and/ormud-rich / granular intervals within the reservoir.4.Granular facies with higher porosities yieldconsiderably lower anisotropy ratios without anysignificant fluctuations. In other words, the bestreservoir facies are expected to present fewer problemsduring production.5.Very high values of the anisotropy ratio are generallydue to unusually low vertical permeabilitymeasurements recorded in compact and undisturbedmud-rich intervals acting as barriers to vertical flow.

ACKNOWLEDGEMENTS

This study is partly based on a paper (SPE 81472)originally presented at the 2003 SPE Middle East Oil& Gas Show and Conference, held in Bahrain. SaudiAramco provided the basic data, and the study wasundertaken at the Research Institute, King Fahd

University of Petroleum and Minerals (KFUPM).Financial support was provided by Saudi Aramco, Al-Khafji Joint Operations, and Schlumberger DhahranCarbonate Research Center . The authors wish to thankthe management of the above-mentioned organizationsfor their support and permission to publish this paper.Review comments on a previous version by DeborahBliefnick and Wayne Wright are acknowledged withthanks.

Nomenclature

kh1 = Horizontal permeability (maximum)kh2 = Horizontal permeabilitykh = Average horizontal permeabilitykv = Vertical permeabilityR1, R2, R3= Anisotropy ratiosNPHI = Neutron porosityPHIT = Total porosityRHOB = Bulk densityGR = Gamma ray

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