-
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:
[email protected]
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 = /
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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).
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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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