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Artificial-Intelligence Technology

Predicts Relative Permeability of Giant

Carbonate Reservoirs

Saud M. Al-Fattah, SPE, and Hamad A. Al-Naim, SPE, Saudi Aramco

Summary

Determination of relative permeability data is required for almost

all calculations of fluid flow in petroleum reservoirs. Water/oil

relative permeability data play important roles in characterizing

the simultaneous two-phase flow in porous rocks and in predicting

the performance of immiscible displacement processes in oil

reservoirs. They are used, among other applications, for determin-

ing fluid distributions and residual saturations, predicting future

reservoir performance, and estimating ultimate recovery. Un-

doubtedly, these data are considered probably the most valuable

information required in reservoir-simulation studies. Estimates

of relative permeability are generally obtained from laboratory

experiments with reservoir-core samples. In the absence of the

laboratory measurement of relative permeability data, developing

empirical correlations for obtaining accurate estimates of relative

permeability data showed limited success, and it proved difficult,

especially for carbonate reservoir rocks.

Artificial-neural-network (ANN) technology has proved suc-

cessful and useful in solving complex structured and nonlinear

problems. This paper presents a new modeling technology to

predict accurately water/oil relative permeability using ANNs.

The ANN models of relative permeability were developed using

experimental data from waterflood-core-tests samples collected

from carbonate reservoirs of giant Saudi Arabian oil fields. Three

groups of data sets were used for training, verification, and testing

the ANN models. Analysis of results of the testing data set shows

excellent agreement with the experimental relative permeability

data. In addition, error analyses show that the ANN models devel-

oped in this study outperform all published correlations.

The benefits of this work include meeting the increased de-

mand for conducting special core analysis (SCA), optimizing the

number of laboratory measurements, integrating into reservoir-

simulation and reservoir-management studies, and providing

significant cost savings on extensive laboratory work and substan-

tial required time.

Introduction

ANNs have seen a great increase of interest during the past

few years. They are powerful and useful tools for solving

practical problems in the petroleum industry (Mohaghegh

2005; Al-Fattah and Startzman 2003). Advantages of neural

network techniques (Bishop 1995; Fausett 1994; Haykin 1994;

Patterson 1996) over conventional techniques include the ability

to address highly nonlinear relationships, independence from

assumptions about the distribution of input or output variables,

and the ability to address either continuous or categorical data

as either inputs or outputs. In addition, neural networks are

intuitively appealing because they are based on crude low-level

models of biological systems. Neural networks, as in biological

systems, simply learn by examples. The neural-network user

provides representative data and trains the neural networks to

learn the behavior of the data.

Design and Development of ANN Models

In regression problems, the objective is to estimate the value of a

continuous variable given the known input variables. Regression pro-

blems can be solved using the following network types: multilayer

perceptrons (MLPs), radial basis function (RBF), generalized-regres-

sion neural network (GRNN), and linear. In this study, we experimen-

ted with the first three types: MLP, RBF, and GRNN. The linear

model is basically the conventional linear-regression analysis. Since

the problem at hand is a regression type and because of its power and

advantages, we found that GRNN performs the best for this particular

study. This is because GRNN has several advantages.

•It usually trains extremely quickly, making the large number

of evaluations required by the input-selection algorithm feasible.

•It is capable of modeling nonlinear functions quite accurately.

•It is relatively sensitive to the inclusion of irrelevant input

variables. This is actually an advantage when trying to decide

whether input variables are required.

Hence, it is worth giving a brief description of this neural-

network type. GRNN uses kernel-based approximation to perform

regression (Patterson 1996; Bishop 1995). It is one of the

so-called Bayesian networks. GRNN has exactly four layers: the

input layer, radial centers’ layer, regression nodes’ layer, and an

output layer, as shown by Fig. 1. The input layer has the same

number of nodes as there are input variables. The radial-layer

nodes represent the centers of clusters of known training data.

This layer must be trained by a clustering algorithm such as sub-

sampling, K-means, or Kohonen training. The regression layer,

which contains linear nodes, must have exactly one node more

than the output layer. There are two types of nodes: The first type

of node calculates the conditional regression for each output vari-

able, whereas the second type of node calculates the probability

density. The output layer performs a specialized function such that

each node simply divides the output of the associated first-type

node by that of the second-type node in the previous layer.

GRNNs can be used only for regression problems. A GRNN

trains almost instantly, but tends to be large and slow. Although it

is not necessary to have one radial neuron for each training data

point, the number still needs to be large. Like the RBF network,

the GRNN does not extrapolate.

There are several important procedures that must be taken into

consideration during the design and development of an ANN

model. Fig. 2 is a flowchart illustrating the ANN-development

strategies proposed and implemented in this study.

Data Preparation

Data acquisition, preparation, and quality control are considered

the most important and most time-consuming task (Fig. 2). The

quantity of data required for training a neural network frequently

presents difficulties. There are some heuristic rules, which relate

the number of data points needed to the size of the network. The

simplest of these indicates that there should be 10 times as many

data points as connections in the network. In fact, the number

needed is also related to the complexity of the underlying function

that the network is trying to model, and to the variance of the

additive noise. As the number of input variables increases, the

number of input data points required increases nonlinearly. Even

a fairly small number of input variables (perhaps 50 or less)

requires a huge number of input data points. This problem is

known as “the curse of dimensionality.” If there is a larger, but

Copyright ã2009 Society of Petroleum Engineers

This paper (SPE 109018) was accepted for presentation at Offshore Europe, Aberdeen,

4–7 September 2007, and revised for publication. Original manuscript received for review

16 September 2007. Revised manuscript received for review 14 April 2008. Paper peer

approved 10 June 2008.

96 February 2009 SPE Reservoir Evaluation & Engineering

still restricted, data set, then it can be compensated to some extent

by forming an ensemble of networks, with each network being

trained using a different resampling of the available data and then

averaging across the predictions of the networks in the ensemble.

Water/oil relative permeability measurements were collected

for all wells having SCAL of carbonate reservoirs in Saudi Arabi-

an oil fields. These reservoirs include Arab-D, Shuaibah, Arab-C,

Arab-AB, Fadhili, Upper Fadhili, Hanifa, and Hadriyah. The

major fields included in this study are the Ghawar field, which is

the largest oil field in the world; and Abqaiq; Shaybah; Qatif;

Khurais; and Berri. SCAL reports were studied thoroughly, and

each relative permeability curve was carefully screened, exam-

ined, and checked for consistency and reliability. Hence, a large

database of water/oil relative permeability data for carbonate

reservoirs was created. All relative permeability experimental data

measurements were conducted using the unsteady-state method.

Developing ANN models for water/oil relative permeability

with easily obtainable input variables was one of the objectives

of this study. Initial water saturation, residual-oil saturation,

porosity, well location, and wettability are considered the main

input variables that contribute significantly to the prediction of

relative permeability data. We made from these input variables

several transformational forms or functional links that are thought

to play a role in predicting the relative permeability. Table 1

presents a list of all input variables and functional links used in

this study. The initial water saturation, residual-oil saturation, and

porosity of each well can be obtained easily from either well logs

or routine core analysis. Wettability is an important input variable

for predicting the relative permeability data and is, thus, included in

the pool of input variables. We found that not all wells with relative

permeability measurements have wettability data. For those wells

missing wettability data, we used Craig’s rule (Craig 1971) to deter-

mine the wettability of each relative permeability curve, which is

classified as oil-wet, water-wet, or mixed-wet. It should be noted

that Craig’s rule helps to distinguish between strongly-water-wet

and -oil-wet systems on the basis of relative permeability curves. If

no information is available on the wettability of a well, it then can be

estimated by use of offset-well data, or sensitivity analysis can be

performed. The output of each network in this study is a single

variable, either water or oil relative permeability.

Because of the variety of reservoir characteristics, and using

data statistics, the database was divided into three categories of

reservoirs: the Arab-D reservoir, the Shuaibah reservoir, and all

other reservoirs having limited data. This necessitates the devel-

opment of six ANN models for predicting water and oil relative

permeability, resulting in two ANN models for each reservoir

category. The database of relative permeability that is used in this

study comprises of a total of 3,711 records or cases. Table 2

presents the distribution of these data cases in the three categories

of reservoirs (Arab-D, Shuaibah, and the others).

Data Preprocessing

Data preprocessing is an important procedure in the development

of ANN models. All input and output variables must be converted

into numerical values to be introduced to the network. Nominal

values require special handling. Since the wettability is a nominal

input variable, it is converted into a set of numerical values. Oil-

wet was represented as {1, 0, 0}, mixed-wet as {0, 1, 0}, and

water-wet as {0, 0, 1}. In this study, we applied two normalization

algorithms—mean/standard deviation, and minimax—to ensure

that the network’s input and output will be in a sensible range

(Al-Fattah and Startzman 2003). The simplest normalization

function is the minimax, which finds the minimum and max-

imum values of a variable in the data and performs a linear

transformation using a shift and a scale factor to convert the

values into the target range, which is typically [0.0, 1.0]. After

network execution, denormalizing of the output follows the

reverse procedure: subtraction of the shift factor, followed by

Fig. 2—Flowchart of procedure of ANN design and develop-

ment proposed in this study.

Fig. 1—Design of a GRNN used in this study.

February 2009 SPE Reservoir Evaluation & Engineering 97

division by the scale factor. The mean/SD technique is defined

as the data mean subtracted from the input variable value divided

by the SD. Both methods have advantages in that they process

the input and output variables without any loss of information,

and their transform is mathematically reversible.

Input Selection and Dimensionality Reduction

One of the most difficult tasks in the design of the neural network

is the decision on which of the available variables to use as inputs

to the neural network. The only guaranteed method to select the

best input set is to train networks with all possible input sets and

all possible architectures, and to select the best. Practically, this is

impossible for any significant number of candidate input vari-

ables. The problem is complicated further when there are inter-

dependencies or correlations between some of the input variables,

which means that any of a number of subsets might be adequate.

To some extent, some neural-network architectures can actual-

ly learn to ignore useless variables. Other architectures are affect-

ed adversely; and in all cases, a larger number of inputs implies

that a larger number of training cases is required to prevent over-

learning. As a consequence, the performance of a network can be

improved by reducing the number of input variables, even some-

times at the cost of losing some input information. There are

sophisticated algorithms that determine the selection of input vari-

ables. The following describes the input-selection and dimension-

ality-reduction techniques that are used in this study.

Genetic Algorithm. A genetic algorithm is an optimization algo-

rithm that can search efficiently for binary strings by processing

an initially random population of strings using artificial mutation,

crossover, and selection operators, in an analogy with the process

of natural selection (Goldberg 1989). It is applied in this study to

determine an optimal set of input variables that contribute signif-

icantly to the performance of the neural network. The method is

used as part of the model-building process, in which variables

identified as the most relevant are then used in a traditional

model-building stage of the analysis. Genetic algorithm is a

particularly effective technique for combinatorial problems of

this type, in which a set of interrelated yes/no decisions needs

to be made. For this study, it is used to determine whether the

input variable under evaluation is significantly important or not.

The genetic algorithm is therefore a good alternative where there

are large numbers of variables (e.g., more than 50), and it also

provides a valuable second opinion for smaller numbers of vari-

ables. It is particularly good at spotting interdependencies be-

tween variables located close together on the masking strings.

The genetic algorithm can sometimes identify subsets of inputs

that are not discovered by other techniques. However, the meth-

od is time consuming; it typically requires building and testing

many thousands of networks, resulting in running the program

for a couple of days.

Forward and Backward Stepwise Algorithms. These algo-

rithms (Hill and Lewicki 2006) are usually quicker than the genet-

ic algorithm if there is a reasonably small number of variables.

They are also equally effective if there are not too many complex

interdependencies between variables. Forward and backward

stepwise-input-selection algorithms work by adding or removing

variables one at a time. Forward selection begins by locating the

single input variable that, on its own, best predicts the output

98 February 2009 SPE Reservoir Evaluation & Engineering

variable. It then checks for a second variable that, when added to

the first, improves the model most, repeating this process until

either all variables have been selected or no further improvement

is made. Backward stepwise feature selection is the reverse pro-

cess; it starts with a model including all variables, and then

removes them one at a time, at each stage finding the variable

that, when it is removed, degrades the model least.

Forward- and backward-selection methods each have their

advantages and disadvantages. The forward-selection method is

generally faster. It may miss key variables if they are interdepen-

dent or correlated. The backward-selection method does not suffer

from this problem, but because it starts with the whole set of

variables, the initial evaluations are most time consuming. Fur-

thermore, the model can actually suffer strictly from the number

of variables, making it difficult for the algorithm to behave sensi-

bly if there are a large number of variables, especially if there is

only a few weakly predictive ones in the set. In contrast, because

it selects only a few variables initially, forward selection can

succeed in this situation. Forward selection is also much faster if

there are few relevant variables because it will locate them at the

beginning of its search, whereas backward selection will not whit-

tle away the irrelevant ones until the very end of its search.

In general, backward selection is to be preferred if there is a

small number of variables (e.g., 20 variables or less), and forward

selection may be better for larger numbers. All of the above-

mentioned input-selection algorithms, including the genetic

algorithm and forward and backward selection, evaluate feature-

selection masks. These are used to select the input variables for a

new training set, and a GRNN is tested on this training set.

Sensitivity Analysis. This is performed on the inputs to a neural

network to indicate those input variables that are considered most

important by that particular neural network. Sensitivity analysis

can be used purely for informative purposes or to perform input

pruning, which is removing excess neurons from input or hidden

layers. In general, input variables are not independent. Sensitivity

analysis gauges variables according to the deterioration on model-

ing performance that occurs if that variable is not available to the

model. However, the interdependence between variables means

that no scheme of single ratings per variable can ever reflect the

subtlety of the true situation. In addition, there may be interdepen-

dent variables that are useful only if included as a set. If the entire

set is included in a model, they can be accorded significant sensi-

tivity, but this does not reveal the interdependency. Worse, if only

part of the interdependent set is included, their sensitivity will be

zero because they carry no discernable information. In summary,

precautions should be exercised when drawing conclusions about

the importance of variables because sensitivity analysis does not

rate the usefulness of variables in modeling in a reliable or abso-

lute manner. Nonetheless, in practice, sensitivity analysis is quite

useful. If a number of models are studied, it is often possible to

identify variables that are always of high sensitivity, variables that

are always of low sensitivity, and ambiguous variables that change

ratings and probably carry mutually redundant information.

Another common approach to dimensionality reduction is the

principle-component analysis (Bishop 1995), which can be repre-

sented in a linear network. It can often extract a very small num-

ber of components from quite high-dimensional original data and

still retain the important structure.

Applying the above-mentioned input-selection methods in this

study, we first used the genetic algorithm to identify redundant input

variables from the 25 variables given in Table 1. For the Arab-D-

reservoir ANN model, this step identified four redundant input vari-

ables that can be removed from the input pool. In the second step,

we applied forward and backward stepwise selection on the remain-

ing input variables. Both the forward and the backward algorithms

yielded the same results by identifying six additional redundant

input variables. We then ran the network with the remaining 15 input

Fig. 3—Error ratio and ranking of the influence of input vari-

ables on ANN model for Arab-D-reservoir water relative perme-

ability.

Fig. 4—Results of ANN model compared to experimental data

for oil relative permeability.

February 2009 SPE Reservoir Evaluation & Engineering 99

variables while running the sensitivity analysis simultaneously. The

network gave a very good performance; however, sensitivity anal-

ysis indicated that two input variables can be removed from the

network without affecting the performance of the ANN model.

Fig. 3 presents the results of sensitivity analysis for the top 10 most

influential input variables for the Arab-D-reservoir ANN model.

Fig. 3 shows the error that will be given by the model if that

particular input variable is excluded from the network. Fig. 3

shows that the wettability gives the highest error if it is removed

from the network, indicating its significance to the performance of

the ANN model; thus, it was ranked the first among other vari-

ables. In this study, we determined that input variables that have

error ratios greater than one are significant and influential to the

network performance. Input variables having error ratios less than

one are removed from the network. The final ANN model con-

sisted of 13 input variables as an optimum input set.

Training, Verifying, and Testing

By exposing the network repeatedly to input data, the weights and

thresholds of the post-synaptic potential function are adjusted

using special training algorithms until the network performs very

well in predicting the output correctly. In this study, the data are

divided into three subsets: training set (50–60% of data), verifica-

tion or validation set (20–25% of data), and testing set (20–25%

of data), as presented in Table 2. Typically, the training-data

subset is presented to the network in several or even hundreds of

iterations. Each presentation of the training data to the network for

adjustment of weights and thresholds is referred to as an epoch.

The procedure continues until the overall error function has been

minimized sufficiently. The overall error is also computed for the

second subset of the data, which is sometimes referred to as the

verification or validation data. The verification data act as a

watchdog and take no part in the adjustment of weights and

thresholds during training, but the networks’ performance is

checked against this subset as training continually. The training

is stopped when the error for the verification data stops decreasing

or starts to increase. Use of the verification subset of data is

important because with unlimited training, the neural network

usually starts “overlearning” the training data. Given no restric-

tions on training, a neural network may describe the training data

almost the perfectly but may generalize very poorly to new data.

The use of the verification subset to stop training at a point when

generalization potential is best is a critical consideration in train-

ing neural networks. A third subset of testing data is used to serve

as an additional independent check on the generalization capabil-

ities of the neural network, and as a blind test of the performance

and accuracy of the network. Several neural-network architectures

and training algorithms have been attempted to achieve the best

results. The results were obtained using a hybrid approach of

genetic algorithm and neural network.

Results

All the six networks developed in this study were successfully

well trained, verified, and checked for generalization. An

important measure of the network performance is the plot of the

root-mean-square error vs. the number of iterations or epochs. A

well-trained network is characterized by decreasing errors for both

the training and verification data sets as the number of iterations

increases (Al-Fattah and Startzman 2003). Statistical analysis used

in this study to examine the performance of a network are

the output-data SD, output error mean, output error SD, output

absolute error mean, SD ratio, and Pearson-R correlation coefficient

(Hill and Lewicki 2006). The most significant parameter is the SD

ratio, which measures the performance of the neural network. It is

the best indicator of the goodness of a regression model, and it is

defined as the ratio of the prediction-error SD to the data SD. One

minus this regression ratio is sometimes referred to as the explained

variance of the model. The degree of predictive accuracy needed

Fig. 6—Results of ANN model compared to experimental data

for water relative permeability.

Fig. 7—Results of ANN model compared to experimental data

for water relative permeability of Well U-628.

Fig. 5—Results of ANN model compared to experimental data

for oil relative permeability.

Fig. 8—Results of ANN model compared to experimental data

for water relative permeability of Well SB-50.

100 February 2009 SPE Reservoir Evaluation & Engineering

varies from application to application. Generally, an SD ratio of 0.3

or lower indicates a very good regression-performance network.

Another important parameter is the standard Pearson-R correlation

coefficient between the network’s prediction and the observed

values. A perfect prediction will have a correlation coefficient of

1.0. In this study, we used the network verification-data subset to

judge and compare it with the performance of a network among

other competing networks.

Because of its large quantity of data (70% of the database), most

of the results presented in this paper belong to the ANN models

developed for the Arab-D reservoir. Tables 3 and 4 present statisti-

cal analysis of the ANN models for determining oil and water

relative permeability, respectively, for Arab-D reservoir. Table 3

shows that Arab-D-reservoir ANN models for predicting oil relative

permeability achieved excellent accuracy by having low values of

SD ratios, which are lower than 0.2 for all data subsets including

training-, verification-, and testing-data set. Table 3 also shows that

a correlation coefficient of 99% was achieved for all data subsets of

the Arab-D-reservoir model, indicating the high accuracy of the

ANN models for predicting the oil relative permeability data. Table 4

shows that the water relative permeability ANN model yielded a

correlation coefficient of 96% for all all three data subsets of the

Arab-D-reservoir model, with SD ratios less than 0.3 indicating a

high degree of accuracy and excellent performance.

Figs. 4 through 8 show that the results of ANN models are in

excellent agreement with the experimental data of oil and water

relative permeability. Crossplots of measured vs. predicted data of

oil and water relative permeability are presented in Figs. 9 and 10,

respectively. The majority of the data fall close to the perfect 45

straight line, indicating the high degree of accuracy of the ANN

models. Figs. 11 and 12 are histograms, respectively, of residual

errors of oil and water relative permeability ANN models for Arab-

D reservoir.

Sensitivity analysis was performed on all input variables to

identify significant variables that are influential on the network’s

performance. Wettability was not found to be an important input

parameter for determining oil relative permeability for all ANN

models. On the other hand, wettability was found to be the

most influential input parameter for determining water relative

permeability. Fig. 3 presents the most influential input variables

that play an important role on the network’s outcome for deter-

mining water relative permeability. As can be seen from this

figure, wettability is placed first as the most significant input

parameter for predicting water relative permeability. To study the

effect of wettability on the network predictions, we removed the

wettability from the input variables and ran the network. Statisti-

cal analysis of the network performance is presented in Table 5.

The results of accuracy are badly deteriorated after removing the

wettability, indicating the significance of the wettability on deter-

mining water relative permeability. Without using the wettability

as input, the ANN model has a correlation coefficient of 79% for

the verification subset and 51% for the testing subset. In addition,

SD ratios of more than 0.6 were given by this model, indicating

the poor performance of the ANN model for water relative perme-

ability after removing the wettability as input.

Comparison of ANN against Correlations

The newly developed ANN models for predicting water/oil

relative permeability of carbonate reservoirs were validated using

data that were not used in the training of the ANN models.

Fig. 9—Crossplot of ANN predicted vs. measured k

ro

for Arab-D

reservoir.

Fig. 10—Crossplot of ANN predicted vs. measured k

rw

for Arab-

D reservoir.

Fig. 11—Histogram of k

ro

residual error for the Arab-D-reservoir

model.

Fig. 12—Histogram of k

rw

residual error for the Arab-D-

reservoir model.

February 2009 SPE Reservoir Evaluation & Engineering 101

This step was performed to examine the applicability of the

ANN models and to evaluate their accuracy against correlations

previously published in the literature. The new ANN models were

compared with published correlations of Wyllie (1951), Pirson

(1958), Naar et al. (1962), Jones and Roszelle (1978), Land

(1968), and Honarpour et al. (1986, 1982). The relative perme-

ability data used for the comparison are for wells in the testing-

data subset. No attempt was made in this study to generate new

coefficients of the published correlations by use of the same data

used for the comparison. The correlations were used with their

original coefficients to be compared with the GRNN predictions

using the testing-data subset. Fig. 13 shows the results of compar-

ison of the ANN model against published correlations for predict-

ing oil relative permeability for one of the oil wells in the

carbonate reservoir. The results of comparison showed that the

ANN models reproduced more accurately the experimental rela-

tive permeability data than the published correlations. Although

the Honarpour et al. (1986) correlation gives the closest results

to the experimental data among other correlations, it does not

honor the oil relative permeability data at the initial water satura-

tion by yielding a value greater than one.

Fig. 14 presents a comparison of results of ANN models

against the correlations for predicting water relative permeability

data for an oil well in the Ghawar field. The results clearly show

the excellent agreement of the ANN model with the experimental

data and the high degree of accuracy achieved by the ANN model

compared to all published correlations considered in this study.

This study differs from others’ ANN work (Slipngarmlers et al.

2002) in that this study used a large database of relative permeability

for giant carbonate reservoirs, it used fewer input variables such that

the developed ANN models use mainly six input variables that can be

obtained easily without performing additional complicated experi-

ments, it used a different network type (GRNN), and it achieved a

higher degree of accuracy and performance. In addition, for the de-

velopment of the ANN models, this study implemented several input-

selection methods and also used three data subsets (training, verifica-

tion, and testing), making sure that the network trained very well

and avoiding the overlearning problem. Slipngarmlers et al. (2002)

used only two data subsets (training and testing).

Conclusion

In this study, we developed new prediction models for determining

water/oil relative permeability using ANN modeling technology for

giant and complex carbonate reservoirs. The ANN models were

developed by use of a hybrid approach of genetic algorithms and

ANNs. The models were successfully trained, verified, and tested

using the GRNN algorithm. To the authors’ knowledge, this is the

first study that uses this type of network, GRNN, in the application

of relative permeability determination. Variable-selection and

dimensionality-reduction techniques, critical procedures in the

design and development of ANN models, were also presented and

applied in this study.

Analysis of results of the blind testing-data set of all ANN

models shows excellent agreement with the experimental relative

permeability data. Results showed that the ANN models outper-

form all published empirical equations by achieving excellent

performance and a high degree of accuracy.

It is hoped that this study will have a great impact on reservoir-

simulation and reservoir-management studies. It minimizes the

cycle time of the history-matching process, which leads to

improved performance predictions. It provides best estimates

of relative permeability for existing and newly drilled wells for

which experimental data are unavailable.

Nomenclature

S

on

=normalized oil saturation

S

or

=residual-oil saturation, fraction

S

w

=water saturation, fraction

S

wi

=irreducible water saturation, fraction

S

wn

=normalized water saturation

f=porosity, fraction

Acknowledgments

The authors would like to thank Saudi Aramco management for

their permission to publish this paper. Special thanks to Ahmed A.

Al-Moosa, Faisal Al-Shuraidah, and Fawzi Al-Matar, all of Saudi

Aramco, for the great support received during the course of this

project. Thanks are extended to the Petrophysics Unit of Saudi

Aramco’s EXPEC Advanced Research Center for providing the

data used in this work.

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Fig. 13—Comparison of ANN model and correlations for pre-

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ro

for one well in the Ghawar field.

Fig. 14—Comparison of ANN model and correlations for pre-

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rw

for one well in the Ghawar field.

102 February 2009 SPE Reservoir Evaluation & Engineering

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Saud M. Al-Fattah is a researcher currently at Saudi

Aramco’s corporate planning in Dhahran, Saudi Arabia.

E-mail: saud.fattah@aramco.com. He worked in several

departments of E&P at Saudi Aramco including reservoir

management, production and facilities development, and

petroleum engineering applications services. Al-Fattah’s

areas of specialty include reservoir engineering, artificial

intelligence, operations research, economic evaluation,

and energy forecasting. He holds a PhD degree from Texas

A&M University, College Station, Texas, and MS and BS

degrees with honors from King Fahd University of Petroleum

and Minerals (KFUPM), Dhahran, Saudi Arabia, all in petro-

leum engineering. Al-Fattah was awarded the 2006 SPE

Saudi Arabia Technical Symposium’s Best Paper of the Year

award (first place). Al-Fattah is an active member of SPE; he

is a technical editor of SPE Reservoir Evaluation and Engi-

neering, a mentor in the SPE e-Mentoring program since

2005, vice chairman of the 2006 SPE Saudi Arabia Annual

Technical Symposium, and chairman of the 2007 SPE Saudi

Arabia Annual Technical Symposium. Hamad A. Al-Naim is

currently on assignment as a reservoir engineer in the reser-

voir management department at Saudi Aramco, Dhahran,

Saudi Arabia. E-mail: hamad.naim@aramco.com. He

worked previously as a petroleum engineering systems ana-

lyst in the petroleum engineering applications services de-

partment at Saudi Aramco. Al-Naim holds a BS degree

from KFUPM, Saudi Arabia, in computer engineering in 2001,

and an MS degree in petroleum engineering from the

University of Calgary in 2006.

February 2009 SPE Reservoir Evaluation & Engineering 103