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Artificial-Intelligence Technology Predicts Relative Permeability of Giant Carbonate Reservoirs

Copyright 2007, Society of Petroleum Engineers
This paper was prepared for presentation at the 2007 SPE Offshore Europe held in Aberdeen,
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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 predicting the performance of immiscible
displacement processes in oil reservoirs. They are used,
among other applications, for determining fluid distributions
and residual saturations, predicting future reservoir
performance, and estimating ultimate recovery. Undoubtedly,
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,
empirical correlations are usually used to estimate relative
permeability data. Developing empirical correlations for
obtaining accurate estimates of relative permeability data
showed limited success, and proved difficult, especially for
carbonate reservoir rocks.
Artificial neural network (ANN) technology has proved
successful and useful in solving complex structured and
nonlinear problems. This paper presents a new modeling
technology to predict accurately water-oil relative
permeability using ANN. 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 show
excellent agreement with the experimental data of relative
permeability. In addition, error analyses show that the ANN
models developed in this study outperform all published
The benefits of this work include meeting the increased
demand for conducting special core analysis, optimizing the
number of laboratory measurements, integrating into reservoir
simulation and reservoir management studies, and providing
significant cost savings on extensive lab work and substantial
required time.
Artificial neural networks have seen an explosion of interest
over 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
as 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 problems can be solved using the following
network types: Multilayer Perceptrons (MLP), Radial Basis
Function (RBF), Generalized Regression Neural Network
(GRNN), and Linear. In this study, we experimented 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 GRNN performs the best for this
particular study. 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 equal number of nodes as 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
SPE 109018
Artificial-Intelligence Technology Predicts Relative Permeability of
Giant Carbonate Reservoirs
Saud M. Al-Fattah, SPE, and Hamad A. Al-Naim, SPE, Saudi Aramco
2 SPE 109018
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 nodes calculates
the conditional regression for each output variable, whereas
the second type of nodes 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 only be used 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.
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; and 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.
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
Data Preparation
Data acquisition, preparation, and quality control are
considered the most important and most time consuming task,
Fig. 2. The number 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 ten 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 which 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 fifty or less) require a huge
number of input data points. This problem is known as “the
curse of dimensionality.” If there is a larger, but still restricted,
data set, then it can be compensated to some extent by forming
an ensemble of networks, each network is trained using a
different resampling of the available data and then average
across the predictions of the networks in the ensemble.
Water-oil relative permeability measurements were
collected for all wells having special core analysis (SCAL) of
carbonate reservoirs in Saudi Arabian 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, Abqaiq, Shaybah, Qatif, Khurais, and
Berri. SCAL reports were thoroughly studied, and each
relative permeability curve was carefully screened, examined,
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
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 significantly
contribute 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. The initial water
saturation, residual oil saturation, and porosity of each well
can be easily obtained from either well logs or routine core
analysis. Wettability is an important input variable for
predicting the relative permeability data, thus to be 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 determine the wettability of each relative
permeability curve which is classified as oil-wet, water-wet, or
mixed wettability. It should be noted that Craig’s rule helps to
distinguish between strongly water wet and oil wet systems
based on relative permeability curves. If no information is
available on the wettability of a well, then it can be estimated
using offset wells 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.
Due to the variety of reservoir characteristics and using
data statistics, the database was divided into three categories
of reservoirs: Arab-D reservoir, Shuaibah reservoir, and all
other reservoirs having limited data. This necessitates the
development 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 constitutes of a total of 3711 records or
cases. Table 1 presents the distribution of these data cases in
the three categories of reservoirs (Arab-D, Shuaibah, and the
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. That is 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
maximum 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, de-normalizing of the output follows
the reverse procedure: subtraction of the shift factor, followed
by division by the scale factor. The mean/standard deviation
technique is defined as the data mean subtracted from the
input variable value divided by the standard deviation. Both
methods have advantages in that they process the input and
SPE 109018 3
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 of 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 variables. The problem is further
complicated when there are interdependencies 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
actually learn to ignore useless variables. Other architectures
are adversely affected, and in all cases a larger number of
inputs imply that a larger number of training cases are
required to prevent over-learning. As a consequence, the
performance of a network can be improved by reducing the
number of input variables, even sometimes at the cost of
losing some input information. There are highly sophisticated
algorithms that determine the selection of input variables. The
following describes the input selection and dimensionality
reduction techniques that are used in this study. Table 2 lists
and defines all input variables that have been used in this
Genetic Algorithm
A genetic algorithm is an optimization algorithm 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 significantly to the performance of the neural
network. The method is used as part of the model building
process, where 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, where a set of interrelated
yes/no decisions need 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 (more than fifty, say), and also provides a valuable
second opinion for smaller numbers of variables. It is
particularly good at spotting interdependencies between
variables located close together on the masking strings.
Genetic algorithm can sometimes identify subsets of inputs
that are not discovered by other techniques. However, the
method 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 algorithms (Hill and Lewicki 2006) are usually quicker
than the genetic algorithm if there are 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 variable. It
then checks for a second variable that when added to the first
it most improves the model, repeating this process until either
all variables have been selected, or no further improvement is
made. Backward stepwise feature selection is the reverse
process; 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, least degrades the model.
Forward and backward selection methods each have their
advantages and disadvantages. Forward selection method is
generally faster. It may miss key variables if they are
interdependent or correlated. Backward selection method does
not suffer from this problem, but as it starts with the whole set
of variables, the initial evaluations are most time consuming.
Furthermore, the model can actually suffer purely from the
number of variables, making it difficult for the algorithm to
behave sensibly if there are a large number of variables,
especially if there are 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,
as it will locate them at the beginning of its search, whereas
backwards selection will not whittle away the irrelevant ones
until the very end of its search.
In general, backward selection is to be preferred if there
are a small number of variables (say, twenty or less), and
forward selection may be better for larger numbers. All of the
above mentioned input selection algorithms 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
Sensitivity Analysis
It is performed on the inputs to a neural network to indicate
which input variables 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
modeling 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 interdependent variables that are useful only if
included as a set. If the entire set is included in a model, they
can be accorded significant sensitivity, but this does not reveal
the interdependency. Worse, if only part of the interdependent
set is included, their sensitivity will be zero, as they carry no
discernable information. In summary, precautions should be
exercised when drawing conclusions about the importance of
variables as sensitivity analysis does not rate the usefulness of
variables in modeling in a reliable or absolute manner.
Nonetheless, in practice sensitivity analysis is extremely
useful. If a number of models are studied, it is often possible
to identify variables that are always of high sensitivity, others
that are always of low sensitivity, and ambiguous variables
4 SPE 109018
that change ratings and probably carry mutually redundant
Another common approach to dimensionality reduction is
the principle component analysis (Bishop 1995) which can be
represented in a linear network. It can often extract a very
small number of components from quite high-dimensional
original data and still retain the important structure.
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 correctly predicting the output. In this
study, the data are divided into three subsets: training set (50-
60% of data), verification or validation set (20-25% of data),
and testing test (20-25% of data), as presented in Table 1.
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 sufficiently
minimized. 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 acts as a
watchdog and takes no part in the adjustment of weights and
thresholds during training, but the networks’ performance is
continually checked against this subset as training continues.
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 restrictions on training, a neural network may
describe the training data almost perfectly but may generalize
very poorly to new data. The use of verification subset to stop
training at a point when generalization potential is best is a
critical consideration in training neural networks. A third
subset of testing data is used to serve as an additional
independent check on the generalization capabilities 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 algorithms and neural network.
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 versus 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 standard
deviation, output error mean, output error standard deviation,
output absolute error mean, standard deviation ratio, and
Pearson-R correlation coefficient (Hill and Lewicki 2006).
The most significant parameter is the standard deviation (SD)
ratio that 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 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 the performance of a network among other
competing networks.
Due to its large size 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
statistical analysis of the ANN models for determining oil and
water relative permeability, respectively, for the Arab-D
reservoir. Both tables show that the Arab-D reservoir ANN
models for predicting oil and water relative permeability
achieved excellent results of accuracy by having low values of
SD ratios that are lower than 0.3 for all data subsets including
training, verification, and testing data set. Tables 3 and 4 also
show 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 and
water relative permeability data.
Figs. 3 to 7 show that the results of ANN models are in
excellent agreement with the experimental data of oil and
water relative permeability. Crossplots of measured versus
predicted data of oil and water relative permeability are
presented in Figs. 8 and 9, respectively. The majority of the
data fall close to the perfect 45o straight line, indicating the
high degree of accuracy of the ANN models. Figs. 10 and 11
are histograms of residual errors of oil and water relative
permeability ANN models for the 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 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. Figure
12 presents the most influential input variables that
significantly play an important role on the network’s outcome
for determining water relative permeability. Figure 12 shows
that the network performance is significantly get deteriorated
when removing wettability from the network by having the
highest error. It also shows that wettability is ranked first as
the most influential parameter on the network performance. To
study the effect of wettability on the network predictions, we
removed the wettability from the input variables and run the
network. Statistical analysis of the network performance is
presented in Table 5. The result of accuracy was badly
deteriorated indicating the significance of the wettability on
determining 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. Also, the SD ratios for the verification and
testing subsets are very high 0.6 and 0.9, respectively.
SPE 109018 5
This study differs from others work (Slipngarmlers et al.
2002) in that it used a large database of relative permeability
for giant carbonate reservoirs, it used less input variables such
that the developed ANN models use mainly six input variables
that can be easily obtained without performing additional
sophisticated experiments, and it achieved higher degree of
accuracy and performance. In addition, for the development of
the ANN models this study implemented several input
selection techniques, and used three data subsets (training,
verification, and testing) making sure that the network trained
very well avoiding the overlearning problem. Slipngarmlers et
al. (2002) used only two data subsets (training and testing),
and did not use input selection methods.
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 utilized in the training of the ANN
models. 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 (1950); Pirson (1958); Naar et al. (1962); Jones (1978);
Land (1968); and Honarpour et al. (1986, 1982). Fig. 13
shows the results of comparison of the ANN model against
published correlations for predicting 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 relative-permeability data than the
published correlations. Although Honarpour’s (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 saturation 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.
In this study, we developed new prediction models for
determining water-oil relative permeability using artificial
neural network modeling technology for giant and complex
carbonate reservoirs. The ANN models were developed using
a hybrid approach of genetic algorithms and artificial neural
networks. The models were successfully trained, verified, and
tested using the GRNN algorithm. To the author’s 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, a
critical procedure in the design and development of ANN
models, were 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 data
of relative permeability. Results showed that the ANN models
outperform all published empirical equations by achieving
excellent performance and a high degree of accuracy.
The author would like to thank Saudi Aramco management for
their permission to publish this paper. Special thanks to
Ahmed A. Al-Moosa, and Fawzi Al-Matar, 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.
Al-Fattah, S.M., and Startzman, R.A. 2003. Neural Network
Approach Predicts U.S. Natural Gas Production. SPEPF 18
(2): 84-91. SPE-82411-PA. DOI: 10.2118/82411-PA.
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for Determining Relative Permeability from Displacement
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6 SPE 109018
Patterson, D. 1996. Artificial Neural Networks. Singapore:
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Pirson, S.J. 1958. Oil Reservoir Engineering. New York:
McGraw-Hill Book Co. Inc.
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Profile : GRNN 24:24-485-2-1:1 , Index = 10
Train Perf. = 0.076232 , Select Perf. = 0.102937 , Test Perf. = 0.137917
Fig. 1-Design of a Generalized Regression Neural Network
used in this study.
TABLE 1- Distribution of data records/cases for relative
permeability data sets.
Reservoir/Data set
TABLE 3- Statistical analysis of ANN model for Kro Arab-D
Data S.D.
Error Mean
Error S.D.
Abs. E. Mean
S.D. Ratio
TABLE 4- Statistical analysis of ANN model for Krw Arab-D
Data S.D.
Error Mean
Error S.D.
Abs. E. Mean
S.D. Ratio
Fig. 2- Flowchart of procedure of ANN design and
development proposed in this study.
Input Layer Radial Layer
Output Layer
SPE 109018 7
TABLE 2- List of all input variables that have been tried in
this study.
Water saturation
Irreducible water saturation
Residual oil saturation
Wettability (oil-wet, water-wet, mix-wet)
X-coordinate of the well location
Y-coordinate of the well location
orwSS SS
wiwSS SS
orwSS SS
 
 
 
 
wiwwi SSS 1
 
orwor SSS 11
orwSS SS
 
wior SS 1
Scatterplot (Prediction (20 ) (Train) (FinalRelPerm_ARBD_noendpt_May29_2007) 6v*2443c)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
ANN Model
Fig. 3-Results of ANN model compared with experimental
data for oil-relative permeability.
Scatterplot (Prediction (20 ) (Train) (FinalRelPerm_ARBD_noendpt_May29_2007) 6v*2443c)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
ANN Model
Fig. 4-Results of ANN model compared with experimental
data for oil-relative permeability.
Scatterplot (Prediction (1 ) (FinalRelPerm_OTHERS_noendpt_May15_07) 6v*586c)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
ANN Model
Fig. 5-Results of ANN model compared with experimental
data for water-relative permeability.
8 SPE 109018
Scatterplot (Prediction (1 ) (FinalRelPerm_ARBD_noendpt_Jan30_2007) 7v*2449c)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
ANN Model
Fig. 6-Results of ANN model compared with experimental
data for water-relative permeability of Well U-628.
Scatterplot (Prediction (4 ) (FinalRelPerm_SHUB_noendpt_May27_07) 6v*676c)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
ANN Model
Fig. 7-Results of ANN model compared with experimental
data for water-relative permeability of Well SB-50.
Kro NN Model
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Measured Kro
Predicted Kro
Fig. 8- Crossplot of ANN predicted and measured Kro for
Arab-D reservoirs.
Crossplot of Predicted Krw vs. Measured Krw
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Measured Krw
Predicted Krw
Fig. 9- Crossplot of ANN predicted and measured Krw for
Arab-D reservoirs.
Histogram of kro, Residual (T.20)
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
kro, Residual
No cases
Fig. 10- Histogram of Kro residual error for the Arab-D
reservoir model.
Histogram of krw, Residual (14)
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4
krw, Residual
No cases
Fig. 11- Histogram of Krw residual error for the Arab-D
reservoir model.
SPE 109018 9
00.5 11.5 22.5
Error Ratio
Fig. 12- Error ratio and ranking of the influence of input
variables on water relative permeability ANN model for Arab-
D reservoir.
TABLE 5- Statistical analysis of ANN model for Krw Arab-D
reservoir without the Wettability.
Data S.D.
Error Mean
Error S.D.
Abs. E. Mean
S.D. Ratio
UTMN 1051
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Water Saturation, fraction
Oil Relative Permeability, fraction
Fig. 13- Comparison of ANN model and correlations for
predicting Kro for one well in the Ghawar field.
SDGM 222
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Water Saturation, fraction
Water Relative Permeability, fraction
ANN Model
Fig. 14- Comparison of ANN model and correlations for
predicting Krw for one well in the Ghawar field.
... For example, the oil industry has successfully applied CT (computer topography) scan, MRI (magnetic resonance induction), microwave, and expert system in solving petroleum engineering problems. Today, artificial intelligence (AI) is also gaining wider applications in the oil industry to perform complex correlation computations where conventional techniques have not been so successful (Mohaghegh et al., 1994;Nikravesh and Aminzadeh, 2001;Al Fattah, 2007). ...
... AI has successfully been used in predicting properties of rock and other porous media such as relative permeabilities (Kalam and Al-Shekaili, 1997;Al-Fattah, 2007), porosity and permeability (Lim and Kim, 2004;Hamada and Elshafei, 2009;Anifowose and Abdulraheem, 2010;Weldu et al., 2010;Olatunji et al., 2011), reservoir heterogeneity characterization (Mohaghegh et al., 1994), oilfield production problems (Adebayo et al., 2013), ther-mal conductivity (Bhoopal et al., 2013), and many different other reservoir properties (Aifa, 2014). However, limited application is available in predicting water saturation. ...
The effect of shale on the evaluation of water saturation in shaly porous media is yet to be fully understood.Wide varieties of water saturation models for shaly sands are currently in use. However, none is universally accepted by log analysts and each model estimates water saturation value significantly different from the others. Error in water saturation can result in either underestimation or overestimation of hydrocarbon reserves, which will influence management decision on a given field. A laboratory measurement of water saturation is the most accurate but limited by time and cost, thereby forcing the industry to rely on these models. In this paper, we show how a computer artificial intelligence (AI) system can predict water saturation with an accuracy of 93% compared to selected saturation models. Three saturation models were selected and subjected to same well log data as the AI model to estimate water saturation. The estimated saturation values for AI and other saturation models were then compared with experimental values for 147 core samples and results showed that the AI model was able to use shale affected log data to accurately predict water saturation while the saturation models did the same with lesser accuracy of 63, 50, and 43%. A statistical and graphical comparison of accuracy and error between the AI technique and selected models is presented.
... The results showed the hybrid models performed better than using the individual techniques. [Al-Fattah 2007] presented a modeling technology to predict accurately the water-oil relative permeability of giant Saudi Arabian carbonate oil fields reservoirs using ANN. The results showed excellent agreement with the experimental data. ...
There are two schools of thought on the application of Artificial Intelligence (AI) techniques in reservoir characterization and modeling. The first school considers AI as a step forward in the future of reservoir characterization and modeling in line with the increased advancement in technology. The other school argues that AI techniques are "black boxes" with vague architectures, whose concepts do not follow fundamental petroleum engineering principles. This paper presents AI as a "white box", highlighting its basic concepts, revealing the architectural composition of some of its techniques, and showcasing examples of its successful applications in various reservoir characterization and modeling tasks. AI techniques are used in the prediction of oil and gas reservoir properties such as porosity, permeability, water saturation, well-bore stability and identification of lithofacies. The recent developments in the hybridization and "ensemblage" of some AI techniques are also discussed. The outcome of this paper will provide a better understanding of the basic concepts of AI and offer a strong background for further study of AI techniques. Overall, it will provide an appraisal of the successful applications of AI in petroleum engineering and increase the necessary synergy required for a multi-disciplinary collaboration among petroleum engineers, computer scientists and mathematicians; and to ensure the delivery of the future AI-driven/AI-assisted reservoir models for better exploration, production and management of petroleum resources.
... These procedures include: 1. Data acquisition and preparation, 2. Data preprocessing, 3. Inputs selection and dimensionality reduction, 4. Network design, 5. Network training, 6. Verifying, and 7. Testing.Figure 2 is a flowchart illustrating the ANN development strategies implemented in this study (Al Fattah & Al-Naim, 2009). ...
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Energy market volatility affects macroeconomic conditions and can unduly affect the economies of energy-producing countries. Large price swings can be detrimental to both producers and consumers. Market volatility can cause infrastructure and capacity investments to be delayed, employment losses, and inefficient investments. In sum, the growth potential for energy-producing countries is adversely affected. Undoubtedly, greater stability of oil prices can reduce uncertainty in energy markets, for the benefit of consumers and producers alike. Therefore, modeling and forecasting crude oil price volatility is critical in many financial and investment applications. The purpose of this paper to develop new predictive models for describing and forecasting the global oil price volatility using artificial intelligence with artificial neural network (ANN) modeling technology. Two ANN models were successfully developed: one for WTI futures price volatility and the other for WTI spot prices volatility. These models were successfully designed, trained, verified, and tested using historical oil market data. The estimations and predictions from the ANN models closely match the historical data of WTI from January 1994 to April 2012. These models appear to capture very well the dynamics and the direction of the oil price volatility. The ANN models developed in this study can be used: as short-term as well as long-term predictive tools for the direction of oil price volatility, to quantitatively examine the effects of various physical and economic factors on future oil market volatility, to understand the effects of different mechanisms for reducing market volatility, and to recommend policy options and programs incorporating mechanisms that can potentially reduce the market volatility. With this improved method for modeling oil price volatility, experts and market analysts will be able to empirically test new approaches to mitigating market volatility. The outcome of this work provides a roadmap for research to improve predictability and accuracy of energy and crude models.
Conference Paper
Relative permeability is one of the most significant reservoir characteristics in the petroleum industry. It captures the fluids behavior inside the porous space within the reservoir. It considers the effective permeability of the fluids in the reservoir which ultimately lead to the understanding of the fluid behavior inside the pores. Also, using relative permeability curves, we can estimate the reservoir's oil or gas recovery. Furthermore, enhanced oil recovery techniques utilize relative permeability curves to evaluate their performance. The well-known practice to develop any relative permeability curve is by conducting core flooding experiments which are relatively time consuming especially if it is needed to be done on several wells with different core samples. Also, it would be costly data set to acquire since it requires special lab sets and conditions. Time and cost are the main factors making relative permeability a very hard to obtain information for any reservoir. Several models and empirical relations have been built to calculate and present relative permeability without going through the lab experiments, each model has its uncertainty. This paper captures the approach to predict relative permeability curves (oil and water) from a set of data collected from one reservoir using machine learning. Data used is generated from special core analysis lab experiments (core flooding) of unsteady state oil and water relative permeability. Core flooding experiments represents several water saturations at which the core been flooded to, at every water saturation a water and an oil relative permeability value is obtained. To represent the reservoir efficiently and addressing several aspects of its 56 relative permeability curves (from 56 composites) have been collected from different wells in the same reservoir. Adding up to a total of more than 7,000 data sets (different water saturations). Two models have been built, one for predicting the relative permeability of oil at several water saturations and the second model is for the relative permeability of water. Main input data are water saturations, connate water saturation, residual oil saturation, porosity, oil viscosity, water viscosity, (several basic core properties) and wettability. The outcome for each model is one, either oil or water relative permeability. The main added value of this work is creating a workflow and models to predict water and oil relative permeability using main reservoir data with high accuracy and without conducting any special core analysis.
This paper develops a rigorous and advanced data-driven model to describe, analyze, and forecast the global crude oil demand. The study deploys a hybrid approach of artificial intelligence techniques, namely, the genetic-algorithm, neural-network, and data-mining approach for time-series models (GANNATS). The GANNATS was developed and applied to two country cases, including one for a high oil producer (Saudi Arabia) and one for a high oil consumer (China), to develop crude oil demand forecasts. The input variables of the neural network models include gross domestic product (GDP), the country’s population, oil prices, gas prices, and transport data, in addition to transformed variables and functional links. The artificial intelligence predictive models of oil demand were successfully developed, trained, validated, and tested using historical oil-market data, yielding excellent oil demand predictions. The performance of the intelligent models for Saudi Arabia and China was examined using rigorous indicators of generalizability, predictability, and accuracy. The GANNATS forecasting models show that the crude oil demand for both Saudi Arabia and China will continue to increase over the forecast period but with a mildly declining growth, particularly for Saudi Arabia. This decreasing growth in the demand for oil can be attributed to increased energy efficiency, fuel switching, conversion of power plants from crude oil to gas-based plants, and increased utilization of renewable energy, such as solar and wind for electricity generation and water desalination. In this study, the feature engineering of variables selection techniques has been applied to identify and understand significant factors that impact and drive the crude oil demand. The proposed GANNATS methodology optimizes and upgrades the conventional process of developing oil demand forecasts. It also improves and enhances the predictability and accuracy of the current oil demand forecasting models.
Full-text available
This paper presents the results about using a methodology that combines two artificial intelligence (AI) models to predict the oil, water and gas production in a Colombian petroleum field. By combining fuzzy logic (FL) and artificial neural networks (ANN) a novelty data mining procedure is implemented, including a data imputation strategy. The FL tool determines the most useful variables or parameters to include into each well production model. ANN and FIS (fuzzy inference systems) predictive models identification is developed after the data mining process. The FIS models are capable to predict specific behaviors, while ANN models are able to forecast an average behavior. The combined use of both tools under few iterative steps, allows to improve forecasting of well behavior until reach a specified accuracy level. The proposed data imputation procedure is the key element to correct false or to complete void positions into operation data used to identify models for a typical oil production field. At the end, two models are obtained for each well product, conforming an interesting tool given the best accurate prediction of fluid phase production.
Conference Paper
There are two schools of thought on the application of Artificial Intelligence (AI) techniques in reservoir characterization and modeling. The first school considers AI as a step forward in the future of reservoir characterization and modeling in line with the increased advancement in technology. The other school argues that AI techniques are "black boxes" with vague architectures, whose concepts do not follow fundamental petroleum engineering principles. This paper presents AI as a "white box", highlighting its basic concepts, revealing the architectural composition of some of its techniques, and showcasing examples of its successful applications in various reservoir characterization and modeling tasks. AI techniques are used in the prediction of oil and gas reservoir properties such as porosity, permeability, water saturation, well-bore stability and identification of lithofacies. The recent developments in the hybridization and "ensemblage" of some AI techniques are also discussed. The outcome of this paper will provide a better understanding of the basic concepts of AI and offer a strong background for further study of AI techniques. Overall, it will provide an appraisal of the successful applications of AI in petroleum engineering and increase the necessary synergy required for a multi-disciplinary collaboration among petroleum engineers, computer scientists and mathematicians; and to ensure the delivery of the future AI-driven/AI-assisted reservoir models for better exploration, production and management of petroleum resources.
Full-text available
The industrial and residential market for natural gas produced in the United States has become increasingly significant. Within the past ten years the wellhead value of produced natural gas has rivaled and sometimes exceeded the value of crude oil. Forecasting natural gas supply is an economically important and challenging endeavor. This paper presents a new approach to predict natural gas production for the United States using an artificial neural network. We developed a neural network model to forecast U.S. natural gas supply to the Year 2020. Our results indicate that the U.S. will maintain its 1999 production of natural gas to 2001 after which production starts increasing. The network model indicates that natural gas production will increase during the period 2002 to 2012 on average rate of 0.5%/yr. This increase rate will more than double for the period 2013 to 2020. The neural network was developed with an initial large pool of input parameters. The input pool included exploratory, drilling, production, and econometric data. Preprocessing the input data involved normalization and functional transformation. Dimension reduction techniques and sensitivity analysis of input variables were used to reduce redundant and unimportant input parameters, and to simplify the neural network. The remaining input parameters of the reduced neural network included data of gas exploratory wells, oil/gas exploratory wells, oil exploratory wells, gas depletion rate, proved reserves, gas wellhead prices, and growth rate of gross domestic product. The three-layer neural network was successfully trained with yearly data starting from 1950 to 1989 using the quick-propagation learning algorithm. The target output of the neural network is the production rate of natural gas. The agreement between predicted and actual production rates was excellent. A test set, not used to train the network and containing data from 1990 to 1998, was used to verify and validate the network performance for prediction. Analysis of the test results shows that the neural network approach provides an excellent match of actual gas production data. An econometric approach, called stochastic modeling or time series analysis, was used to develop forecasting models for the neural network input parameters. A comparison of forecasts between this study and other forecast is presented. The neural network model has use as a short-term as well as a long-term predictive tool of natural gas supply. The model can also be used to examine quantitatively the effects of the various physical and economic factors on future gas production.
This paper presents graphical constructions that simplify the calculation of relative permeability from displacement data. These constructions convert raw data to relative permeability in a less tedious, more accurate manner than the usual computations. Fractional-flow saturation curves derived from waterflood displacements are always concave downward and never yield multiple-value saturations. Introduction To find oil and water relative permeabilities by the displacement or unsteady-state method, a small linear core usually is saturated with water, then oilflooded to irreducible water saturation. Subsequently, the core is waterflooded, and during the process, pressure drop (either constant or variable) across the entire core and water injection rate (constant or variable) are determined. Effluent fractions are collected and the amount of water and oil in each is measured. Augmented by the absolute permeability and pore volume of the core and by oil and permeability and pore volume of the core and by oil and water viscosities, these data are sufficient to develop relative permeability curves. The average saturation in the core at any time in the flood can be found from an over-all material balance. However, to calculate relative permeability, the saturation history at some point in the core must be determined, not the average saturation history. The Welge equation yields saturations at the effluent end of the core when the average saturation history is known. Similarly, to compute relative permeability, the point pressure gradient per unit injection rate is needed, not the pressure gradient per unit injection rate is needed, not the average. The equation developed by Johnson et al. converts average relative injectivity to a point value, accomplishing the required task. While the equations of Welge and Johnson et al. have been used successfully for years, they require tedious computation and are subject to error because of the evaluation of derivatives. The graphical techniques presented in this study are equivalent to these equations, but are easier to use and can give a more accurate evaluation of relative permeability. Lefebvre du Prey has presented graphical constructions based on curves of volume of oil produced vs time and pressure drop vs time to develop the required point functions. These constructions are limited to constant rate displacements. The constructions presented here are general and apply to constant rate, constant pressure, or variable rate-pressure displacements. Constant-rate and constant-pressure examples are given to help clarify the methods. The graphical techniques make it easy to see that double or triple saturation values, so extensively discussed in the past simply do not result from the fractional flow curve generated by a single displacement, such as a waterflood or an oilflood. Theory Ignoring gravity effects and capillary pressure, water and oil relative permeabilities (expressed as functions of saturation) are (1) (2) To use these equations, the fractional flow of water or oil and effective viscosity, lambda-1, must be determined as functions of saturation. JPT P. 807
Relative permeability functions are developed for both two- and three-phase systems with the saturation changes in the imbibition direction. An empirical relation between residual nonwetting-phase saturation after water imbibition and initial nonwetting-phase saturations is found from published data. From this empirical relation, expressions are obtained for trapped and mobile nonwetting-phase saturations which are used in connection with established theory relating relative permeability to pore-size distribution. The resulting equations yield relative permeability as a function of saturation having characteristics believed to be representative of real systems. The relative permeability of water-wet rocks for both two- and three-phase systems, with the saturation change in the imbibition direction, may be obtained by this method after properly selecting two rock properties: the residual nonwetting-phase saturation after the complete imbibition cycle, and the capillary pressure curve. Introduction Relative permeability is a function of saturation history as well as of saturation. This fact was first pointed out for two-phase flow by Geffen et al. and by Osaba et al. Hysteresis in the relative permeability-saturation relation also has been reported for three-phase systems. Since saturations may change simultaneously in two directions in a three-phase system, four possible relationships arise between relative permeability and saturation for a water-wet system. The four saturation histories of this system were given by Snell as II, ID, DI and DD. I refer to the direction of saturation change (imbibition and drainage), with the first letter of the symbol indicating the direction of change of the water phase. As used in this paper, the second letter of the symbol refers to the direction of saturation change of the gas phase, i.e., D and I indicate an increase and decrease, respectively, in gas saturation. Only a few three-phase relative permeability curves have been published. Leverett and Lewis published three-phase curves for unconsolidated sand, and Snell reported results of several English authors for both drainage and imbibition three-phase relative permeability of unconsolidated sands. Three-phase relative permeability curves for a consolidated sand were published by Caudle et al. for increasing water and gas saturations (ID). Corey et al. reported drainage (DD) three-phase relative permeability for consolidated sands. Recently, Donaldson and Dean and Sarem calculated three- phase relative permeability curves from displacement data on consolidated sands, also for saturation changes in the drainage direction. The only published three - phase relative permeability curves for consolidated sands with saturation changes in the imbibition direction (II) are those of Naar and Wygal. These curves are based on at theoretical study of the model of Wyllie and Gardner as modified by Naar and Henderson. Interest in three-phase relative permeability has increased recently due to the introduction of new recovery methods and refinements in calculation procedures brought about by the use of large-scale digital computers. The scarcity of empirical relations for three-phase flow, and the experimental difficulty encountered in obtaining such data, have made the theoretical approach to this problem attractive. RELATIVE PERMEABILITY AS A FUNCTION OF PORE-SIZE DISTRIBUTION Purcell used pore sizes obtained from mercury-injection capillary pressure data to calculate the permeability of porous solids. Burdine extended the theory by developing a relative permeability-pore size distribution relation containing the correct tortuosity term. SPEJ P. 149ˆ
Experimental work is reported which shows that consolidated rocks and unconsolidated porous media exhibit different imbibition flow behavior. At a given saturation the imbibition nonwetting permeabilities for a rock are smaller than the drainage permeabilities. The contrary happens for unconsolidated aggregates - imbibition nonwetting permeabilities are larger than drainage ones. A similar difference is observed for the wetting phase. Imbibition permeabilities are larger than drainage ones for a consolidated rock but smaller than drainage permeabilities for an unconsolidated medium. The results of these differences are examined for two cases.Flooding Efficiency - Craig's scheme for the computation of production history of a five-spot water flood is shown to agree extremely well with experimental results obtained when using a system packed with glass spheres if imbibition relative permeability curves are used.Alcohol-Slug Displacement - Published theory on oil displacement by alcohol slugs bas been questioned despite the apparent agreement between predicted and observed results. The present work suggests that, if imbibition relative permeability curves characteristic of the unconsolidated media used in the early experiments had been available to make the predictions, the inadequacy of the theory would have been immediately evident. The experimental work shows that poorly consolidated formations tend to behave like unconsolidated media. Finally, it is shown that the difference in imbibition behavior is directly related to pore-size distribution and cementation. PART 1 - THE FLOW BEHAVIOR OF UNCONSOLIDATED AGGREGATES Introduction Experiments on scaled models of field reservoirs are useful for studying new displacement processes which are incompletely understood. Even when a mathematical description is possible, the solution might be difficult and complex. An answer obtained from a scaled model is extremely valuable in such cases. A great amount of work, therefore, has been devoted to the derivation of scaling laws. Similarity groups have been defined which assumethat the relative permeability curves of the prototype and the model are the same whether the displacement is an imbibition or a drainage process andthat there is a linear relationship between the capillary pressure of the model and the prototype. For practical reasons (simplicity in the preparation of models, duration of the experiments, etc.), the porous media of laboratory models are usually unconsolidated packs of sand or glass particles. Hence, unless the capillary and flow characteristics of unconsolidated and consolidated systems are identical, the model data are applicable only to unconsolidated formations. The usefulness of scaled-model studies may then be seriously restricted since most oil-bearing sands are consolidated. Perkins and Collins suggested the use of model and prototype curves normalized with respect to both relative permeability and saturation to improve compliance with scaling criteria. Even this technique does not give a satisfactory model-prototype match. This paper reports an observation of two-phase flow in unconsolidated sands which shows that, for most displacements, "scaling" in the strict sense of the word is not even qualitatively feasible with a sand model. It provides, however, a firm foundation for testing a theory by matching it with observed performance of laboratory-size models. EXPERIMENTAL As a part of a basic study of packed aggregates, the relative permeability of glass-spheres and sand-grain packs was measured with capillary control. The fluids were oil and air. SPEJ
Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized to be experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering. Abstract With the recent interest and enthusiasm in the industry toward smart wells, intelligent fields, and real-time analysis and interpretation of large amounts of data for process optimization, our industry's need for powerful, robust, and intelligent tools has significantly increased. Operations such as asset evaluation; 3D- and 4D-seismic-data interpretation; complex multilateral-drilling design and implementation; log interpretation; building of geologic models; well-test design, implementation, and interpretation; reservoir modeling; and simulation are being integrated to result in comprehensive reservoir management. In recent years, artificial intelligence (AI), in its many integrated flavors from neural networks to genetic optimization to fuzzy logic, has made solid steps toward becoming more accepted in the mainstream of the oil and gas industry. In a recent set of JPT articles, fundamentals of these technologies were discussed. This article covers some of the most recent and advanced uses of intelligent systems in our industry and discusses their potential role in our industry's future. Introduction On the basis of recent developments, it is becoming clear that our industry has realized the immense potential offered by intelligent systems. Our daily life as petroleum professionals is full of battling highly complex and dynamic problems and making high-stakes decisions. Moreover, with the advent of new sensors that are permanently placed in the wellbore, very large amounts of data that carry important and vital information are now available. To make the most of these exotic hardware tools, one must have access to proper software to process the data in real time. Intelligent systems in their many flavors are the only viable techniques capable of bringing real-time analysis and decision-making power to the new hardware.