A publication of
CHEMICAL ENGINEERING TRANSACTIONS
VOL. 35, 2013
The Italian Association
of Chemical Engineering
www.aidic.it/cet
Guest Editors: Petar Varbanov, Jiří Klemeš, Panos Seferlis, Athanasios I. Papadopoulos, Spyros Voutetakis
Copyright © 2013, AIDIC Servizi S.r.l.,
ISBN 978-88-95608-26-6; ISSN 1974-9791
Modeling of Crude Oil Properties Using Artificial Neural
Network (ANN)
Wirit Cuptasantia, Farshid Torabib, Chintana Saiwan*a
a
Petroleum and Petrochemical College, Chulalongkorn University, Bangkok 10330, Thailand
Petroleum Technology Research Centre, University of Regina, Saskatchewan S4S7J7, Canada
Chintana.Sa@chula.ac.th
b
Crude oil properties data were gathered from the published sources for modeling correlations and artificial
neural networks (ANN), which could be used to predict crude oil’s physical properties, such as bubble
point pressure and bubble point oil formation volume factor. The data sets were preprocessed for
representativeness of each data points. Each data set was selected randomly and divided into developing,
and test data sets. The input parameters for bubble point pressure and oil formation volume factor
prediction models were reservoir temperature, solution-gas-oil ratio, gas specific gravity and API gravity, or
oil specific gravity. Nonlinear regression was the technique used to develop each correlation. For ANN
development, the developing data sets were randomly divided into training, validation, and testing sets.
Different network architectures and transfer functions were used for developing the best ANN models. The
developed correlations and ANNs were tested with the testing data sets, which had not been used for
developing correlations and ANNs, to ensure their accuracy and applicability. Moreover, the developed
models were compared and evaluated with other published correlations. The results showed that the
developed models gave better accuracy in terms of average absolute errors over other published
correlations.
1. Introduction
Physical properties of reservoir fluid are necessary for various field applications, such as field
development, production optimization, reservoir performance evaluation, wellbore hydraulic calculations,
enhanced oil recovery processes, and etc. These properties are essentially determined at reservoir
temperature with various pressures for reservoir system studies as well as at both various parameters for
wellbore calculations. It implies that the fluid properties have a profound influence on petroleum and
reservoir engineering calculations (Cosentino, 2001). This valuable information of reservoir fluid can be
obtained through vast laboratory testing either on bottom-hole or sub-surface samples, PVT laboratory
analysis and field production data. In order to acquire the accurate results from the laboratory, the
reservoir fluid samples must be appropriately collected and kept for the representative quality of the
original reservoir condition. Extremely care and precaution must be taken from a specialized sampler since
it is possible to have accurate laboratory results from poor samples, which leads to severely fallacious
unrepresentative data resulting in devastating consequences throughout the life of a reservoir (Cosentino,
2001). Moreover, apart from the inherent difficulties of the sampling measurements, these extensive
procedures are very expensive and time-consuming. Since the last century, many empirical correlations of
reservoir fluid properties have been developed and used in order to solve the aforementioned obstacles.
Therefore, they can be incorporated with reservoir simulations or used in many cases where laboratory
data become unavailable. These correlations can predict fluid properties based on the measured data from
various sources, but fail to predict fluid properties in a wide range of conditions due to the complexity of
fluid composition of hydrocarbon molecules, different crude characteristics in each area or region, and
insufficient information (Sutton and Farshad, 1990). Artificial neural network (ANN) can be another
approach among artificial intelligence techniques for prediction of reservoir fluid physical properties.
The objective of this work was to develop ANN models and correlations for predicting crude oil properties
such as bubble point pressure and bubble point oil formation volume factor using data points available in
literature. The gathered data sets were screened, and used for training ANN models. Different neural
model architectures were investigated and then the best neural model would be chosen. Finally, the
developed ANN models were evaluated and compared to the developed correlations and other published
empirical correlations, using data sets for testing, which had not been used in developing the models.
2. Methodology
2.1 Data Preparation
It is essential to select the effective inputs to develop an ANN model. However, availability of data is
another major factor for choosing the input parameters since ANN demands large volume of data to be
used for training and cross-validation in order to solve complex, nonlinear problems accurately. In this
study, large PVT data were collected from available sources and literature. Collected Data were checked
based on following criteria. Redundant data points or data points with errors were removed. The data sets
were divided into data sets for developing and testing ANNs and correlations.
2.2 Developing ANNs and correlations
The prepared data sets were utilized for developing ANNs by using neural network toolbox (nntool)
embedded in Matlab software. In addition, the data sets were used for developing correlations by using
nonlinear regression technique from Minitab software. The best correlations and ANNs resulted from
numerous trials were selected.
2.3 Statistical Analysis
As a consequence of testing the developed ANNs and correlations, the statistical parameters, such as
minimum error (Ermin), maximum error (Ermax), average absolute error (AEravg), and coefficient of
determination (R2) were determined and compared with the results from some published correlations.
3. Results and discussion
3.1 Data Available
For bubble point pressure modeling, after removing redundant data, a total of 757 data points with 3,785
measurements were used. The data were collected from Glaso (1980), Ostermann and Owolabi (1983),
Al-Marhoun (1988), Dokla and Osman (1991), Omar and Todd (1993), De Ghetto and Villa (1994),
Mahmood and Al-Marhoun (1996), Velarde et al. (1997), Gharbi and Elsharkawy (1999), Wu and
Rosenegger (1999), and Bello et al. (2008). The crude oil data consist of reservoir temperature (Tres, ºF),
solution gas oil ratio (Rs, scf/stb), gas specific gravity (γg), oil API gravity (APIº), and bubble point pressure
(Pb, psia). The data were randomly classified into two sets. A set of 557 data points were used in
developing correlation and ANN, and another set of 200 data points were used for testing the models. The
data summaries for developing and testing bubble point pressure models are shown in Tables 1-2.
Similarly, for the bubble point oil formation volume factor (Bob) modeling, after removing redundant data, a
total of 1,175 data points with 5,875 measurements were used. The data were collected from Glaso
(1980), Ostermann and Owolabi (1983), Al-Marhoun (1988), Abdul-Majeed et al. (1988), Dokla and Osman
(1991), Omar and Todd (1993), De Ghetto and Villa (1994), Mahmood and Al-Marhoun (1996), Gharbi
and Elsharkawy (1997), Velarde et al. (1997), Wu and Rosenegger (1999), and Bello et al. (2008). The
crude oil data consist of Tres, Rs, γg, API, and Bob. The data were randomly divided into two sets. A set of
875 data points were used in developing correlation and ANN, and another set of 300 data points were
used for testing the models. The data summaries for developing and testing bubble point oil formation
volume factor are shown in Tables 3-4.
Table 1: Data summary for developing Pb models (557 points)
Properties
Rs (scf/stb)
Tres (ºF)
γg
APIº
Pb (psia)
Min
8.61
74
0.61
6
79
Max
3298.66
341.6
3.4445
56.8
7127
AVG
639.685
197.875
1.12292
34.8083
1978.68
S.D.
514.78
52.5279
0.42212
8.27712
1400.58
Skewness
1.52654
-0.2074
1.59279
-0.9992
0.84701
Kurtosis
2.95075
-0.5608
2.86265
1.44669
0.42249
Table 2: Data summary for testing Pb models (200 points)
Properties
Rs (scf/stb)
Tres (ºF)
γg
APIº
Pb (psia)
Min
17.21
80
0.61
6.3
95
Max
3020
334.4
2.98
56.5
6641
AVG
657.41
204.357
1.16574
35.972
1970.43
S.D.
528.524
51.8959
0.44579
8.41313
1438.43
Skewness
1.43495
-0.2426
1.63334
-1.2479
0.72348
Kurtosis
2.55253
-0.1802
2.9683
2.17911
-0.0341
S.D.
480.242
54.1197
0.37987
10.0429
0.28297
Skewness
1.66484
0.47773
2.08889
-0.5984
1.77547
Kurtosis
3.57134
2.71979
5.32879
-0.341
4.47046
S.D.
481.115
54.102
0.3922
9.72234
0.29277
Skewness
1.75751
0.08627
2.02137
-0.6421
2.15482
Kurtosis
4.27439
-0.6121
4.72544
0.19895
6.97319
Table 3: Data summary for developing Bob models (875 points)
Properties
Rs (scf/stb)
Tres (ºF)
γg
APIº
Bob
Min
0
74
0.511
6
1.028
Max
3298.66
593.996
3.4445
59.5
2.916
AVG
523.534
187.693
1.01727
32.8496
1.34781
Table 4: Data summary for testing Bob models (300 points)
Properties
Rs (scf/stb)
Tres (ºF)
γg
APIº
Bob
Min
0
75.002
0.525
6.3
1.028
Max
3020
341.6
2.98
56.8
2.903
AVG
552.867
187.153
1.03774
33.2908
1.36313
3.2 Developed correlations
After numerous trails on nonlinear regression technique in Minitab software using the developing data
sets, the Pb correlation was developed by modifying Calhoun’s correlation (Calhoun, 1976), as expressed
in Eq(1).
Pb  577.747( Rs0.444689  4.43941)e
( 0.00252849Tres 0.0217755API 0.976346 g )
(1)
where Pb is a function of solution gas oil ratio (Rs), reservoir temperature (Tres), oil API gravity (API), and
gas specific gravity (γg).
Likewise, the Bob expression in Eq(2) was correlated using Petrosky Jr. and Farsahd’s correlation
(Petrosky Jr. and Farshad, 1993).
1.99881
 R 0.601715 1g.47844

0.68077

Bob  4.25999 10   s 1.47844
 0.968331 Tres


o


5
 1.00387
(2)
where Bob is a function of solution gas oil ratio (Rs), reservoir temperature (Tres), gas specific gravity (γg),
and oil specific gravity (γo).
3.3 Developed ANNs
The similar developing data sets as used for developing correlations were also used for developing ANN
models. In this work, 70% of the developing data were randomly used for training, and 30% were used for
validation and testing each network. Feed-forward, back-propagation neural network model with one
hidden-layer was used for each model. Gradient descent with momentum (GDM) training algorithm and
Levenberg-Marquardt (LM) learning algorithm were used for developing the models. Hyperbolic tangent
sigmoid transfer function (TANSIG) was used for calculation between input layer and hidden layer, while
linear transfer function (PURELIN) was chosen to calculate the output from the hidden layer to the output
layer. For Pb neural network model, four input parameters including Rs, Tres, γg, and API were used. A
neural network with 10 neurons in the hidden layer was regarded as the best model with the mean square
error (MSE) for validation performance of 1177883.51. In other words, the 4-10-1 (input layer-hidden layeroutput layer) neural network architecture was selected. For Bob neural network model, four input
parameters, which are Rs, Tres, γg, and γo, were used for Bob prediction. The 4-12-1 neural network
architecture was chosen for Bob prediction. A value of the MSE for validation performance of B ob ANN is
0.0039261. The neural network architectures and the regression plots resulted from the developed
network outputs with respect to targets for training, validation, and testing the developing data sets for Pb
ANN and Bob ANN are shown in Figure 1.
a) b)
Figure 1: Neural network architectures and regression plots resulted from the developed ANNs: a) Pb ANN,
b) Bob ANN.
3.4 Testing Results
The developed correlations and ANNs were tested against published correlations using data sets for
testing. The testing results from Pb and Bob predictions are shown in Tables 5-6.
Table 5: Statistical results of Pb using testing data
Method
Standing (1947)
Calhoun (1976)
Glaso (1980)
Vazquez and Beggs (1980)
Al-Marhoun (1988)
Petrosky Jr. and Farshad (1993)
Dokla and Osman (1991)
Kartoatmodjo and Schmidt (1991)
De Ghetto and Villa (1994)
Frashad et al. (1996)
Almehaideb (1997)
Velarde et al. (1997)
Hanafy et al. (1997)
Al-Shammasi (1999)
Valkó and McCain Jr (2003)
Dindoruk and Christman (2004)
Nikpoor and Khanamiri (2011)
Pb correlation (this work)
Pb ANN (this work)
Ermin
-3139.93
-1882.76
-4181.29
-3869.91
-4049.08
-3035.26
-1830.10
-4685.30
-2617.00
-1620.52
-3979.12
-1611.32
-1882.76
-1862.15
-1566.93
-1314.32
-2731.29
-1633.87
-1519.51
Ermax
AEravg (%)
AErmax (%)
1579.84
25.69
372.01
1654.84
53.76
614.80
1228.53
27.62
247.00
1307.29
30.15
403.90
1894.29
23.20
131.62
1521.86
86.39
766.86
2243.37
29.80
206.23
1179.75
34.54
487.43
1624.93
30.22
466.61
1624.93
39.08
230.77
1724.54
34.32
427.18
2117.66
21.12
110.45
1645.84
53.77
614.80
1642.29
18.09
105.65
1829.55
18.76
112.73
2703.91
25.94
152.31
2077.11
20.72
115.40
1693.76
22.36
185.92
1512.67
21.32
240.19
R2
0.88929
0.86888
0.87955
0.88920
0.83649
0.90579
0.79883
0.87637
0.89587
0.88458
0.82125
0.87761
0.86888
0.89788
0.91467
0.80465
0.85476
0.91846
0.93176
3.5 Testing Results
The developed correlations and ANNs were tested against published correlations using data sets for
testing. The testing results from Pb and Bob predictions are shown in Tables 5-6.
Table 6: Statistical results of Bob using testing data
Method
Standing (1947)
Glaso (1980)
Al-Marhoun (1988)
Al-Marhoun (1992)
Omar and Todd (1993)
Petrosky Jr. and Farshad (1993)
Almehaideb (1997)
Hanafy et al. (1997)
Al-Shammasi (1999)
Hemmati and Kharrat (2007)
Nikpoor and Khanamiri (2011)
Bob correlation (this work)
Bob ANN (this work)
Ermin
-0.0214
-0.1674
-0.1014
-0.0726
-0.0015
-0.2337
-0.2062
-01.268
-0.2136
-0.1789
-0.1421
-0.1377
-0.1951
Ermax
AEravg (%)
AErmax (%)
1.5944
16.70
54.92
0.2695
2.84
11.61
0.2821
1.99
10.90
0.5773
3.56
20.00
1.6115
17.87
55.51
0.1530
2.46
15.08
0.3171
4.23
17.73
0.1512
7.97
43.93
0.4123
3.06
16.66
0.1805
1.89
11.53
0.4129
2.00
14.30
0.2189
1.67
8.21
0.1876
2.13
9.67
R2
0.81238
0.97351
0.98026
0.97846
0.84345
0.97582
0.93238
0.93602
0.95197
0.98179
0.97513
0.98395
0.98134
Regarding the Pb prediction results, the developed Pb ANN gave competitive performance compared to
some of the correlations. Although the AEravg (21.32 %) from the developed Pb ANN was higher than some
published correlations, the developed Pb ANN had the highest R2 of 0.93176 with the narrowest range
between Ermin (-1519.51) and Ermax (1512.67). The developed Pb correlation (Equation 1) also gave
competitive performance for Pb prediction compared to most of the published correlations with R2 of
0.91846. For the prediction of Bob, both developed Bob correlation (Equation 2) and Bob ANN outperformed
the published correlations in term of AErmax, which are 8.21 % for Bob correlation and 9.67 % for Bob ANN.
Moreover, the result from the developed Bob correlation was slightly better than Bob ANN in term of R2
(0.98134) and AEravg (1.67 %).
4. Conclusions
The ANNs and correlations were developed for the prediction of bubble point pressure and bubble point oil
formation volume factor using data gathered from various published sources. The prepared data sets were
divided into data sets for developing and testing correlations and ANNs. The developed Pb ANN and the Pb
correlation could competitively predict bubble point pressure when compared to the other published
correlations. On the other hand, the developed Bob ANN and Bob correlation could be satisfactorily
employed in the prediction of bubble point oil formation volume factor under an acceptable range of data.
Acknowledgements
I would like to thank University of Regina, Petroleum Technology Research Centre for research funding.
Also thanks to Petroleum and Petrochemical College and Petroleum and Petrochemical Research Unit
Center for Petroleum, Petrochemicals, and Advanced Materials, Chulalongkorn University, Thailand.
References
Abdul-Majeed G.H., Salman N.H., Scarth B.R., 1988, An empirical correlation for oil Fvf prediction, Journal
of Canadian Petroleum Technology, 27.
Al-Marhoun M.A., 1988, PVT Correlations for Middle East crude oils, SPE Journal of Petroleum
Technology, 40, 650-666.
Al-Marhoun M.A., 1992, New correlations for formation volume factors of oil and gas mixtures, Journal of
Canadian Petroleum Technology, 31.
Al-Shammasi A.A., 1999, Bubble Point pressure and oil formation volume factor correlations, Middle East
Oil Show and Conference. Bahrain: Copyright 1999, Society of Petroleum Engineers Inc.
Almehaideb R.A., 1997, Improved PVT Correlations for UAE Crude Oils, Middle East Oil Show and
Conference. Bahrain: 1997 Copyright 1997, Society of Petroleum Engineers, Inc.
Bello O.O., Reinicke K.M., Patil P.A., 2008, Comparison of the performance of empirical models used for
the prediction of the PVT properties of crude oils of the Niger Delta, Petroleum Science and
Technology, 26, 593-609.
Calhoun J.C.J., 1976, Fundamentals of reservoir engineering.
Cosentino L., 2001, Integrated Reservoir Studies, Editions Technip.
De Ghetto G., Villa M., 1994, Reliability analysis on PVT correlations, European Petroleum Conference.
London, United Kingdom: 1994 Copyright 1994, Society of Petroleum Engineers, Inc.
Dindoruk B., Christman P.G., 2004, PVT properties and viscosity correlations for Gulf of Mexico oils, SPE
Reservoir Evaluation & Engineering, 7, 427-437.
Dokla M.E., Osman M.E., 1991, Correlation of PVT properties for U.A.E. Crudes, Middle East Oil Show
and Conference. Bahrain: 1990.
Frashad F., Leblanc J.L., Garber J.D., Osorio J.G., 1996, Empirical PVT correlations for Colombian crude
oils.
Gharbi R.B., Elsharkawy A.M., 1997, Universal neural network based model for estimating the PVT
properties of crude oil systems, SPE Asia Pacific Oil and Gas Conference and Exhibition. Kuala
Lumpur, Malaysia: 1997 Copyright 1997, Society of Petroleum Engineers, Inc.
Gharbi R.B.C., Elsharkawy A.M., 1999, Neural network model for estimating the PVT properties of Middle
East crude oils, SPE Reservoir Evaluation & Engineering, 2, 255-265.
Glaso O., 1980, Generalized pressure-volume-temperature correlations, SPE Journal of Petroleum
Technology, 32, 785-795.
Hanafy H.H., Macary S.M., Elnady Y.M., Bayomi A.A., El Batanony M.H., 1997, A new approach for
predicting the crude oil properties, SPE Production Operations Symposium. Oklahoma City, Oklahoma:
1997.
Hemmati M.N., Kharrat R., 2007, A Correlation approach for prediction of crude-oil PVT properties, SPE
Middle East Oil and Gas Show and Conference. Bahrain: Society of Petroleum Engineers, Inc.
Kartoatmodjo T.R.S., Schmidt Z., 1991, New correlations for crude oil physical properties. Society of
Petroleum Engineers, Inc.
Mahmood M.A., Al-Marhoun M.A., 1996, Evaluation of empirically derived PVT properties for Pakistani
crude oils, Journal of Petroleum Science and Engineering, 16, 275-290.
Nikpoor M.H., Khanamiri H.H., 2011, New empirical correlations for predicting crude oil properties,
Petroleum Science and Technology, 29, 1649-1658.
Omar M.I., Todd A.C., 1993, Development of new modified black oil correlations for Malaysian crudes,
SPE Asia Pacific Oil and Gas Conference. Singapore: 1993 Copyright 1993, Society of Petroleum
Engineers, Inc.
Ostermann R.D., Owolabi O.O., 1983, Correlations for the reservoir fluid properties of Alaskan crudes,
SPE California Regional Meeting. Ventura, California: 1983 Copyright 1983 Society of Petroleum
Engineers of AIME.
Petrosky Jr. G.E., Farshad F.F., 1993, PVT correlations for Gulf of Mexico crude oils, SPE Annual
Technical Conference and Exhibition. Houston, Texas: 1993 Copyright 1993, Society of Petroleum
Engineers, Inc.
Standing M.B., 1947, A PVT correlation for mixtures of California oils and gases. American Petroleum
Institute.
Sutton R.P., Farshad F., 1990, Evaluation of empirically derived PVT properties for Gulf of Mexico crude
oils, SPE Reservoir Engineering, 5, 79-86.
Valkó P.P., Mccain Jr W.D., 2003, Reservoir oil bubblepoint pressures revisited; solution gas–oil ratios and
surface gas specific gravities, Journal of Petroleum Science and Engineering, 37, 153-169.
Vazquez M., Beggs H.D., 1980, Correlations for fluid physical property prediction, SPE Journal of
Petroleum Technology, 32, 968-970.
Velarde J., Blasingame T.A., W. D. Mccain J., 1997, Correlation of black oil properties at pressures below
bubble point pressure - A New approach, annual technical meeting. Calgary, Alberta: Petroleum
Society of Canada.
Wu R., Rosenegger L., 1999, Comparison of PVT properties from equation of state analysis and PVT
correlations for reservoir studies, Annual technical meeting. Calgary, Alberta: Petroleum Society of
Canada.