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Energy & Fuels 1999, 13, 454-458
Universal Neural-Network-Based Model for Estimating the PVT Properties of Crude Oil Systems Ridha B. Gharbi,*,† Adel M. Elsharkawy,† and Mansour Karkoub‡ Department of Petroleum Engineering and Department of Mechanical Engineering, College of Engineering & Petroleum, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait Received June 25, 1998
This study presents a universal neural-network-based model for the prediction of PVT properties of crude oil samples obtained from all over the world. The data, on which the network was trained, contains 5200 experimentally obtained PVT data sets of different crude oil and gas mixtures from all over the world. They were collected from major-producing oil fields in North and South America, the North Sea, Southeast Asia, the Middle East, and Africa. This represents the largest data set ever collected to be used in developing PVT models. An additional 234 PVT data sets were used to investigate the effectiveness of the neural-network models to predict outputs from inputs that were not used during the training process. The neural network model is able to predict the solution gas-oil ratio and the oil formation volume factor as a function of the bubble-point pressure, the gas relative density, the oil specific gravity, and the reservoir temperature. The neural-network models were developed using back-propagation with momentum for error minimization to obtain the most accurate PVT models. A detailed comparison between the results predicted by the neural-network models and those predicted by other correlations are presented for these crude oil samples. This study shows that artificial neural networks, once successfully trained, are excellent reliable predictive tools for estimating crude oil PVT properties better than available correlations. These neural-network PVT models can be easily incorporated into reservoir simulators and production optimization software.
Introduction Empirical correlations for predicting reservoir fluid properties have been used in evaluating newly discovered formations, studying fluid recoveries, designing production equipment and surface facilities, planning future production, and economics. In 1949, Katz1 introduced the first correlation to predict the oil-formation volume factor for midcontinent U.S. crudes. Since then, several correlations for the prediction of crude oil properties from various locations worldwide have been presented in the literature.2-21 †
Department of Petroleum Engineering. Department of Mechanical Engineering. (1) Katz, D. L. Prediction of the shrinkage of crude oils. API Drill. Prod. Prac. 1942, 137. (2) Standing, M. B. A pressure-volume-temperature correlation for mixtures of California oils and gases. API Drill. Prod. Prac. 1947, 275-87. (3) Borden, G.; Rzasa, M. J. Correlation of bottom hole sample data. Trans. AIME 1950, 189, 345-348. (4) Elam, F. M. Prediction of bubble-point pressure and formation volume factors from field data, M.Sc. Thesis, Texas A&M University, 1957. (5) Lasater, J. A. Bubble point pressure correlation. Trans. AIME 1958, 213, 379-81. (6) Knopp, C. R.; Ramsey, L. A. Correlation for oil Formation volume factor and solution gas-oil ratio. J. Pet. Technol. 1960, 27-29. (7) Standing, M. B. Oil-system correlations. In Petroleum Production Handbook; Frick, T. C., Ed.; SPE: Richardson, TX, 1962; Vol. 2, Chapter 19. (8) Cronquist, C. Dimensionless PVT behavior of gulf coast crude oils. J. Pet. Technol. 1973, 1-8. (9) Caixerio, E. Correlation of reservoir properties, Miranga field, Brazil. M.Sc. Report, Stanford University, 1976. (10) Standing, M. B. Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems; SPE: Richardson, TX, 1977; p 124. ‡
Ideally, the PVT properties such as bubble-point pressure, gas-oil ratio, and oil formation volume factor are measured on collected bottom-hole samples or recombined surface samples. In some occasions, experimentally measured PVT data are not available because adequate samples cannot be obtained or the production horizon does not warrant the expense of detailed reservoir fluid studies. In these cases, field-measured data such as reservoir pressure, temperature, crude oil API gravity, and gas specific gravity are used to estimate the PVT properties using these empirical (11) Vasquez, M. E.; Beggs, H. D. Correlations for fluid physical property prediction. J. Pet. Technol. 1980, 968-70. (12) Galsø, O. Generalized pressure-volume-temperature correlations. J. Pet. Technol. 1980, 785-95. (13) Obomanu, D. A.; Okpobiri, G. A. Correlating the PVT properties of Nigerian crudes. J. Energy Resour. Technol. 1987, 109, 214-217. (14) Al-Marhoun, M. A. PVT Correlations for Middle East Crude Oils. J. Pet. Technol. 1988, 650-66; Trans. AIME 1988, 285. (15) Abdul Majeed, G. H.; Salman, N. H. An empirical correlation for oil FVF prediction. J. Can. Pet. Technol. 1988, 27 (6) 118-122. (16) Labedi, R. Use of production data to estimate volume factor density and compressibility of reservoir fluids. J. Pet. Sci. Eng. 1990, 4, 357-90. (17) Farshad, F. F.; LeBlance, J. L.; Garbeer, J. O.; Osorio, J. G. Empirical PVT correlations for Colombian crudes; Unsolicited SPE paper, 1992; 24538. (18) Dokla, M. E.; Osman, M. E. Correlation of PVT properties for UAE crudes. SPE Form. Eval. 1992, 41-46. (19) Petrosky, G. E.; Farshad, F. F. Pressure volume temperature correlations for Gulf of Mexico crude oils. SPE 26644, October 3-6, 1993. (20) Kartoatmodjo, T.; Schmidt, Z. Large data bank improves crude oil Physical property correlations. Oil Gas J. 1994, 51-55. (21) Elsharkawy, A. M.; Alikhan, A. A. Correlations for Predicting Solution Gas-Oil Ratio, Oil Formation Volume Factor, and Undersaturated Oil Compressibility. J. Pet. Sci. Eng. 1997, 17, 291-302.
10.1021/ef980143v CCC: $18.00 © 1999 American Chemical Society Published on Web 02/02/1999
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correlations. Local PVT correlations for a particular field or region can also be used to check the accuracy of the PVT report for a given crude from the same field or region. The accuracy of the well-known empirical PVT correlations such as Standing,2,7,10 Vasquez and Beggs,11 and Glasø12 and the recently developed ones13-21 has been the subject of numerous studies.22-28 All of these studies have indicated that these correlations are not accurate enough to be generalized to predict crude oil properties from various locations. All the correlations mentioned above were developed using conventional regression methods, which may not give reliable results. Artificial neural networks, on the other hand, were shown to have excellent and reliable predictive capabilities. The objective of this paper is two-fold: (1) to develop a universal network model using a large collection of crude oil properties representing oils from different oil fields in the world to predict the PVT properties of various crude oil systems and (2) to compare the accuracy of the neural-network model to several published correlations. In recent years, the application of artificial neural networks to petroleum engineering problems has been the subject of much study.29-40 This new interest in this approach to modeling is due to the fact that neural (22) Abdus Sattar, A. A correlation technique for evaluating formation volume factor and gas solubility of crude oil in Rocky Mountain regions; Petroleum Engineering Department: Colorado School of Mines, 1959. (23) Ostermann, R. D.; Ehlig-Economides, C. A.; Owolabi, O. O. Correlations for the reservoir fluid properties of Alaskan crudes; SPE 11703, March 23-25, 1983. (24) Abdul Majeed, G. H. Evaluation of PVT correlations; Unsolicited SPE Paper 14478, 1985. (25) Saleh, A. M.; Mahgoub, I. S.; Assad, Y. Evaluation of empirically drived PVT properties for Egyptian crudes. SPE 15721, March 7-10, 1987. (26) Abdul Majeed, G. H. Statistical evaluation of PVT correlation solution gas-oil ratio. J. Can. Pet. Technol. 1988, 27 (4), 95-101. (27) Sutton, R. P.; Farshad, F. F. Evaluation of empirically derived PVT properties for Gulf of Mexico crude oils. SPE Res. Eng. 1990, 7986. (28) Elsharkawy, A. M.; Elgibly, A. A.; Alikhan, A. A. Assessment of the PVT correlations for predicting the properties of Kuwaiti crude oils. J. Pet. Sci. Eng. 1995, 13, 219-232. (29) Gharbi, R.; Karkoub, M.; Elkamel, A. An Artificial Neural Network for the Prediction of Immiscible Flood Performance. Energy Fuels 1995, 9, 894-900. (30) Gharbi, R.; Elsharkawy, A. M. Neural-Network Model for Estimating the PVT Properties of Middle East Crude Oils. In Situ 1996, 20, 4. (31) Gharbi, R. Estimating the isothermal compressibility coefficient of undersaturated Middle East Crudes Using Neural Networks. Energy Fuels 1997, 11, 372-378. (32) Mohaghegh, S.; Arefi, R.; Ameri, S. Design and Development of an Artificial Neural Network for the Prediction of Formation Permeability. Proc. SPE Pet. Comput. Conf., Dallas, TX, 1994. (33) Baldwin, J. L. Using a Simulated Bi-Directional Associative Neural Network Memory with Incomplete Prototype Memories to Identify Facies from Intermittent Logging Data Acquired in a Siliciclastic Depositional Sequence. A case Study. Proc. SPE Annu. Technol. Conf. Exhib. 1991, 273-286. (34) Garcia, G.; Whitman, W. W. Inversion of a Lateral Log Using Neural Networks. Proc. SPE Petr. Comput. Conf. 1992, 295-304. (35) Smith, M.; Carmichael, N.; Reid, I.; Bruce, C. Lithofacies Determination from Wire-Line Log Data Using a Distributed Neural Network. Proc. IEEE Workshop Neural Networks Signal Processing, Princeton, NJ, 1991; pp 482-292. (36) Juniardi, I. R.; Ershaghi, I. Complexities of Using Neural Network in Well Test Analysis of Faulted Reservoirs. Proceedings of the SPE Annual Western Regional Meeting, Anchorage, AK, 1993; pp 711-721. (37) Kumoluyi, A. O.; Daltaban, T. S. Higher-Order Neural Networks in Petroleum Engineering. Proceedings of the SPE Annual Western Regional Meeting, Long Beach, CA, 1994; pp 555-570. (38) Waller, M. D.; Rowsell, P. J. Intelligent Well Control. Trans. Inst. Min. Metall. 1994, 103, a47-a51.
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Figure 1. Multiple-layer neural-network model. Table 1. Range of PVT Data Used for Training bubble-point pressure, psia bubble-point formation volume factor, rb/stb solution gas-oil-ratio, scf/stb gas relative density (air ) 1) stock-tank oil gravity, oAPI reservoir temperature, oF
79-7130 1.02-2.92 9-3370 0.50-1.67 14.3-59 74-342
networks generally have large degrees of freedom, thus they can capture the nonlinearity of the process being studied better than regression techniques. In addition, neural networks have the ability to model systems with multiple inputs and multiple outputs. Since the theory of neural networks has been described in great detail in many recent publications, the main idea of the neural networks will only be described here. Artificial neural networks are composed of many elements called neurons. The neurons are arranged in layers as shown in Figure 1. Neural networks have one input layer, one output layer, and one or more hidden layers. A set of input and output variables are entered, and the neural network attempts to map (train) the process by which the input variables become the output variables. Neural networks are trained by adjusting the connection weights (wijk) by some suitable algorithm so that the difference between the predicted and the observed outputs is as small as possible. One common algorithm used for training is the back-propagation algorithm with momentum.41 This algorithm was used in this study. The output from one neuron is calculated by applying a transfer function to the weighted summation of its input to give an output, which in turn can serve as an input to other neurons. One commonly used transfer function is the sigmoidal function, which gives values that range from 0 to 1. Readers interested in the theory behind neural networks should consult ref 29. Developing the Neural-Network Model Input Data. The data on which the neural network was trained contains 5200 PVT data analysis. This (39) Habiballah, W. A.; Startzman, R. A.; Barrufet, M. A. Use of Neural Networks for the Prediction of Vapor-Liquid Equilibrium K Values. In Situ 1993, 17, 227-242. (40) Briones, M. F.; Rojas, G. A.; Moreno, J. A.; Hidaigo, O. Thermodynamic Characterization of Volatile Hydrocarbon Reservoirs by Neural Networks. Proceedings of the SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, 1994; pp 235-243. (41) Hertz, J.; Krogh, A.; Palmer, R. G. Introduction to the Theory of Neural Computation; Addison-Wesley Publishing: New York, 1991.
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Table 2. Connection Weights and Biases for the Retained Neural-Network Model j/i
1
2
1 2 3 4 5
-0.004373 -0.008733 -0.033895 0.000455 0.009606
-0.052962 0.097769 0.185221 -0.002072 -0.102837
1 2
0.484744 -0.539092
-2.102122 0.232258
wij 3
4
Input Layer -0.008207 6.888934 3.17277 -0.005059 -7.067945
-0.000788 0.000182 0.003661 0.000278 -0.001301
Output Layer 0.082344 0.005046
represents 350 different crudes collected from all over the world. This data was enough to develop an accurate model for the prediction of PVT properties. Each of these PVT data points contains the bubble-point pressure Pb, the solution gas-oil ratio Rs, the gas specific gravity γg, the oil API gravity oAPI, the reservoir temperature T, and the oil formation volume factor Bob. The range of data used to train the neural network is listed in Table 1. The bubble-point pressure and the oil formation volume factor were considered to be the output variables, whereas the other four variables (T, oAPI, γg, Rs) were considered to be the input variables. To eliminate the unstability of the neural network during the training process, the normalized bubble-point pressure and the oil formation volume factor were used.41 Each normalized output variable is calculated by subtracting the minimum value from each data point and then dividing the result by the difference between the maximum and the minimum of the output variable. This operation yields a normalized output variable with a domain of variation that ranges from 0 to 1. To obtain the most accurate model for predicting Pb and Bob as a function of the other four variables, several neural-network architectures were investigated. A single neural-network design with one-hidden layer and twohidden layer architectures were considered in this study. The number of neurons in each hidden layer was systematically varied. At the end of each successful training, the model is tested to ensure that oscillation or “overfitting” does not occur42 and also to make sure that it can predict outputs from inputs that were not seen by the model during its training phase. These two conditions must be both satisfied in order for the model to be accurate and can be generalized. Only the onehidden layer network with five neurons met these two conditions, and consequently, it was chosen to predict the bubble-point pressure and the oil formation volume factor for crude oil systems. The corresponding connection weights and biases of the retained neural-network model for the estimation of Pb and Bob are shown in Table 2. The top portion of Table 2 shows the inputlayer connections, which are the connection weights from each input node to each of the five nodes in the hidden layer. The bottom part of Table 2 shows the output-layer connections, which are the connection weights from the five hidden nodes to the two output nodes which correspond to the dependent variables Pb and Bob. (42) Sjo¨berg, J.; Ljung, L. Overfitting, Regularization, and Searching for Minimum in Neural Networks. Proceedings of the Fourth IFAC International Symposium on Adaptive Systems in Control Signal and Processing, Grenoble, France, 1992; pp 663-674. (43) Garson, G. D. Interpreting Neural-Network Connection Weights. AI Expert, 1991; pp 47-51.
bias bj
5
5.105344 -5.411592 -4.80704 0.215902 5.601545 -2.014758 0.188104
4.525415 3.078434
-0.889433 -1.394353
Table 3. Relative Importance of Input Variables on the Output Variables for the Retained Neural-Network Model input variables API γg
output variables
T
Pb Bob
13.92% 14.27%
20.27% 17.34%
22.74% 5.74%
Rs 43.07% 62.59%
Interpreting the Connection Weights. Connection weights in neural networks are usually presented as numbers, and their interpretation is seldomly done. The reason is that neural networks are taught through a long complicated process which requires a large amount of computation, thus making the interpretation of the weights very difficult. Therefore, the importance of each input variable on the output cannot be described. One of the methods that has been used to assess the relative importance of each input variable on the output variable has been described by Garson43 and later used by Gharbi.31 In this method, all the weights, except the bias, are used to partition the sum of effects on the output layer. The following equation is used to perform this computation for a one hidden-layer network with N1 hidden nodes N1
∑j
( ) ( ) |wij1|
Im
aj1
∑k |wij1|
Im N1
∑i ∑j
|wij1|
Im
100%
(1)
aj1
∑k |wij1|
where aj1 is the connection weight of the output node for hidden node j. Application of eq 1 to a set of connection weights yields the percent factor of the input variable on the output variable. For further information on the application of this equation, refer to Gharbi.31 Table 3 lists the relative importance of each of the four input variables (T, oAPI, γg, Rs) for the retained PVT neural-network model. As shown, the solution gasoil ratio is the most important input for both the bubblepoint pressure and the oil formation volume factor (43.07% for Pb and 62.59% for Bob). The gas gravity is of great importance to the bubble-point pressure (22.74%); however, it is the least important input parameter for the oil formation volume factor (5.74%). It should be noted that the least-accurate measured parameter in
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Energy & Fuels, Vol. 13, No. 2, 1999 457
Table 4. Statistical Parameters for Pb Calculations (Data Used in the Training Process) method
Er (%)
Ea (%)
Emax (%)
Sx (%)
neural network -0.02 15.38 45.76 19.14 standing 18.81 25.20 369.23 36.48 Vasquez and Beggs 29.99 32.98 418.80 45.42 Glasø 30.96 34.23 356.00 44.91 Al-Marhoun 45.30 49.61 666.07 69.44 Dokla and Osman 30.88 39.82 681.00 59.24 Labedi 22.59 27.82 411.11 40.72 Farshad 11.48 22.73 298.00 30.77 Kartaotmodjo 22.78 28.17 339.00 39.19
correlation coefficient % 96.00 92.22 86.40 85.65 68.58 83.74 92.45 93.11 85.33
Table 5. Statistical Parameters for Bob Calculations (Data Used in the Training Process) method
Er (%)
Ea (%)
Emax (%)
Sx (%)
correlation coefficient %
neural network standing Vasquez and Beggs Glasø Al-Marhoun Dokla and Osman Labedi Farshad Kartaotmodjo Petrosky Abdelmajeed Elsharkawy Obomano
1.39 -1.32 -2.67 -3.93 -1.60 -1.76 -1.68 -1.95 -1.35 -1.52 -0.73 1.21 1.18
2.04 2.47 3.51 4.32 2.35 3.21 2.62 2.38 2.10 2.52 2.53 3.40 2.49
6.86 21.85 18.40 17.67 15.24 20.26 18.14 13.27 11.24 24.77 43.17 19.43 26.63
2.52 3.42 4.74 5.11 3.23 4.02 3.60 3.13 2.79 3.35 3.65 4.53 3.59
98.89 97.38 94.48 94.72 97.36 97.17 97.06 97.89 98.24 97.55 95.43 95.85 97.28
Figure 2. Comparison of the estimated vs experimental bubble-point pressure (data used for testing: neural network).
Table 6. Range of PVT Data Used for Testing bubble-point pressure, psia bubble-point formation volume factor, rb/stb solution gas-oil-ratio, scf/stb gas relative density (air ) 1) stock-tank oil gravity, oAPI reservoir temperature, oF
200-5980 1.05-2.31 52-1860 0.56-1.23 21.9-48.5 112-293
PVT analysis is the gas specific gravity. This explains why most PVT correlations predict the oil formation volume factor more accurately than the bubble-point pressure. The API gravity was of substantial importance for both output variables (20.27% for Pb and 17.34% for Bob). On the other hand, the reservoir temperature was of substantial but somewhat lesser importance (13.92% for Pb and 14.27% for Bob). Comparison of the Neural-Network Model with Other Correlations. A comparison between the results predicted by the neural-network model and those predicted by several published correlations is performed for these crude oil samples. The statistical results of this comparison are shown in Tables 4 and 5 for both Pb and Bob, respectively. As shown, the neural-network model shows very high accuracy as compared to any other correlations. The neural-network model achieved the lowest relative errors, standard deviation, and highest correlation coefficient for both Pb and Bob. The artificial neural-network model for predicting Pb achieved a correlation coefficient of 96%, whereas for Bob, the correlation coefficient was 98.89%. The correlation coefficient for the prediction of Pb obtained from the other PVT correlations ranges from 68.58% for Al-Marhoun’s to 93.11% for Farshad’s correlation. For the oil formation volume factor (Bob), the value ranges from 94.72% for Glasø’s to 98.24% for Kartoatmodjo’s correlation. As shown for all correlations, the accuracy for the prediction of Bob was better than that of Pb.
Figure 3. Comparison of the estimated vs experimental bubble-point oil formation volume factor (data used for testing: neural network). Table 7. Statistical Parameters for Pb Calculations (Data Used for Testing) method
Er (%)
Ea (%)
Emax (%)
Sx (%)
neural network -2.13 6.48 19.93 7.81 standing 14.39 16.69 101.90 24.26 Vasquez and Beggs 15.78 16.44 84.97 22.35 Glasø 23.72 23.75 83.45 29.15 Al-Marhoun 55.04 56.93 285.77 70.66 Dokla and Osman 12.48 23.44 157.85 34.62 Labedi 16.58 19.20 125.95 28.15 Farshad -1.44 14.86 69.92 18.65 Kartaotmodjo 3.08 10.96 56.87 15.21
correlation coefficient % 98.91 96.52 95.12 92.32 50.69 91.36 96.43 93.87 95.48
The neural-network model was then subjected to data points not seen during the training process. If the neural network was successfully trained, then its prediction performance would be accurate. To test the prediction performance, an additional 234 measured PVT data points were used. The range of the data used for testing is shown in Table 6. As shown, all of the data used for testing fall in the range of the data used in the training phase of the model. Figures 2 and 3 show the scatter diagrams (cross plots) that compare the experimental Pb and Bob versus the neural-network-computed Pb and Bob, respectively. As shown, a tight cloud of points about the 45° line was
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Table 8. Statistical Parameters for Bob Calculations (Data Used for Testing) method
Er (%)
Ea (%)
Emax (%)
Sx (%)
correlation coefficient %
neural network standing Vasquez and Beggs Glasø Al-Marhoun Dokla and Osman Labedi Farshad Kartaotmodjo Petrosky Abdelmajeed Elsharkawy Obomano
1.53 -0.96 -1.16 -3.92 -0.78 0.38 -1.38 -1.64 -0.41 -1.84 0.30 4.23 2.18
1.97 2.52 3.13 4.78 2.23 2.43 2.67 2.20 1.86 3.11 2.59 5.43 2.89
6.41 21.84 14.89 17.57 10.44 17.47 18.12 8.59 7.79 18.17 16.06 16.03 26.53
2.43 3.99 4.64 5.58 3.33 3.42 4.03 3.00 2.64 4.03 3.38 6.48 4.68
98.75 95.81 93.21 92.49 96.49 97.37 95.52 97.62 97.94 96.12 96.39 91.25 94.79
obtained for these additional data points. This indicates an excellent agreement between the experimental and the calculated data. The statistical parameters for the prediction capability obtained from the neural-network and the PVT correlations are shown in Tables 7 and 8. As shown, the overall performance of the neural network for predicting both Pb and Bob is better than that of any correlations. The correlation coefficient achieved by the neural-network model for predicting Pb was 98.91%, whereas for Bob, the correlation coefficient was 98.75%, with an average absolute relative error of 6.48% for Pb and 1.97% for Bob. The other PVT correlations showed a correlation coefficient for Pb that ranges from 50.69% for Al-Marhoun’s to 96.52% for Standing’s correlation. For Bob, this value ranges from 91.25% for Elsharkawy’s to 97.94% for Kartoatmodjo’s correlation. Conclusions A universal neural-network-based model is presented for the prediction of the bubble-point pressure (Pb) and
the oil formation volume factor (Bob) of crude oil systems from the all over the world. The neural-network model was shown to be more accurate than existing PVT correlations, which were developed using conventional regression techniques. The model predicts Pb and Bob as a function of the solution gas-oil ratio (Rs), the gas specific gravity (γg), the oil specific gravity (γo), and the reservoir temperature (T). The neural-network model was trained using 5200 PVT data sets representing 500 different crudes from the all over the world. This represents the largest data set ever collected to be used to train a neural-network model to estimate Pb and Bob. The model successfully predicted outputs from inputs that were not used during the training process. The most successful neural-network architecture contains one-hidden layer with five neurons. Nomenclature ai ) element i of output vector ajk ) output of neuron j in layer k bjk ) bias for neuron j in layer k Bob ) bubble point oil formation volume factor Ea ) average absolute relative error Emax ) maximum absolute relative error Im ) element m of input vector Nk ) number of neurons in layer k Pb ) bubble-point pressure Rs ) solution gas-oil-ratio Sx ) standard deviation T ) reservoir temperature wijk ) weight for input i, neuron j, and layer k oAPI ) oil API gravity γg ) gas specific gravity EF980143V
