Proceedings of ICEE 2009 3rd International Conference on Energy and Environment, 7-8 December 2009, Malacca, Malaysia

978-1-4244-5145-6/09/$26.00 ©2009 IEEE 1

Prediction of PVT Properties In Crude Oil Systems Using Support Vector Machines

Jawad Nagi, Tiong Sieh Kiong, Syed Khaleel Ahmed Department of Electronics and Communication Engineering

Universiti Tenaga Nasional KM 7, Jalan Kajang-Puchong, 43009 Kajang, Malaysia

{jawad, siehkiong, syedkhaeel}@uniten.edu.my

Farrukh Nagi Department of Mechanical Engineering

Universiti Tenaga Nasional KM 7, Jalan Kajang-Puchong, 43009 Kajang, Malaysia

farrukh@uniten.edu.my

Abstract— Calculation of reserves in an oil reservoir and the determination of its performance and economics require good knowledge of its physical properties. Accurate determination of the pressure–volume–temperature (PVT) properties such as the bubble point pressure (Pb) and the oil formation volume factor (Bob

Keywords- Support vector machine; support vector regression; PVT properties; bubble point pressue; oil formation volume factor.

) are important in the primary and subsequent development of an oil field. This paper proposes Support Vector Machines (SVMs) as a novel machine learning technique for predicting outputs in uncertain situations using the ε-Support Vector Regression (ε-SVR) method. The objective of this research is to investigate the capability of SVRs in modeling PVT properties of crude oil systems and solving existing Artificial Neural Network (ANN) drawbacks. Three datasets used for training and testing the SVR prediction model were collected from distinct published sources. The ε-SVR model incorporates four input features from the datasets: (1) solution gas-oil ratio, (2) reservoir temperature, (3) oil gravity and, (4) gas relative density. A comparative study is carried out to compare ε-SVR performance with ANNs, nonlinear regression, and different empirical correlation techniques. The results obtained reveal that the ε-SVR once successfully trained and optimized is more accurate, reliable, and outperforms the other existing approaches such as empirical correlation for estimating crude oil PVT properties.

I. INTRODUCTION Reservoir fluid properties are very important in reservoir

engineering computations such as material balance calculations, well test analysis, reserve estimates, and reservoir simulations [1]. Knowledge of the pressure–volume–temperature (PVT) properties is a requirement for all types of petroleum calculations such as determination of hydrocarbon flowing properties, design of fluid handling equipment, and reservoir volumetric estimates. For the development of a correlation, the geological condition is considered important because the chemical composition of crude oil differs from region to region [3]. Among the PVT properties is the bubble point pressure (Pb) and oil formation volume factor (Bob), which is defined as the volume of reservoir oil that would be occupied by one stock tank barrel oil plus any dissolved gas at the bubble point pressure and reservoir temperature [4]. Since it is crucial that all calculations in reservoir performance,

production operations and design, and formation evaluation be as good as the PVT properties, therefore precise prediction of Pb and Bob

There are many empirical correlations for predicting different PVT properties such as the equation of state (EOS), linear or non-linear multiply regression or graphical techniques [4]. Many correlations already exist in the oil and gas industry such as the: Standing [5], Glaso [6], Beggs and Vasquez [7] correlations etc. Many researchers have investigated that artificial neural networks (ANNs) are able to solve the PVT correlation problems in the petroleum industry [8]. Therefore, in recent years researchers have utilized ANNs to predict more accurate PVT correlations [4]. However, ANN developed correlations do not perform accurately and suffer from a number of drawbacks. They have some limitations as they were originally developed for a certain range of reservoir fluid characteristics and geographical area with similar fluid compositions and API oil gravity [3].

properties is necessary.

The objective of this study is to investigate the capability of support vector machines (SVMs), i.e. the ε-Support Vector Regression (ε-SVR) method in modeling PVT properties of crude oil systems and to overcome the limitations and drawbacks of ANNs. The ε-SVR is an intelligence paradigm which is based on the statistical learning theory and the structural risk minimization (SRM) principle. In this research study, the capability of ε-SVR in modeling both Pb and Bob

II. LITERATURE SURVEY

is investigated, using worldwide published experimental PVT databases. Comparative studies are also carried out to compare the performance of the proposed ε-SVR model with the ANNs, nonlinear regression, and different empirical correlation techniques.

In the oil and gas industry PVT properties such as, permeability and porosity, liquid-holdup flow regimes, lithofacies types etc are very important properties in reservoir engineering computations. Predicting these properties in the laboratories is very expensive and the accuracy of such predictions is critical and not often known in advance. This section briefly summarizes the most common empirical PVT correlations and different computational intelligence schemes published for predicting PVT properties in the recent years.

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A. Common Empirical Correlation Methods In the last six decades, researchers and engineers have

realized the importance of developing and using empirical correlations for PVT properties [1]. Many studies have been carried out in this field to develop new correlations. Standing [5] and [9] presented correlations for the bubble point pressure (Pb) and the oil formation volume factor (Bob). Standing’s correlations were based on laboratory experiments carried out on 105 samples from 22 different crude oils in California. Katz [10] presented five methods for predicting reservoir oil shrinkage. Vazquez and Beggs [7] presented correlations for Bob by dividing oil mixtures into two groups, above and below 30° API gravity. Glaso [6] developed correlation for Bob using 45 oil samples from North Sea hydrocarbon mixtures. Al-Marhoun [11] published correlations for estimating Pb and Bob for the Middle East oils. He used 160 datasets from 69 Middle Eastern reservoirs to develop the correlation. Abdul-Majeed and Salman [12] published a Bob

B. Predicting PVT Properties Using ANNs

correlation based on 420 datasets. A detailed literature of PVT correlation models and schemes proposed by researchers and engineers over the last six decades can be reviewed from Osman et al. [1] and Al-Marhoun et al. [4]. This research only concentrates on the most common three empirical correlations, namely: Al-Marhoun et al. [13], Glazo [6], and Standing [5] for the purpose of a comparative study.

In recent years, Artificial Neural Networks (ANNs) have gained much popularity in petroleum engineering applications. Few studies have been carried out for predicting PVT properties using feed-forward ANNs such as: Al-Shammasi [14], Elsharkawy [16], Gharbi [2] and [17], Kumoluyi [18], McCain et al. [19], Osman et al. [1] and Varotsis et al. [20]. In [14] Al-Shammasi presented neural network models and compared their performance to numerical correlations. He used a two hidden layer neural network (4-5-3-1) structure for predicting both Pb and Bob

Gharbi and Elsharkawy [17] and Osman et al. [1] conducted comparative studies to determine the performance between feed-forward ANNs and four empirical correlations, Standing [5], Al-Marhoun et al. [13], Glaso [6], and Vasquez and Beggs [7] correlation. In 1997, Gharbi et al. [2], [17] published ANN models for estimating P

properties. He concluded that the statistical and trend performance analysis showed some of the correlations violate the physical behavior of hydrocarbon fluid properties [4].

b and Bob for Middle Eastern crude oils based on a neural system with a sigmoid activation function. Gharbi et al. [2] developed a universal ANN model for predicting PVT properties for any oil reservoir. In [17] Gharbi and Elsharkawy trained two ANNs separately to estimate Pb and Bob

III. IMPLEMENTATION

. The input data consisted of the solution gas-oil ratio, reservoir temperature, oil gravity, and gas relative density. They used a two hidden layers neural network [1]. Results obtained from their comparative studies indicated that the feed-forward ANNs outperformed conventional empirical correlation schemes for predicting PVT properties. A detailed literature of PVT correlation models using ANN schemes proposed by researchers in the past two decades can be reviewed from Osman et al. [1] and Al-Marhoun et al. [4].

The prediction model developed in this paper is implemented using datasets from authors who have published work in this research area [1], [4], [11], [22–24]. Prediction of the Pb and Bob

A. Data Acquisiton

uses the ε-Support Vector Regression (ε-SVR) method in SVMs. The ε-SVR model is trained and optimized using cross-validation (CV) and is tested using these datasets.

Datasets used to implement the ε-SVR prediction model were collected from three distinct published sources. Properties of the three datasets acquired are explained below:

1. The first dataset was retrieved from work conducted by Al-Marhoun [11]. This dataset consists of 160 observations collected from 69 Middle Eastern reservoirs, which published correlations for estimating Pb and Bob

2. The second dataset was obtained from work conducted by Al-Marhoun [4] and Osman et al. [22] and [23]. This dataset consists of 283 observations collected from different Saudi oil fields to predict the P

for Middle Eastern oils.

b and Bob at the Pb

3. The third dataset was retrieved from the work conducted by Goda et al. [24] and Osman et al. [1]. This dataset contains 782 observations. This dataset was collected from the oil fields of Malaysia, Middle East, Gulf of Mexico and Columbia.

for Saudi crude oils.

B. SVR Model Development For development of the prediction model, LIBSVM v2.86

[25], a library for support vector machines is used in MATLAB R2009a. LIBSVM is used as the core of the SVM to accurately predict Pb and Bob values using a ε-SVR model. Four features from the three datasets were selected to build ε-SVR model for predicting the Pb and Bob

In order for the all features to fit the ε-SVR model properly, all data points from the four features were linearly scaled (normalized) in the range from 0 to 1. To evaluate the performance of the ε-SVR model, the datasets were divided using a stratified criterion such that 70% of the data was used for training the ε-SVR and the remaining 30% of the data was used for testing and validation. Therefore, of the 782 data points: 382 were used to train the ε-SVR, 200 were used to cross-validate (CV) the relationships established during the training process, and the remaining 200 were used to test ε-SVR model for evaluation of its accuracy and trend stability. The internal and external validation processes were repeated 1000 times for 10-fold CV trials.

. The four input features are: (1) solution gas-oil ratio, (2) reservoir temperature, (3) oil gravity, and (4) gas relative density.

The radial basis function (RBF) kernel is used for training the ε-SVR. Model optimization was performed by optimizing the three important ε-SVR hyper-parameters: (1) Cost of error, “C” (2) Width of the ε-tube “ε” and the, (3) RBF kernel parameter, “γ”. Experimentally though 1000 iterative trials the best 10-fold CV accuracy was achieved by selecting ε = 0.56.

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Optimal ε-SVR hyper-parameters (C, γ) were selected using the SVM “Grid-Search” method [26], by using exponentially growing sequences of parameters (C, γ) and iterating them for all possible combinations to determine the optimal ε-SVR hyper-parameter set. The optimal ε-SVR hyper-parameters (C, γ) were found to be (1, 0.89) respectively. The 10-fold CV method utilized in this study is used as a checking mechanism to prevent both over fitting and complexity criterion based on the root mean square error (RMSE).

C. Quality Control and Dataset Domain A statistical summary of the investigated quality measures

corresponding to proposed ε-SVR modeling scheme, ANNs and the three common empirical correlations (Standing [5], Al-Marhoun et al. [13] and Glaso [6]) using the three distinct datasets were found. The following are the most common domains for the variables that are used in both the input and output layers of the modeling schemes for PVT analysis:

1. Input variables: a. Solution gas-oil ratio range: 26 and 1602, scf/stb. b. Reservoir temperature range: 74° F to 240° F. c. Oil gravity (API) range: 19.4 and 44.6. d. Gas relative density: 0.744 to 1.367.

2. Output variables: a. Oil formation volume factor: 1.032 to 1.997 bbl/stb. b. Bubble point pressure: 130 to 3573 psia.

D. Statistical Quality Measures To compare the performance of the proposed ε-SVR model

to other schemes such as ANNs and empirical correlations, seven quality measures based on statistical error analysis were computed. The statistical parameters calculated were: average percent relative error (Er), average absolute percent relative error (Ea), minimum absolute percent error (Emin), maximum absolute percent error (Emax), root mean square errors (Erms), standard deviation (σ), and the correlation coefficient (r). Detailed information corresponding to the equations of these statistical parameters can be found in Osman et al. [1]. The best model in terms of the Pb and Bob

IV. EXPERIMENTAL RESULTS

prediction accuracy is the model with the highest correlation coefficient (r) and the smallest RMSEs.

Comparative studies were conducted to compare the performance of the proposed ε-SVR model with ANNs and the three common empirical correlations (Standing [5], Al-Marhoun et al. [13] and Glaso [6]) for all three distinct datasets. Graph plots of the average absolute percent relative error (Ea) versus the correlation coefficients (r) for all modeling schemes are shown in Figure 1 and Figure 2 for Bob and Pb respectively. Figure 1 and Figure 2 are based on the dataset used by Osman et al. [1]. It is observed that the SVR scheme for both the bubble point pressure (Pb) and oil formation volume factor (Bob) prediction has the lowest error and highest correlation coefficient, while the ANN and all other schemes fall below the SVR.

Figure 1. Average absolute percent relative error (Ea) versus correlation coefficients (r) for all modeling schemes for predicting Bob

Figure 2. Average absolute percent relative error (Ea) versus correlation coefficients (r) for all modeling schemes for predicting P

The comparative prediction results of both the P

b

b and Bob

V. CONCLUSION

for all modeling schemes (SVR, ANN and empirical correlations) using all three distinct datasets, are summarized in Tables I through VI respectively.

In this study, three distinct published datasets were used to investigate the capability of SVR in modeling a new framework for predicting PVT properties of oil crude systems. The ε-SVR, a novel machine learning technique was used predict both the bubble point pressure (Pb) and oil formation volume factor (Bob) using four input variables: (1) solution gas-oil ratio, (2) reservoir temperature, (3) oil gravity, and (4) gas relative density. The prediction results obtained revealed that the developed ε-SVR modeling scheme outperforms both ANNs and the three most common empirical correlations.

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TABLE I. MODEL TESTING RESULTS (USING EL-SEBAKHY ET AL. [15] AND OSMAN ET AL. [1] DATASET) FOR PREDICTING B

Correlation

OB

E Er Ea Emin r max Standing (1947) [5] -0.170 2.724 0.008 20.180 0.974 Glaso (1980) [6] 1.8186 3.374 0.003 17.776 0.972 Al-Marhoun (1992) [13] -0.115 2.205 0.003 13.179 0.981 ANN System 0.3024 1.789 0.008 11.775 0.980 SVR System 0.18 1.37 0.002 7.751 0.984

TABLE II. MODEL TESTING RESULTS (USING EL-SEBAKHY ET AL. [15] AND OSMAN ET AL. [1] DATASET) FOR PREDICTING P

Correlation

B

E Er Ea Emin r max Standing (1947) [5] 67.60 67.73 0.1620 102.08 0.867 Glaso (1980) [6] -1.616 18.52 0.1056 138.96 0.945 Al-Marhoun (1992) [13] 8.008 20.01 0.0254 109.12 0.906 ANN System 8.129 21.02 0.0182 145.29 0.943 SVR System 7.547 15.12 0.009 104.73 0.963

TABLE III. MODEL TESTING RESULTS (USING AL-MARHOUN [4] AND OSMAN [22] DATASET) FOR PREDICTING B

Correlation

OB

E Er Ea Emin σ max r Standing (1947) [5] -1.054 1.6833 0.066 7.7997 2.1021 0.9947 Glaso (1980) [6] 0.4538 1.7865 0.0062 7.3839 2.1662 0.9920 Al-Marhoun (1992) [13] -0.392 0.8451 0.0003 3.5546 1.1029 0.9972 ANN System 0.217 0.5116 0.0061 2.6001 0.6626 0.9977 SVR System 0.006 0.353 0.0013 2.5835 0.4743 0.997

TABLE IV. MODEL TESTING RESULTS (USING AL-MARHOUN [4] AND OSMAN [22] DATASET) FOR PREDICTING P

Correlation

B

E Er Ea Emin σ max r Standing (1947) [5] -8.441 10.4562 0.2733 47.0213 11.841 0.8974 Glaso (1980) [6] -18.48 20.7569 2.0345 63.7634 16.160 0.9837 Al-Marhoun (1992) [13] 0.941 8.1028 0.0935 38.085 11.41 0.9905 ANN System -0.222 5.8915 0.2037 38.1225 8.678 0.9930 SVR System -0.326 3.260 0.0016 25.447 4.978 0.995

TABLE V. MODEL TESTING RESULTS (USING GODA ET AL. [24] AND OSMAN ET AL. [1] DATASET) FOR PREDICTING B

Correlation

OB

E Er Ea Emin r max Standing (1947) [5] -2.628 2.7202 0.0167 13.2922 0.9953 Glaso (1980) [6] -0.5529 0.9821 0.0086 6.5123 0.9959 Al-Marhoun (1992) [13] -0.4514 2.0084 0.0322 11.0755 0.9935 ANN System 0.3251 1.4592 0.0083 5.3495 0.9968 SVR System 0.065 0.386 0.007 2.502 0.9971

TABLE VI. MODEL TESTING RESULTS (USING GODA ET AL. [24] AND OSMAN ET AL. [1] DATASET) FOR PREDICTING P

Correlation

B

E Er Ea Emin r max Standing (1947) [5] 12.811 24.684 0.62334 59.038 0.8657 Glaso (1980) [6] -18.887 26.551 0.28067 98.78 0.9675 Al-Marhoun (1992) [13] 5.1023 8.9416 0.13115 87.989 0.9701 ANN System 4.9205 6.7495 0.16115 65.3839 0.9765 SVR System 3.426 4.0757 0.128 53.219 0.9808

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Thus, the proposed ε-SVR prediction model has a far better, efficient, and reliable performance compared to ANNs and empirical correlations. In addition, the proposed scheme shows higher prediction accuracy for Bob

Hence, the proposed prediction model is flexible and shows a bright future for implementation in the oil and gas industry. SVR models similar to this can be easily incorporated into reservoir simulators and production optimization software. Future work using this ε-SVR framework can be achieved by modeling other oil and gas industry problems such as: permeability and porosity prediction, identifying liquid-holdup flow regimes, fracture corridor, identifying lithofacies types, seismic pattern recognition, estimating pressure drops in the pipes and wells, optimizing well production, and other reservoir characteristics.

by achieving the lowest error metrics and the highest correlation coefficient among other techniques.

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