Kerman, Kerman, Iran Published online: 01 Jul 2014.

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1 This article was downloaded by: [ ] On: 11 July 2014, At: 12:18 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Petroleum Science and Technology Publication details, including instructions for authors and subscription information: Prediction of Oil Recovery Factor in CO 2 Injection Process M. Mohammadi a, M. Kouhi a & A. Mohebbi a a Department of Chemical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran Published online: 01 Jul To cite this article: M. Mohammadi, M. Kouhi & A. Mohebbi (2014) Prediction of Oil Recovery Factor in CO 2 Injection Process, Petroleum Science and Technology, 32:17, , DOI: / To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at

2 Petroleum Science and Technology, 32: , 2014 Copyright C Taylor & Francis Group, LLC ISSN: print / online DOI: / Prediction of Oil Recovery Factor in CO 2 Injection Process M. Mohammadi, 1 M. Kouhi, 1 and A. Mohebbi 1 1 Department of Chemical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran In this study, prediction of recovery factor (RF) for CO 2 injection into oil reservoirs based on artificial neural networks (ANNs) and mathematical models were investigated. To design the optimum ANN model, number of neurons, hidden layers, and training function were studied. Finally, efficiency of the models was evaluated using new data. As a result of this work, it can be concluded that it is possible to predict RF in CO 2 injection process by ANN and mathematical model. However, values that obtained from ANN were in the best agreement with the actual values than regression model. The proposed artificial neural network predicted RF during CO 2 injection with error about 0.396%. Keywords: artificial neural network, CO 2 injection, enhanced oil recovery, flooding, recovery factor 1. INTRODUCTION Recovery prediction under the predominant reservoir mechanism(s) is one of the important functions of the reservoir engineer. Calculation of recovery factor (RF) and production rate is useful for determination of company financial grade and it is important in petroleum products sailing. Although it is usually possible to determine a reasonably accurate RF, this number will be unrealistic for problem of fluid migration in the reservoir or a particular lease or portion of a reservoir (Craft and Hawkins, 1991). Several researchers tried to find a relationship between the widely available parameters in reservoir with oil recovery (Linker et al., 1997; Huang et al., 2003; Zhou et al., 2011; Melzer. 2012), for example; in a statistical study of Craze and Buckley s (1945) water drive recovery data, Guthrie and Greenberger (1955), using multiple correlation analysis methods, found the following correlation between water-drive recovery and five variables that affect recovery in sandstone reservoirs (Craft and Hawkins, 1991): RF = log k S w log μ O 1.538ϕ h (1) Where, k is permeability (md), S w is water saturation fraction, is oil viscosity (cp), and h is reservoir thickness (ft). Nonlinear regression is one of the methods for reaching the oil recovery indirectly. However, due to high reservoir heterogeneity these equations in the most of the conditions are not reliable. For this aim, using a method which is able to predict the oil recovery in different heterogeneity conditions of reservoir is necessary. Moreover, a comprehensive study requires hundreds Address correspondence to M. Kouhi, Department of Chemical Engineering, Shahid Bahonar University of Kerman, P.O. Box , Kerman, Iran. masoume.kouhi@gmail.com Color versions of one or more of the figures in the article can be found online at

3 2094 M. MOHAMMADI ET AL. FIGURE 1 The schematic of used feed-forward MLPNN for prediction of RF. of simulation runs; therefore, use of ANN model as an optimizing tool that capable of representing and quantifying the complex phenomena, can reduced the number of these runs. In the recent years, the applications of artificial intelligent methods due to their intrinsic abilities to capture the nonlinearity and complex heterogeneity in reservoir have been widespread and can finds several applications such data mining, Prediction, risk assessment, uncertainty quantification TABLE 1 Constants of Linear Regression Constant Value Constant Value a i b j c k d l e m f n g o h 0.935

4 PREDICTION OF OIL RECOVERY FACTOR IN CO 2 INJECTION PROCESS 2095 FIGURE 2 Determination of optimal neurons for the (a) first hidden layer and (b) second hidden layers based on minimum training error by the trial and error procedure. and data integration (Sahimi, 2000; Nikravesh, 2004; Lashkarbolooki et al., 2011; Tahmasebi and Hezarkhani, 2010; Karimpouli et al., 2010). Artificial intelligent methods (e.g. ANN, fuzzy logic [FL], genetic algorithm [GA]), or more specifically, artificial neural network (ANN) methods due to flexibility and ability to solve the nonlinear problems, have become increasingly popular in predicting some affecting parameters on enhanced oil recovery (EOR) such as CO 2 minimum miscibility pressure (Huang et al., 2003; Emera and Sarma, 2005; Mousavi et al., 2008; Nezhad et al., 2011) and permeability (Saemi et al., 2007; Karimpouli et al., 2010; Tahmasebi and Hezarkhani, 2012) but there are not extensive related studies about the application of ANN in evaluation of recovery factor of the EOR processes (e.g. gas injection [Shahsavand et al., 2011], water flooding [Sipöcz et al., 2011]). Therefore, in this study ANNs were used to predict the oil recovery factor in a CO 2 injection process. The results were compared with a regression model.

5 2096 M. MOHAMMADI ET AL. FIGURE 3 testing data. Comparison of the network response (predicted RF) with actual values, for (a) validating data and (b)

6 PREDICTION OF OIL RECOVERY FACTOR IN CO 2 INJECTION PROCESS 2097 FIGURE 4 Error values for training, testing and validating data for predicted RF by ANN. FIGURE 5 Scatter plot between measured and predicted RF with the regression model.

7 2098 M. MOHAMMADI ET AL. FIGURE 6 Comparison of the output values of the ANN and the regression model with desired outputs for testing data. 2. METHODOLOGY 2.1 Data Acquisition and Selection of Optimal Configuration of ANN Because of the large number of effective parameters on RF in CO 2 flooding process, it is suitable to use important parameters for frugality in time and money, for this purpose, Ramirez and Salazar (2009) used two-level fractional design because could supply as a proper tool for screening purposes. Fourteen independent variables (Figure 1), namely (horizontal permeability (K h [md]), vertical to horizontal permeability (k v /k h ), rate of injection (U inj [MMscfd]), pressure (P [psia]), flowing bottom hole pressure at the producers (P p [psia]), reservoir effective porosity (ϕ [fraction]), dip angle of the reservoir (α [rad]), mobility of each fluids (λ ri ), length, depth, thickness of reservoir (L, H, and W, respectively [ft]) and volume of CO 2 ) were utilized as input signals and the network output consisted of a one-element vector, RF, which was the dependent variable of the ANN and the regression model. In CO 2 flooding, RF relates to both primary recovery and recovery obtained from EOR, which is expressed as percent. All 252 data sets that used for the network training were obtained from (Ramirez and Salazar, 2009). 177 data sets were used in training step. Also, 37 and 38 data sets were used for test and validation of the neural network, respectively. For selection of the optimal configuration for multilayer perceptron (MLP) network, a trial and error procedure was used by changing the number of hidden layers and number of neurons in each layer as well as applying different training algorithms. The MLP network that has two hidden layers is capable to estimate almost any type of nonlinear mapping. Accordingly, the network structure used in this research for predicting the RF had two hidden layers. The number of neurons in first and second hidden layers were determined through an optimization procedure, which minimized some error indexes from training. 2.2 Regression Model For comparison of ANN results, with a regression model, a linear model was developed by Data Fit 9.0 software that presented in Eq. (2). The general purpose of this equation is to learn more about

8 PREDICTION OF OIL RECOVERY FACTOR IN CO 2 INJECTION PROCESS 2099 the relationship between several independent variables and a dependent variable. In this method, a large number of input variables lead to a polynomial with many coefficients that involves tedious computation. RF(%) = a (K h ) + b (K v /K h ) + c (U inj ) + d (P) + e (P p ) + f (ϕ) + g (λ r1 ) +h (λ r2 ) + i (λ r3 ) + j (L) + k (H) + l (W) + m (α) + n (CO 2 ) + O (2) The constants of this model are given in Table 1. Also, units of the variables were mentioned in section 2.1. In order to evaluate the regression model in all stages, total average absolute error was performed, which is defined as: total averageerror = 1 N N i=1 d p y p d p (3) Where N is total number of data in each stage, y p is the calculated RF by the ANN model or regression model, and d p is the target value from (Ramirez and Salazar, 2009). 3.1 Artificial Neural Networks 3. RESULTS AND DISCUSSION ANN model was developed to simulate the RF from CO 2 injection project using MLP neural network with two hidden layers. Tan-sigmoid activation function was used for input and hidden layers and purelin function was used for output layer. Figure 2 shows the total training error calculated for different neural network configurations, differing with respect to the number of neurons in their first and second hidden layers. The network with minimum error was chosen as the optimal network configuration. Since the final values of total training error could be affected by the initial guess of the network parameters (weight and bias coefficients), network was trained several times by applying different randomly generated initial values of the network parameters. The values showed in Figure 2a are the best values of total training error, which obtained from the network training for several initial guesses. For the RF prediction, the best approach, which had minimum errors, was performed by Bayesian regulation (BR) or trainbr algorithm with nine neurons in first hidden layer and five neurons in second hidden layer. Figure 3 shows a comparison between the predicted RF by the ANN model and the actual values obtained from (Ramirez and Salazar, 2009). Moreover, the error values for three data sets showed the accuracy of ANN in prediction. Total obtained errors were %, %, and % for training, testing, and validating data sets, respectively. The error values are showed in Figure 4, that the black, blue, and red points are error values for training, testing, and validating data, respectively. Maximum errors for training, testing and validating data sets were 1.17%, 0.723%, and 3.23%, respectively. 3.2 Regression Model The scatter plot (see Figure 5) obtained from the regression model shows some tendency for the model to under or overestimate RF values. According to this figure the correlation coefficient of the regression model is versus 1 as ANN model. Hence, data points for the regression are more widely dispersed about the fitted line than with ANN. The correlation coefficients for the ANN and the regression show that the RF prediction by best-fit ANN model is significantly superior to the

9 2100 M. MOHAMMADI ET AL. regression model obtained with selected input data. Moreover, average error for the proposed model was about 7.918% that it was severe than ANN model. Also, the results showed that, in the case of the testing data obtained values from the ANN had more adjustment with the target values than the regression model. Figure 6 shows a comparison between the results of the ANN, the regression model and the target values. 4. CONCLUSIONS In this study, accuracy of ANN and regression model were compared for RF prediction in CO 2 injection process. ANN model was developed and compared with the mathematical model based on 252 data points from the literature. The optimal neural network configuration for the estimation of RF had two hidden layers with nine and five neurons in the first and second hidden layers, respectively. The feed-forward MLP neural network had been trained by BR algorithm. The results demonstrated that, under conditions with limited field data, the ANN could produce a higher accuracy than the statistical model. Prediction of an accurate value of RF will bring significant economic benefits in EOR processes. Our results show that the new ANN model is a reliable, on-time, and useful model for the modeling hydrocarbon recovery in CO 2 -EOR to perform complex functions. Predicted values, which obtained from the ANN, were in the best agreement with experimental data than the regression model. The proposed ANN predicted RF during CO 2 injection with error about 0.396%. ACKNOWLEDGMENTS The authors are grateful to Mr. Zabihi, Mr. Jafari, and Mr. Ghannadshirazi for their guidance and assistance. REFERENCES Craft, B. C., and Hawkins, M. F. (1991). Applied petroleum reservoir engineering. Englewood Cliffs, NJ: Prentice-Hall Press. Craze, R. C., and Buckley, S. E. (1945). A factual analysis of the effect of well spacing on oil recovery. Drilling and Production Practice, New York, January 1, pp Emera, M. K., and Sarma, H. K. (2005). Use of genetic algorithm to estimate CO 2 oil minimum miscibility pressure a key parameter in design of CO 2 miscible flood. Pet. Sci. Eng. 46: Guntis, M. (2008). Special report: More US EOR projects start but EOR production continues decline. Oil and Gas. Guthrie, R. K., and Greenberger, M. K. (1955). The use of multiple correlation analysis for interpreting petroleum-engineering data. Drilling and Production Practice, New York, January 1, pp Huang, Y. F., Huang, G. H., and Dong, M. Z. (2003). Development of an artificial neural network model for predicting minimum miscibility pressure in CO 2 flooding. Pet. Sci. Eng. 37: Karimpouli, S., Fathianpour, N., and Roohi, J. (2010). A new approach to improve neural networks algorithm in permeability prediction of petroleum reservoirs using supervised committee machine neural network (SCMNN). Pet. Sci. Eng. 73: Lashkarbolooki, M., Vaferi, B., and Rahimpour, M. R. (2011). Comparison the capability of artificial neural network (ANN) and EOS for prediction of solid solubilities in supercritical carbon dioxide. Fluid Phase Equilibria 308: Linker, R., Seginer, I., and Gutman, P. O. (1998). Optimal CO2 control in a greenhouse modeled with neural networks. Comput. Electron. Agric. 19: Melzer, S. (2012). Carbon dioxide enhanced oil recovery (CO 2 EOR): Factors involved in adding carbon capture, utilization and storage (CCUS) to enhanced oil recovery, CO 2 Consultant and Annual CO 2 Flooding Conference, Midland, TX, pp

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