Kerman, Kerman, Iran b Petroleum Engineering Department, National Iranian South. Oilfield Company, Ahwaz, Iran Published online: 24 May 2013.

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1 This article was downloaded by: [Universiti Teknologi Malaysia] On: 07 August 2013, At: 01:35 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: A Dew Point Pressure Model for Gas Condensate Reservoirs Based on an Artificial Neural Network H. Kaydani a, A. Hagizadeh b & A. Mohebbi a a Chemical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran b Petroleum Engineering Department, National Iranian South Oilfield Company, Ahwaz, Iran Published online: 24 May To cite this article: H. Kaydani, A. Hagizadeh & A. Mohebbi (2013) A Dew Point Pressure Model for Gas Condensate Reservoirs Based on an Artificial Neural Network, Petroleum Science and Technology, 31:12, , 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, 31: , 2013 Copyright Taylor & Francis Group, LLC ISSN: print/ online DOI: / A Dew Point Pressure Model for Gas Condensate Reservoirs Based on an Artificial Neural Network H. Kaydani, 1 A. Hagizadeh, 2 and A. Mohebbi 1 1 Chemical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran 2 Petroleum Engineering Department, National Iranian South Oilfield Company, Ahwaz, Iran Dew point pressure (DPP) is one of the most important parameters to characterize gas condensate reservoirs. Experimental determination of DPP in a window pressure-volume-temperature cell is often difficult especially in case of lean retrograde gas condensate. Therefore, searching for fast and robust algorithms for determination of DPP is usually needed. This paper presents a new approach based on artificial neural network (ANN) to determine DPP. The back-propagation learning algorithms were used in the network as the best approach. Then equations for DPP prediction by using weights of the network were generated. With the obtained correlation, the user may use such results without a running the ANN software. Consequently, this new model is compared with results obtained using other conventional models to make evaluation among different techniques. The results show that the neural model can be applied effectively and afford high accuracy and dependability for DPP forecasting for the wide range of gas properties and reservoir temperatures. Keywords: artificial neural network, condensate gas reservoir, dew point pressure 1. INTRODUCTION Gas condensate reservoirs exhibit complex phase and flow behaviors due to the formation of condensate banking in the near well region and changing composition of each phase dynamically. Natural production from these reservoirs leads to pressure drop of the reservoir, which results in gas condensation and liquid dropout in the reservoir. The phenomenon exhibits itself in the vicinity of the wellbore first and then propagates in a cylindrical form to the reservoir volume. The most important effect of liquid condensation is the reduction of gas relative permeability and as the result the loss of production. So, accurate determination of dew point pressure (DPP) is considerable (Danesh, 1998). In general, there are two classes of estimation methods for calculation of DPP. The first class is determined experimentally from collected laboratory samples. Constant volume depletion (CVD) is the most common test in DPP prediction. The depletion process is simulated by CVD, assuming Address correspondence to H. Kaydani, Chemical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran. kaydani3038@yahoo.com 1228

3 DEW POINT PRESSURE MODEL 1229 immobility of dropped out condensate in porous media. The test consists of a series of expansion followed by expelling the excess gas at constant pressure in such a way that the cell volume remains constant at the end of each stage. The first droplet of condensate will be formed at the DPP. The experimental determination of DPP is expensive, time consuming and frequently these measurements are not available and sometimes subjected to many errors (Pedersen et al., 1988). The second classes of estimation methods for calculation of DPP are empirical correlations or they can be determined iteratively using an equation of state (EOS). Generally, the performance of the EOS is good for simple hydrocarbon systems, predominantly oil. However, it deteriorates for phase behavior modeling of complex hydrocarbons such as volatile oils and gas condensates especially in the retrograde region (Saker et al., 1991). The DPP correlations have been studied by several investigators. Eilerts and Smith (1942) developed four correlations relating DPPs to temperature, composition, molar average boiling point and oil-to-gas volume ratio. Olds et al. (1945) studied the behavior of reservoir fluids from Paloma field, and the influence of composition on the DPP. They indicated that removal of the intermediate molecular weight components from the mixtures resulted in considerable increase in the DPP. Olds et al. (1949) studied experimentally the behavior of five paired samples of oil and gas. Their investigations resulted in developing a rough correlation relating the retrograde DPP to the gas-oil ratio, temperature, and stock tank API oil gravity. The results of this correlation were presented in tabulated and graphical forms. Reamer and Sage (1950) attempted to extend existing correlation to higher gas-to-oil ratio by studying combinations of five different pairs of fluids. Numerous diagrams depicting the effect of temperature and gas-to-oil ratio on DPP were presented. They concluded that, due to complexity of the influence of composition, it was doubtful that a useful correlation could be established. Nementh and Kennedy (1967) proposed a relationship between the DPP of a hydrocarbon reservoir fluid and its composition, temperature and characteristics of the heptanes-plus fraction, such as molecular weight and specific gravity. Crogh (1996) performed several evaluations to improve the Nemeth Kennedy correlation to fit better the DPP versus composition and C 7C properties in the retrograde dew point range. A test correlation was developed using the Nemeth Kennedy database. However, temperature was not considered in their DPP correlation, which correlates DDP with hydrocarbon and nonhydrocarbon reservoir composition, specific gravity, and mass of C 7C. Carison and Cawston (1996) investigated the influence of hydrogen sulfide on DPP. According to their researches, as H 2 S content increases, the volume of liquid drop out decreases. Yisheng et al. (1998) studied the behavior of reservoir fluids from China oilfields and presented a new empirical correlation to predict the DPP of gas condensate as a function of gas composition, temperature, characteristics of the heptanes-plus fraction, and average molecular weight of fluid mixture. Humoud and Al-Marhoun (2001) published a new empirical correlation to predict the DPP of gas condensate fluids from readily available field data. This correlation relates the DPP of a gas condensate fluid directly to its reservoir temperature, pseudoreduced pressure and temperature, primary separator gas-oil ratio, the primary separator pressure and temperature, and relative densities of separator gas and heptanes-plus fraction. Elsharkawy (2002) presented a new empirical model to estimate DPP for gas condensate reservoirs as a function of routinely measured gas analysis and reservoir temperature. The proposed model was developed using experimental data covering a wide range of gas properties and reservoir temperature. Elsharkawy s empirical model contains 19 terms. It correlates DPP with reservoir temperature, reservoir composition of hydrocarbon and a non-hydrocarbon expressed as mole fraction, with molecular weight of C 7C and with specific gravity of C 7C.

4 1230 H. KAYDANI ET AL. Generally, the statistical approach is comparatively a more versatile approach to the problem of pressure-volume-temperature (PVT) parameters prediction. However, it requires the assumption and satisfaction of multinormal behavior and linearity, and hence it must be applied with caution. The complexity and uncertainty existent in addition to non-linear behavior of most reservoir parameters require a powerful tool to overcome these challenges. In recent years, intelligent technique such as artificial neural network (ANN) has had noticeable part in reservoir engineering applications (Gharbi, 1997). This paper proposes a new approach based on ANN to determine a formula for DDP. The advantages of ANNs compared to classical methods are the speed, the simplicity, and the capacity to learn from examples. Instead of the complex rules and mathematical routines, ANNs are able to learn the key information patterns within multidimensional information domain. So, engineering effort can be reduced in the areas. Then equations for DPP prediction by using the weights of network will be generated. Finally, the performance of this model will be compared with that of other models. 2. ARTIFICIAL NEURAL NETWORKS In order to find relationship between the input and output data derived from experimental work, a more powerful method than the traditional ones are necessary. ANN is an especially efficient algorithm to approximate any function with finite number of discontinuities by learning the relationships between input and output vectors (Gharbi, 1997). These algorithms can learn from different experiments, and also are fault tolerant that is they are able to handle noisy and incomplete data. The ANNs are able to deal with nonlinear problems, and once trained can perform prediction and generalization rapidly (Bean and Jutten, 2000). Previous investigations (Mohaghegh et al., 1996) have revealed that neural network is a powerful tool for identifying the complex relationship among permeability, porosity, fluid saturations, depositional environments, lithology, and well log data. Back-propagation type neural networks have an input, an output and, in most of the applications, have one hidden layer. The number of inputs and outputs of the neural networks are determined by considering the characteristics of the application. Each neuron of a layer is generally connected to the neurons in the proceeding layer. Repeating forward propagating and backward-propagating steps performs the required learning. When a pattern is given to the input pattern, the forward propagation step begins. The activation levels are calculated and the results are propagated forward through the following hidden layers until they reach the output layer. A neuron has two components: (a) a weighted summer which perform a weighted summation of its inputs with components (X 1 ; X 2 ; X 3 : : : X n ; i.e., S D W i X i C b, where b is the bias of the networks), and (b) a linear, nonlinear or logic function that gives an output corresponding to S. The output of the network is created at the output layer. The bias units of input and hidden layer add a constant term to the weighted sum, which improves convergence. In general, the output from neural j in layer k can be calculated by the following equation:! NX k 1 u jk D F k w ijk u i.k 1/ C b jk (1) id1 Coefficients w ijk and b jk are connection weight and bias of the network, respectively; they are fitting parameters of the model. After the network s output pattern is compared with the target vector, error values for the hidden units are calculated, and their weights are changed. The backward propagation starts at the output layer and moves backward through the hidden layers until it reaches the input layer (Bean and Jutten, 2000).

5 DEW POINT PRESSURE MODEL MODELING OF MMP BY USING NEURAL NETWORK By considering the ability of ANN on developing an effective model, ignoring uncertainty and nonlinearity of a system, and also avoiding the complex mathematical modeling, it can be used to predict DPP of retrograded gas reservoirs. Figure 1 shows the offered flowchart of neural networks modeling for DPP prediction. The following steps are those performed to develop the ANN model Data Acquisition A set of 100 measurements experimental data points of CVD test were available for this study. Some of data includes experimentally measured values in Iranian oil fields and other collected from the literature (Guo and Du, 1989; Zhang and Mei, 1998; Elsharkawy, 2002; Nasrifar and Moshfeghian, 2002). The overall range of PVT experimental data points used for developing the ANN model are summarized in Table 1. FIGURE 1 A flowchart of working principle of neural networks modeling.

6 1232 H. KAYDANI ET AL. TABLE 1 Range of Input Parameters Uses for Normalizing Data Reservoir temperature, ı F Mole fraction of volatile gas fraction, % Mole fraction of intermediate gas fraction, % 0 40 Mole fraction of heavy gas fraction, % 0 15 C 7C molecular weight Experimental DPP, psia 2,000 12, Neural Network Input Data DPP determination of retrograded gas reservoirs has been studied extensively, and various correlations to estimate DPP have been proposed. In most of correlations, reservoir temperature and gas composition including volatile fractions (C 1, N 2 ), intermediate fractions (C 2 -C 6, H 2 S) and heavy fraction (C 7C ), and molecular weight of C 7C (MC 7C ) are the parameters for prediction of DPP. Those parameters are selected as input data for training the network and experimental data from the CVD test are used as a target data. Using a linear transformation first, data is normalized between (0.2 1), in order to data rate reduction, noise suppression and avoiding ill conditioning (Kasabov, 1998). Inputs and outputs are normalized according to Eq. (2). R min D 0:8 C 0:2 (2) max where R is replaced by all of input and output parameters and the values of maximum and minimum for each parameter is obtained from Table Neural Network Modeling For obtaining ANN model to predict DPP of retrograded gas reservoirs as shown in Figure 2, reservoir temperature, light fraction (C 1, N 2 ), intermediate fraction (C 2 -C 4, H 2 S), heavy fraction (C 7C ), and MC 7C are selected as input parameters. min FIGURE 2 Basic components of network.

7 DEW POINT PRESSURE MODEL 1233 The back-propagation learning algorithm has been used in feed-forward and single hidden layer network. Conjugate Gradient, Quasi-Newton, and Levenberg-Marquardt (LM) use standard numerical optimization techniques and they are faster algorithms than other algorithms. Tan- Sigmoid (tansig) and pure line transfer functions have been used in hidden and output layers, respectively. The computer program has been developed under MATLAB R2008 software (The MathWorks, Natick, MA). In the training, the number of neurons has been increased (i.e., from 3 to 8) in hidden layer to obtain more accurate outputs. The neurons in the hidden layer perform two tasks: they sum the weighted inputs connected to them and pass the resulting summations through a non-linear activation function to the output neuron or adjacent neurons of the corresponding hidden layer. To train the ANN, no more patterns are necessary. The aim of ANN is to estimate the interval values accurately. According to statistical values such as R 2 and RMSE, the training can be achieved with sufficient data. When network training was successfully finished, network was tested with test data. 4. RESULTS AND DISCUSSION In this work, a new approach based on artificial neural network is applied to determine the DPP for gas retrograded reservoirs. The best approach that has minimum errors is performed the LM algorithm with five neurons in hidden layer. Performance of network is illustrated in Figure 3. According to the previous network training, formulation of DPP prediction has been prepared by using algorithm s weights. Neurons in input layer have no transfer function. Tan-Sigmoid (tansig) transfer function has been used in hidden layer where the transfer function used for this FIGURE 3 Performance of network due to experimental data in DDP prediction.

8 1234 H. KAYDANI ET AL. TABLE 2 Weight Values Obtained LM Algorithm With Five Neurons for DPP Prediction E i D C 1i T R C C 2i X vol C C 3i X int C C 4i C 7C C C 5i MW C 7C C C 6i i C 1i C 2i C 3i C 4i C 5i C 6i approach is given in Eq. (3) (Demuth et al., 2006): f.z/ D 2 1 C exp. 2z/ 1 (3) Therefore Eqs. (4) and (5) have been prepared by using this algorithm s weights for DPP prediction. Ei values in Eq. (4) should be taken from Table 2. Data in the network are normalized as said previously. Therefore, in this study to use Eq. (4), data in input layer should be normalized according to Eq. (2). Similarly, output data should be changed to original values by using Eq. (2). F i D 2 D 1I i D 1 W 5 (4) 1 C exp. 2E i / DPP D 0:427F 1 0:345F 2 1:367F 3 2:477F 4 C 0:795F 5 0:893 (5) Results have been demonstrated in Table 3 for DPP prediction using this formulation based on algorithm s weights and some other correlations. It is clear that this novel model gives a very accurate representation of the statistical values such average absolute deviation (AAD), RMSE, correlation coefficient (R), and R 2 over the full range of operating conditions for DPP prediction. Table 3 shows that the average absolute deviation, RMSE, correlation coefficient, and R 2 values for the new proposed model are 5.84%, 7.54%, 0.963, and 0.93 respectively, which gives the best results compared with the other methods. In order to investigate of the ability of the new developed model further, it was tested against an equation of state based method to calculate DPP. Table 4 gives the compositions of some gases used for calculating DPP by Elsharkawy (2002). The results of DPP calculations using Soave- Redlich-Kwong (SRK-EOS) and Peng-Robinson equation of state (PR-EOS) also are presented in Table 4 (Elsharkawy, 2001). EOS calculations require critical pressure (Pc), critical temperature TABLE 3 Accuracy of the Various Methods for Predicting DPP of Gas Condensate Samples Parameter Presented Model Nemeth and Kennedy (1967) Yisheng et al. (1998) Elsharkawy (2001) AAD, % RMSE, % R R

9 TABLE 4 Comparison of the DDP Obtained From the Formulation Model to the Calculated From Different Equations of State Composition, mol% Sample H2S CO N C C C ic nc ic nc C C7C (C7C) MW (C7C) Reservoir Temperature, ı F Measured DPP, psi 3,337 2,651 11,830 8,750 5,780 5,229 4,203 4,173 5,219 4,172 4,160 7,871 Calculated DPP, psi Estimated Model 3,779 2,775 11,525 8,720 5,250 5,100 4,818 4,864 5,097 4,790 4,989 6,943 SRK-EOS (Method 1) 6,808 2,911 12,914 9,850 5,602 5,147 4,152 4,153 4,823 4,089 4,055 6,208 SRK-EOS (Method 2) 4,739 2,902 12,689 9,599 6,500 5,141 4,157 4,152 4,830 4,098 4,105 6,762 PR-EOS (Method 1) 5,947 2,682 11,738 9,172 5,092 5,330 4,256 4,243 4,709 3,855 4,159 6,163 PR-EOS (Method 2) 4,909 2,675 11,426 9,138 5,427 5,307 4,258 4,243 4,712 4,863 4,935 6,374 Presented Model SRK-EOS (Method 1) SRK-EOS (Method 2) PR-EOS (Method 1) PR-EOS (Method 2) AAD, % RMSE, % R

10 1236 H. KAYDANI ET AL. (Tc), and accentric factor (!) for every component forming the gas condensate. However, critical properties for the sub-fraction are estimated from correlations (Elsharkawy, 2001). Elsharkawy considered two of the most well-known methods for characterizing the sub-fraction are: These methods are Kesler and Lee (KL) and Pedersen correlations. Thus, method 1 involves using KL correlation to calculate the critical pressure and temperature of the pseudocomponent. Method 2 involves using Pedersen correlation to calculate the critical pressure, the critical temperature, and the accentric factor of the pseudocomponent. The results shown in Table 4 reveal that the new model can be effectively used along by EOS based approach without any doubt. 5. CONCLUSION Accurate determination of DPP has been the main challenge in gas reservoir development and management. This paper shows that values predicted with ANN can be used to define the DPP instead of approximate and complex empirical correlations. An attempt was made to develop the formula based on ANN model for prediction of DDP in gas retrograded reservoirs. With the obtained correlation, the user may use such results without a running the ANN software. In other words, they may be put in a spreadsheet application to provide useful results. The comparison of the prediction accuracies of formulas based on ANN model and other conventional methods indicated that this model approach was more accurate than other statistical methods in predicting MMP. Especially under conditions with limited field information, this approach could produce a higher accuracy than other estimating methods. ACKNOWLEDGMENTS The authors would like to gratefully acknowledge the financial support for this study provided by National Iranian Oilfield Company, Petroleum Engineering Department of National Iranian South Oilfield Company, and Research & Development Center of National Iranian South Oilfield Company. REFERENCES Bean, M., and Jutten, C. (2000). Neural networks in geophysical applications. Geophys. J. 65: Carison, M. R., and Cawston, W. B. (1996). Obtaining PVT data for very sour retrograde gas and volatile oil reservoirs: A multi-disciplinary approach. SPE 35653, SPE Gas Technology Symposium, Calgary, Canada, April 28 May 1. Crogh, A. (1996). Improved correlations for retrograde gases. M.Sc. thesis, College Station, TX: Texas A&M University. Danesh, A. (2003). PVT and phase behavior of petroleum reservoir fluids, 3rd ed. Amsterdam, the Netherlands: Elsevier Science. Demuth, H., Beale, M., and Hagan, M. (2006). Neural network toolbox user s guide. Natick, MA: The MathWorks. Eilerts, K., and Smith, R. V. (1942). Specific volumes and phase boundary properties of separator-gas and liquidhydrocarbon mixtures. U.S. Bureau of Mines Report of Investigation Elsharkawy, A. M. (2001). Characterization of the plus fraction and prediction of the dewpoint pressure for gas condensate reservoirs. SPE 68776, SPE Western Regional Meeting, March Elsharkawy, A. M. (2002). Predicting the dewpoint pressure for gas condensate reservoir: Empirical models and equations of state. Fluid Phase Equilib. 193: Gharbi, R. (1997). Estimating the isothermal compressibility coefficient of under saturated Middle East crudes using neural networks. Energy Fuels 11: Guo, T. M., and Du, L. (1989). A new three-parameter cubic equation of state for reservoir fluids-iii. Application to gas condensates, SPE

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