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Application of Recurrent Networks to Classification of Oil Reservoir Models in Well-testing Analysis

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Application of Recurrent Networks to Classification of Oil Reservoir Models in Well-testing Analysis
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  F    o  r    P    e  e  r    R   e  v   i    e  w    O   n  l     y                                       ! "  #$% # & "& '" ($ ) * "& +*, -&.%/ &. 0, (&$ % 1$ !! $, ./ &. 0, (&$ % 1$ !! "&, % &&#%%/ &. 0, (! * !! 23%   34, $   34, 3 !,  %00 ,  0 $% % URL: http://mc.manuscriptcentral.com/ueso Email: JamesSp8@aol.comEnergy Sources, Part A: Recovery, Utilization, and Environmental Effects  F    o  r    P    e  e  r    R   e  v   i    e  w    O   n  l     y    Application of recurrent networks to classification of oil reservoir models in well-testing analysis    Behzad Vaferi, Reza Eslamloueyan 1  , Shahab Ayatollahi  Chemical and Petroleum Engineering School, Shiraz University, Mollasadra Avenue, Shiraz, Iran Abstract  The main objective of this study is utilizing of recurrent neural networks (RNN) to categorize pressure derivative plots of well testing data into various reservoir models. The training and test data have been generated through analytical solution of commonly-used reservoir models. The accuracy of the designed RNN has been examined by the simulation test data and actual field data. The accuracy of the developed RNN has been compared to a multilayer perceptron neural network (MLPNN). The results indicate that the RNN can identify the correct reservoir models from test data with an accuracy of 98.39%, while MLPNN represent an accuracy of 95.83%. Keywords: Recurrent neural networks, well testing, pressure derivative plots, oil reservoirs model detection 1. Introduction The success of a hydrocarbon reservoir simulator in imitating the reservoir current behavior and forecasting its future performance depends highly on the accuracy of the reservoir description and its detailed information. Well testing analysis is a well-known 1   Corresponding Autour: Tel.: +987112303071; fax: +987116474619 E-mail address : eslamlo@shirazu.ac.ir (R. Eslamloueyan) Chemical and Petroleum Engineering School, Shiraz University, Shiraz, Iran Page 1 of 16URL: http://mc.manuscriptcentral.com/ueso Email: JamesSp8@aol.comEnergy Sources, Part A: Recovery, Utilization, and Environmental Effects 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960  F    o  r    P    e  e  r    R   e  v   i    e  w    O   n  l     y    2 and widely used technique for hydrocarbon reservoirs characterization. Determination of the correct reservoir model is a pre-requirement and an important step prior to estimating parameters from transient pressure data and interpreting the test results. Up to now, this technique has been one of the most important available tools to estimate some of the essential properties of the oil and gas reservoirs such as initial reservoir pressure, the degree of reservoirs damage (Jeirani and Mohebbi, 2006) Fissure Volume, Block Size and so on (Bourdet and Gringarten, 1980). Pressure derivative (the rate of alteration of pressure with respect to superposition time function) plots are among the most useful graphs for reservoir characterization and model identification through well testing analysis (Bourdet, 2002). The previous study indicates that when the srcinal plot does not provide much information, derivative plot always indicate special features of the hydrocarbon reservoirs (Amanat, 2004). 2. Method In this section a short summary of well testing, the procedure for generating well testing data, the technique of converting the transient pressure curves to derivative plots, and the structure of the neural network that employed in this study are explained. 2.1 Drawdown Well Testing Interpretation In drawdown test, the production from a well is started at a constant flow rate, and the temporal variation of the bottom-hole pressure of the wellbore is measured. The transient pressure response moves radially through the reservoir and away from the well. At first, this movement is rapid, but it becomes slow while spreads out further from the wellbore, and senses progressively larger reservoir volume. Page 2 of 16URL: http://mc.manuscriptcentral.com/ueso Email: JamesSp8@aol.comEnergy Sources, Part A: Recovery, Utilization, and Environmental Effects 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960  F    o  r    P    e  e  r    R   e  v   i    e  w    O   n  l     y    3 2.2 Recurrent Neural Networks The developed RNN by Elman is a partially recurrent network whose connections are generally feed-forward, but contains some of the feedback links (Elman, 1990). In this network, a number of context neurons are existed, which are extra input neurons whose their values are fed-back from the hidden layer. The Elman’s model recalls the situation, which obtained from the presentation at time t-1 , of the input, and fed back as an additional input to the network at time t  . In this research, the Elman’s RNN has been utilized as a classifier for detecting oil reservoir models from normalized pressure derivative plots. Up to now, there is no study in the literature relating to the assessment of accuracy of RNNs in analysis of the well testing data, only some works have been done on the application of conventional feed-forward network for reservoirs model detection. For instance, Ershaghi et al., developed several MLPNNs specialized for detecting a various reservoir models (Ershaghi et al., 1993). Athichanagorn and Horne have applied MLPNN to recognize special parts of pressure derivative plots of some candidate reservoir models (Athichanagorn and Horne, 1995). 2.3 Well testing simulation, data generation and pre-processing  In this study, the following eight different reservoir models have been chosen and the RNNs have been trained to discriminate among them. Homogeneous Reservoir, Infinite Acting Boundary (HI) Homogeneous Reservoir, Single Sealing Fault Boundary (HS) Homogeneous Reservoir, Constant Pressure Outer Boundary (HCP) Page 3 of 16URL: http://mc.manuscriptcentral.com/ueso Email: JamesSp8@aol.comEnergy Sources, Part A: Recovery, Utilization, and Environmental Effects 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960  F    o  r    P    e  e  r    R   e  v   i    e  w    O   n  l     y    4 Homogeneous Reservoir, Closed Outer Boundary (HCB) Dual Porosity Reservoir, Infinite Acting Boundary (DPI) Dual Porosity Reservoir, Single Sealing Fault Boundary (DPS) Dual Porosity Reservoir, Constant Pressure Outer Boundary (DPCP) Dual Porosity Reservoir, Closed Outer Boundary (DPCB) For each reservoir model 120 pressure transient data have been generated for different ranges of well testing parameters. The percentages of the data used for the network training and validation are 75 and 25 respectively. Each transient pressure data have been converted to pressure derivative using the method of Bourdet et al., (Bourdet et al., 1989). The aforementioned algorithm is given in the Eq. 1. 11111111 )]()([ )( −+−+++−− −−−−+−−−= iiiiiiiiiiiiiii t t t t t t  p pt t t t  p pdt dp  (1) Where  p  is pressure data and t is   time function (ln  t for drawdown). Normalization in the interval [-1 1] is performed, in order to speed up of convergence of the network and avoiding saturation of its weights. The schematic of normalized derivative plots of homogeneous and dual porosity reservoirs with various boundaries are shown in Fig. 1a and Fig. 1b, respectively. Fig. 1   2.4 Selection of optimal configuration The optimal configuration of both networks has been chosen using a trial and error. Two layers RNN with nine and eight neurons in its hidden and output layers has been found as an optimal topology. The MLP network with twelve hidden neurons shows the best performance, and is considered as an optimal configuration. The back-propagation Page 4 of 16URL: http://mc.manuscriptcentral.com/ueso Email: JamesSp8@aol.comEnergy Sources, Part A: Recovery, Utilization, and Environmental Effects 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960
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