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Petroleum and Coal Petroleum and Coal Article Open Access IMPROVED ESTIMATION OF PERMEABILITY OF NATURALLY FRACTURED CARBONATE OIL RESER- VOIRS USING WAVENET APPROACH Mohammad M. Bahramian 1, Abbas Khaksar-Manshad 1*, Nader Fathianpour 2, Amir H. Mohammadi 3, Bengin Masih Awdel Herki 4, Jagar Abdulazez Ali 4 1 Department of Petroleum Engineering, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology (PUT), Abadan, Iran 2 Department of Mining Engineering, Isfahan University of Technology, Isfahan, Iran 3 Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa 4 Faculty of Engineering, Soran University, Kurdistan-Iraq Received June 18, 2017; Accepted September 30, 2017 Abstract One of the most important parameters which is regarded in petroleum industry is permeability that its accurate knowledge allows petroleum engineers to have adequate tools to evaluate and minimize the risk and uncertainty in the exploration of oil and gas reservoirs. Different direct and indirect methods are used to measure this parameter most of which (e.g. core analysis) are very time -consuming and cost consuming. Hence, applying an efficient method that can model this important parameter has the highest importance. Most of the researches show that the capability (i.e. classification, optimization and data mining) of an Artificial Neural Network (ANN) is suitable for imperfections found in petroleum engineering problems considering its successful application. In this study, we have used a Wavenet Neural Network (WNN) model, which was constructed by combining neural network and wavelet theory to improve estimation of permeability. To achieve this goal, we have also developed MLP and RBF networks and then compared the results of the latter two networks with the results of WNN model to select the best estimator between them. Keywords: Permeability; Wavelet; Neural Network; MLP; RBF; Model. 1. Introduction Permeability prediction is one of the main challenges in reservoir engineering. On the other hand, suggesting engineering methods to solve reservoir modeling and managements is impo- ssible without the knowledge of the actual permeability values. The reservoir rock permeability cannot be measured directly with exception of using core plugs as direct measurement. However, direct measuring methods are expensive and time-consuming. In recent years, intelligent techniques such as Artificial Neural Networks (ANNs) have been increasingly applied to esti- mate reservoir properties using well log data. Moreover, previous investigations have indicated that neural networks can estimate formation permeability even in highly heterogeneous reser- voirs using geophysical well log data with good accuracy [1]. Intelligent methods generally utilize raw well log data to estimate permeability, and core plug measurements are used to validate the estimations. Thus, intelligent technique can be utilized as a powerful tool for reservoir properties estimation from well logs in oil and natural gas development projects .Neural network has accurate results but complex structures need more improvement in network [2]. Wavenet is a feed forward and new class of network that combines the classic sigmoid neural networks (NNs) and the wavelet analysis (WA). To detect relation between variables in the main signal, WNN finds family of wavelets in estimation space. WNN has two properties: transfer Pet Coal (2017); 59(6): 785-796 ISSN 1337-7027 an open access journal 785 Petroleum and Coal wavelet and a global estimator. At the same time, wavelets functions in addition to perpen- dicular properties have good local properties. These properties cause a quick homogeneity than normal neural network. These networks can estimate a function with every accuracy by using multi resolution technique [3]. The main objectives of the present study are: - To develop a MLP-NN model to estimate of permeability from well log data; - To develop a RBF-NN model to estimate of permeability from well log data; - To develop a Wavenet-NN model to estimate of permeability from well log data; - To validate models with core data and compare the abovementioned approaches; In this study, a case study of Asmari reservoir located at Ahwaz oil field of Iran is presented. To estimate the permeability of the reservoir, the MLP, RBF and Wavenet methods are used. We designed a Wavenet model to improve estimation of permeability of reservoir. We compare the results of Wavenet, RBF and MLP models to identify the best model to estimate permea- bility to achieve this goal. A summary of literature review is shown in Table 1. Table 1. Summary of literature review. Author Year Methodology Objective Results Create accuracy and easy to Neural network (Back R. Soto B [6] 1997 Estimate K and Ø apply model with satisfactory propagation algorithm) estimations GA was able to sufficiently Neural network(genetic Estimation Mohsen Saemi [7] 2007 estimate the permeability with algorithm) permeability high correlation coefficient Supervised committee The high power and efficiency Sadegh 2010 machine neural network Estimate permeability of SCMNN to compare with Karimpouli [8] (SCMNN) simple network Improve the Better results of proposed reliability and network than simple network Irani and Nasimi [9] 2011 Genetic algorithm predictability of artificial neural network Very low computational time, Tahmasebi and Modular neural network increase R2 and the ability to 2011 Estimate permeability Hezarkhani [10] (MNN) encounter with complex problems Combining cuckoo, par- The COA–LM neural model ticle swarm (PSO) and produces a high accuracy than imperialist competitive without the optimization Kaydani and 2012 algorithms (ICA) with Estimate permeability method Mohebbi [1] Levenberg–Marquardt (LM) neural network algorithm. Accurate, reliable, and outperforms most of the El-Sebakhy [2] 2012 functional networks Forecast permeability existing predictive modeling approaches Compare three FN-SVM hybrid model had versions of Adaptive better performance, the Neuro-Fuzzy highest R2, lowest MSE, but Adaptive Neuro-Fuzzy Inference System taking longer time to execute Inference System (ANFIS) (ANFIS) hybrid model than the 3 ANFIS algorithms Anifowose [11] 2012 and two innovative hybrid and two innovative models hybrid models in the prediction of oil and gas reservoir properties Hybrid neural network Increases permeability model consisting of modelling accuracy Maslennikova [12] 2013 several computational and Predict permeability one clustering neural networks Pet Coal (2017); 59(6): 785-796 ISSN 1337-7027 an open access journal 786 Petroleum and Coal Author Year Methodology Objective Results estimate (k), (ϕ) and Found nonlinear relations that Viveros and Parra Artificial Neural Network 2014 intrinsic attenuation were not visible to linear [13] (ANN) models (1/Q) regression Shokooh Increase R 2 and decrease MSE Wavelet network Saljooghi and 2014 Estimate porosity than MLP (wavenet) Hezarkhani [5] Substituting different wavelet functions as feed forward Shokooh Wavelet network neural network transfer 2015 Estimate permeability Saljooghi [14] (wavenet) functions can enhance the network performance and efficiency 2. Artificial neural networks One of the types of intelligence methods is artificial neural networks (ANNs). This method is inspired by biological neural networks. ANNs are created with neurons that are arranged to create input, hidden and output layers. Neurons are the large number of simple calculating parameters. They further include interconnections between the nodes of successive layers through the so-called weights. Weight modifies the signal carried from one node to the other and improves the influence of the specific connection. Each neuron in a layer receives weighted inputs from a previous layer and transmits its output to the neuron in the next layer then plus it with bias. The internal weights of the network are adjusted in the course of an iterative process termed training and the algorithm used for this purpose so-called training algorithm. A back- propagation neural network is a supervised training technique that sends the input values forward through the network then computes the difference between calculated output and corresponding desired output from the training dataset. The error back-propagation (BP) algorithm is the most common form of learning, utilized today in artificial neural networks. There exist many network architectures but Multilayer Perception is one of the most popular among them. The number of nodes in the feed forward neural network input layer is equal to the number of inputs in the process, whereas the number of output nodes is equal to the number process output. Basically, the back-propagation training procedure is intended to obtain an optimal set of the network weight, which minimizes an error function. The commonly employed error function is the mean squared error (MSE) as defined by [4]: MSE= ½ ∑ (yiobs – yiout) for i=1,…, n. (1) obs out where yi and yi are respectively the observed and estimated values. 2.1. Multi-layer perceptron (MLP) MLP with back propagation (BP) algorithm is the most popular artificial neural network, as mentioned earlier. MLP is a network with an input layer, an output layer and one or more hidden layers that consist of neurons. For assignment number of hidden layers and neurons, we can use trial and error procedure. Thus, we select the number of neurons with highest regression (R)
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