Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 287816, 10 pages

http://dx.doi.org/10.1155/2015/287816

## Extreme Learning Machine for Reservoir Parameter Estimation in Heterogeneous Sandstone Reservoir

College of Computer Science and Information Engineering, Tianjin University of Science and Technology, Tianjin 300222, China

Received 21 August 2014; Revised 8 November 2014; Accepted 10 November 2014

Academic Editor: Zhan-li Sun

Copyright © 2015 Jianhua Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study focuses on reservoir parameter estimation using extreme learning machine in heterogeneous sandstone reservoir. The specific aim of work is to obtain accurate porosity and permeability which has proven to be difficult by conventional petrophysical methods in wells without core data. 4950 samples from 8 wells with core data have been used to train and validate the neural network, and robust ELM algorithm provides fast and accurate prediction results, which is also testified by comparison with BP (back propagation) network and SVM (support vector machine) approaches. The network model is then applied to estimate porosity and permeability for the remaining wells. The predicted attributes match well with the oil test conclusions. Based on the estimations, reservoir porosity and permeability have been mapped and analyzed. Two favorable zones have been suggested for further research in the survey.

#### 1. Introduction

In geosciences, reservoir is defined as the underground accumulation of oil or natural gas in sedimentary basins, and it is of great importance for petroleum exploration and development. Among the steps for well planning decisions, reservoir characterization is the essential one, and physical parameters estimation, including porosity and permeability, is the basic requirement in the characterization workflow.

As for the two geophysical parameters, porosity describes the fraction of void space in the sedimentary rocks, where the void may contain fluids, such as oil or natural gas. The more porous the rock is, the more the oil or gas may be preserved in the void spaces. And permeability describes the ability of rocks to transmit fluids. The more permeable the rock is, the easier the oil or gas could flow through. These two types of reservoir parameters are to some extent determining factors for reserve estimation and oil or gas production.

Practically, it is very complex and difficult for porosity and permeability estimation since lots of factors could affect the estimation accuracy, such as depositional formations, lithologic mineral components, measurement tools, data quality, and computational method.

There are mainly two types of approaches that have been used to acquire porosity and permeability data in reservoir research workflow. The first one is laboratory core analysis. Cores are obtained from drilled wells. Porosity and permeability can be determined precisely under strict core test principles. The results are reliable and are often used as reference for further estimation using mathematical ways. Due to the expensive cost, cores are often few in numbers for most of the oilfields. The second one is borehole log interpretation. The logs data are physical measurements performed by electric instruments lowered into the borehole. Specific physical characteristics of the rocks surrounding the borehole are recorded by logs with depth variations. Conventional logs include gamma ray (GR), acoustic slowness (AC), density (DEN), compensated neutron logs (CNL), and deep resistivity (RT). Among these logs, GR is often used to predict rock lithology, and the three logs of AC, DEN, and CNL have largely been used to estimate rock porosity. Permeability is estimated by combination of RT log and the former-estimated porosity. Empirical mathematical equations are often used when carrying out log interpretations. These equations are regression models built based on the correlation between geophysical logs and core-measured reservoir parameters. Since logs are run for all wells in oilfield and the mathematical empirical equations are feasible to be used, log interpretation becomes the most used method in porosity and permeability estimation. But the estimation results rely greatly on the equations or the correlation models. Meanwhile, the relations between logs and geophysical parameters of rocks are nonlinear and very complicated. It is hard to get a universal solution for all wells in one survey or for all oilfields. So some nonlinear numerical method and artificial intelligence are brought into the log interpretation process and proposed as supplementary approach, so that more reliable and precise estimation data could be obtained for further reservoir evaluation.

Artificial neural networks have been proved to be capable of approximating any nonlinear function to any degree of accuracy provided that there are sufficient number of samples for network training and learning and have some successful applications in petroleum engineering, such as sedimentary microfacies prediction [1], lithology classification [2, 3], and reservoir prediction [4–6].

In petrophysical analysis, the neural network models have always acted as a predictor or estimator of deriving geophysical parameters, such as porosity and permeability where no core data is available [7–12]. Among the neural networks, BP network and SVM are the two commonly used learning algorithms in porosity and permeability estimation. BP neural network is a typical full-connected neural network with forward and error backpropagation part. The error could be backpropagated by adjusting weights in the learning process until it converges to a targeted value, which is very effective in solving nonlinear problems [13]. Support vector machine (SVM) is a network based on statistical learning theory and is especially designed for classification problems with different convolution kernel functions [14]. Satisfactory accuracy of estimations has been achieved when the networks are optimized with appropriate model parameters [15–19], although there still are some shortcomings in the applications, such as time-consuming and overfitting problems [20].

Extreme learning machine (ELM) is a single-hidden layer feedforward neural network (SLFN) proposed by Huang et al. [21, 22]. The ELM approach to training SLFN consists in the random generation of the hidden layer weights, followed by solving a linear system of equations by least squares for the estimation of the output layer weights. This learning strategy is very fast and gives good prediction accuracy. Theoretically and practically, this algorithm can produce good generalization performance in most cases and the speed has been proved to be much faster than conventional popular learning algorithms for feedforward neural networks. Till now, ELM has been widely studied and accepted by researchers and has demonstrated good generalization and prediction performance in many real-life applications [23–26]. But in petroleum reservoir prediction, there are still few applications.

In this paper, we examine the potential of ELM to predict porosity and permeability parameters in a heterogeneous sandstone reservoir in Permian formation, Yanqi survey of Ordos basin, China. Prediction models are established by SLFN trained with ELM and optimally pruned ELM (OP-ELM). OP-ELM is a variation of the ELM introducing an optimal selection of the number of hidden units and variables modeling the problem [27, 28]. It is more robust and generic than conventional ELM [26]. In the study, reservoir parameters measured from cores and logs value at the same depth are paired as samples. Optimal prediction models for porosity and permeability estimation are established, which are finally used to interpret reservoir porosity and permeability for all wells in the survey.

The outline of this paper is as follows: Section 2 is the geologic background of the survey and brief introduction about the sandstone reservoir. Section 3 gives a short review of ELM and OP-ELM. Section 4 describes the preparation for the network model establishment. Section 5 gives the prediction results. Finally, Section 6 gives the conclusion of this work.

#### 2. Geological Background

Yanqi survey is located in eastern Ordos basin, China. In the survey, there are 15 wells that encountered Permian sandstone reservoir. Oil has been discovered in 6 wells, which are marked with red color-filled circles in Figure 1.