Support-Vector Regression for Permeability Prediction in a Heterogeneous Reservoir: A Comparative Study

Summary Permeability is a key parameter in reservoir-engineering computation, and the relationship between rock petrophysical properties and permeability is often complex and difficult to understand by using conventional statistical methods. Neural-network-based methods can be employed to develop more-accurate permeability correlations, but the correlations from these methods have limited generalizability and the global correlations are usually less accurate compared to local correlations. In this research, the objective is to build a permeability model with promising generalization performance. Recently, support-vector machines (SVMs) based on statistical-learning theory have been proposed as a new intelligence technique for both prediction and classification tasks. The formulation of SVMs embodies the structural-risk-minimization (SRM) principle, which has been shown to be superior to the traditional empirical-risk-minimization (ERM) principle employed by conventional neural networks. This new formulation deals with kernel functions, allows projection to higher planes, and solves more-complex nonlinear problems. SRM minimizes an upper bound on the expected risk, as opposed to ERM, which minimizes the error on the training data. It is this difference that equips SVMs with a greater ability to generalize, which is the goal in reservoir-characterization statistical learning. This novel support-vector-regression (SVR) algorithm was first introduced in well-logs intelligent analysis. Here, a permeability-prediction model using SVR from well logs in a heterogeneous sandstone reservoir is developed. Also, an attempt has been made to review the basic ideas underlying support-vector machines for function estimation. To demonstrate the potential of the proposed SVM's regression technique in prediction permeability, a study was performed to compare its performance with multilayer perceptron neural network, generalized neural network, and radial-basis-function neural networks. Accuracy and robustness were investigated, and statistical-error analysis reveals that the SVM approach is superior to the other methods for generalizing previously unseen permeability data.