On Support Vector Regression to Predict Poisson’s Ratio and Young’s Modulus of Reservoir Rock

Accurate prediction of rock elastic properties is essential for wellbore stability analysis, hydraulic fracturing design, sand production prediction and management, and other geomechanical applications. The two most common required material properties are Poisson’s ratio and Young’s modulus. These elastic properties are often reliably determined from laboratory tests by using cores extracted from wells under simulated reservoir conditions. Unfortunately, most wells have limited core data. On the other hand, wells typically have log data. By using suitable regression models, the log data can be used to extend knowledge of core-based elastic properties to the entire field. Artificial neural networks (ANNs) have proven to be successful in many reservoir characterization problems. Although nonlinear problems can be well resolved by ANN-based models, extensive numerical experiments (training) must be done to optimize the network structure. In addition, generated regression models from ANNs may not perfectly generalize to unseen input data. Recently, support vector machines (SVMs) have proven successful in several real-world applications for their potential to generalize and converge to a global optimal solution. SVM models are based on the structural risk minimization principle that minimizes the generalization error by striking a balance between empirical training error and learning machine capacity. This has proven superior in several applications to the empirical risk minimization (ERM) principle adopted by ANNs that aims to reduce the training error only. Here, support vector regression (SVR) to predict Poisson’s ratio and Young’s modulus is described. The method uses a fuzzy-based ranking algorithm to select the most significant input variables and filter out dependency. The learning and predictive capabilities of the SVR method is compared to that of a backpropagation neural network (BPNN). The results demonstrate that SVR has similar or superior learning and prediction capabilities to that of the BPNN. Parameter sensitivity analysis was performed to investigate the effect of the SVM regularization parameter, the regression tube radius, and the type of kernel function used. The result shows that the capability of the SVM approximation depends strongly on these parameters.