Fracture identification in tight reservoirs by multiple kernel Fisher discriminant analysis using conventional logs

Abstract

Kernel Fisher discriminant analysis (KFD) can map well-log data into a nonlinear feature space to make a linear nonseparable problem of fracture identification into a linear separable one. Commonly, KFD uses one kernel. However, the prediction capacity of KFD based on one kernel is limited to some extent, especially for a complex classification problem, such as fracture identification in tight sandstone reservoirs. To alleviate this problem, we have used a multiple kernel Fisher discriminant analysis (MKFD) method to recognize fracture zones. MKFD uses multiscaled Gaussian kernel functions instead of a single kernel to realize optimal nonlinear mapping. To assess the effectiveness of MKFD in fracture identification for complex reservoirs, we chose a data set from tight sandstone reservoirs in China to implement comparison experiments. In the experiments, we used the MKFD with 20 Gaussian kernels to map the original well logs into nonlinear feature spaces so that we could obtain appropriate features for fracture identification. The comparison results demonstrated that the accuracy of fracture identification by MKFD improved about 13.4% over KFD and that MKFD also outperformed KFD in the blind well test, although the improvement of the generalization ability of MKFD was not very obvious. Overall, MKFD can provide an accurate means for the identification of fracture zones in tight reservoirs. We also evaluate the problems for fracture identification by MKFD.