A quantification method for shale reservoir heterogeneity using the empirical mode decomposition technique and the analytical hierarchy process

Heterogeneity is an intrinsic property of shale reservoirs that exhibit long-standing puzzles that are difficult to optimize the hydraulic fracturing design and may render suboptimal performance. At present, the selection of a single influencing factor is not appropriate due to bias and upscaling problems. In this study, the multiple influencing factors were first selected from geophysical logging data to establish a structural hierarchy model. The heterogeneity index of single parameters was then obtained from the relationships between the intrinsic mode function (IMF) number decomposed by the empirical mode decomposition technique (EMDT) and its average wavenumber. In addition, the weighting coefficient of multiple influencing factors was determined based on the analytical hierarchy process (AHP). Finally, the composite heterogeneity index of the multi-stage process was calculated and combined with the weighting coefficient of multiple influencing factors. A shale gas well was analysed using this new quantification method. The results indicate that the multi-stage composite heterogeneity index is in good agreement with the fracture pressure derived from hydraulic fracturing data, and better than that from the coefficient of variation (CV) and the Lorentz coefficient method. Therefore, a quantification method for integrating the multiple influencing factors is of significant importance in order to comprehensively evaluate the degree of heterogeneity within a shale reservoir.