The T-matrix approach for the mathematical modeling of the effective elastic properties of hydrocarbon reservoirs

Abstract

Various methods of the effective medium theory (EMT)—the T-matrix approach (optical potential approximation and coherent potential approximation), Mori–Tanaka method, generalized singular approximation, etc.—for modeling the effective elastic properties of hydrocarbon reservoir rocks are considered. The relationship of the different approaches (perturbation theory, self-consistent methods, and variational principles) is demonstrated. The classification of the methods by the degree of complexity of solving the inverse problem is suggested. An example of the theoretical modeling of an oil-, gas-, and water-saturated rock with the oriented axis of the fractures is presented. Conclusions about the applicability of different methods for rock modeling are made. In this study we review and compare different methods of the EMT and present the guidelines for determining the effective properties of the medium in rock physics modeling.