An Extended Differential Effective Medium Theory: Linking Pore Geometry and Elastic Moduli in Carbonate Rocks

Summary The differential effective medium (DEM) theory is widely used to estimate the elastic properties of reservoir rocks based on their constituent minerals and pore fluids. However, its dependence on ideal ellipsoidal pores limits its applicability to rocks with irregular and complex pore geometries, particularly carbonate rocks. In this study, we present an extension to the DEM framework that incorporates a perturbation tensor to account for deviations from ideal ellipsoidal inclusions. For isotropic composites, this tensor reduces to two scalar coefficients that quantify the mechanical impact of pore shape irregularities. The physical significance of these coefficients is investigated through numerical simulations on synthetic rocks with controlled pore geometries, where pore shape complexity is quantified using a convexity-based metric. The simulations show that the perturbation coefficients systematically increase with decreasing convexity within a given shape family, indicating enhanced compliance associated with more irregular pore shapes. The extended DEM model is further validated using well-log and micro-computed tomography (μCT) data from carbonate reservoirs in the Mumbai Offshore Basin, India. The inclusion of perturbation coefficients substantially improves the prediction of shear-wave velocity compared to the standard DEM approach. Overall, the extended DEM framework provides a practical means of incorporating the mechanical effects of irregular pore geometries into rock-physics models, thereby improving the characterisation of elastic properties in heterogeneous carbonate systems.