Homogenization of elastic properties utilizing the Mori-Tanaka method for formations containing stiff inclusions embedded in soft rock matrix

ABSTRACT: The Avalon formation located in the Delaware Basin, southeast New Mexico, is an unconventional reservoir with complex heterogeneity, consisting of organic-rich mudstones interbedded with carbonates and debris flows containing chert nodules. These nodules alter the elastic properties of the formation, influencing fracture dimensions during hydraulic fracturing. This study presents a method for homogenizing the elastic properties of formations with stiff inclusions, such as chert, for hydraulic fracture modeling. The approach utilizes micromechanical models from composite science, specifically the Mori-Tanaka method, which estimates effective elastic properties of materials with inclusions. The homogenization results were validated with finite element analysis (FEA), which modeled the chert inclusions as stiff ellipsoids in a soft matrix. Sensitivity analyses examined how variations in mechanical properties of inclusions affected the homogenized elastic properties. The results showed that differences in elastic moduli between the chert and shale increase fracture half-length and height, while decreasing fracture width. This approach provides a computationally efficient method for homogenizing heterogeneous formations that contain ellipsoidal inclusions to then be used in hydraulic fracture modeling.