Elasticity of porous rocks with microscopic pore adaptivity

ABSTRACT: Modeling rock deformation is crucial for a variety of subsurface technologies, such as the multiphysics of carbon storage. Here, a new class of microstructure-enhanced continuum models is formulated to quantify at multiple length scales the elastic properties and storage capacity of potential host rocks. Specifically, a theoretical framework accounting for nonlinear alterations of the rock stiffness is derived through homogenization procedures considering the evolution of microscopic quantities such as the size, shape, orientation, and distribution of pores and cracks. By combining the Ponte Castañeda-Willis micromechanical model with the Biot theory of poromechanics, a new formulation is obtained to derive elastic constitutive equations for rocks comprising a wide range of idealized microstructural units, including pores with spherical, penny-, or needle-shaped geometry. The formulation is further enhanced by introducing a scheme allowing for microscopic pore adaptivity, which enables reversible segmentation and/or merging of pores. While multiple choices are possible for this scheme, here a classic strategy for pore/crack segmentation is used as a working hypothesis to test the model. The versatility and reliability of the proposed model are illustrated by comparing its predictions against laboratory measurements collected for specimens of rocks regarded as potential targets for subsurface carbon storage.