A Darcy-Brinkman-Biot Approach to Modeling the Hydrology and Mechanics of Porous Media Containing Macropores and Deformable Microporous Regions

Abstract

The coupled hydrology and mechanics of soft porous materials (such as clays, hydrogels, membranes, and biofilms) is an important research area in several fields, including water and energy technologies as well as biomedical engineering. Well-established models based on poromechanics theory exist for describing these coupled properties, but these models are not adapted to describe systems with more than one characteristic length scale, that is, systems that contain both macropores and micropores. In this paper, we expand upon the well-known Darcy-Brinkman formulation of fluid flow in two-scale porous media to develop a “Darcy-Brinkman-Biot” formulation: a general coupled system of equations that approximates the Navier-Stokes equations in fluid-filled macropores and resembles the equations for poroelasticity in microporous regions. We parameterized and validated our model for systems that contain either plastic (swelling clay) or elastic microporous regions. In particular, we used our model to predict the permeability of an idealized siliciclastic sedimentary rock as a function of pore water salinity and clay content. Predicted permeability values are well described by a single parametric relation between permeability and clay volume fraction that agrees with existing experimental data sets. Our novel formulation captures the coupled hydro-chemo-mechanical properties of sedimentary rocks and other deformable porous media in a manner that can be readily implemented within the framework of Digital Rock Physics.