Mesoscale saturated & unsaturated poroelasticity of highly heterogeneous porous solids- discrete solid fluid descriptions

Abstract

The capacity of the continuum approach to capture the effective poromechanical response of highly heterogeneous porous solids is limited. Specifically, the mean-field theories of continuum micromechanics cannot capture the full spatial variations of mechanical properties and restricted to scale separability. Additionally, any approach to unsaturated poromechanics requires a description for fluids that accounts for confinement, temperature variations and the strength of fluid-fluid and fluid-solid interactions. Most prevailing models are phenomenological in approach and hinge on the concept of effective stress for capturing liquid and gas interactions with solid(s). Thus, a framework is implemented based on discrete descriptions for solids and fluids. The behavior of solids is captured through Lattice Element Method.

This method utilizes a finite number of mass points, each interacting with their nearest neighbors through linear or non-linear effective interaction potentials while capable to account for anisotropy. The fluid behavior is described in the grand canonical ensemble in a statistical mechanics approach which paves the way to study the behavior of confined fluids while providing access to the capillary stress tensorial field in the pore domain. The two descriptions are brought together via a local pore pressure force formulation that links capillary pressures to solid deformation. For the case of fully saturated poroelasticity, generalized discrete expressions for Biot poroelastic coefficients defined in statistical mechanics ensembles are presented. The developed theoretical model and its implementation are validated on simple porous media for which micromechanics based solution exist.

By way of application to real heterogeneous materials imported from computed tomography (CT) scans, a methodology is presented to merge lab-measured nanoindention data and CT scans into the developed computational framework. Finally, capillary condensation in disordered granular packings is studied. The results provide insights into confined fluid behavior, fluid criticality, the interplay of disorder, temperature and capillary stress fields as well as liquid clustering formation, growth and coalescence.