A three-scale poromechanical model for swelling porous media incorporating solvation forces: Application to enhanced coalbed methane recovery

• Published in: Mechanics of materials Vol. 131; pp. 47 - 60
• Main Authors: Le, Tien Dung, Moyne, Christian, Murad, Marcio A., Panfilova, Irina
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2019; Elsevier
• Subjects: Computer Science; Density functional theory; Engineering Sciences; Enhanced coalbed methane recovery; Homogenization; Mechanics; Modeling and Simulation; Poromechanics; Solvation force; Swelling porous media; Thermics; Homogenization; Density functional theory; Solvation force; Swelling porous media; Poromechanics; Enhanced coalbed methane recovery
• ISSN: 0167-6636; 1872-7743
• DOI: 10.1016/j.mechmat.2019.01.021

•Development of a new poromechanical model for expansive porous media with two levels of porosity.•Incorporation of solvation forces through formal homogenization coupled with density functional theory.•Numerical reconstruction of the homogenized non-linear poroelastic coefficients dependent on the solvation force.•Computation of cleat closure due to CO2 injection in coalbed methane recovery. In this work we develop an innovative three-scale poromechanical model for expansive porous media characterized by two levels of porosity associated with nano and macropores (or fissures). New versions of the effective stress principle and the constitutive law for the Lagrangian porosity are rigorously reconstructed within the framework of the formal homogenization procedure in the upscaling of the anomalous behavior of a fluid mixture in the nanopores. Local adsorption isotherms are computed within the framework of Thermodynamics of inhomogeneous fluids in nanopores by exploring the tools of the Density Functional Theory (DFT) for calculating fluid density profiles based on the minimization of grand canonical potential under uniformity of the chemical potential. At the microscale, a modified form of the effective stress principle is derived incorporating the disjoining pressure effects. By linearizing the poromechanics around a reference state, the microscopic governing equations are rephrased in the framework of an incremental nonlinear elastic formulation with coefficients strongly dependent on the disjoining pressure. The poromechanics of the matrix is then homogenized with the macropore/fissure network giving rise to a new three-scale model ruled by the effective stress, Lagrangian porosity and permeability. Within the framework of DFT, the profiles of structural component of the disjoining pressure and partition coefficient are numerically constructed for a binary mixture of CH4/CO2 in the nanopores of an organic matter aiming application to enhanced coalbed methane recovery. Computational simulations illustrate the behavior of the effective coefficients. Among the numerical results we highlight the appearance of two regimes of closure and mild-opening of the cleats strongly dependent on the CO2-partial pressure.