Characterization of Swelling Modulus and Effective Stress Coefficient Accommodating Sorption-Induced Swelling in Coal

Abstract

The effective stress law transforms external stress (σ) and pore pressure (p), into a single equivalent variable (σeffective), expressed as σeffective = σ – αp, where α is the effective stress coefficient. For porous media, every property such as drained deformability, permeability, storage capacity, and acoustic velocity has its own particular effective stress coefficient. We extend the effective stress law for deformation in sorbing porous media (coal and organic-rich shales), accommodating sorption-induced swelling, by introducing the concept of an effective modulus of swelling/shrinkage. This attributes the volumetric strain (ev) of the sorbing medium to changes in the effective stress as ev = (σ – αsp)/K, with the effective stress coefficient αs = 1 – K/Ks + K/Zp, in terms of the bulk modulus (K) of the sorbing porous medium, the bulk modulus (Ks) of the solid grains and the swelling modulus (Zp). Thus, the static problem of deformation in sorbing porous media can be simplified into an elastic proble...