LAUSR

Abstract The evolution of coal permeability has been studied exhaustively and a broad array of permeability models developed. These models are normally derived under the assumption of fluid pressure equilibrium between matrix and fractures. Under this assumption, these models define coal permeability as a function of either gas pressure or effective stress. However, experimental observations indicate that coal permeability may change significantly under a constant observed gas pressure or assumed effective stress. The goal of this study is to resolve this contradiction. In this study, we hypothesize that coal permeability is closely related to the expansion of gas-invaded area/volume as a concentration front propagates from the fracture wall into the matrix. When this invaded volume/area is localized around the fracture, the gas-induced swelling reduces the coal permeability. When the area spreads throughout the entire matrix, gas-induced swelling may increase coal permeability. This important mechanism of transition from local (to the fracture) swelling to global (into the matrix medium) swelling is incorporated into an overlapping dual permeability approach. In this approach, the coal is characterized by a well-defined macroscopic model consisting of four overlapping/interpenetrating continua comprising: (1) coal matrix system; (2) coal fracture system; (3) gas flow in the matrix system; and (4) gas flow in the fracture system. These four continua are connected through a full set of cross-coupling relations, including (1) local force balance between the matrix and the fracture; (2) local deformation compatibility between the matrix and the fracture; and (3) mass exchange between the matrix and the fracture. We apply this approach to generate coal permeability maps under the influence of multiple coupled processes. For a particular coal sample, the permeability is bounded by the solutions for the free-swelling case (upper bound) and for the constant volume case (lower bound). The variations of permeability between the upper and lower bounds under a constant gas pressure are determined by the dynamics of matrix-fracture interactions. Current experimental measurements are bounded by these limits depending on the state of equilibrium between matrix and fractures. These model results are verified against experimental observations reported in the literature.