Non-equilibrium thermodynamics approach to mass transport in sorptive dual continuum porous media: A theoretical foundation and numerical simulation

Modeling gas flow in sorptive porous materials (e.g. coal) offers significant challenges compared to that of nonsorptive porous media (e.g. conventional hydrocarbon reservoirs). Sorption processes in the matrix, gas flow in the fractures (cleats) and induced strains in the bulk of coal interact in a coupled manner, affecting the sorption, mechanical and hydraulic characteristics of the media. Despite extensive research on constitutive models that take into account the coupling processes in gas sorbing systems, these developed constitutive models are often phenomenological and thermodynamically inconsistent (violate thermodynamic laws). The models developed based on equilibrium thermodynamics on the other hand are unable to capture the time dependency of coupling processes. We, therefore, use the non-equilibrium thermodynamics along with continuum mechanics to derive a thermodynamically consistent formulation for the constitutive equations of mechanical, hydraulic and sorption processes in gas sorbing media considering the time dependency of the involved coupling processes. The model, also referred to as NETCoal in this study, considers changes in gas content in the tight coal matrix through sorption and diffusion processes along with gas leakage from the matrix into fractures (cleats) where Darcy type flow takes place. The model also accounts for the time dependency of coupling processes especially the volumetric strains induced by gas sorption and their overall effects on changes in the fracture aperture, hence in the bulk flow conductivity. The finite element method is then employed to discretize and solve the set of governing equations for the bulk displacement (and stress), the gas pressure in coal fractures and the gas content in the matrix. Simulation results are analyzed based on conceptualized cases with input data from a coal seam located in eastern Australia. We also present a parametric study to demonstrate the sensitivity of results to main coupling parameters.