Viscoelastic Behavior of Rocks Saturated with Sorptive Gases: A Heuristic Internal Variables Approach

Recent thermodynamics-based constitutive modeling has enabled robust formulations for complex coupled mechanical, hydraulic, thermal, and chemical interactions. Despite such advances, the constitutive modeling of fractured sorptive media with complex mechanical behavior has attracted less attention. We present a new sorptive poroviscoelastic model for fractured rocks that specifically integrates the rate-dependent viscous flow into the coupled fracture fluid flow and matrix gas desorption processes using the two-potential framework, mixture theory, and continuum mechanics. The proposed dissipative viscoelastic strain rate evolution law is governed by the applied stress variable and the amount of gas adsorbed in the matrix pores. The model is exemplified through the simulation of gas production from a sorptive shale formation. The numerical results show that poroviscoelasticity becomes dominant at late production times when the pore-pressure and desorption fronts have progressed significantly. It is revealed that time-dependent stress accumulation can reach high magnitudes which can cause fracture closure that risks impedance to further gas production. Neglecting viscoelastic multiphysics effects in the modeling of fractured sorptive rocks can reduce the accuracy of the predicted production data. In addition, the contribution of desorption-induced viscoelasticity to bulk rock deformation may be substantial in shales and other highly adsorbing rocks and may also be the key to explaining some of the complexities encountered during drilling or hydraulic fracturing operations.