Theoretical and Modelling Insights into Rate-Dependent Sorptive Viscoelasticity

ABSTRACT Recent thermodynamics-based constitutive modelling has enabled robust formulations for complex coupled mechanical, hydraulic and chemical interactions. Despite such advances, constitutive modelling of fractured sorptive media with complex mechanical behaviour has attracted little attention. This study presents a new sorptive poro-viscoelastic model for fractured rocks specifically integrating 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 adsorbed gas in the matrix pores. The model is exemplified through the simulation of gas production from a sorptive shale formation. The numerical results show that poro-viscoelasticity becomes dominant at late times of production when pore pressure and desorption fronts have progressed significantly. It is also revealed that time-dependent stress accumulation can reach high magnitudes relatively early in the production phase which can cause fracture closure risking impedance to further gas production. Neglecting viscoelastic multiphysics effects in the modelling of fractured sorptive rocks can reduce 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 be the key to explaining some of the complexities encountered during hydraulic fracturing operations such as shale water loss and fracture closures. INTRODUCTION Shale formations are among the most abundant and widely distributed geological formations on earth, with enormous potential as a source of energy. Understanding the mechanical behavior of shales is essential for optimizing the hydraulic fracturing and gas production processes and the long-term stability of shale formations (Algazlan et al., 2022; Huang & Ghassemi, 2013; Siddiqui et al., 2022). The viscoelasticity and sorption behavior of shales are critical parameters that influence the stress-strain response of shale rocks, particularly under dynamic loading conditions as experience during gas production. In this context, a constitutive model that captures the sorptive viscoelasticity of shales can provide valuable insights into the mechanical response of shale formations.