A Coupled Model of Multiscaled Creep Deformation and Gas Flow for Predicting Gas Depletion Characteristics of Shale Reservoir at the Field Scale

The viscoelastic behavior of shale reservoirs indeed impacts permeability evolution and further gas flow characteristics, which have been experimentally and numerically investigated. However, its impact on the gas depletion profile at the field scale has seldom been addressed. To compensate for this deficiency, we propose a multiscaled viscoelasticity constitutive model, and furthermore, a full reservoir deformation–fluid flow coupled model is formed under the frame of the classical triple-porosity approach. In the proposed approach, a novel friction-based creep model comprising two distinct series of parameters is developed to generate the strain–time profiles for hydraulic fracture and natural fracture systems. Specifically, an equation considering the long-term deformation of hydraulic fracture, represented by the softness of Young’s modulus, is proposed to describe the conductivity evolution of hydraulic fractures. In addition, an effective strain permeability model is employed to replicate the permeability evolution of a natural fracture system considering viscoelasticity. The coupled model was implemented and solved within the framework of COMSOL Multiphysics (Version 5.4). The proposed model was first verified using a series of gas production data collected from the Barnett shale, resulting in good fitting results. Subsequently, a numerical analysis was conducted to investigate the impacts of the newly proposed parameters on the production process. The transient creep stage significantly affects the initial permeability, and its contribution to the permeability evolution remains invariable. Conversely, the second stage controls the long-term permeability evolution, with its dominant role increasing over time. Creep deformation lowers the gas flow rate, and hydraulic fracturing plays a predominant role in the early term, as the viscoelastic behavior of the natural fracture system substantially impacts the long-term gas flow rate. A higher in situ stress and greater formation depth result in significant creep deformation and, therefore, a lower gas flow rate. This work provides a new tool for estimating long-term gas flow rates at the field scale.