Poro-viscoelastic modeling of production from shale gas reservoir: An adaptive dual permeability model

In most simulations of gas production from shale reservoirs, only the elastic deformation of reservoir rock and fractures is modeled. However, many experimental studies and field investigations indicate shale experiences viscoelastic deformation. In this work, a numerical model is constructed by implementing a poro-viscoelastic model into a dual permeability model (DPM) by using finite element method (FEM), to investigate the coupled time-dependent viscoelastic deformation of shale, and fracture permeability evolution in response to compressible flow of gas and gas desorption. The viscoelastic effect is considered through both deviatoric and mean effective stresses to allow for the effect of shear strain localization. The geomechanical model is first verified against available analytical and numerical solutions. Then, the model is applied to a few synthetic production cases to investigate the geomechanical evolution of a fractured reservoir. Comparing the case of poroelasticity and poro-viscoelasticity shows that the pore pressure differences throughout the domain are small, however, the stress evolution is quite divergent, with higher fracture closure in the poro-viscoelastic case. Comparison of the cumulative gas productions for poroelastic and poro-viscoelastic cases shows that cumulative gas production predicted by the poro-viscoelastic case is always lower than that of the poroelastic one. The difference between the two cases increases for long production times, as the viscous deformation (creep) of the reservoir rock closes the fracture. Results of the numerical simulations suggest that viscous deformation-enhanced closure of natural fractures that feed the main propped fractures can have a critical role in production decline.