Investigation on Nonlinear Behaviors of Seepage in Deep Shale Gas Reservoir with Viscoelasticity

The nonlinear behaviors in deep shale gas seepage are investigated, involving the non-Darcy effect, desorption, and viscoelasticity. The seepage model accounts for the nonlinear compressibility factor and gas viscosity due to their stronger non-linearity at a high pressure and temperature. The viscoelastic behavior in deep shales, including matrix deformation and proppant embedment, is quantified, and the evolution of the time-varying and pressure-dependent porosity and permeability is derived. A semi-analytical approach with explicit iteration schemes is developed to solve the pressure field. The proposed model and method are verified by comparing the simulation results with the field data. The results show that the gas production contributed by the non-Darcy effect and desorption is much higher in deep shale than in shallow shale. However, Darcy flow contributes 85% of the total gas production of deep shales. If the effect of viscoelastic behavior is neglected, the accumulative gas production would be overestimated by 18.2% when the confining pressure is 80 MPa. Due to the higher pressure and temperature, the accumulative gas production in deep shale is 150% higher than that in shallow shale. This investigation helps to clarify the performance of the non-Darcy effect, desorption, and viscoelastic behavior in deep shales, and the proposed model and approach can facilitate the optimization simulations for hydraulic fracturing strategy and production system due to its high efficiency.