Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

The nonlinear effects of unsteady multi-scale shale gas percolation, such as desorption, slippage, diffusion, pressure-dependent viscosity, and compressibility, are investigated by numerical simulation. A new general mathematical model of the problem is built, in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability. Based on the Boltzmann transformation, an efficient semi-analytical method is proposed. The problem is then converted into a nonlinear equation in an integral form for the pressure field, and a related explicit iteration scheme is constructed by numerical discretization. The validation examples show that the proposed method has good convergence, and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature. Desorption, slippage, and diffusion have significant influence on shale gas flows.The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.