The nonlinear effects of unsteady multi-scale shale gas percolation,such as desorption,slippage,diffusion,pressure-dependent viscosity,and compressibility,are in-vestigated by numerical simulation.A new general mathematical model of the problem is built,in which the Gaussian distribution is used to describe the inhomogeneous in-trinsic permeability.Based on the Boltzmann transformation,an effcient semi-analytical methon in proposed.The problem is then converted into a nonlinear equation in an inte-gral form for the pressure field, and a related explicit iteration scheme is constructed by numerical discretization.The validation examples show that the proposed mathod 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 litera-ture.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.