Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells

摘要

A unified mathematical model is established to simulate the nonlinear unsteady percolation of shale gas with the consideration of the nonlinear multi-scale effects such as slippage,diffusion,and desorption.The continuous inhomogeneous models of equivalent porosity and permeability are proposed for the whole shale gas reservoir includ ing the hydraulic fracture,the micro-fracture,and the matrix regions.The corresponding semi-analytical method is developed by transforming the nonlinear partial differential governing equation into the integral equation and the numerical discretization.The nonlinear multi-scale effects of slippage and diffusion and the pressure dependent effect of desorption on the shale gas production are investigated.