Similar Structure of Solutions for Percolation Model in Dual-Permeability of Shale Gas Reservoirs

As for the shale gas of complex seepage problems about adsorption & desorption, diffusion, slippage, seepage and so on, we established respectively shale gas reservoir seepage equations with the premise on adsorption & desorption according to the shale gas seepage theory. During the establishment, we considered slippage effect in the matrix porosity, the slippage effect and gas diffusion in micro-matrix porosity, synthesis, stress-sensitivity, gas diffusion and so on. The percolation model in dual- permeability of Shale Gas Reservoirs was composed of every kind of shale gas reservoir seepage equations, three kinds of outer boundary conditions (closed, constant pressure, infinity), initial conditions and boundary conditions. With the dimensionless transform and Laplace transform, the nonlinear model in dual-permeability of Shale gas reservoirs was transformed into a definite solution problem of ordinary differential equation and solutions of the model in Laplace space were obtained. Then, we analyzed the solutions in depth and found that the solutions of the model had a characteristic of the similar structure. It is great convenience for well test analysis software. It helps to avoid a tedious and complicated calculation process and improve the computational efficiency and, and has a guiding significance on shale gas productivity model.