| The study of fluid seepage in fractured porous media is one of the main basic problems in the study of unconventional oil and gas reservoirs and karst groundwater seepage in recent years.In fractured porous media,the width of the fractured region is very small compared to the characteristic length of the surrounding porous media region.In order to reduce the computation,the dimension of the fracture region can be reduced,and the fracture is regarded as an interface of the porous media region,and a codimensional porous media seepage coupling model is obtained.The model is composed of the Darcy equation,the mass conservation equation and the coupling conditions of the porous media and the reduced dimension fracture region.Because of its local mass conservation and easy realization,block-centered difference is widely used to discreteness of spatial derivatives of differential equations in fluid seepage models.In this paper,block central difference method is used to deal with the equations of seepage,coupling equations and boundary conditions in codimension fractured porous media,and a large scale linear equations system is obtained.Because the convergence of the multi-grid iteration method is not affected by the discrete grid scale,it is very suitable for the rapid solution of the codimension fracture seepage model,so the multi-grid method can be used to solve the discrete linear equations system numerically.Finally,numerical experiments are carried out to verify the effectiveness of the proposed method in porous media with different fracture distributions.By comparing The Times and time of Gauss-seidel and other iterative methods when converging,the efficiency of the method is verified.At the same time,by changing the permeability parameters of the crack and the spatial scale of the discrete grid,it is verified that the stability and convergence of the multi-grid method based on block central difference are not affected by the grid scale. |
