Numerical Simulation Of Flow In Porous Media With Fracture

In this paper,the block center finite difference method is used to simulate the singlephase Darcy flow problem in two-dimensional fractured porous media.It is divided into the following parts:(1)A reduced dimensional model is established to describe the singlephase Darcy flow in fracture,(2)the mixed finite element method is equivalent to block center finite difference method,(3)solving the fluid flow equation derived from the reduced model by block center finite difference method.A dimensionality reduction model is established to describe the flow problem of single-phase Darcy flow in fractures.Compared with the whole area,the width of the crack is very small,which simplifies the crack into an interface between two connected areas.The source term in the conservation equation at the fracture represents the flow of the subdomain into the fracture.Darcy's law is a vector equation.The average value of the tangential component of the fracture is obtained,and the Darcy's law in the fracture is obtained.The Darcy's law links the tangential component of the average pressure with the tangential component of the average Darcy velocity.By averaging the whole fracture and writing it into the flow equation in the form of mixing,a flow equation along the fracture is obtained,which is coupled with the flow equation in the adjacent two subdomains.The mixed finite element method is equivalent to the block center finite difference under a specific numerical integration,and the existence and uniqueness of the solution of the previous dimensionality reduction model is proved by the theoretical knowledge of the mixed finite element method.The block center finite difference method is used to solve the fluid flow equation derived from the dimensionality reduction model.The equations of the dimensionality reduction model are discretized by the block center finite difference method.The numerical examples show that the fracture is a fast channel or a geological barrier,which depends on the value of permeability tensor at the fracture.