Numerical simulation of single-phase fluid flow in fractured porous media

The models of single-phase fluid filtration in the fractured medium have been considered. Fractures have a significant impact on filtration processes, because they act as highly conductive channels. The mathematical model has been described by a parabolic pressure equation. Two approaches to flow approximation in fractures have been discussed: Approach 1 (by defining the nonhomogeneous coefficient for a cell occupied by the fracture); Approach 2 (by using a discrete model of fractures). Both approaches enable the explicit flow simulation in fractures by means of grid methods. Approximation of the problem has been performed using the method of finite differences and the method of finite elements. Numerical comparison of the two methods based on the model two-dimensional problem has been carried out. The results of simulation for the three-dimensional case have been presented.