Multiphase flow simulation of hydraulically fractured wells with pre-existing natural fractures is a challenging task. Discrete fracture network (DFN) is an effective method to simulate a system of anisotropic fracture network. In DFN method unlike double porosity approach, fractures can be defined in different scales and in different apertures and directions such that all details of fractures will be included in the simulation. Also all the interactions and fluid flow in and between the fractures and within the matrix are modelled in a unified manner, using the same computational grid.
We developed software based on DFN model in which both induced fractures and pre-existing natural fractures can be placed at any location and direction in the geological model. Then, quadrilateral unstructured grids are generated using Paving method. Quadrilateral grids are more efficient and more flexible than triangular grids such that the number of quadrilateral grids is reduced to half. A drawback of algorithm in this mesh generation process is that very small grids are generated in the intersection of fractures and in the ends of the fracture grids due to the size difference between the fracture and the matrix. In order to avoid severe time-step restrictions associated with small cells, an endpoint transformation method is used to replace the quadrilateral grids with the triangular grids at both ends of the fracture. As a result, the number of very small grids at the ends of fractures is notably decreased.
In this paper, the results of two-phase flow simulation in a hydraulically fractured well with pre-existing natural fractures are presented. For solving the pressure and saturation equations in each grid, the inter region of quadrilateral mesh is taken as a control volume cell and the governing equations are solved using MPFA (Multi-Point Flux Approximation) technique which is designed to give a correct discretization of the flow equations for general non-orthogonal grids. Finally the results of our software are tested to verify its validity in theory, algorithm, and efficiency in calculation.