A new Matrix Equivalent Discrete Fracture Network model for variable density flow in fractured porous media

• Modeling variable density flow in fractured porous media with complex fracture network is challenging. • A new model is proposed where the low-permeable matrix is replaced by an equivalent uniform fracture network. • The variable density flow problem is solved on the global network, formed by the combination of the initial fracture network with the uniform matrix equivalent fracture network. • Several numerical experiments are performed to validate the new model by comparison with the discrete fracture model (DFM) • Numerical simulations show the high efficiency of the new model for variable density flow in fractured porous media, especially in the case of complex fracture networks. Modeling variable density flow (VDF) in fractured reservoirs is a challenging task because of ( i ) the high contrast of permeability between the fractures and the matrix, ( ii ) the complexity of the fracture network and ( iii ) the nonlinearities induced by density variation. The dual-porosity model (DPM) and the discrete fracture-matrix (DFM) model are among the most used models for the simulation of flow in fractured reservoirs. The DPM is efficient as it uses an implicit representation of the fractures but is not sufficiently accurate since it cannot account for the effect of individual fractures. The DFM model uses an explicit representation of the fractures but suffers from lack of efficiency induced by the poor quality of meshes in the case of complex fracture networks. In this study, a new efficient model named matrix-equivalent discrete fracture network (MEDFN) model is developed for VDF in fractured porous media. The main idea of the VDF-MEDFN model is to use an explicit representation of the high-conductive fractures and to replace the low-permeable matrix by an equivalent rectangular fracture network. The flow and the transport equations are then solved on the global fracture network formed by the combination of the initial high-conductive fracture network and the fictitious rectangular low-permeable fracture network representing the matrix. The VDF-MEDFN model is developed in this work leveraging the method of lines (MOL) with the upwind finite volume method for the spatial discretization and high-order methods for the time integration. Performed numerical experiments show the validity of the new model and highlight its high performances against the VDF-DFM model, based on DFM and the mixed finite element method.