A Green element method-based discrete fracture model for simulation of the transient flow in heterogeneous fractured porous media

Advances in hydraulic fracturing technology are promoting global interest in the simulation of the transient flow in fractured porous media. Boundary element method (BEM) is widely used in pressure transient analysis because of its high precision and simple discretization of the boundaries and the fractures. However, BEM is computationally expensive when real heterogeneities and large numbers of fractures are modeled. A Green element method (GEM)-based discrete fracture model (DFM) is proposed in this paper to address this problem, and this is the first study to enrich the GEM in modeling the transient behavior of heterogeneous porous media with discrete fracture networks. GEM is applied to handle formation heterogeneities and discrete fractures. First, a new mathematic model and integral formulation are proposed with the consideration of formation heterogeneities and discrete fractures. Next, structured Cartesian grids are used to discretize the domain and characterize the heterogeneities, and discrete fracture networks are embedded into the domain grids. Then, GEM is used to handle fluid flow between connected domain blocks and between a domain block and connected discrete fracture segments. The finite difference method (FDM) is used to model fluid flow between connected discrete fracture segments. The solution of the model is obtained by coupling the two systems. Two validation cases and several synthetic cases are used to verify the precision, efficiency, and application of the proposed GEM-based DFM. The results show that the proposed model is precise and efficient by comparing it to the BEM and a commercial simulator. The number of integrals and the computation are largely decreased by applying the boundary integral equation to each local block. Finally, a field example with several synthetic cases is studied to show the model's application. The proposed GEM-based DFM serves as a good tool for simulation of the transient flow in heterogeneous fractured porous media.