Extended finite element method for analysis of multi-scale flow in fractured shale gas reservoirs

Economic exploration for shale gas is highly dependent on the complexity of the fracture network caused by hydraulic fracturing technology, so it is necessary to accurately assess the effect of the fracture network on gas flow behavior and productivity. Having multiple scales is a remarkable characteristic of gas flow in fractured shale gas reservoirs, which involves multiple flow regimes, including the gas desorption from shale matrix, Knudsen flow in nanoscale pores, Darcy flow in general porous media, Darcy flow in the fracture networks and fluid exchange between the matrix system and the fracture system. The extended finite element method (XFEM) has been integrated with the dual-permeability method (DPM) to investigate the multi-scale problem. Some previous studies have adopted the same solution scheme, but usually considered gas flow in the natural fracture network and in the hydraulic fractures as belonging to the same scale, and in addition, the coverage area of the stimulated reservoir volume (SRV) was underestimated. Based on the XFEM–DPM, this paper subsumes flow in the micro-mecro fractures and macro-hydraulic fractures under two scales because of their different effects on shale gas flow and then presents a new multi-scale extended finite element model to study the multi-scale flow problem in shale gas reservoirs. Moreover, the Lagrangian multiplier method is integrated to introduce the internal well boundary conditions into the XFEM, so the arbitrariness and the asymmetry of the complex fracture network can be taken into account easily to reflect the real flow mechanisms in fractured shale. Case studies indicate that the improved extended finite element model constructed in this paper is effective, especially for complicated asymmetrical physical condition problems.