Meshless Generalized Finite Difference Method for Gas–Water Two-Phase Flow Equation of Complex-Shape Shale Gas Reservoirs

In this paper, the meshless generalized finite difference method (GFDM) is applied to the gas–water two-phase flow equation of complex-shape shale gas reservoirs. GFDM is a regional meshless method, in which the partial derivatives of unknown functions at any node can be expressed as differential approximations of other node functions in the node influence domain by using Taylor series expansion of multiple functions and least squares approximation. It overcomes the dependence of the discrete fracture method (DFM) on the grids and can obtain the finite difference approximation with higher precision. Compared with DFM, the meshless GFDM is based on the point cloud discretization which is more flexible to describe the complex geometric of the field case. Thus, reducing the computational freedom of the numerical model and the calculation cost. In the last, the numerical examples of the complex boundary demonstrate the computational performance of the proposed method for gas–water two-phase flow in shale gas reservoirs. In conclusion, this work provides an efficient meshless GFDM-based calculation method for solving the gas–water two-phase flow problem with the complex boundary conditions in shale gas reservoirs, and reveals the tremendous application potential of meshless GFDM in the numerical simulation of shale reservoirs with the complex boundary conditions.