Two-dimensional black-oil simulation using the meshless extended finite volume method

This paper has developed the first meshless numerical solver for the reservoir black-oil model. The meshless solver uses a point cloud that is virtually unrestricted by topological constraints during generation and the extended finite volume method to discretize the reservoir computational domain and the governing equations, respectively. It can directly use the mature nonlinear solvers in grid-based simulators to calculate the global nonlinear discrete equations and obtain the distribution of oil, gas, and water saturations and pressures. This paper has implemented four examples with regular and irregular computational domains to test the computational performance of the meshless simulator. The results of the examples demonstrate that, compared to grid-based methods, the meshless simulator can effectively manage heterogeneous reservoir models and significantly mitigate the challenges associated with discretizing complex reservoir computational domains. Moreover, it avoids the grid orientation effect of the finite volume method that utilizes Cartesian grids by reducing the computational error by more than six times and exhibits good convergence.