Generalized finite difference method (GFDM) based analysis for subsurface flow problems in anisotropic formation

Abstract

This paper applies the meshless generalized finite difference method (GFDM) to analyze the subsurface flow problem in anisotropic formations for the first time, and develops the treatment methods of anisotropic permeability tensor in continuous function and discrete distribution expressions respectively. In particular, in case of the common discrete distribution expression of anisotropic permeability tensor in reservoir simulation, this paper suggests combining general difference operators and harmonic average scheme to simply and efficiently obtain the meshless discrete scheme of the anisotropic flow equation. Three numerical examples of steady and transient flow in the rectangular computational domain, transient flow with complex boundary, and steady flow with strongly discontinuous anisotropic permeability are used to verify the high accuracy and good convergence of GFDM to handle anisotropic flow problems. Compared with the traditional mesh-based reservoir numerical simulation method that replies on laborious gridding to discretize the reservoir domain and complicated multi-point flux approximation (MPFA) to handle discrete distribution anisotropic permeability tensor, the meshless GFDM can be more practically applied to the anisotropic flow problems in the reservoir domain with complex geometry and complex boundary conditions. Besides, it is found that the radius of the influence domain has little impact on the accuracy of steady flow. For the transient flow, it generally holds that the larger the radius of the influence domain, the lower the calculation accuracy in case of Cartesian collocation. In sum, this work provides an efficient and simple meshless solver to handle anisotropic flow problems in porous media under GFDM framework, which reveals the great application potential of GFDM in reservoir numerical simulation.