A novel discontinuous Galerkin model for two-phase flow in porous media using an improved IMPES method

Abstract

Purpose

The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme.

Design/methodology/approach

The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method.

Findings

Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media.

Research limitations/implications

The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible.

Practical implications

The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers.

Originality/value

The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.

Citation

Jamei, M. and Ghafouri, H. (2016), "A novel discontinuous Galerkin model for two-phase flow in porous media using an improved IMPES method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 1, pp. 284-306. https://doi.org/10.1108/HFF-01-2015-0008