An Effective Time-Splitting Technique for Full-Tensor Flow Model

<jats:title>Abstract</jats:title> <jats:p>A flux-continuous model incorporating full-tensor permeability has been developed for two-phase flow of immiscible and incompressible fluids. Full-tensor permeability is often required to characterize flow from the upscaling process in fine grids heterogeneous reservoirs.</jats:p> <jats:p>The governing equations can effectively be formulated in fractional flow equations; i.e. in terms of global pressure and saturation equations. An algorithm is implemented applying a highly accurate numerical approach based on the mixed finite volume element (MFVE) method for discretizing the pressure equation, and a combination of the MFVE and the finite volume element (FVE) methods for the saturation equation. The saturation equation is discretized by means of a time-splitting algorithm that allows an explicit time stepping for FVE applied to the advection equation, and an implicit time stepping for MFVE applied to the corrective equation of capillary diffusion.</jats:p> <jats:p>Numerical experiments of 1-D and 2-D flow are presented to demonstrate the efficiency and robustness of the time-splitting technique. The 1-D Buckley-Leverett displacements verify accuracy and numerical behavior of the proposed scheme. It is also used to determine the optimum time-stepping strategy. The 2-D simulation also show accurate results for full-tensor models and a highly heterogeneous reservoir. It is proved that proposed method can significantly reduce computational time for both 1-D and 2-D displacements.</jats:p>