A locally conservative multiphase level set method for capillary-controlled displacements in porous media

Abstract

We present a multiphase level set method with local volume conservation for capillary-controlled displacement in porous structures. Standard numerical formulations of the level set method for capillary-controlled (or, curvature-driven) motions assume phase pressures and interface properties are spatially uniform and disregard the fact that separate phase ganglia typically have distinct pressures. This is a major problem for the suitability of such methods to simulate capillary trapping in porous rocks as it will lead to severe mass loss. The method presented here preserves volumes of individual phase ganglia, while it predicts capillary pressures between ganglia and surrounding phases. A conservative volume redistribution algorithm handles ganglia breakup and coalescence. The method distinguishes between three-phase systems, where separate level set functions describe the different phases, and two-phase systems, where one level set function represents interfaces. We present sequential and parallel algorithms for the new method and emphasize important aspects specific to the patch-based parallel implementation.We validate the method numerically by applying local volume conservation to simulations of two and three phase systems in both two and three spatial dimensions. The model is tested for both saturation and pressure controlled systems and handles both merging and splitting of phase ganglia.