Investigating pore scale configurations of two immiscible fluids via Level Set Method

Abstract

The study of pore level displacement of immiscible fluids has scientific appeal as well as a plethora of engineering applications, notably in oil reservoir engineering and in environmental problems in the shallow subsurface. Pore network models have been used for numerical simulation of fluid displacement over relevant physical volume sizes. An accurate description of the mechanics of 3D displacement could significantly improve the predictions from network models of capillary pressure - saturation curves, interfacial areas and relative permeability in real porous media. If we assume quasi-static displacement, the criteria for interface movement can be deduced from capillary pressure and local pore geometry. The capillary pressure (pressure difference between the non-wetting and wetting fluid phase) at the fluid interface is determined by the Young-Laplace equation Pc = 2*S*C, where S is the interfacial tension and C is mean curvature of the interface. At constant pressure and surface tension, pore scale interfaces are modeled as constant mean curvature surfaces. Extremely irregular geometry of natural porous media makes it difficult to evaluate surface curvature values and corresponding geometric configurations of two fluids. A purely mechanistic set of pore level criteria for fluid advancement through pore space implemented by [1] relied on idealizing the interfacial surface as locally spherical. Even with spherical idealizations, simulating the topological changes of the interface, such as splitting and merging fronts, is nontrivial. We apply the Level Set Method (using Level Set Toolbox [2]) and the Surface Evolver software [3] for tracking and propagating interfaces in order to robustly handle topological changes and to obtain geometrically correct interfaces. For the level set method, we describe a simple model for mechanical equilibrium between capillary pressure and surface tension. The results from the models are illustrated at the pore scale in two and three dimensions. The pore scale grain boundary conditions are extracted from model porous media and from measured geometries in real rocks [4]. 1. M. Gladkikh and S. L. Bryant. Prediction of imbibition in unconsolidated granular materials. Journal of Colloid and Interface Science 288 (2005) 526-539 2. K. Brakke. Surface Evolver, an interactive program for the modeling of liquid surfaces shaped by various constraints. http://www.susqu.edu/facstaff/b/brakke/evolver/html/intro.htm#overview 3. I. M. Mitchell and J. A. Templeton. A Toolbox of Hamilton-Jacobi Solvers for Analysis of Nondeterministic Continuous and Hybrid Systems. Springer-Verlag. Lecture Notes in Computer Science (LNCS) 3413, 480-494. 4. W. B. Lindquist. 3DMA-Rock, A Software Package for Automated Analysis of Rock Pore Structure in 3-D Computed Microtomography Images http://www.ams.sunysb.edu/~lindquis/3dma/3dma_rock/3dma_rock.html