Investigating pore scale configurations of two immiscible fluids via the level set method

The study of pore level displacement of immiscible fluids has scientific appeal as well as many applications, notably in oil reservoir engineering and in subsurface environmental engineering. Pore network models have been used for numerical simulation of fluid dis-placement over relevant physical volume sizes. An accurate description of the mechanics of displacement could significantly improve the predictions from network models of capil-lary 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 de-duced from capillary pressure and local pore geometry. Several challenges arise in deter-mining these criteria. At constant pressure and surface tension, pore scale interfaces are modeled as constant mean curvature surfaces, which are not easy to calculate. Moreover, extremely irregular geometry of natural porous media makes it difficult to evaluate sur-face curvature values and corresponding geometric configurations of two fluids. Finally, accounting for the topological changes of the interface, such as splitting or merging, is nontrivial. We apply the level set method and the Surface Evolver software for tracking and prop-agating interfaces in order to robustly handle topological changes and to obtain geomet-rically correct interfaces. We describe a simple but robust model based on the level set method for determining critical curvatures for throat drainage and pore imbibition. The model is set up for pseudo-static displacements and thus simulates only the approach to spontaneous events (Haines jump, pore body imbibition). The pore scale grain boundary conditions are extracted from model porous media and from imaged geometries in real rocks. 1