Numerical modeling of microscopic fluid distribution in porous media

Abstract

Three numerical methods have been developed to model the equilibrium distribution of fluid phases in a multiphase saturated porous medium. The basic assumption made is that the distribution of phases is governed by the static interfacial free energy of the system, such that the equilibrium phase distribution corresponds to a minimum in the total interfacial free energy of the system. The example of determining the distribution of water vapor and liquid water in 2D numerical models of the pore space in a rock is considered. Starting with a numerical model of the pore space, the objective of each method is to obtain the minimum energy configuration of water vapor and liquid water in the pore space for some set level of water saturation. Two of the methods are simple and computationally fast methods that can produce fluid distributions close to, or matching, the equilibrium configuration. These methods can, however, produce metastable configurations due to the simplistic nature of the algorithms. The third method applied to this problem is a simulated annealing method. This method consistently produced the lowest possible energy configuration. It is concluded that simulated annealing can be successfully used to numerically model fluid distribution in multiphase saturated porous media.