Pore-Network Approach for Calculating the Interfacial Area of Wetting/Non-Wetting Phases in Porous Media

In order to better understand and quantify many flow and transport processes in porous media (e.g. soil remediation strategies, reactive transport, CO2 sequestration, etc.) it is important to acquire a detailed knowledge of fluid-fluid and fluid-solid interfacial areas since they play a key role in the dynamics of multiphase flow and transport in porous media. Fluid-fluid interfacial areas (e.g., between wetting and non-wetting phases) control many mass transfer processes in porous media such as phase partitioning (adsorption) and volatilization as well as colloidal and microbial transport since it has been shown that they can serve as sorption sites. Fluid-solid interfacial areas (e.g., in partially saturated media) controls mineral reaction rates and adsorption phenomena. During CO2 sequestration in a saline aquifer, the brine/CO2 interface controls the amount of CO2 dissolved in the brine phase and the amount of H2O dissolved in the CO2 plume, while the fluid/solid interface controls the dissolution of the porous media and precipitation of reaction products (thus affecting mineral sequestration of CO2). Due to the complicated nature of experimentally measuring the fluid-fluid interfaces it is useful to have a predictive approach. In this study, a 3-D pore-network approach is introduced to calculate the interface between wetting and non-wetting phases in porous media. We consider a regular, cubic lattice of pores and throats of different geometries and sizes. The pores have either spherical or cubic geometry and the throats have cylindrical, rectangular, or triangular geometries. The constructed network can contain one or multiple types of pores/throats and can have variable saturation of wetting and/or non-wetting phases, resulting in different interfacial areas. In a first step, different network saturations are obtained by randomly distributing wetting/non-wetting phases in the network based on concepts borrowed from Ordinary Percolation Theory. In a further step, we study the effect of the history of the fluid displacement (drainage, imbibition, etc.) on the resulting interfacial areas. These simulations are based on principals from Invasion Percolation Theory. We further report results on how the calculated interfacial areas are affected by parameters such as the range and distribution of pore/throat characteristic lengths, the wetting saturation, the pore-size distribution, and the extent of overlapping of pore/throat distributions.