A pore network model for calculation of interfacial velocities

Abstract

Two-phase flow in porous media is characterized by fluid–fluid interfaces that separate fluid phases at the pore scale. These interfaces support pressure differences between phases, and their dynamics lead to changes in phase saturation within the porous medium. Dynamic pore-scale network models mathematically track the dynamic position of each fluid–fluid interface through a pore network, based on imposed boundary conditions, fluid and solid properties, and geometric characteristics of the network. Because these models produce a detailed description of both phase and interface dynamics, results from these models can be volume-averaged to provide values for many upscaled variables. These include traditional variables such as saturation and macroscopic capillary pressure, as well as non-traditional variables such as amount of interfacial area in the averaging volume. With appropriate geometric definitions in the dynamic pore-scale model, a new algorithm may be included in the pore-scale network model to calculate a new variable: average interfacial velocity. This algorithm uses local information in any pore that contains a fluid–fluid interface to estimate the velocity of that interface over a time step. Summation over all interfaces in the network provides a measure of average velocity. Computations for dynamic drainage experiments indicate that this average interfacial velocity is well defined and exhibits distinct behavior for stable and unstable displacements. Comparison of calculated interfacial velocities to a theoretical conjecture on the functional dependence of this macroscopic variable demonstrates another important use of pore-scale model, namely testing of new theories involving non-traditional variables.