Dynamic pore-scale network models for two-phase flow in porous media

Pore-scale network models for two-phase flow in porous media describe fluid movement and interface displacements at the scale of individual pores. Aggregation of many pores, into an interconnected network structure, allows for simulations from which volume-averaged properties may be computed. These averaged variables include fluid saturations, average capillary pressures, specific interfacial areas, and measures of contact-line length. Quantification of variables like interfacial areas and contact-line length have allowed new constitutive relationships to be evaluated, and many specific aspects of multi-phase flow to be explored. Most pore-scale network models are quasi-static, in that fluid-fluid interfaces are displaced from one location to another but no consideration is given to the rates of motion of the interfaces. Displacements are based strictly on static equilibrium conditions. While such models have proven useful, and are consistent with the assumption at the averaged scale of an algebraic relationship between average saturation and average capillary pressure, they fail to provide any insights into dynamic elements associated with capillary pressures and saturations. We have developed two different kinds of dynamic pore-scale network models, both of which account for dynamics associated with interface motions. One focuses on pore throats, and computes explicit velocities for each interface as it moves along a given pore throat. Pore bodies, which are located at the junctions of pore throats, are given no volume, and serve only to connect different pore throats. A second model focuses the network structure in the pore bodies. In this second model, all of the volume is partitioned among the pore bodies, and the pore throats serve as connections between the pore bodies. While the pore throats provide resistance to flow, they are assumed volumeless. Each of these approaches has advantages and disadvantages, from both the computational and the physical points of view. In this paper, we present the basic computational components of both models and report on initial comparisons between the two models for problems involving dynamic displacements in two-phase flow systems.