This paper presents an approximate semianalytical solution for predicting the average steady-state saturation during multiphase coreflood experiments across a wide range of capillary and gravity numbers. Recently, the influences of flow rate, gravity, and subcore heterogeneity on brine displacement efficiency have been studied with the 3D simulator TOUGH2 (Kuo et al. 2010). These studies have demonstrated that the average saturation depends on the capillary and gravity numbers in a predictable way.
The purpose of this paper is to provide a simple and approximate semianalytical solution for predicting the average saturation (during two-phase coreflood experiments across a wide range of flow rates) for different average rock properties and fluid pairs. A 2D analysis of the governing equations for the multiphase-flow system at steady state is used to develop the approximate semianalytical solution. We have developed a new criterion to identify the viscous-dominated regime at the core scale. Variations of interfacial tension (IFT), core permeability, and length of the core and the effects of buoyancy, capillary, and viscous forces are all accounted for in the semianalytical solutions. We also have shown that three dimensionless numbers (NB, Ngv, Rl) and two critical gravity numbers (Ngv,c1, Ngv,c2) are required to properly capture the balance of viscous, gravity, and capillary forces. There is good agreement between the average saturations calculated from the 3D simulations and the analytical model. This new model can be used to design and interpret multiphase-flow coreflood experiments, gain better understanding of multiphase-flow displacement efficiency across a wide range of conditions and for different fluid pairs, and perhaps even provide a tool for studying the influence of subgrid-scale multiphase-flow phenomena on reservoir-scale simulations.