This paper presents an approximate semi-analytical solution for predicting the average steady-state saturation during multiphase core flood experiments over a wide range of capillary and gravity numbers. Recently, the influences of flow rate, gravity, and sub-core heterogeneity on the brine displacement efficiency have been studied using the 3-D 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 approximate semi-analytical solution for predicting the average saturation during core flood experiments, thus avoiding the need for 3-D simulations. A two dimensional analysis of the governing equations for the CO2/brine multiphase flow system at steady-state is used to develop the approximate semi-analytical solution. We have developed a new criterion to identify the viscous-dominated regime at core scale. Variations of interfacial tension, core permeability, length of the core, and the effects of buoyancy, capillary and viscous forces are all accounted in the theoretical solutions. We have also 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 of the average saturations between the 3-D simulations and the model. This new model can be used to design and interpret multiphase flow core-flood experiments.

You can access this article if you purchase or spend a download.