Analytical theory for three-phase partially miscible flow in ternary systems

Three-phase flow often occurs in reservoirs, particularly during secondary or tertiary oil recovery. There is significant mutual solubility of components in the phases for near miscible gas floods or chemical floods. Unfortunately there is insufficient understanding of how three partially miscible phases can affect flow. Furthermore, there are currently no benchmark analytical solutions available to validate numerical simulations for this complex flow regime. In this research, compositional solution routes are developed by the method of characteristics (MOC) for one-dimensional, dispersion-free flow where up to three partially miscible flowing phases may be present. The method is applied to a water/alcohol/oil system that exhibits a large three-phase region in laboratory experiments. Unique solutions are found based on continuity arguments, shock-jump conditions, entropy constraints, and velocity constraints. The analytical solutions are compared to fine-grid finite-difference simulations to verify that they converge to the same dispersion-free limit. The results show that within the three-phase region one phase is below its residual saturation so that only two phases are flowing. As miscibility is approached, cumulative oil recovery initially declines because of the development of constant states in the solution, which cause the leading shock to speed up. We show that multi-contact miscibility is developed along the boundary of the three-phase region where all shocks and waves flow at a dimensionless velocity of one. Last, we show that injectivity (or inverse flow resistance) changes by a factor of two over the range of injection compositions considered for the specific relative permeabilities used.