Mathematics of partially miscible three-phase flow

Partially miscible flow of several components in three or more phases occurs in both enhanced oil recovery and remediation of contaminated aquifers. There is insufficient understanding of how the formation of multiple phases affects subsurface flow.{09}The main objective of this work is to develop compositional solution routes using the method of characteristics (MOC) for one-dimensional, dispersion-free flow where up to three partially miscible flowing phases may be present; a problem that is poorly understood. Analytical solutions provide insight into the behavior of multi-phase flow and can be used as benchmarks for numerical simulation.; Unique composition routes are found for a ternary system that can form three flowing phases and is analogous to carbon dioxide and methane injection into an oil reservoir. A single-component, single-phase initial composition is assumed and injection of the other two components is studied. A ternary system modeling surfactant-enhanced remediation of a non-aqueous phase contaminant is also studied for a two-phase initial composition and a series of injection compositions. Analytical solutions are found for three different relative permeability models. Finally, the analytical solutions are compared to core floods and simulations.; The results show that recovery of oil or contaminant often declines with surfactant enrichment for a range of injection compositions. Multiple-contact miscibility (MCM) is developed at the critical point of the alcohol/oleic two-phase region and on the boundary of the three-phase region for the single-phase initial composition. When the initial composition is two-phase miscibility is not developed; a substantial divergence from two-phase flow.; Analytical composition routes match the experimental data in most cases. Numerical dispersion may cause simulated routes to differ from analytical routes at shock fronts, but as dispersion is minimized the simulated routes converge to the analytical solutions. Numerical dispersion causes a decrease in recovery, particularly near MCM and may not adequately model the true physical dispersion in the core floods.; Two-phase partially miscible flow is also studied for the case when the initial composition has two hydrocarbon phases. The flow in MCM condensing and condensing/vaporizing drives is dependent on the relative permeability curves and recovery of heavy hydrocarbons may be substantially delayed.