Compositional gravity drainage 1. Equilibrium solutions and controlling Bond numbers for a two-phase,three-component system

The amount of wetting phase that is recovered by gravity drainage is determined by an interplay of gravitational and capillary forces. The relative importance of those forces is often expressed in terms of a Bond number. For compositional gravity drainage, where the initial and displacing fluids are not in chemical equilibrium, there is no single Bond number, as phases that form during a displacement will be associated with a different interfacial tension and density for each equilibrium tie line encountered as the compositions change during flow. We study vertical compositional displacements to determine how the Bond numbers of the initial and displacing fluids control the ultimate recovery. We find analytical solutions to the capillary/gravity equilibrium for a simplified model three-component, two-phase system. The equilibrium phase composition versus distance profiles are different than those predicted from standard viscous dominated displacements. We calculate the recovery as a function of the Bond numbers of the initial and displacing phases, and the degree of diffusion for this simple system. We discuss the important role of molecular diffusion in the ultimate recovery for condensing displacements. Finally, we find that the simple numerical average of the Bond numbers provides a reasonable estimate of an effective Bond number for calculating the retained wetting phase for many compositional gravity drainages.