The Development of Stability Theory for Miscible Liquid-Liquid Displacement

Abstract

A stability theory is developed for miscible liquidliquid displacement within a porous medium. In the usual case considered, a high-density high-viscosity "oil" is displaced downdip by a low-density lowviscosity "solvent". Perturbation methods are used to find the conditions under which the spreading mechanism changes from the stable dispersion process to unstable viscous fingering. We find that Instability is conditional, that there is a dependence on the shape of a disturbance leading to a "diameter" effect and that very difficult experimental scaling problems may result. A useful consequence is the definition of a minimum "slug size" for stable miscible displacement. This should make possible optimum use of the solvent process for oil recovery. The results may apply to many situations in which one fluid displaces another of somewhat different fluid properties within a porous medium.