Instability of parallel flow of two immiscible liquids in a pore and application to steam-assisted gravity drainage

Abstract

The instability at the interface between two parallel flows of immiscible liquids through a uniform planar pore is studied by using linear stability analysis. A characteristic equation determines the growth rate versus wavenumber, and instability conditions are determined. The instability is governed by a dimensionless group relating the ratio of gravity to interfacial tension. Interfacial tension has a stabilizing effect resisting the destabilizing gravitational force, limiting the range of wavelengths of unstable disturbances to be longer than a minimum critical wavelength. Application to flow of steam condensate and mobilized bitumen in the steam-assisted gravity drainage process shows that the instability is possible only over a specific range of temperatures given the densities of the steam condensate and oil in the reservoir. This instability may contribute to forming an emulsion which could help support oil drainage if the oil is hosted by the more mobile water phase.