Onset of viscous fingering for miscible liquid-liquid displacements in porous media

The displacement of one fluid by another miscible fluid in porous media is an important phenomenon that occurs in petroleum engineering, in groundwater movement, and in the chemical industry. This paper presents a recently developed stability criterion which applies to the most general miscible displacement. Under special conditions, different expressions for the onset of fingering given in the literature can be obtained from the universally applicable criterion. In particular, it is shown that the commonly used equation to predict the stable velocity ignores the effects of dispersion on viscous fingering.Nomenclature C Solvent concentration - Unperturbed solvent concentration - D _L Longitudinal dispersion coefficient m²/s] - D _T Transverse dispersion coefficient m²/s] - g Gravitational acceleration m/s²] - I _sr Instability number - k Permeability m²] - K Ratio of transverse to longitudinal dispersion coefficient - L Length of the porous medium m] - L _x Width of the porous medium m] - L _y Height of the porous medium m] - M Mobility ratio - V Superficial velocity m/s] - V _c Critical velocity m/s] - V _s Velocity at the onset of instability m/s] - µ Viscosity Pa/s] - Unperturbed viscosity Pa/s] - µ ₀,µ _s Viscosities of oil and solvent, respectively Pa/s] - Density kg/m³] - ₀, _s Densities of oil and solvent, respectively kg/m³] - Porosity - Dimensionless length