Effect of Capillary Forces on Immiscible Displacement in Porous Media

Abstract

Abstract The complete fractional flow equation obtained previously by the authors from capillary models of both counter-current and co-current imbibition has been solved numerically, together with the mass conservation equation of water to obtain saturation profile histories in waterfloods in models of lengths ranging from lm to 200m, at an injection rate of 10−4cm/s. The saturation profiles change from near horizontal in the lm long model to near piston like in the 200m model. Equivalent roles are played by model length and by water injection rate in determining saturation profile history. Calculated saturation profiles match those determined in the laboratory when plotted against dimensionless distance coordinates. The complete and the simplified fractional flows, derived from calculated saturation profiles, have been compared: unlike the former ones, the latter are s-shaped curves. It is demonstrated with the help of the simple capillary model of imbibition that development of the Buckley-Leverett front under conditions when viscous forces dominate is nevertheless due to capillary forces. Capillary pressure gradient in the fractional flow equation can be neglected only at very low interfacial tensions when the relative permeability curves become straight lines. Multiple-valued saturation profiles are obtained from physically inconsistent simplified fractional flow equation in which the capillary pressure gradient is neglected but relative permeability data obtained under conditions of non-negligible capillarity are used.