The effect of displacement rate on imbibition relative permeability and residual saturation

A dynamic network model for imbibition based on a physically realistic description of the complex dynamics of film flow, film swelling and snap-off is described. The model shows that film swelling is a capillary driven nonlinear diffusive process and that the competition between snap-off and frontal displacements is rate dependent resulting in rate dependent relative permeability curves and residual saturations. In contrast to existing quasi-static network models where snap-off is suppressed by contact angle alone, the dynamic model introduces displacement rate as an additional snap-off inhibiting mechanism. The network model is used to analyse the complex interaction between displacement rate, contact angle, aspect ratio and pore and throat shapes on relative permeability. Computed relative permeabilities and residual saturations are compared with laboratory measured data for strongly water-wet Berea sandstone. It is concluded that the magnitude of the rate effect on relative permeability for a particular rock and wetting state depends largely on the aspect ratio. Higher aspect ratios produce larger rate effects than smaller aspect ratios.