Evaluation of Two‐Phase Relative Permeability and Capillary Pressure Relations for Unstable Displacements in a Pore Network

At the pore scale, unstable displacement is often observed for two‐fluid systems, depending on the capillary number and fluid viscosity ratio. At the continuum scale, unstable displacement is usually not considered. In this work, relations between nonwetting fluid relative permeabilities ( k rn ), fluid saturations ( S n ), and capillary pressure heads ( h c ) are evaluated to predict average S n values using a continuum‐based simulator for displacements in a micromodel. To this end, a series of displacement experiments was conducted using five wetting–nonwetting immiscible fluid pairs in a homogenous pore network. The micromodel was initially saturated with either polyethylene glycol 200 (PEG) or water as a wetting fluid, which was subsequently displaced by a nonwetting fluid (dodecane, hexadecane, or mineral oil) at different flow rates. Nonwetting fluid saturations increased with increasing flow rates for all five fluid pairs. Viscous fingering occurred when PEG was displaced by either dodecane or hexadecane. For the displacements of water, capillary fingers were observed at low capillary numbers. Fitting the experimental S n and h c data with the BrooksCorey relationship indicated that the fitted and computed entry pressure heads, based on pore geometry and fluid properties, compare reasonably well. However, the fitted pore geometry factor values for these displacements are considerably lower than what is expected for displacements in homogeneous, highly uniform, porous systems, demonstrating the impact of unstable displacement. It was shown that a continuum‐based multiphase simulator could be used to reasonably estimate the average S n behavior for unstable wetting fluid displacement in a pore network as long as independently fitted h c – S n and k rn – S n relations were used.