New Capillary Number Definition for Micromodels

Abstract

A new capillary number (N
ca
) definition is proposed for 2-D etched micromodels. We derive the new definition from a force balance on a nonwetting ganglion trapped by capillarity. It incorporates the impact of pore microstructure on mobilization. The geometrical factors introduced can be estimated directly from image analysis of the pore network etched in the micromodel, without conducting flow experiments. The improved fit of the new N
ca
to published data supports its validity. The new definition yields a consistent trend in the capillary-desaturation curve. The conventional N
ca
definitions proposed for porous rock give a large scatter in the capillary-desaturation curve for data in micromodels. This is due to the different type of flow in micromodels, as 2-D networks, relative to 3-D geological porous media. In particular, permeability is dominated by channel depth in micromodels with shallow depth of etching, and generally, there is no simultaneous multiphase flow under capillary-dominated conditions. Applying the conventional definitions to results in micromodels may lead to misleading conclusions for fluid transport in geological formations.