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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.

Plain Language Summary Mobilization or trapping of fluids in porous media, fundamentally, is a result of a force competition. Numerous studies investigate mobilization efficiency using the capillary number (N-ca), which represents a ratio of driving force for mobilization, that is, pressure or hydrostatic effects of gravity, to capillary resistance. The conventional N-ca definitions were initially proposed for 3-D porous media, yet many experimental studies use these definitions for 2-D networks. Experimental observations and theoretical analysis show that flow in a 2-D pore network, for example, a microfluidic device, is very different from that in 3-D porous rock. We here propose a new definition of N-ca to describe the efficiency of one phase displaced by another in a microfluidic device. The new definition is derived from a force balance on a trapped ganglion. The validity of the new definition is experimentally tested using data from micromodels in the literature. The new N-ca definition, as an indicator for mobilization, may be applied to microfluidic studies of a variety of processes across the fields of groundwater, energy, and climate: removal of Nonaqueous Phase Liquid contaminants from aquifers and soils; enhanced recovery of oil in reservoirs; or trapping efficiency of CO2 in Carbon Capture, Utilization, and Storage.