New capillary number definition for displacement of residual nonwetting phase in natural fractures

We propose a new capillary number for flow in fractures starting with a force balance on a trapped ganglion in a fracture. The new definition is validated with laboratory experiments using five distinctive model fractures. Capillary desaturation curves were generated experimentally using water-air forced imbibition. The residual saturation-capillary number relationship obtained from different fractures, which vary in aperture and roughness, can be represented approximately by a single curve in terms of the new definition of the capillary number. They do not fit a single trend using the conventional definition of the capillary number.