“…It is well established that k w , k o , and p c are functions of both saturation and saturation history (Bear, 1988) and a number of empirical models have been proposed to describe them (e.g., Brooks and Corey, 1964;Skjaeveland et al, 2000;Lomeland et al, 2005;Duchenne et al, 2015;Honarpour et al, 1982). For imbibition, which we define in this paper as increasing water saturation, S w , irrespective of whether or not the porous medium is hydrophilic, all models assume water is immobile when the fractional volume of the pore space that it occupies falls below the irreducible water saturation, S w = S wi (> 0), or above S w = 1 − S or (< 1), where S or is the residual oil saturation.…”