Comments on Capillary Equilibrium

In previous Technical Notes, W. R. Rose and W. Purcell have discussed thecapillary pressure data presented by Welge. Welge obtained capillary pressurecurves of the imbibition type in which it was necessary to apply to theapparent wetting phase a greater pressure than that of the non-wetting phase tocomplete the cycle and reduce the non-wetting phase saturation to low values.Rose suggests in his Note that conditions of equilibrium could not haveprevailed, since the non-wetting phase pressure must always be the greater.Purcell in his Note, proceeds to postulate a pore system consisting of a seriesof "holes in a doughnut," in which he contends that under equilibriumconditions it is necessary to resort to negative capillary pressures beforesignificant wetting phase displacement can take place. There is a remarkablesimilarity between the shape of the capillary pressure curve calculated byPurcell and those measured by Welge. It is the purpose of this Note to show that, because Purcell neglected toaccount for the behavior of the residual wetting phase saturation, his systemwas not in equilibrium during imbibition; and, furthermore, that if his systemhad been in equilibrium, negative capillary pressures would not have beenpossible. In Purcell's pore system, the residual wetting phase will form pendularrings at the interstitial spaces existing somewhere within the system, forexample, such as those spaces between "doughnuts" as shown in Fig. 1.The true capillary pressure is that across the pendular ring interface, and forthe system to be in equilibrium the pressure drop across all interfaces must bethe same, including that across the interface in the tight pores A of diaphragmB (Fig. 1). As the pressure across the cell is reduced, the advancing interfacewill move into the pore from the diaphragm, but at each pressure, the curvatureof the pendular rings must be the same as that of the advancing interface ifequilibrium is to prevail. Since equilibrium conditions are the basis for theentire argument, it follows that pendular rings must grow as wetting phaseenters the pore, that is, as the pressure across the cell is lowered. InPurcell's calculated curve, the residual wetting phase saturation remainsconstant as the capillary pressure decreases. Thus, his curve does notrepresent an equilibrium process. T.N. 152