Technical Notes - Comments on Capillary Equilibrium

In previous Technical Notes, W. R. Rose' and W. Purcell have discussed the capillary pressure data presented by Welge.' Welge obtained capillary pressure curves of the imbibition type in which it was necessary to apply to the apparent wetting phase a greater pressure than that of the non-wetting phase to complete the cycle and reduce the non-wetting phase saturation to low values. Rose suggests in his Note that conditions of equilibrium could not have prevailed, since the. non-wetting phase pressure must always be the greater. Pur-cell in his Note, proceeds to postulate a pore system consisting. of a series of "holes in a doughnut," in which he contends that under equilibrium conditions it is necessary to resort to negative capillary pressures before significant wetting phase displacement can take place. There is a remarkable similarity between the shape of the capillary pressure curve calculated by Purcell and those measured by Welge. It is the purpose of this Note to show that, because Purcell neglected to account for the behavior of the residual wetting phase saturation, his system was not in equilibrium during imbibition; and, furthermore, that if his system had been in equilibrium, negative capillary pressures would not have been possible. In Purcell's pore system, the residual wetting phase will form pendular rings at the interstitial spaces existing somewhere within the system, for example, such as those spaces between "doughnuts" as shown in Fig. 1. The true capillary pressure is that across the pendular ring interface, and for the system to be in equilibrium the pressure drop across all interfaces must be the same, including that across the interface in the tight pores A of diaphragm B (Fig. 1). As the pressure across the cell is reduced, the advancing interface will move into the pore from the diaphragm, but at each pressure, the curvature of the pendular rings must be the same as that of the advancing interface if equilibrium is to prevail. Since equilibrium conditions are the basis for the entire argument, it follows that pendular rings must grow as wetting phase enters the pore, that is, as the pressure across the cell is lowered. In Purcell's calculated curve, the residual wetting phase saturation remains constant as the capillary pressure decreases. Thus, his curve does not represent an equilibrium process.