Three-phase threshold capillary pressures in noncircular capillary tubes with different wettabilities including contact angle hysteresis.

We use the Helmholtz free energy balance and the Mayer-Stowe-Princen method to derive general expressions governing multiphase pistonlike displacements in noncircular capillary elements with arbitrary wettability. We take into account hysteresis in oil/water, gas/water, and gas/oil contact angles. We study both two- and three-phase systems. We find threshold capillary pressures for gas invasion into oil, oil invasion into gas, and water invasion into oil for capillaries with an irregular triangular cross section. Finally we study the effects of shape factor, oil/water capillary pressure, and oil/water and gas/oil contact angles on the threshold capillary pressure for gas invasion into oil for spreading and nonspreading systems. In many cases the threshold pressures of the three-phase displacements are not the same as those of the equivalent pseudo-two-phase displacements. It is possible that gas invasion can occur resulting in a configuration without oil layers, even if oil layers are geometrically possible. This emphasizes the distinction between geometric and thermodynamic stability-it is the latter that controls threshold pressures.