Three-phase mixed-wet capillary pressure curves from a bundle of triangular tubes model

We present a bundle of triangular tubes model that simulates three-phase mixed-wet capillary pressure curves for any sequences of gas, oil, and water invasion processes. A diversity of cross-sectional fluid configurations may occur because of pore shape and different combinations of the contact angles. We use expressions for the capillary entry pressures that truly accounts for the mixed wettability condition and the possibility of simultaneous displacement of the fluids occupying the cross-sections. As a consequence, invasion does not necessarily proceed in the order of monotonic increasing or decreasing pore size. We simulate primary drainage and imbibition first. The saturation dependencies of the three-phase capillary pressures are analyzed for the subsequent gas injections and waterfloods and compared with the results from a similar bundle of cylindrical tubes model. Simulations are performed for three sets of contact angles representing oil-wet conditions with variable contact angle hysteresis. It is shown that the capillary pressure at the end of primary drainage, Pcowmax, strongly affects the saturation dependencies in the bundle of triangular tubes. For moderate values of Pcowmax, we have identified regions in the saturation space where two or all three capillary pressures are functions of two saturations, while the corresponding results from the bundle of cylindrical tubes often show that only one of the capillary pressures depends on more than one saturation, regardless of Pcowmax. The differences are caused by the capillary entry pressures in the triangular tubes that are strongly affected by the hinging interfaces in the corners when contact angle hysteresis is assumed. This leads to different bulk pore occupancies in the two bundle models, and hence different saturation dependencies. Furthermore, the level of gas–water and oil–water capillary pressure is higher for the bundle of triangular tubes during the gas and water invasion processes. The saturation dependencies, capillary levels and pore occupancies calculated from triangular tubes approach the corresponding results calculated from cylindrical tubes when Pcowmax is increased.