Relationship between capillary pressure, saturation, and interfacial area from a model of mixed-wet triangular tubes

A simple bundle of triangular tubes model is employed to calculate specific interfacial area for primary drainage, imbibition, and secondary drainage for mixed-wet conditions. In this model, only the interfaces between bulk and corner fluid are contributory to the interfacial area. Accurate expressions for the capillary entry pressures are employed, which account for the possibility of hinging interfaces in the corners due to contact angle hysteresis. The results show that very different trends in the specific interfacial area versus saturation curves can occur during imbibition, depending on the advancing contact angle and the reversal point after primary drainage. For water-wet conditions, interfacial area scanning curves coincide with the bounding imbibition curve, while for oil-wet conditions, the scanning curves may cross each other because of the impact that hinging interfaces in the pore corners have on the invasion order of the pore sizes. Analytical expressions for specific interfacial area as a function of saturation and capillary pressure are derived for primary drainage of triangular tubes. Approximate correlations for interfacial area as a function of saturation are suggested for the subsequent imbibition and drainage processes. The correlations are fitted to the simulated data, and good agreement is obtained. We also demonstrate that hysteresis remains present in the relationship between interfacial area, capillary pressure, and saturation when contact angle hysteresis is assumed. Hysteresis may be significant for both water-wet and mixed-wet conditions. A more sophisticated model is required to examine if this is also the case when hysteresis is caused by phase entrapment.