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

Abstract

Fluid-fluid interfacial area is recognized as an important parameter in understanding various multiphase flow processes in porous media. Mass transfer processes such as dissolution, adsorption and volatilization occur across interfaces and are strongly related to interfacial area. Moreover, the coefficient for interfacial mass transfer is assumed to be proportional to the interfacial area. It has also been observed experimentally that surfactants and bacteria may preferentially accumulate at the interfaces and affect the subsequent fluid transport. To quantify the efficiency and consequences of these processes, the magnitude of the interfacial area is required. In this paper we use a simple, yet physically-based, bundle-of-triangular-tubes model to calculate interfacial area for mixed-wet conditions and contact angle hysteresis. In such a representation of the pore network, capillary displacements may either occur as piston-like displacements of the fluids occupied in the bulk, or as piston-like displacements of fluids in layers. Accurate expressions for the associated capillary entry pressures are implemented. The simulated interfacial area vs. saturation data displays the same general trends as experimental measurements. We also derive analytical expressions for the relationship between specific interfacial area, capillary pressure and saturation for primary drainage. Based on these expressions, we formulate flexible correlations for subsequent invasion processes. The correlations are compared with the simulated data, and good agreement is obtained. The proposed correlations are consistent with the well-known Brooks- Corey correlation and may also be implemented in reservoir simulators. Finally, we use our model to explore the conjecture by Hassanizadeh and Gray who suggested that hysteresis can be eliminated in the relationship between capillary pressure, saturation and specific interfacial area. We find that hysteresis may be significant for both water-wet and mixed-wet conditions as long as contact angle hysteresis is assumed.