A thermodynamically consistent characterization of wettability in porous media using high-resolution imaging

Conservation of energy is used to derive a thermodynamically-consistent contact angle, θ_t, when fluid phase 1 displaces phase 2 in a porous medium. Assuming no change in Helmholtz free energy between two local equilibrium states we find that Δa_1scosθ_t=κϕΔS₁+Δa₁₂, where a is the interfacial area per unit volume, ϕ is the porosity, S is the saturation and κ the curvature of the fluid-fluid interface. The subscript s denotes the solid, and we consider changes, Δ, in saturation and area. With the advent of high-resolution time-resolved three-dimensional X-ray imaging, all the terms in this expression can be measured directly. We analyse imaging datasets for displacement of oil by water in a water-wet and a mixed-wet sandstone. For the water-wet sample, the curvature is positive and oil bulges into the brine with almost spherical interfaces. In the mixed-wet case, larger interfacial areas are found, as the oil resides in layers. The mean curvature is close to zero, but the interface tends to bulge into brine in one direction, while brine bulges into oil in the other. We compare θ_t with the values measured geometrically in situ on the pore-scale images, θ_g. The thermodynamic angle θ_t provides a robust and consistent characterization of wettability. For the water-wet case the calculated value of θ_t gives an accurate prediction of multiphase flow properties using pore-scale modelling.