Conservation of energy is used to derive a thermodynamically-consistent contact angle, theta(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 Delta a(1s) cos theta(t) = kappa phi Delta S-1 + Delta a(12), where a is the interfacial area per unit volume, phi is the porosity, S is the saturation and kappa the curvature of the fluid-fluid interface. The subscript s denotes the solid, and we consider changes, Delta 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 theta(t) with the values measured geometrically in situ on the pore-scale images, theta(g). The thermodynamic angle theta(t) provides a robust and consistent characterization of wettability. For the water-wet case the calculated value of theta(t) gives an accurate prediction of multiphase flow properties using pore-scale modelling. (C) 2019 The Authors. Published by Elsevier Inc.