Linking continuum-scale state of wetting to pore-scale contact angles in porous media

Hypothesis: Wetting phenomena play a key role in flows through porous media. Relative permeability and capillary pressure-saturation functions show a high sensitivity to wettability, which has different definitions at the continuum- and pore-scale. We hypothesize that the wetting state of a porous medium can be described in terms of topological arguments that constrain the morphological state of immiscible fluids, which provides a direct link between the continuum-scale metrics of wettability and pore-scale contact angles. Experiments: We perform primary drainage and imbibition experiments on Bentheimer sandstone using air and brine. Topological properties, such as Euler characteristic and interfacial curvature are measured utilizing X-ray micro-computed tomography at irreducible air saturation. We also present measurements for the United States Bureau of Mines (USBM) index, capillary pressure and pore-scale contact angles. Additional studies are performed using two-phase Lattice Boltzmann simulations to test a wider range of wetting conditions. Findings: We demonstrate that contact angle distributions for a porous multiphase system can be predicted within a few percent difference of directly measured pore-scale contact angles using the presented method. This provides a general framework on how continuum-scale data can be used to describe the geometrical state of fluids within porous media.