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Wetting phenomena play a key role in flows through porous media. Relativepermeability and capillary pressure-saturation functions show a highsensitivity to wettability, which has different definitions at the continuum-and pore-scale. At the continuum-scale, the state of wetting is defined asAmott-Harvey or USBM (United States Bureau of Mines) by capillary pressuredrainage and imbibition cycles. At the pore-scale, the concept of contact angleis used, which until recently was not experimentally possible to determinewithin an opaque porous medium. Recent progress on measurements of pore-scalecontact angles by X-ray computed micro-tomography has therefore attractedsignificant attention in various research communities. In this work, theGauss-Bonnet theorem is applied to provide a direct link between capillarypressure saturation $P_c(S_w)$ data and measured distributions of pore-scalecontact angles. We propose that the wetting state of a porous medium can bedescribed in terms of geometrical arguments that constrain the morphologicalstate of immiscible fluids. The constraint describes the range of possiblecontact angles and interfacial curvatures that can exist for a given system. Wepresent measurements in a tested sandstone for which the USBM index,$P_c(S_w)$, and pore-scale contact angles are measured. Additional studies arealso performed using two-phase Lattice Boltzmann simulations to test a widerrange of wetting conditions. We show that mean pore-scale contact anglemeasurements can be predicted from petrophysical data within a few differences.This provides a general framework on how continuum-scale data can be used todescribe the geometrical state of fluids within porous media.

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