Capillary pressure–saturation relationships for porous granular materials: Pore morphology method vs. pore unit assembly method

In studies of two-phase flow in complex porous media it is often desirable to have an estimation of the capillary pressure–saturation curve prior to measurements. Therefore, we compare in this research the capability of three pore-scale approaches in reproducing experimentally measured capillary pressure–saturation curves. To do so, we have generated 12 packings of spheres that are representative of four different glass-bead packings and eight different sand packings, for which we have found experimental data on the capillary pressure–saturation curve in the literature. In generating the packings, we matched the particle size distributions and porosity values of the granular materials. We have used three different pore-scale approaches for generating the capillary pressure–saturation curves of each packing: i) the Pore Unit Assembly (PUA) method in combination with the Mayer and Stowe–Princen (MS–P) approximation for estimating the entry pressures of pore throats, ii) the PUA method in combination with the hemisphere approximation, and iii) the Pore Morphology Method (PMM) in combination with the hemisphere approximation. The three approaches were also used to produce capillary pressure–saturation curves for the coating layer of paper, used in inkjet printing. Curves for such layers are extremely difficult to determine experimentally, due to their very small thickness and the presence of extremely small pores (less than one micrometer in size). Results indicate that the PMM and PUA-hemisphere method give similar capillary pressure–saturation curves, because both methods rely on a hemisphere to represent the air–water interface. The ability of the hemisphere approximation and the MS–P approximation to reproduce correct capillary pressure seems to depend on the type of particle size distribution, with the hemisphere approximation working well for narrowly distributed granular materials.