Abstract
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.
Highlights
The relationship between capillary pressure and saturation plays an important role in many applications of porous materials, such as inkjet printing (Rosenholm, 2015), water flow in hygienic products (Diersch et al, 2010), water distribution in fuel cells (Qin, 2015), oil and gas reservoir engineering, and unsaturated soils (Lins and Schanz, 2005)
Pore bodies and pore throats is typically complex and highly irregular. This network can be constructed by, for example, one of the following methods: (1) it can be randomly generated based on the pore throat size distribution, pore body size distribution, the distribution in number of pore throats per pore body, and either the porosity value or permeability value of the granular material (Lindquist et al, 2000, Raoof and Hassanizadeh, 2010), (2) it can be extracted from the pore geometry inside an artificially generated pack of spheres (Gladkikh and Bryant, 2005; Sweijen et al, 2016; Yuan et al, 2016) or (3) it can be extracted from a 3-dimensional reconstruction of the porous material, based on advanced imaging methods such as X-ray tomography and micro-CT (Joekar-Niasar et al, 2010; Lindquist et al, 1996)
To investigate the ability of Pore Unit Assembly (PUA) and Pore Morphology Method (PMM) to estimate capillary pressure–saturation curves of granular materials, we studied 12 granular materials for which experimental data are reported in the literature
Summary
The relationship between capillary pressure and saturation plays an important role in many applications of porous materials, such as inkjet printing (Rosenholm, 2015), water flow in hygienic products (Diersch et al, 2010), water distribution in fuel cells (Qin, 2015), oil and gas reservoir engineering, and unsaturated soils (Lins and Schanz, 2005) This relationship depends on both the geometry and dimensions of the pore space (Likos and Jaafar, 2013; Mousavi and Bryant, 2012; Øren and Bakke, 2003; Torskaya et al, 2014). This network can be constructed by, for example, one of the following methods: (1) it can be randomly generated based on the pore throat size distribution, pore body size distribution, the distribution in number of pore throats per pore body (i.e. coordination number), and either the porosity value or permeability value of the granular material (Lindquist et al, 2000, Raoof and Hassanizadeh, 2010), (2) it can be extracted from the pore geometry inside an artificially generated pack of spheres (Gladkikh and Bryant, 2005; Sweijen et al, 2016; Yuan et al, 2016) or (3) it can be extracted from a 3-dimensional reconstruction of the porous material, based on advanced imaging methods such as X-ray tomography and micro-CT (Joekar-Niasar et al, 2010; Lindquist et al, 1996)
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