Absorption Rate and Volume Dependency on the Complexity of Porous Network Structures

Abstract

Results of simulated supersource imbibition into model network structures are compared with experimental observations of real network structures determined by dynamical gravimetric fluid uptake. A computer model, Pore-Cor, has been used previously to simulate the imbibition of fluid into porous structures by applying an imbibition algorithm for fluids undergoing both inertial and viscous dynamical absorption (Schoelkopf et al., 2000). The structures comprise cubic pores connected by cylindrical throats on a three-dimensional 10 × 10 × 10 position matrix. The absorption curves for model structures with monosized pore and throat size ranges and for polydisperse pore and throat size distributions centred around 0.1 µm, increasing from 0.1 µm as a lower limit, and decreasing from 0.1 µm as an upper limit, respectively, are analysed. A relevant observable porosity and 50% volume intrusion radius (r ₅₀) are obtained using simulated mercury intrusion. Experimental network pore structures were made using compressed tablets, formed under a series of pressures, of two finely ground calcium carbonates with defined differences in skeletal particle size distribution. The surface chemical, particulate and morphological pore characteristics were maintained constant over a range of porosities using controlled wet grinding and careful use of dispersant levels such that the ratio of dispersant to BET surface area was held constant. The experimental porosities were determined by mercury intrusion porosimetry applying corrections for mercury compression and penetrometer expansion together with a correction for sample skeletal compression (Gane et al., 1996). The applicability of the Lucas–Washburn equation is examined by defining two equivalent hydraulic radii, one based on a Darcy absorption length (r _ehcDarcy) and the other on a volume uptake (r _ehc), respectively. The results from the model structures having distributions of pores and throats, which contain either small or large pores, respectively, follow the experimental results qualitatively. Both approaches show a long timescale macroscopic absorption rate depending approximately, but not exactly, on the square root of time. The two experimental series, however, fail to scale with each other via the Lucas–Washburn equation in accordance with pore size, r ₅₀. Porosity is shown to be the main factor determining the volume absorption rate, and, when used as a weighting factor, gives linear correlation-scaling between r ₅₀ and a derived volume-based r′_ehc equivalent hydraulic radius, obtained from an analytical expression of the observed Darcy-based r _ehcDarcy. The experimental samples showed that the directly observed r _ehc and the calculated r′_ehc, derived from Darcy length, were equal, but this was not the case for the model values. A factor β = r′_ehc/r ₅₀ is shown to be a possible descriptor of the sample network complexity and an indicator for the probability level of pore filling during the absorption dynamic.