Relating the macroscopic properties of porous media such as capillary pressure with saturation is an on-going problem in many fields, but examining their correlations with microstructural traits of the porous medium is a challenging task due to the heterogeneity of the solid matrix and the limitations of laboratory instruments. Considering a capillarity-controlled invasion percolation process, we examined the macroscopic properties as functions of matrix saturation and pore structure by applying the throat and pore network model. We obtained a relationship of the capillary pressure with the effective saturation from systematic pore network simulations. Then, we revisited and identified the microstructure parameters in the Brooks and Corey capillary pressure model. The wetting phase residual saturation is related to the ratio of standard deviation to the mean radius, the ratio of pore radius to the throat length, and pore connectivity. The size distribution index in the Brooks and Corey capillary pressure model should be more reasonably considered as a meniscus size distribution index rather than a pore size distribution index, relating this parameter with the invasion process and the structural properties. The size distribution index is associated with pore connectivity and the ratio of standard deviation to mean radius (σ0/r), increasing with the decline of σ0/r but the same for networks with same σ0/r. The identified parameters of the Brooks and Corey model might be further utilized for correlations with other transport properties such as permeability.
Low density permeations of some gases (He, H2, N2, CH4, CO2 and CF4) through micro‐ and mesocarboneous pores were investigated using Knudsen and Oscillator models. Lennard‐Jones model in single layer pores was used to simulate the gas–solid interactions in the Oscillator model. The effects of the pore radius as well as the molecular size and the temperature on the pore diffusivity and the activation energy were studied. The Monte Carlo simulation was then performed to calculate the permeability of these gases in three‐dimensional cubic networks of different connectivities (2.5–6) and different pore size distributions (ra = 2.74 and 6.95 nm). It was shown that for networks with larger pores there is a minor difference between the two models, while a large discrepancy exists in networks with fine pores. Both models tend to have the same permeability as the coordination number decreases. To investigate the accuracy of the models, the simulation results were compared with the experimental selectivities of some pure gases in two different membranes extracted from the literature. It was shown that the Oscillator model can better predict the experimental data in the membranes of smaller pores (i.e. ra = 2.74 nm). However, both models were comparable in membranes of larger pores (ra = 6.95 nm). The capability of the models to predict the activation energy of the diffusion was also studied.
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