Effect of capillary condensation on gas transport properties in porous media

We investigate the effect of capillary condensation on gas diffusivity in porous media composed of randomly packed spheres with moderate wettability. To simulate capillary phenomena at the pore scale while retaining complex pore networks of the porous media, we employ density functional theory (DFT) for coarse-grained lattice gas models. The lattice DFT simulations reveal that capillary condensations preferentially occur at confined pores surrounded by solid walls, leading to the occlusion of narrow pores. Consequently, the characteristic lengths of the partially wet structures are larger than those of the corresponding dry structures with the same porosities. Subsequent gas diffusion simulations exploiting the mean-square displacement method indicate that while the effective diffusion coefficients significantly decrease in the presence of partially condensed liquids, they are larger than those in the dry structures with the same porosities. Moreover, we find that the ratio of the porosity to the tortuosity factor, which is a crucial parameter that determines an effective diffusion coefficient, can be reasonably related to the porosity even for the partially wet porous media.

Figure 1

Representative porous medium constructed using the drop-and-roll algorithm with the sphere diameter 10L. Domain dimensions are 160L×160L×480L with the periodic boundary conditions in the horizontal directions. The origin of the coordinates is located at a vertex of the bottom plane. The contact angle and porosity are 0° and 0.42.

Figure 2

(a) Definition of contact angle θ between two contacting spheres. The contact angle is spanned by the two lines, one of which connects the sphere center with the center of the contact area, and the other with the circumference of the contact area. (b) Porosity as a function of the contact angle. The error bars of each marker are standard deviations obtained using five different structures.

Figure 3

Lattice DFT simulation system. The porous medium with the contact angle 0° is immersed in the system with the volume of 320L×320L×960L, where the side length of each cubic lattice is L. Periodic boundary conditions (PBCs) are imposed in all directions.

Figure 4

Adsorption and desorption isotherms for the porous medium with $\theta =0^{\circ }$. Left axis shows the mean density of fluid sites in the structure. Right axis shows the apparent porosity during the adsorption process calculated on the assumption that the fluid sites with the densities >0.5 are occluded by condensed liquids.

Figure 5

Fluid density distributions in the plane of $z=240L$ during the adsorption process. Gray regions correspond to solids. (a) Relative activity $\lambda /{\lambda }_0=0$ and apparent porosity ${\varepsilon }_{\mathrm{a}}=0.42$, (b) $\lambda /{\lambda }_0=0.50$ and ${\varepsilon }_{\mathrm{a}}=0.35$, (c) $\lambda /{\lambda }_0=0.60$ and ${\varepsilon }_{\mathrm{a}}=0.30$, (d) $\lambda /{\lambda }_0=0.66$ and ${\varepsilon }_{\mathrm{a}}=0.25$, (e) $\lambda /{\lambda }_0=0.70$ and ${\varepsilon }_{\mathrm{a}}=0.20$, and (f) $\lambda /{\lambda }_0=0.74$ and ${\varepsilon }_{\mathrm{a}}=0.14$.

Figure 6

Chord length distributions of the dry $\left(\lambda /{\lambda }_0=0\right)$ and partially wet $\left(\lambda /{\lambda }_0=0.74\right)$ structures with $\theta =0^{\circ }$.

Figure 7

Comparison of chord length distributions between the dry and partially wet structures with the same porosities. (a) Dry structure with $\theta ={21}^{\circ }$ and partially wet structure with $\theta =0^{\circ }$ and $\lambda /{\lambda }_0=0.60$, both of which have $\varepsilon =0.30$; (b) dry structure with $\theta ={33}^{\circ }$ and the partially wet structure with $\theta =0^{\circ }$ and $\lambda /{\lambda }_0=0.74$, both of which have $\varepsilon =0.14$.

Figure 8

Structural parameters of the dry and partially wet structures. Contact angle θ is varied for the dry structures, while θ is kept at 0° and $\lambda /{\lambda }_0$ is varied for all partially wet structures. (a) Mean chord length $\langle l\rangle$, (b) the ratio $\langle l^2\rangle /\phantom{\langle l^2\rangle 2{\langle l\rangle }^2}2{\langle l\rangle }^2$ in Eq. (10) with the theoretical value 1 for an exponential chord length distribution indicated by a dashed line, (c) β given by Eq. (11) with the theoretical value 4/13 for the Knudsen cosine law in random packings of monodisperse spheres indicated by a dashed line, and (d) characteristic length $d$ given by Eq. (10).

Figure 9

MSDs (on a log-log scale) in the dry $\left(\lambda /{\lambda }_0=0\right)$ and partially wet ($\lambda /{\lambda }_0=0.60$, 0.70, and 0.74) structures with $\theta =0^{\circ }$.

Figure 10

Comparison of the MSDs (on a log-log scale) between the dry and partially wet structures with the same porosities. (a) Dry structure with $\theta ={21}^{\circ }$ and the partially wet structure with $\theta =0^{\circ }$ and $\lambda /{\lambda }_0=0.60$, both of which have $\varepsilon =0.30$; (b) dry structure with $\theta ={33}^{\circ }$ and the partially wet structure with $\theta =0^{\circ }$ and $\lambda /{\lambda }_0=0.74$, both of which have $\varepsilon =0.14$.

Figure 11

Effective diffusion coefficients obtained from the slopes of the MSDs based on Eq. (12) (a) and the ratio of a porosity ε to the tortuosity factor τ (b) of the dry and partially wet structures with the same porosities. Contact angle θ is varied for the dry structures, while θ is kept at 0° and $\lambda /{\lambda }_0$ is varied for all the partially wet structures.