Percolation and Grain Boundary Wetting in Anisotropic Texturally Equilibrated Pore Networks

In texturally equilibrated porous media the pore geometry evolves to minimize the energy of the liquid-solid interfaces, while maintaining the dihedral angle $\theta$ at solid-solid-liquid contact lines. We present computations of three-dimensional texturally equilibrated pore networks using a level-set method. Our results show that the grain boundaries with the smallest area can be fully wetted by the pore fluid even for $\theta >0$. This was previously not thought to be possible at textural equilibrium and reconciles the theory with experimental observations. Even small anisotropy in the fabric of the porous medium allows the wetting of these faces at very low porosities, $\varphi <3\%$. Percolation and orientation of the wetted faces relative to the anisotropy of the fabric are controlled by $\theta$. The wetted grain boundaries are perpendicular to the direction of stretching for $\theta >60°$ and the pores do not percolate for any investigated $\varphi$. For $\theta <60°$, in contrast, the grain boundaries parallel to the direction of stretching are wetted and a percolating pore network forms for all $\varphi$ investigated. At low $\theta$ even small anisotropy in the fabric induces large anisotropy in the permeability, due to the concentration of liquid on the grain boundaries and faces.

Figure 1

(a) Texturally equilibrated pore network with $\theta =30^{\circ }$ and $\varphi =1.5\%$ in a polycrystalline solid comprising truncated octahedral grains. (b) Definition of the dihedral angle $\theta$ in a cross section of a channel along a three-grain corner. (c) Melt network with $\theta \approx 0°$ in a copper-silver alloy [1]. (d) Melt network with $\varphi =5\%$ in an olivine-basalt aggregate [8] (used with permission from The American Association for the Advancement of Science). (e) Quadruple junction of a melt network between ice grains near $0°\mathrm{C}$ [9] (used with permission from Nature Publishing Group). (f) Drained brine network in halite with $\theta \approx 45°$ at 1.5 kbar and $395°\mathrm{C}$ [10] (used with permission from the Geological Society of America).

Figure 2

Texturally equilibrated pore networks in a polycrystalline solid with an isotropic fabric. Only a single grain extracted from a network of 200 grains is shown.

Figure 3

The center shows a regime diagram for percolation and grain boundary wetting in $\varphi \theta$ space. Black dots indicate the parameter combinations that have been investigated in this study. The dark gray region corresponds to conditions where isotropic media do not percolate. The black circles indicate the previously determined percolation boundary [14]. The expanded no percolation region for anisotropic media is shown in light gray. The colored contours indicate the boundaries where grain boundary wetting occurs for different anisotropies. The top row illustrates the formation of wetted grain boundaries for $\theta =90°$ and $f=1.5$ as $\varphi$ increases from 0.5% to 2%. The bottom row illustrates the formation of wetted grain boundaries for $\theta =10°$ and $f=1.5$ as $\varphi$ increases from 1% to 3%.

Figure 4

Fluid distribution between grains in textural equilibrium with $f=2$, porosity 3%. (a) $\theta =10°$, (b) 60°. The polycrystalline material is stretched in the $z$ direction.

Figure 5

(a-c) Development of permeability anisotropy in texturally equilibrated pore networks as function of $\varphi$, $\theta$, and $f$. (d-e) Absolute permeability in texturally equilibrated pore networks as function of $\varphi$, $\theta$, and $f$. In all cases, the polycrystalline material is stretched in the $z$ direction.