Scale dependence of intragranular porosity, tortuosity, and diffusivity

[1] Diffusive exchange of solutes between intragranular pores and flowing water is a recognized but poorly understood contributor to dispersion. Intragranular porosity may also contribute to the “slow sorption” phenomenon. Intragranular pores may be sparsely interconnected, raising the possibility that accessible porosity and diffusive exchange are limited by pore connectivity. We used a pore-scale network model to examine pore connectivity effects on accessible porosity, tortuosity, and diffusivity in spherical particles. The diffusive process simulated was release of a nonsorbing solute initially at equilibrium with the surrounding solution. High-connectivity results were essentially identical to Crank's analytical solution. Low-connectivity results were consistent with observations reported in the literature, with solute released at early times more quickly than indicated by the analytical solution, and more slowly at late times. Values of accessible porosity, tortuosity, and diffusivity scaled with connection probability, distance to the sphere's exterior, and/or the sphere's radius, as predicted by percolation theory. When integrated into a conventional finite difference model, the scaling relationships provide a consistent and physically sound way to incorporate such nonuniformities into models of intragranular diffusion.