Scale Dependence of Intra-Granular Accessible Porosity, Diffusivity, and Tortuosity.

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, diffusivity, and tortuosity in spherical particles.  The diffusive process simulated was release of a non-sorbing solute initially at equilibrium with the surrounding solution.  High-connectivity results were essentially identical to Crank’s analytical solution, while low-connectivity results were consistent with experimental observations.  In particular, at low connectivity the simulated solute release showed the same deviation from the analytical solution that is often observed experimentally: solute released too quickly at early times, and too slowly at late times.  The scale dependence of accessible porosity, diffusivity, and tortuosity was well described by percolation theory.  The scaling relationships should be useful in conventional modeling of diffusive processes in porous spherical particles.