Structural Controls on Solute Diffusion in Porous Media

Diffusion in natural porous media, e.g., in soils, rocks and geological formations, is a widely observed phenomenon and is critical to many subsurface applications, such as deep nuclear waste disposal and contaminated aquifer remediation. In much of the existing literature, diffusion is considered to be effectively Fickian. However, recent experimental studies have shown that diffusion can exhibit non-Fickian behavior. To explain this behavior, and in the spirit of percolation theory, we hypothesize that non-Fickian diffusion arises from the low-connectivity nature of pore networks, even when percolating channels exist. Based on a systematic study involving a large number of particle tracking simulations in two- and three-dimensional domains, with low and high connectivity, we demonstrate that non-Fickian diffusion appears in domains nearer the percolation threshold, while it approaches Fickian behavior in high-connectivity domains. Low-connectivity domains contain primary diffusive channels as well as dead ends and even isolated pore clusters that can trap diffusive plumes over extremely long times. This leads to diffusion occurring with power-law transition time behavior. This study highlights the limitations of using purely Fickian models to characterize diffusion behavior in geological settings, as structural features such as pore network connectivity can have a significant influence.