Quantifying anomalous chemical diffusion through disordered porous rock materials

Abstract

Fickian (normal) diffusion models show limitations in quantifying diffusion-controlled migration of solute species through porous rock structures, as observed in experiments. Anomalous diffusion prevails and can be interpreted using a Continuous Time Random Walk (CTRW) framework with a clear mechanistic underpinning. From the associated fractional diffusion equation we derive solutions over a broad range of anomalous diffusion behaviours, from highly anomalous to nearly Fickian, that yield temporal breakthrough curves and spatial concentration profiles of diffusing solutes. We illustrate that these solutions can be tailored to match realistic experimental conditions and resulting measurements that display anomalous diffusion. In particular, our analysis enables clear differentiation between early-time Fickian and anomalous diffusion, which becomes more pronounced over longer durations. It is shown that recent measurements of diffusion in natural rocks display distinct anomalous behaviour, with significant implications for critical assessment of solute migration in diverse geological and engineering applications.