Sharp transition to strongly anomalous transport in unsaturated porous media - Modelling and prediction

Transport processes in unsaturated porous media flows play a key role in a broad range of environmental and industrial systems. The simultaneous presence of liquid and gas in the pore space increases flow heterogeneity and fundamentally alters the observed flow patterns when compared to fully saturated systems. The introduction of the air phase leads to the development of highly structured water flow fields with preferential flow localized on a backbone and flow re-circulation occurring in flow dead-ends. However, it is unclear how saturation controls both flow statistics and transport dynamics. Here we use millifluidic experiments and high-resolution numerical simulations to develop a general theoretical framework that describes this flow re-organisation in the pore space and captures its impact on the statistics of pore-scale velocities. We observe, and predict theoretically, that this previously-identified flow structure of backbone and dead-ends induces both a drastic change in the scaling of the probability density function (PDF) of flow velocities compared to fully saturated conditions, and a sharp transition to strongly anomalous transport. From the theoretically derived velocity PDFs, we successfully predict the dynamics of advective transport for all saturation degrees using a continuous time random walk approach. These findings hence provide a new modelling framework linking flow heterogeneity to parameters that describe the liquid phase heterogeneity within the pore space.