Molecular diffusion and pore-scale mechanical dispersion controls on time-variant travel time distribution in hillslope aquifers

Abstract

The travel time distribution (TTD) is a lumped representation of the age composition of water leaving the system. Under nonstationary rainfall injection conditions, the TTD varies with transient groundwater flow, leading to a time-variant TTD. It reflects water and solute exports responding to rainfall. The time-variant TTD, time-variant residence time distribution (RTD) and storage selection function (SAS function) provide fundamental insights into transport and mixing processes in groundwater flow system. This study investigates the control of local-scale mixing (i.e., molecular diffusion and pore-scale mechanical dispersion) on time-variant TTD, RTD and SAS function. A solute transport model is constructed to simulate the time-variant TTD, RTD and SAS function under the influence of local-scale mixing; and a particle tracking model is applied to simulated time-variant TTD, RTD and SAS function without the influence of local-scale mixing. Generally, the TTD and cumulative TTD are found to be more sensitive to local-scale mixing than RTD and cumulative RTD due to the ‘volume effect’. The local-scale mixing smoothens the sharp fluctuations of backward TTD and SAS function. The differences of cumulative breakthrough curves and cumulative backward TTDs between two models deviate to negative value except the tails of the two functions, and this verifies the random velocity theory. The differences of cumulative RTDs between the two models indicate the hydrodynamic dispersion can result in more young water leaving the system and more old water remaining in the storage. Meanwhile, two rainfall time series, one with seasonality and one without seasonality, are applied in the two models separately; it is found that the hydrodynamic dispersion shapes the 2-dimensional backward TTD by increasing its continuity along the 45° direction. Finally, the spatial distribution of mean groundwater age is used to illustrate the local-scale mixing in the aquifer and further explain the controls of local-scale mixing on time-variant TTD, RTD and SAS function mechanistically.