Influence of initial water content on hydrodynamic dispersion in an unsaturated limestone column under transient flow regime

When solutes such as fertilizers or pesticides applied to the soil surface are transported through the vadose zone to the underlying aquifer by rainfall infiltration or irrigation, hydrodynamic dispersion significantly contributes to the spreading and attenuation of the resulting contaminant plume. Dispersion is governed by the longitudinal dispersivity, a parameter that is not intrinsic to the medium. Dispersivity has long been recognized to be approximately proportional to the distance traveled by the solute plume. It has also been recognized to be dependent of the water content. This paper analyzes the effect of transient flow on solute dispersion during a rewetting phase after a long drying period, a topic of practical relevance because dispersivity is an input parameter in models simulating nitrogen or pesticide transport to aquifers through the vadose zone, where water flows generally do not reach steady state, at least in its upper part.

A unique set of hydraulic and transport parameters is obtained by modeling simultaneously a dataset of 19 tracer experiments conducted in the lab in a vertical unsaturated limestone column, under various water contents and flow regimes.

To assess the variation in dispersivity between tracer experiments in transient flow conditions initiated from a dry state under rewetting and those initiated under steady flow conditions, the dispersivity value assigned by the numerical model to the column is chosen during calibration from two values, depending on the initial state at the start of each experiment: one for tracer tests in a rewetting phase, and the other for those starting in steady flow conditions.

The calibration results demonstrate that dispersivity under transient flow starting with rewetting conditions is twice that obtained for a tracer test starting in steady flow. This highlights the impact of the initial water content on the limestone’s dispersivity.

The paper demonstrates how the addition in the numerical model of a novel time-dependent relationship, defining dispersivity as a function of water content and cumulative volume of injected water, makes it possible to simulate complex scenarios involving successive tracer injections under varying flow regimes.