Local Solute Sinks and Sources Cause Erroneous Dispersion Fluxes in Transport Simulations with the Convection-Dispersion Equation

The convection-dispersion equation (CDE) is the most widely used model for simulating the transport of dissolved substances in porous media. The dispersion term in the CDE lumps molecular diffusion and hydromechanical dispersion into an effective diffusive solute flux. This is possible by describing hydrodynamic dispersion with Fick's first law of diffusion. We critically analyzed this concept for specific water flow situations where the solute concentration is locally increased by processes like root water uptake or water evaporation. The local accumulation of solutes in these situations leads to high concentration gradients and a dispersive solute flux component opposite to the direction of the water flux. This is physically wrong because it assumes that molecules or ions are moving against the flow direction by dispersion. The aim of this study was to investigate the magnitude of the resulting error by means of numerical modeling. We simulated solute transport from a groundwater table to a bare soil surface during steady-state evaporation using the HYDRUS-1D code. The simulations showed that in the region where dissolved substances accumulate due to the transition from liquid water to vapor, the resulting incorrect dispersive flux against the mean transport direction can reach the same order of magnitude as the convective solute flux. Under such conditions, application of the CDE is questionable.