The Advection-Dispersion Equation

The one-dimensional (vertically and laterally integrated) equation for the con­servation of mass of a substance in a solution, i.e. the one-dimensional advection-dispersion equation reads:

where

-          –         C : concentration

-          –         D : dispersion coefficient

-          –         A : cross-sectional area

-          –         K : linear decay coefficient

-          –         C2 : source/sink concentration

-          –         q : lateral inflow

-          –         x : space coordinate

-          –         t : time coordinate

The equation reflects two transport mechanisms:

·         Advective (or convective) transport with the mean flow;

·         Dispersive transport due to concentrations gradients.

The main assumptions underlying the advection-dispersion equation are:

·         the considered substance is completely mixed over the cross-section, implying that a source/sink term is considered to mix instantaneously over the cross-section;

·         the substance is conservative or subject to a first order reaction (linear decay);

·         Fick's diffusion law applies, i.e. the dispersive transport is proportional to the concentration gradient.