Calculation of kinetic rate constants from steady-state soil profile concentration measurements

We derive a simple approximation for the steady-state distribution of solute subject to an arbitrary, irreversible transformation in a soil profile under the condition of steady fluid flow. The approximation accounts for the effect of dispersion in both the surface boundary condition and the transport equation. The accuracy of the approximation is determined explicitly for the cases of zero- and first-order kinetics, where exact solutions are available. Data from a numerical scheme are used to check the approximation's accuracy for the widely used Michaelis Menten kinetic rate. It is shown that existing approximations in which the effect of dispersion in the transport equation is ignored can affect significantly the value determined for the Michaelis-Menten saturation constant. Parameters found when the new method is applied to experimental data are found to agree closely with those estimated directly from a least-squares fitting.