SOME APPROXIMATE SOLUTIONS OF THE TRANSPORT EQUATION WITH IRREVERSIBLE REACTIONS

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Abstract
We discuss the influence of dispersion on solute movement for zero-order, first-order, and Michaelis-Menten kinetics. In general, dispersion enters both the transport equation and the boundary condition at the soil surface. The method of characteristics yields an accurate analytical solution for arbitrary kinetics by ignoring dispersion effects in the transport equation. When those effects are taken into account, exact analytical solutions exist only for zero- and first-order kinetics. An analytical approximation is obtained here for arbitrary kinetics, and its accuracy is analyzed by considering specific examples. It is suggested that, in general, the accuracy of the solution for arbitrary kinetics can be assessed by comparison with the exact solutions for zero-and first-order kinetics, i.e., for high and low solute concentrations. We discuss the influence of dispersion on solute movement for zero-order, first-order, and Michaelis-Menten kinetics. In general, dispersion enters both the transport equation and the boundary condition at the soil surface. The method of characteristics yields an accurate analytical solution for arbitrary kinetics by ignoring dispersion effects in the transport equation. When those effects are taken into account, exact analytical solutions exist only for zero- and first-order kinetics. An analytical approximation is obtained here for arbitrary kinetics, and its accuracy is analyzed by considering specific examples. It is suggested that, in general, the accuracy of the solution for arbitrary kinetics can be assessed by comparison with the exact solutions for zero-and first-order kinetics, i.e., for high and low solute concentrations. © Williams & Wilkins 1984. All Rights Reserved.