A SEMIANALYTICAL SOLUTION FOR ONE-DIMENSIONAL SOLUTE TRANSPORT IN SOILS

Analytical solutions to the convection-dispersion model (CDM) of solut e transport require linear reaction terms, strict initial and boundary concentration conditions, and are often complex to evaluate because o f the inherent mathematical functions. We present a flexible and mathe matically very simple solution to the CDM at steady water flow, labele d a semi-analytical (SA) solution. The SA solution allows for nonlinea r reaction terms, variable initial and boundary conditions, and is bas ed on the recently presented moving concentration slope (MCS) model fo r solute transport. To derive the SA solution, a solute flux approxima tion at the upper boundary and a small, constant depth increment of 0. 5 cm are used, and two features of the MCS model are exploited, i.e., an explicit, depth-integrated flux equation is already inherent in the model and all numerical error and stability equations are unique func tions of the solute unit mean travel distance (SUMTD). The SA solution contains seven constants; one is the solute dispersivity, and the rem aining six are functions only of the SUMTD. Excellent agreement betwee n the SA solution and ordinary analytical solutions to the CDM was obt ained. For variable boundary conditions, the SA solution was also test ed against data for chloride transport in sandy soil columns. Measured and calculated outlet concentrations compared well. The SA model allo ws for linear or nonlinear reaction terms without increasing the compl exity of the solution. In the case of nonlinear reactions, the SA mode l offers a simple solution in situations where conventional analytical solutions are not available. This was illustrated by successfully com paring the SA solution, including a Michaelis-Menten reaction term, wi th measured data for simultaneous transport and reduction of nitrate i n porous media columns.