Analytical solutions for equations describing coupled transport of two solutes and a gaseous product in soil
1993
Angelakis, A.N. | Kadir, T.N. | Rolston, D.E.
An analytical solution for transient soil-gas diffusion coupled to two convective-dispersive solute transport equations is presented. First-order kinetic transformations, linear equilibrium distribution coefficient for both solutes, and equilibrium gas solubility for the gaseous product were assumed. The solution was obtained by means of Laplace transforms for zero initial concentrations of all three species, pulse application of both solutes, and semi-infinite media. Concentration profiles of the soil gas as a function of soil depth and time were computed. An example problem was used to demonstrate the use of the solution and its sensitivity to various parameters. The solution was verified by comparison to a numerical solution using an explicit finite difference scheme. The analytical solution shows that the soil-gas distributions were highly affected by the gas solubility and by the distribution coefficient and the transformation rate constants of both solutes. However, the gas distributions were not significantly affected by the dispersion coefficient of either solute. The gas distributions are slightly affected by changes in the gas diffusivity over the range expected for different gas species at a single value of air-filled porosity. Changes in soil-water content and the corresponding change in air-filled porosity would result in large changes in the gas concentration profiles.
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