Reaction Kinetics and Transport in Soil: Compatibility and Differences between Some Simple Models

Abstract

Non-equilibrium between the composition of the soil solution and of the sorption sites on the solid matrix of soil may be due to mass transfer resistances and to slow chemical kinetics of elementary or complex reactions. Different mechanistic models have been used to describe the rate of change of the soil solution composition due to sorption, using a good description of experimental results to draw conclusions with respect to the mechanisms involved. Assuming a mono-solute description to be appropriate, some similarities and differences between overall first order kinetics and two mechanistic diffusion-sorption kinetics models are considered. Empirical first order reaction rates can often be fitted well within experimental error on the solutions for the mechanistic diffusion-sorption models. For one of the mechanistic models (un-reacted shrinking core) the behaviour is shown when the reactive solid particle size is exponentially distributed. This model can be recast into a semi-empirical model that allows scaling of reaction time, as its concentration dependence differs from the two other models. This is illustrated with an example taken from metallurgical engineering. Another difference is the effect of nonequilibrium on the solute front in an ideal plug flow reactor. For sorption according to the shrinking core model displacement may lead to a non-Fickian front, as front spreading does not grow with the square root of time. For the two other sorption models Fickian type of displacement results for large enough displacement distances.