APPLICATION OF A LUMPED, NONLINEAR KINETICS MODEL TO METAL SORPTION ON HUMIC SUBSTANCES

Exposure assessment models are needed to predict the sorption behavior of metal ions with humic substances. To address this need, a lumped p arameter nonlinear kinetics model based on the Langmuir-Hinshelwood ki netic model-dC/dt = k(1)C/(1 + k(o)C)-is introduced and evaluated. The model was applied to a mixture of seven metal ions-Cr(III), Pb(II), C u(II), Cd(II), Co(II), Ag(I), and Li(I)-reacted with three individual humic substances. The lumped parameter model employs a dimensional ana lysis technique (i.e., uses dimensionless parameters), Laplace transfo rms, gamma functions, and gamma distributions to produce analytical so lutions for the kinetic equation of metal ion sorption to humic substa nces. During the initial reaction period, the most reactive species-Cr (III) and Pb(II)-dominated the lump parameter value, and the mixture b ehaved like a first-order reaction. At longer periods, the lump follow ed a second-order decay if there were less reactive species involved. The lumped parameter model provides valuable information about the ove rall kinetics behavior of metal ion mixtures with humic substances and could serve as a simulation tool to investigate the transport of meta l ions in and out of landfill sites and the transport/retardation of m etals in contaminated soils and aquifers.