Estimating Freundlich isotherm parameters of heavy metals from multiple batch extraction tests using a Bayesian approach

The sorption isotherm is the key to modeling the fate of many environmental chemicals in soil. Iden and Durner (2008) proposed a simple method, the multiple batch extractions test (MuBaX), to simultaneously estimate the isotherm parameters and the total desorbable heavy metal contents. The method essentially consists of equilibrating soil suspensions at varying liquid to soil (L/S) ratios, which induces desorption of heavy metals, measuring the solution phase concentrations at equilibrium, and using a model to evaluate the measured data. This study was carried out to test the capability of the proposed method to estimate Freundlich parameters of eight heavy metals for 49 topsoil samples from nine soil types. Heavy metals studied were Cd, Cr, Cu, Mo, Ni, Sb, Tl and Zn. Five L/S ratios (1, 2, 10, 30, and 100 L kg− 1) were used. Parameter estimation was carried out using a Bayesian approach. Although measured solution phase concentrations could be reproduced very well (modeling efficiency, EF, between 0.89 and 0.99), the agreement between total desorbable heavy metal contents estimated by MuBaX and those measured by isotope dilution was quite poor as indicated by negative values of the modeling efficiency. We conclude that the MuBaX method is not well suited for application to strongly sorbing topsoils with relatively low heavy metal contents. Nevertheless, the Bayesian parameter estimation proved useful because it enabled the reliable quantification of the uncertainties in the parameter estimates and was not negatively affected by the existence of local minima of the objective function.