Kinetic model selection and the Hill model in geochemistry

This study introduces the Hill model for modelling sorption kinetics and illustrates its efficacy using formal model selection procedures. Although the coeffi- cient of determination (R²) value can be used to ensure goodness-of-fit of a particular model to a set of data, a measure that incorporates the number of model parameters, such as the Bayesian information criterion, law of iterated logarithm criterion, Akaike information criterion, and the extra sum-of-squares F-test is necessary to undertake reliable model selection. This study undertook a formal model selection procedure based on these criteria, in combination with the coefficient of determination, for a range of candidate kinetics sorption models [the pseudo-second order (PSO), the intra-particle diffusion (IPD), Power, Elovich, and the four and five parameter Hill models]. It was found that the model order that statistically best described the data was Hill 5>Hill 4>pseudo-second order>Elovich>Power>IPD as given by the evidence ratios, information criterion weights and Bayes factors. The extra sum-of-squares F-test, only applicable to nested models, confirms the best fit order as Hill 5[Hill 4[PSO models. Two new parameters (T and k_Hill) have also been defined that give the Hill models a mechanistic meaning directly comparable to the well-defined parameters of the pseudo-second-order model, namely, the pseudo-secondorder rate constant k_pso and the instantaneous sorption coefficient h_pso. In the field of geochemistry the use of the four and five parameter Hill models for describing sorption kinetics has been overlooked with many studies favouring the PSO model. It is strongly recommended that the Hill model be considered more widely as a general predictive tool in geochemistry.

Keywords
Hill model; Pseudo-second order; Adsorption; Kinetics; Model selection; AIC