Kinetic model selection and the Hill model in geochemistry

Abstract

This study introduces the Hill model for modelling sorption kinetics and illustrates its efficacy using formal model selection procedures. Although the coefficient of determination (R 2 ) 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.

Revision of adsorption models of xyloglucan on microcrystalline cellulose

“…The following equations were used to calculate those values (El-Khaiary 2008; Danish et al 2011;Turner et al 2015):…”

Kinetics of fluoride removal from spent pot liner leachate (SPLL) contaminated groundwater

“…Methods that account for a model's goodness-of-fit (R 2 ) and its number of parameters are better suited for model selection [14]. Such methods include the akaike information criterion (AIC), the Bayesian information criterion (BIC), and likelihood ratio tests (LRT) such as the statistical F-test.…”

“…Such methods include the akaike information criterion (AIC), the Bayesian information criterion (BIC), and likelihood ratio tests (LRT) such as the statistical F-test. Further information on these tests and their application can be foundin Turner et al [14].…”

“…For each model 1000 Monte Carlo simulations were made to generate the 95% confidence intervals (CIs) for the best fitting model as per the method outlinedin Turner et al [14]. Monte Carlo simulations allow randomized Gaussian resampling of the observed data (based on a known standard deviation) to construct a "new" set of data as per Motulsky and Christopolous [20].…”

“…Reaction kinetics are modelled as a function of pCO 2 , and stirring rate using the pseudo-second order (PSO) model and the four and five parameter Hill models first described in the geochemical literature by Turner et al [14].…”