Statistical analysis of parameters and adsorption isotherm models

Abstract

The present work intends to discuss parameter estimation and statistical analysis in adsorption. The Langmuir and Tóth isotherm models are compared for a set of carbon dioxide adsorption data on 13X zeolite from literature at different temperatures: 303, 323, 373, and 423 K. Statistical analyses were performed under frequentist and bayesian perspectives. Under the frequentist statistical view, the estimation of parameters was performed employing Maximum Likelihood estimation (MLE) using Particle Swarm Optimization (PSO) and a Newton-like method. Statistical analyses of parameters were performed by confidence regions in terms of elliptical approximation and likelihood region, while the evaluation of models was performed by chi-square statistics. The results showed the importance of precisely knowing the experimental errors and obtaining the true confidence region of model parameters. As the model is nonlinear, the elliptical confidence region provides a poor approximation of the confidence region of the parameter estimates. Finally, correlation matrices show that Tóth's equation returned less correlated parameters than the Langmuir's. Under the bayesian perspective, the Markov-chain Monte Carlo (MCMC) technique allowed obtaining the confidence regions of the parameters such as those obtained by the frequentist approach. The bayesian method, however, enables the reconstruction of the parameters' probability density functions and the propagation of parametric uncertainties.