Statistical analysis of parameters and adsorption isotherm models.

Area of Science:

• Adsorption Science
• Chemical Engineering
• Physical Chemistry

Background:

• Adsorption processes are critical in chemical engineering and environmental applications.
• Accurate parameter estimation and statistical analysis are essential for understanding adsorption phenomena.
• Langmuir and Tóth isotherms are commonly used models for describing gas adsorption on solid surfaces.

Purpose of the Study:

• To compare the Langmuir and Tóth isotherm models for carbon dioxide (CO2) adsorption on 13X zeolite.
• To evaluate parameter estimation and statistical analysis methods, including frequentist and Bayesian approaches.
• To assess the influence of experimental uncertainty on model performance and parameter evaluation.

Main Methods:

• Adsorption isotherm data for CO2 on 13X zeolite at various temperatures (303–423 K) were analyzed.
• Frequentist statistical analysis employed Maximum Likelihood Estimation (MLE) with confidence regions (elliptical approximation, likelihood region) and chi-square statistics.
• Bayesian statistical analysis utilized Markov chain Monte Carlo (MCMC) for parameter probability density functions and uncertainty propagation.

Main Results:

• The elliptical approximation for confidence regions provided a poor fit for parameter estimates, particularly for correlated parameters.
• The four-parameter Tóth model exhibited less parameter correlation compared to the three-parameter Langmuir model.
• Bayesian analysis via MCMC effectively reconstructed parameter probability density functions and propagated uncertainties.

Conclusions:

• The Tóth model is advantageous over the Langmuir model due to reduced parameter correlation in this CO2/zeolite system.
• Frequentist confidence region approximations can be unreliable for nonlinear adsorption models.
• Accurate assessment of experimental uncertainty is paramount for robust model selection and parameter determination in adsorption studies.