Global Approach for Simulated Moving Bed Model Identification: Design of Experiments, Uncertainty Evaluation, and Optimization Strategy Assessment

Statistical analysis of parameters and adsorption isotherm models

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, parameters were estimated using Maximum Likelihood estimation (MLE). 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 that, for these nonlinear models, the elliptical region offers a poor approximation of the parameter estimates' confidence region, especially for the most correlated parameter pairs. Additionally, the four-parameter Tóth's equation yields less correlated parameters than the three-parameter Langmuir model. From a Bayesian perspective, the Markov chain Monte Carlo (MCMC) technique facilitated the reconstruction of the probability density functions of parameters as well as enabled the propagation of parametric uncertainties in the model responses. Finally, the accurate assessment of experimental uncertainty significantly influences the evaluation of models and their respective parameters.

A Complete Heterogeneous Model for the Production of n-Propyl Propionate Using a Simulated Moving Bed Reactor

n-Propyl Propionate (ProPro) is a harmless biodegradable product employed in several fields for the production of drugs, inks, coating, food, and perfume. ProPro is synthesized in an equilibrium reaction for which its yield can be enhanced by constant withdraw of the products as the reaction takes place. Simulated Moving Bed Reactor (SMBR) is a candidate for the production of ProPro with high efficiency as it is a multifunction unit able to simultaneously run reaction and separation, hence shifting the equilibrium reaction toward products. This paper proposes a complete phenomenological model for the ProPro synthesis in a Simulated Moving Bed Reactor (SMBR) packed with the heterogeneous catalyst Amberlyst 46 resin. The operating conditions are defined by the Triangle Theory to design an SMBR unit to produce ProPro efficiently and a comprehensive parameter estimation procedure is employed to obtain more representative parameters. The validated phenomenological model was applied to design an SMBR unit to produce high purity (99.28%) ProPro.