Bayesian inference based process design and uncertainty analysis of simulated moving bed chromatographic systems

TL;DR

This paper introduces a Bayesian inference method using MCMC algorithms to analyze uncertainties in operating conditions of simulated moving bed chromatography, providing comprehensive performance assessment and optimization insights.

Contribution

It develops a Bayesian approach with MCMC sampling to quantify uncertainties and identify optimal operating conditions in SMB chromatography, extending applicability beyond linear isotherm models.

Findings

Provides posterior distributions and credible intervals for operating conditions.

Maps uncertainties onto separation performance regions.

Offers a versatile tool for process optimization under uncertainty.

Abstract

Prominent features of simulated moving bed (SMB) chromatography processes in the downstream processing is based on the determination of operating conditions. However, effects of different types of uncertainties have to be studied and analysed whenever the triangle theory or numerical optimization approaches are applied. In this study, a Bayesian inference based method is introduced to consider the uncertainty of operating conditions on the performance assessment, of a glucose-fructose SMB unit under linear condition. A multiple chain Markov Chain Monte Carlo (MCMC) algorithm (i.e., Metropolis algorithm with delayed rejection and adjusted Metropolis) is applied to generate samples. The proposed method renders versatile information by constructing from the MCMC samples, e.g., posterior distributions, uncertainties, credible intervals of the operating conditions, and posterior predictive check and Pareto fronts between each pair of the performance indicators. Additionally, the MCMC samples can be mapped onto the $(m_\text{II}, m_\text{III})$ and $(m_\text{IV}, m_\text{I})$ plains to show the actually complete separation region under uncertainties. The proposed method is a convenient tool to find both optimal values and uncertainties of the operating conditions. Moreover, it is not limited to SMB processes under the linear isotherm; and it should be more powerful in the nonlinear scenarios.