(674d) Parameter Estimation for Reactive Chromatography Model By Bayesian Inference and Parallel Sequential Monte Carlo

Reactive chromatography simultaneously performs reaction synthesis and separation of the product. This principle has been shown to improve the reaction conversion rate, enable the downsizing of equipment, and reduce operating costs. For industrial-scale applications, a simulated moving bed reactor (SMBR) can be a promising technique in which multiple columns are connected to continuously feed reactants to carry out reactions while performing separations simultaneously. This process has been investigated for various applications, including biodiesel production[i] and sugar inversion [ii]. The principle of simulated moving bed has been commercialized for many large-scale separations in the petrochemical industry and sugar production[iii].

Reliable model development is essential for designing complex processes such as SMBRs, which require operating conditions to be determined, so that product requirements are met. In the model-based development of such processes, experimental data are needed to estimate parameters in the model. However, analyzing the uncertainty in the estimated model parameters and quantifying the influence on the predictive performance remains a challenge.

This study aims to quantify the uncertainty in model parameters and develop reliable models to support the development of reactive chromatography. To this end, Bayesian estimation was used to estimate model parameters in this study. In the proposed approach, parameter uncertainty is shown as probability distributions. Since it is challenging to obtain parameters analytically, the sequential Monte Carlo method is applied, a sampling method for approximation. This method allows random sampling in parallel using multiple cores, which reduces the computation time compared to the conventional methods such as Markov chain Monte Carlo[iv]. Furthermore, several thousand points were sampled from the posterior probability distributions of the parameters, which were used in numerical simulations to evaluate predictions.

This study considers the synthesis of methyl acetate and water from acetic acid and methanol as a case study. Experimental data under various conditions were utilized, and parameters were estimated using multiple data sets. Experimental conditions that can successfully reduce parameter uncertainties were also investigated.

References:

[i] Fukumura T, Chiba R, Ono Y, Kubo M. Continuous synthesis of ethyl esters from triglycerides using simulated moving bed chromatographic reactor packed with solid acid catalysts. Kagaku Kogaku Ronbunshu. 2018;44(3):177-184. doi:10.1252/kakoronbunshu.44.177

[ii] Hashimoto K, Adachi S, Noujima H, Ueda Y. A new process combining adsorption and enzyme reaction for producing higher‐fructose syrup. Biotechnol Bioeng. 1983;25(10):2371-2393. doi:10.1002/bit.260251008

[iii] Rodrigues AE, Pereira CSM, Santos JC. Chromatographic Reactors. Chem Eng Technol. 2012;35(7):1171-1183. doi:10.1002/ceat.201100696

[iv] Yamamoto Y, Yajima T, Kawajiri Y. Uncertainty Quantification for Chromatography Model Parameters by Bayesian Inference using Sequential Monte Carlo Method. Chem Eng Res Des. 2021;175:223-237. doi:10.1016/j.cherd.2021.09.003