(412h) Uncertainty Propagation from Batch Experiment Parameters Towards Prediction of Continuous Chromatographic Process

Optimization of process design and operation requires a reliable process model. In order to obtain a process model that gives prediction with sufficient accuracy, it is necessary to reliably estimate unknown parameters in model equations. In chemical processes, practitioners estimate model parameters from laboratory experiments and apply them to a process model¹; however, with the model parameters estimated by lab experiments, the process model often fails to accurately predict the behavior of an actual plant. This is partly because parameter uncertainty is not identified, and the uncertainty that propagates to the prediction of the process model is not quantified.

We took the example of a continuous chromatographic process, or a simulated moving bed (SMB) process, which is a continuous separation technique for sugars, petrochemicals, and enantiomers. To improve the purity, recovery, and throughput of products with model-based optimization,^2,3 a reliable mathematical model of SMBs is essential. Parameters in an SMB model —Henry’s constant, overall mass transfer coefficient, and affinity coefficient— are typically estimated from batch experiments⁴; however, past studies have not considered the uncertainty propagation of estimated parameters towards SMB model predictions.

In this research, we attempted to quantify the effect of the uncertainty on the model prediction as a predictive distribution propagated from parameter uncertainty estimated by Bayesian inference. Our approach is as follows: we estimated parameters from batch chromatographic experimental data using Bayesian inference to quantify uncertainty as a probability distribution. Because the probability distribution of model parameters cannot be obtained analytically, a numerical solution based on random sampling, Markov chain Monte Carlo (MCMC), was employed.⁵ Using parameters sampled from the resulting posterior distributions of parameters, the performance of SMB—product concentrations, purity, and recovery—were evaluated as predictive distributions obtained by carrying out thousands of simulations. From the predictive distributions, the influence of uncertainty in each model parameter was analyzed, which provides insights into the design of batch experiments that assures sufficient model accuracy and allows reliable development of continuous chromatographic separations.

References:

1. Wang Y, Biegler LT, Patel M, Wassick J. Parameters estimation and model discrimination for solid-liquid reactions in batch processes. Chem Eng Sci. 2018;187:455-469. doi:10.1016/j.ces.2018.05.040
2. Kawajiri Y, Biegler LT. Optimization strategies for simulated moving bed and powerfeed processes. AIChE J. 2006;52(4):1343-1350. doi:10.1002/aic
3. Grosfils V, Levrie C, Kinnaert M, Vande Wouwer A. A systematic approach to SMB processes model identification from batch experiments. Chem Eng Sci. 2007;62(15):3894-3908. doi:10.1016/j.ces.2007.04.015
4. Schmidt-Traub H, Schulte M, Seidel-Morgenstern A. Preparative Chromatography. 2nd ed. WILEY-VCH Verlag GmbH & Co.; 2012.
5. Kim H. A First Course in Statistical Methods. Vol 47.; 2005. doi:10.1198/tech.2005.s830