Abstract
Determining the adsorption isotherms is an issue of significant importance in preparative chromatography. A modern technique for estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides with actual experimental results. However, due to the ill-posedness, the high nonlinearity, and the uncertainty quantification of the corresponding physical model, the existing deterministic inversion methods are usually inefficient in real-world applications. To overcome these difficulties and study the uncertainties of the adsorption-isotherm parameters, in this work, based on the Bayesian sampling framework, we propose a statistical approach for estimating the adsorption isotherms in various chromatography systems. Two modified Markov chain Monte Carlo algorithms are developed for a numerical realization of our statistical approach. Numerical experiments with both synthetic and real data are conducted and described to show the efficiency of the proposed new method.
Funding Statement
Z.Y. thanks the research support from the Center of Mathematical Sciences and Applications at Harvard University. Z.Y. would like to thank the Singapore MOE Tier 1 grants R-155-000-196-114, A-0004826-00-00 and Tier 2 grant A-0008520-00-00 at the National University of Singapore.
C.L. would like to thank the Singapore MOE Tier 1 grant A-0004822-00-00 at the National University of Singapore.
Y.Z. would like to thank the National Key Research and Development Program of China (No. 2022YFC3310300) and Beijing Natural Science Foundation (No. Z210001).
Acknowledgments
The authors would like to thank the Fundamental Separation Science Group (FSSG) under the supervision of Professor Torgny Fornstedt at Karlstad University, Sweden for providing the real data (cyclohexanone and cycloheptanone). Correspondence should be addressed to E-mail: zhigang.yao@nus.edu.sg.
Citation
Jiaji Su. Zhigang Yao. Cheng Li. Ye Zhang. "A statistical approach to estimating adsorption-isotherm parameters in gradient-elution preparative liquid chromatography." Ann. Appl. Stat. 17 (4) 3476 - 3499, December 2023. https://doi.org/10.1214/23-AOAS1772
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