Bayesian optimization for quick determination of operating variables of simulated moving bed chromatography

The Simulated Moving Bed (SMB) is a continuous chromatographic separation process that operates on the principle of counter-current movement between the solid and liquid phases. Due to periodic switching of feed and product ports across numerous connected columns, adjusting SMB operating variables such as feed and product flow rates and switching time to achieve desired separations is challenging. While equilibrium theory can help narrow the search space, obtaining essential information such as accurate adsorption isotherms is crucial. This requirement, combined with often highly stringent production specifications, makes it challenging to identify even a feasible operating condition, let alone an optimal one. Trial-and-error-based approaches are often impractical as reaching cyclic steady state can be time-consuming, and any waste produced during this period can lead to significant economic losses. While rigorous dynamic models are available, they are computationally intensive and often do not accurately mirror actual process behavior. To address these challenges, the use of Bayesian Optimization (BO) is proposed to sequentially approach optimal SMB operation. Furthermore, it is suggested to employ the simpler True Moving Bed (TMB) model as a prior for the BO, which significantly accelerates convergence. This approach is demonstrated on an SMB process for cresol separation. Initially, the effectiveness of the BO using the TMB model is examined to gain insights into its behavior. Subsequently, we apply BO to the rigorous SMB model, informed by prior knowledge from the TMB model. Our results show that the developed BO framework rapidly converges to the optimal operating parameters that satisfy the purity constraints. We examine the efficiency improvements over various search algorithms and highlight the advantages of using the TMB model as a prior.