(61t) Use of Bayesian Optimization for Efficient Finding of Optimal Operating Condition of Simulated Moving Bed Process

Simulated moving bed (SMB) is a chromatographic separation process that can be operated continuously. It provides the effect of moving the stationary (solid) phase by arranging several columns and periodically switching the position of inlet and outlet ports. Since the solid phase and the solvent move in opposite directions, components highly adsorbed to the solid phase flow with solid bed movement and poorly adsorbed components flow with the solvent (desorbent), enabling separation of the mixture. Compared to the conventional batch chromatography, SMB process has the advantages of lower production costs (by reducing the amount of stationary phase and desorbent used) and high purity and yield. Due to these advantages, the SMB technology has been broadly applied in petrochemical, carbohydrate, and pharmaceutical industries.

In practice, it is important to quickly find feasible and possibly optimal operating conditions of SMB process for a new separation task, because large amounts of off-spec products are produced during the test runs in searching for them. An SMB process generally takes a long time (sometimes more than 2 days) to reach a cyclic steady state when operating conditions change. Therefore, methods such as random search or grid search are inappropriate. It can be helpful to use a first-principles model to find a good starting guess for the optimal operation condition, but first-principles based high-fidelity SMB process models can be quite complex and take several hours or even days to calculate the cyclic steady state, making it difficult to use for this purpose. On the other hand, the true moving bed (TMB) model based on the assumption of instantaneous equilibrium is conceptually simple and requires much less computational time, but has low accuracy.

To address these challenges, this study develops an automated algorithm based on Bayesian optimization that efficiently recommends a new candidate of operating conditions of SMB by balancing exploration and exploitation. With the algorithm, one can quickly and sequentially approach the optimal condition, both in high-fidelity simulations and actual plant trials. In our case, the optimal operating conditions of the SMB process are defined as those resulting in the minimum desorbent consumption while satisfying product specifications of 99.5% or higher purity. While the objective function (desorbent consumption rate) is inexpensive-to-evaluate, constraints (product purities) are very expensive-to-evaluate because they are defined with respect to the cyclic steady state which takes long time to reach. Operating degrees of freedom are the four m ratios, which are the ratio of the solvent flow rate to the solid flow rate for the four zones of the SMB process. As these m ratios vary, process variables such as the extract flow rate, raffinate flow rate, recycle flow rate, and switch time vary accordingly. In the developed Bayesian optimization framework for SMB process, Gaussian process regression with Matérn32 kernel is used to predict the extract and raffinate purity. As an acquisition function, the typical choice of expected constrained improvement is modified to fit the case of an inexpensive-to-evaluate objective function and expensive-to-evaluate constraints. We also introduced batch Bayesian optimization to recommend multiple candidates in one iteration when function evaluation can be performed in parallel.

To test the suggested algorithm, the separation of m-cresol and p-cresol mixture is studied. Using the 66,510 data from the TMB model as a true function, it turned out that the Bayesian optimization approaches the true optimum faster than either random search or greedy search. Whereas the random search performs inconsistently and the greedy search gets stuck at a sub-optimum, Bayesian optimization effectively reaches the global minimum of desorbent consumption while satisfying the purity constraints, by balancing exploitation and exploration. Next, the complex high-fidelity SMB model is assumed as a real SMB process. The proposed framework is shown to find better operating conditions as iterations progress. Furthermore, we investigate the effect of using the simple TMB model as a baseline of purity prediction. Even though the TMB model is less accurate, it is worthwhile to utilize its results as the initial mean in the Gaussian modeling, because search space can be effectively narrowed in initial iterations by reflecting the physics of the SMB process, albeit only in an approximate manner.

The current industrial practice is that the operating conditions of SMB process are explored by changing them little by little while relying on the experience of experts. The method not only requires many repetitions of experiments, but also may not ultimately find a point that satisfies the purity constraints. The proposed Bayesian optimization framework is more efficient and finds better operating conditions by allowing the algorithm to choose the next operating conditions it wants to learn from. It can lower the dependency on the expert experience and reduce the amounts of off-spec products by minimizing the number of trial runs.