(115a) A Systematic Method to Find Optimal Number of Columns and Zone Configuration of Simulated Moving Bed Processes

The number of columns is one of the most important design parameter for simulated moving bed processes. This choice is not trivial due to the trade-off between the capital cost and separation performance. A low number of columns where the adsorbent is split into a few columns may lead to poor separation performance. On the other hand, a high number of columns where the adsorbent is split into many columns leads to a higher capital cost, but has the potential to improve the separation performance utilizing the greater flexibility in choosing the zone configuration.

In this work, a systematic method to determine the adsorbent split problem based on a deterministic optimization technique using a rigorous dynamic SMB model is proposed. First, it is shown that this SMB optimization problem is classified as a singular optimal control problem, where the optimal operating condition is non-unique. Due to this property, the optimal performance of SMB reaches a plateau when the number of columns is sufficiently high. After finding this performance upper bound, the number of columns can be reduced so that the capital cost is decreased without sacrificing the optimal separation performance. Furthermore, it is shown that the optimal zone configuration differs significantly depending on the unit cost of feed and desorbent. Some case studies of different objectives and isotherms are discussed