A tandem simulated moving bed (SMB) was developed previously for the purification of insulin from two impurities in two sequential steps. In this study, an efficient optimization tool based on the standing wave design is developed to find the optimal tandem SMB for insulin purification. Both system parameters (total number of columns, zone configuration, column diameter, and column length for each ring) and operating parameters (zone flow rates and switching time for each ring) are optimized to achieve the lowest purification cost. In the production range of interest, equipment cost dominates. For this reason, the optimal design has eight or fewer columns in each ring. The optimal design also has a small column length and a large column diameter, as the stationary phase for insulin purification is compressible and has a zone linear velocity limit. Splitting strategies and constraints on the column diameter and column length have significant effects on the optimal design. If there is a limit on the column diameter, optimization of the splitting strategy and column length can result in 24 and 25% savings, respectively, in total purification costs. Finally, if the limit on linear velocity is removed, a lower purification cost can be achieved by using longer columns with smaller diameters. The method developed in this study can be applied to other size-exclusion systems or linear isotherm systems.
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