On the Optimality of Superstructures for Simulated Moving Beds

The past decade has seen a variety of operating modifications for Simulated Moving Bed (SMB) processes, including Three-Zone, VARICOL, and PowerFeed. In recent studies, we have shown that these can all be embedded within a superstructure optimization problem with timevariant flow rates. Moreover, the resulting dynamic optimization problem has yielded a number of interesting and useful insights on novel SMB operations. In many cases, optimal solutions have a “bang-bang” character, i.e., at any instant of time, the feed, desorbent, extract and raffinate streams appear at only one location. Remarkably, this occurs even though the optimization is performed without the introduction of binary decision variables. In this study we analyze and present the conditions where “bangbang” solutions are optimal. We also demonstrate cases where these conditions do not hold and where “bang-bang” solutions are suboptimal. To demonstrate that these properties are independent of the column model and solution strategy, we present both “bang-bang” and “nonbang-bang” cases for two different column models.