Liquid chromatograhpic separation is widely used in life-science,pharmaceutical, chemical, and food industries. Since this separation technique does not require heat, it is suitable for separation of mixtures with similar chemical structures, and thermally unstable products such as proteins.

In a liquid chromatographic process, feed mixture is separated making use of the difference in the migration speed of components in the liquid. A small amount of feed mixture is supplied to an end of a column which is packed with adsorbent particles, and then pushed toward the other end with desorbent (water, organic solvent, or mixture of these). The purified products are withdrawn at the other end of the column.



Simulated moving bed (SMB) chromatographic separation

Simulated Moving Bed (SMB) was developed as a continuous version of liquid chromatography in the 1960s. Its application areas include sugar, petrochemical, and pharmaceutical separations. In particular,enantiomeric separations have been found to be one of the most effective applications in the past decade.

An SMB system consists of multiple columns connected to each other making a circulation loop. Between every column, there are inlet ports for feed and desorbent streams, as well as outlet ports for extract and raffinate streams. The feed and desorbent are supplied continuously and at the same time extract and raffinate are drawn continuously through the ports. These four inlet/outlet ports are switched simultaneously at a regular interval in the direction of the liquid flow (see below).

This system does not reach a steady state but a cyclic steady state (CSS), where the concentration profiles change dynamically, but the profiles of both liquid and solid phase at the beginning of a cycle are identical to those at the end of the cycle (see below).  Because of this behavior, determining the design and operating parameters of SMB processes remains a challenging problem. The cyclic dynamics characterized by CSS complicate numerical treatments.



Other multi-column operations

It is known that by modifying the standard switching operation, the performance of SMB can be improved significantly. For example, the VARICOL systems perform asynchronous valve switchings,where the four inlet/outlet ports are switched independently, not simultaneously.



In the Three-Zone operation, the circulation loop is cut open and the recycle stream is withdrawn as the raffinate stream.




 How to find the best multi-column operation?

In order to find novel optimal operating schemes, we have proposed an SMB superstructure as shown below that embeds numerous kinds of modified SMB operations. This superstructure model is incorporated in the optimization problem.



An optimal control problem technique is applied to this superstructure. Below is an example of optimal operating schemes of a throughput maximization problem. CPU time required to find this operating scheme is only 9.03 minutes on a Xeon 3.2 GHz machine.




Details are given in the following reference:

Kawajiri, Y. and Biegler, L.T.: A Nonlinear Programming Superstructure for Optimal Dynamic Operations of Simulated Moving Processes, Industrial & Engineering Chemistry Research, 45(25), 8503-8513 (2006).