Optimal design and operation of a certain class of asynchronous simulated moving bed processes

A compact representation of the cyclic operation of simulated moving-bed chromatography is established from the governing equations for the analogous single-column model that reproduces the cyclic steady-state (CSS) behavior of the multi-column process. A broad class of physically realizable asynchronous processes is then derived by dropping the integrality condition on the number of columns per zone, which now represents the average over a cycle. The steady periodic solution of the multi-column unit is computed by solving the analogous single-column model using a full-discretization method. The nonlinear algebraic system resulting from the simultaneous discretization of both spatial and temporal coordinates is solved using the gPROMS software. This solution strategy leads to shorter computational times than those previously reported in the literature. Process optimization is handled using single objective functions, to avoid competing effects, which are explicitly constrained by product quality and maximum allowable internal flow rates. The process is optimized for maximum feed throughput, with a possible upper bound on eluent consumption or flow rate, or minimum eluent consumption for a given feed flow rate. The nonlinear programming problem is solved by an external solver while still carrying out the CSS calculations in gPROMS. The feasibility of the approach is demonstrated on the chromatographic separation of an enantiomeric mixture with nonlinear competitive isotherm. Emphasis is given to the benefits that can be gained by upgrading an existing system to asynchronous operation. It is shown that eluent consumption for optimized asynchronous configurations in the higher feed-throughput region can be significantly reduced by modulation of eluent flow rate and selective product withdrawal.