Design of controllable batch processes in the presence of uncertainty

Design of controllable batch processes can be more challenging than continuous processes because of their unsteady nature of operation. The operating strategy of a batch process is characterized by trajectories of manipulated variables. This precludes the use of conventional controllability measures in evaluating the controllability of a given batch process design. Short process development cycles typically accredited to batch processes lead to uncertainty in the model formulation. Integrated approach to batch process design and control addresses the problem of controllability of a batch process during the design phase. This is best achieved by treating the problem as a dynamic optimization problem with time invariant (design) and time variant (operating) variables. The method proposed in this paper uses the decomposition feature of Generalized Benders Decomposition (GBD) to evolve a 2-level nested optimization problem (primal and master), one involving time variant decision (operating) variables and the other involving time invariant decision (design) variables. To enhance the computational efficiency, a relaxed LP formulation of the master problem is proposed. This variant of GBD, termed as ExGBD, is guaranteed to converge to the optimum for convex problems. A simple batch reactor design problem has been chosen to demonstrate ExGBD.