Optimization of a Semi-Batch Reaction System under Safety Constraints

OPTIMIZATION OF A SEMI-BATCH REACTION SYSTEM UNDER SAFETY CONSTRAINTS O. Ubrich+, B. Srinivasan*, F. Stoessel+, D. Bonvin* * Novartis Services AG, CH-4002 Basel, Switzerland Institut d’ utomatique, Ecole Polytechnique Fédérale de Lausanne A CH-1015, Lausanne, Switzerland * Fax: +41 21 693 2574 and e-mail: dominique.bonvin@epfl.ch + An important objective in the chemical industry is to find the operating conditions that maximize profit while ensuring safe operation. The safety considerations arise from the exothermic nature of most industrial chemical reactions. For normal operation, the system must be able to remove the heat produced. But at the same time, the system must be capable of withstanding a cooling failure. These goals are best achieved in a semi-batch reactor, since the contents of the reactor can be controlled by the external feed. In this paper, the maximization of the yield of a second-order reaction by manipulating the inlet flow rate is investigated. Two modes of operation are considered: (a) the isoperibolic mode, where the temperature of the cooling fluid is kept constant, and (b) the isothermal mode, where the temperature of the reaction mass is kept constant by adjusting the temperature of the cooling fluid. Constraints on (i) the amount of heat produced, and (ii) the temperature under cooling failure are imposed for safety considerations. The optimal solution is discontinuous and is first obtained numerically. Analytical expressions for the evolution of the input between the discontinuities and the switching times are obtained. Using the analytical characterization of the optimal solution, an efficient feedback implementation strategy is proposed and tested in simulation.