Uncertainty issues in the modeling and optimization of batch reactors with tendency models

The calculation of optimal input policies for operation of chemical batch reactors is greatly affected by the accuracy of the process model. Approximate process models for batch reactors can be developed via a gray box modeling technique known as tendency modeling. Because these models are approximate models, the introduction of process-model mismatch may have a significant effect on the success of the process optimization. In this paper, the effect the process-model mismatch, represented by the parametric uncertainty of the tendency model, has on the process optimization is examined. We develop techniques that allow confidence limits to be placed on the optimal input policy as well as on the performance index. by considering the sensitivity of the optimal input policy with respect to uncertain model parameters. The uncertainty of the optimal operating policy can indicate whether the next experiment in the tendency modeling algorithm should be used for process optimization or for improvement in model accuracy. Also considered is the issue or operating the next batch with a suboptimal policy that is at a fraction of the distance between the previous policy and the calculated optimal one, so that the uncertainty of the new policy is reduced to an acceptable level.