Chemical Engineering @ChemengFiles.Com

Continuous distillation processes are frequently characterized by uncertainties of their inflow. These may relate to the flow rate, to the composition of the mixture to be separated or to its temperature. Typically, the uncertainties are not completely irregular but follow a certain pattern caused by the operation of upstream units. Then it makes sense to model uncertainty as a stochastic parameter, the distribution of which can be estimated from history but the realization of which in the coming period of optimization is unknown. In the following, we are going to consider the rate of inflow as the only random parameter. As a consequence of possible unpredictable peaks, the inflow cannot be processed immediately but has to be stored in a feed tank before being directed at a controlled rate to the distillation unit (see [9], Figure 1). For technological reasons, one has to impose upper and lower level constraints for the feed tank preventing it from running full or empty. Both cases would require unpleasant compensating actions which are desirable to avoid (see [9], Section 1.3). Therefore, a problem will be formulated which reflects the objective to find a feed control being robust with respect to level constraints yet optimal in the sense of minimum energy consumption subject to product specifications.

From the stochastic nature of the inflow rate it is clear that the level constraints are stochastic too, and there is a choice to apply any of the methods briefly sketched in [9]. As costs of compensating actions for possible level violations are difficult to model on the one hand and a worst case approach is much too conservative or even impossible on the other hand, it is proposed to rely on probabilistic constraints. The
gain over simply using typical profiles (or expected values) for the inflow rate will be illustrated later on. The aim of the subsequent analysis is to present a model of optimal control for continuous distillation with probabilistic feed tank constraints and to present numerical results for different assumptions on the randomness of inflow rate. As an example serves the separation of a methanol/water mixture.

Download Link:
Optimal Control of a Continuous Distillation Process under Probabilistic Constraints