OPTIMAL CONTROL OF TIME-DEPENDENT PROCESSES (DESIGN, BATCH DISTILLATION, CATALYST DEACTIVATION)

Optimization problems for time-dependent processes at the design stage are formulated and analyzed via simple calculus and Pontryagin\u27s Minimum Principle. Two specific time-dependent processes are chosen for this study; a batch distillation process and a process with catalyst deactivation. Since profit is the ultimate goal of most commercial chemical processes, economic performance indices are introduced for both processes (instead of the more popular, simple performance indices in the literature, such as product yield, reactor conversion operating time, etc.). Process economic models to construct the economic performance indices are formulated using the short-cut design technique of Douglas (1978). The use of the economic performance indices makes the solution procedure much more complex than that of the simple performance indices. Moreover, the introduction of max-value functions in the performance index due to equipment sizes, which should be based on the maximum flow rate, adds even more complexity to the optimization problem. A solution procedure for the batch distillation process is developed via a calculus approach for two simplified problems and via Pontryagin\u27s Minimum Principle for the more general problem. The results indicate that the optimal policy falls into the category of easy separations according to the guidelines of Robinson (1971a) and Kerkhof and Vissers (1978) for a wide range of parameter values. In addition, the optimal policy is so close to the constant distillate composition policy, so that the simple constant distillate composition policy can replace the optimal policy for the control of the column. For the process with catalyst deactivation, an IPA plant, which dehydrogenates isopropanol to produce acetone, is chosen as a case study. There are two possible candidates for a control variable to compensate for catalyst deactivation--reactor temperature and fresh feed flow rate. The fresh feed flow rate is chosen as a control variable, since a lot of attention has been paid to using the reactor temperature as a control variable. Application of Pontryagin\u27s Minimum Principle with the introduction of Kuhn-Tucker multiplier suggests that the solution is in the form of several suboptimal policies patched together. The patched solution is divided into 15 possible combinations of one-. two-, and three-piece policies and each policy is analyzed by simple calculus. The optimization results indicate that any patched solution can be the optimal one depending upon the parameter values