Accurate determination of optimal reflux policies for the maximum distillate problem in batch distillation

Abstract: "An approach for the accurate solution of optimal control problems that arise in batch distillation is developed and demonstrated. Since the optimal control problem has a natural partitioning of control variables and state variables, we develop a nonlinear programming decomposition strategy to (1) exploit the block matrix form of the discretized differential equations that results from using collocation on finite elements, and (2) perform the optimization in the reduced space of the control variables. State variables for each finite element are determined by linearized differential equations and information is passed from element to element by chainruling the state information. In addition, the nonlinear programming strategy has a great deal of flexibility to determine control variable discontinuities and enforce a wide variety of state and control variable constraints. In this study, we also consider characteristics of the maximum batch distillate problem and show that our approach is especially useful for the optimization of detailed tray-by-tray models with tray and condenser holdups. Here we discuss two formulations: an inequality path constrained problem and the classical endpoint constrained problem. In both cases interesting and unusual optimal policies are determined and compared to current practice. Moreover, parallels are observed between optimal reflux policies for these two problems, and these are also related to findings from previous studies. To handle these problems, nonlinear programs of up to 8000 variables are solved reasonably quickly on a small workstation. Finally, it is observed that more complex batch distillation problems can be handled in a straightforward manner through this approach."