Solution of the maximum distillate on a batch distillation column by a Pseudo-Newton method

Abstract

This paper presents a new algorithm for the solution of the maximum distillate problem based on Pontryagin's maximum principle. Four cases of study were analyzed with the algorithm. The first case is a literature problem where the column uses twenty trays to distillate ten components, the second case is a binary mixture with no ideal behavior, the third case is a quaternary mixture, and the last case is a reactive mixture. In all cases, the desired purity was settled as a final constraint. The solution algorithm found the optimal control faster than results reported in literature concerning the CPU time.The batch distillation process is modeled by using a rigorous model with no constant volatility. The proposed algorithm uses the Hamiltonian function to reformulate the maximum distillate problem. Then, the optimal control is solved by a Broyden–Fletcher–Goldfarb–Shanno algorithm. The solution procedure of the indirect approach required the forward integration of the states, the integration of the co-state equations backward in time, and the control input is the distillate flow rate which is parameterized. The binary batch distillation column uses six stages, and the maximum recovery is 95% of the light component with a 95% mol percent on the accumulator. The multicomponent batch distillation column uses 17 stages, and the recovery of the lightest component in the product is 90% mol percent. The reactive case reached 80% conversion.