Simultaneous Optimal Design and Control of an Extractive Distillation System for the Production of Fuel Grade Ethanol Using a Mathematical Program with Complementarity Constraints

The simultaneous optimal design and control problem of an extractive distillation system is studied using a rigorous model and solved when the feed is subjected to composition disturbances. First, the problem is formulated as a mixed-integer dynamic optimization (MIDO) problem, and then transformed into a mathematical program with complementarity constraints (MPCC) problem using orthogonal collocation on finite elements. The model allows simultaneous determination of the number of trays, feed tray locations, structural parameters of the column, heat exchanger areas, set points of both the controlled and manipulated variables, and the optimal control policy in order to obtain an optimal design which maximizes profit and also guarantees feasible dynamic operation. The study also demonstrates how the distillation column design problem can be addressed as a MPCC problem instead of as a mixed-integer nonlinear programming (MINLP) problem, containing thousands of continuous variables and constraints, and how can it be solved in reasonable times using state-of-the-art algorithms. The problem is modeled in GAMS and solved using IPOPT. Finally, results obtained by the simultaneous strategy are compared to those obtained by addressing the design and control problem sequentially.