Optimal design and sensitivity analysis of reactive distillation units using collocation models

The optimal design of staged distillation units with chemical reactions is determined using a modeling approach that facilitates both rigorous optimization and sensitivity analysis with detailed models. The values of the design variables are determined so that an economic criterion is optimized while a set of safety, operating, and product quality constraints and specifications is satisfied. An equilibrium stage model with kinetically controlled chemical reactions describes the physical and chemical phenomena in the column. Orthogonal collocation on finite elements (OCFE) techniques that transform the integer-valued stage model into a continuous analogue are employed. OCFE models accurately reproduce the same optimal design as a full-order tray-by-tray model, while using a smaller set of equations and eliminating the use of integer variables associated with the column stages. Furthermore, the effects of multiple process parameter variations on the optimal operating point of the reactive distillation units are investigated on the basis of a sensitivity analysis of the optimal design. The parameter perturbations are performed along the dominant directions that result in the maximum change in the process variables. Sensitivity information regarding the optimal solution for different parameter values is utilized to modify the design variable values in order to improve the feasibility region and profitability of the final process design. The proposed modeling and design procedure is applied successfully in the production of high-purity ethyl acetate from ethanol and acetic acid carried out in a reactive distillation column followed by a recovery column. Design modifications to the process flowsheet allow for the achievement of better economic performance under multiple parameter variations.