Integrating product and process design with optimal control: A case study of solvent recycling

This paper proposes the simultaneous integration of environmentally benign solvent selection (product design), solvent recycling (process design) and optimal control for the separation of azeotropic systems using batch distillation. The previous work performed by Kim et al. (2004. Entrainer selection and solvent recycling in complex batch distillation. Chemical Engineering Communications 191(12), 1606-1633) combines the chemical synthesis and process synthesis under uncertainty. For batch distillation, optimal operation is also important due to the unsteady state nature of the process and high operating costs. Optimal control allows us to optimize the column operating policy by selecting a trajectory for the reflux ratio. However, there are time-dependent uncertainties in thermodynamic models of batch distillation due to the assumption of constant relative volatility. In this paper, the uncertainties in relative volatility were modeled using Ito processes and the stochastic optimal control problem was solved by combined maximum principle and non-linear programming (NLP) techniques. Then the previous work of optimal solvent selection and recycling was coupled with optimal control. As a real world example for this integrated approach, a waste stream containing acetonitrile-water was studied. The optimal design parameters obtained by Kim et al. (2004. Entrainer selection and solvent recycling in complex batch distillation. Chemical Engineering Communications 191(12), 1606-1633), for this separation were used and the optimal control policy is computed first without considering uncertainties by variable transformation technique. The deterministic optimal control policy improves the product yield by 4.0% as compared to the base case, verified using a rigorous simulator for batch distillation. When the stochastic optimal control policy was computed representing the relative volatility as an Ito process, a similar recovery rate was obtained from simulations, but the batch time was reduced significantly, producing the most profitable operation.