(474c) An MINLP Formulation for the Optimization of Heat-Pump Assisted Distillation Configurations

Distillation is the predominant choice of unit operation for the separation of a multicomponent mixture into its constituent components. It is well-known that the number of distillation configurations available increases combinatorially with increase in number of components. All the configurations differ in terms of energy requirement. This gives rise to two questions: For a given system, (a) what is the optimal configuration? (b) What are the optimal operating conditions?

Here, we propose a method that allows the screening of distillation configurations based on the minimum heat pump work required for the separation, which is equal to the net exergy added to the system. Exergy of a stream is its maximum work potential when it is brought to a reference state along a reversible path. In addition to the overall energy requirement, the proposed screening criterion also accounts for temperature levels of condensers and reboilers. This criterion is especially useful for cryogenic distillations, which are work-driven, like air and Natual Gas Liquid (NGL) separations.

Agrawal and Herron (1997) described a method to compute the exergy input solely in terms of relative volatilities and composition of various streams. Using this approach, we formulate a novel Mixed-Integer Nonlinear Program (MINLP) for the identification of exergetically attractive distillation configurations. However, the model, in its natural form, has a large number of nonlinear and non-convex terms. This is exacerbated by the fact that the model is numerically sensitive, which leads to errors in computation of lower bounds. We address these challenges by employing a simple, yet powerful, variable elimination process. This process significantly reduces the number of non-convexities by collapsing the non-convex equilibrium equations onto a single equation. The new equation has several interesting properties that can be exploited to improve the convergence of branch-and-bound method. Furthermore, the reduced model is free from numerical sensitivities. Finally, with the net heat pump work as the objective, the MINLP is solved to global optimality with BARON [2]. The utility of the formulation will be illustrated with a few case studies.

1. Agrawal, R., & Herron, D. M. (1997). Optimal thermodynamic feed conditions for distillation of ideal binary mixtures. AIChE journal, 43(11), 2984-2996.
2. Tawarmalani, M., & Sahinidis, N. V. (2005). A polyhedral branch-and-cut approach to global optimization. Mathematical Programming, 103(2), 225-249.