(171g) A Tightly Constrained MINLP-Based Formulation for the Identification of Energy Efficient Distillation Configurations

Distillation is one of the widely used unit operation to carryout multicomponent separation. It is well known that the number of configurations available to perform the separation increases to millions with increase in number of components in the feed. Identifying the optimal solution from the search space is challenging as the governing equations, Underwood constraints, are nonconvex. Moreover, a sub-optimal solution often results in a severe energy penalty¹.

We propose a novel Mixed-Integer Nonlinear Program (MINLP) based formulation to identify distillation configurations that are energy efficient and cost effective. We will present a novel formulation to describe the search space of basic configurations in a way that is simultaneously tighter and uses fewer binary variables than those available in the literature. The problem is formulated under the assumption of constant overflows and relative volatilities. We use ideas from Nallasivam et al.² and Caballero and Grossmann³, and couple them with convexification techniques, such as the Reformulation-Linearization Technique (RLT), to construct tighter constraints for mass balance and Underwood equations. The formulation can be solved using standard global optimization solvers such as BARON⁴.

The optimal solution to the MINLP may not be easily implementable when the underlying assumptions are relaxed. Hence, we present a method to identify a handful configurations, K, of the top solutions. Rigorous tray-by-tray calculations can then be performed only on these K configurations to determine the appropriate configuration. Towards the end, we present a few five and six-component cases that were solved to global optimality using our formulation.

[1]. Shah, Vishesh H., and Rakesh Agrawal. "A matrix method for multicomponent distillation sequences." AIChE journal 56.7 (2010): 1759-1775.

[2]. Nallasivam, Ulaganathan, et al. "Global optimization of multicomponent distillation configurations: 2. Enumeration based global minimization algorithm." AIChE Journal 62.6 (2016): 2071-2086.

[3]. Caballero, José A., and Ignacio E. Grossmann. "Structural considerations and modeling in the synthesis of heat-integrated− thermally coupled distillation sequences." Industrial & Engineering Chemistry Research 45.25 (2006): 8454-8474.

[4]. Tawarmalani, Mohit, and Nikolaos V. Sahinidis. "A polyhedral branch-and-cut approach to global optimization." Mathematical Programming 103.2 (2005): 225-249.