# (500a) Expanding the Scope of Distillation Network Synthesis Using Superstructure-Based Methods

- Conference: AIChE Annual Meeting
- Year: 2019
- Proceeding: 2019 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time: Wednesday, November 13, 2019 - 12:30pm-12:49pm

In state-of-the-art distillation sequencing approaches, the Underwood method [4] is frequently used to estimate the (minimum) vapor flow of individual columns. To use the Underwood method, the key as well as the distributed components (i.e. components more volatile than the heavy key but less volatile than the light key) must be specified, so that the set of active roots can be determined a priori. However, when the set of components to be separated is not predefined and the variable component flowrates can be zero, the set of active roots cannot be defined a priori, which leads to numerical challenges when using the Underwood method as a submodule in the superstructure optimization model.

Accordingly, we develop a novel approach to design non-azeotropic distillation sequences for both conventional and thermally coupled columns to facilitate the integration of reactor and distillation column network synthesis. The proposed approach includes (1) a distillation column superstructure constructed using a â€œmatrixâ€ representation [5], and (2) a modified Underwood method to account for the possibility that (1) the keys cannot be defined prior to optimization and (2) some distributed components have zero flowrate.

In the distillation column superstructure, distillation column candidates (i.e. nodes) are â€œplacedâ€ in an upper-triangular matrix according to the set of components in the feed stream. For each distillation column candidate, there is a one-to-one correspondence of its indices in the matrix and the components in its feed stream. This mapping allows us to systematically generate all the feasible connections (i.e. arcs) between the product streams of one column and the feed stream of another. A set of logical relationships is introduced for the (de)activation of the nodes and arcs to represent the selection of columns and separation tasks. The proposed superstructure can deal with systems where some component flowrates are equal to zero. For example, if A, B, and C are the potential components in the feed stream of column and the optimization determines that the flowrate of B is equal to zero, then the model â€œrecognizesâ€ that ABC should be separated into A and C, determining, automatically, components A and C as the key components. This type of separation is not admissible in the previous methods.

Our modified Underwood method utilizes a set of mixed-integer constraints to determine the values of all the *potentially* active roots. When a root candidate is not active (e.g. due to zero component flowrate), it will be equal to a neighboring active root. In this way, the number and value of the active roots are determined by the optimization models. In the previous example where the flowrate of B is equal to zero, the two potentially active roots become one.

**Reference**

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