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

Distillation is the most commonly used unit operation for separations. When the mixture contains three or more components, a network (sequence) of distillation columns is typically needed and the design of this network has a significant impact on the capital and energy cost of the separation. Since the 1980s, numerous optimization-based approaches have proposed for finding the optimal distillation sequence [1-3]. These existing approaches focus on optimizing the distillation network assuming that information such as the set of components to be separated and their feed flowrates are given as inputs. However, in the context of process synthesis, where the distillation column network is designed along with the reactor network, the set of components to be separated can vary due to, for example, the selection of different reaction strategies in the reactor network synthesis. Meanwhile, the component flowrates in the effluent streams of the reactor network (i.e. the feed of the distillation column network) are variables, which may be equal to zero.

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 “matrix” 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 “placed” 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 “recognizes” 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

1. Aggarwal, A. and C.A. Floudas, Synthesis of General Distillation Sequences - Nonsharp Separations. Computers & Chemical Engineering, 1990. 14(6): p. 631-653 DOI: Doi 10.1016/0098-1354(90)87033-L.
2. Caballero, J.A. and I.E. Grossmann, Generalized disjunctive programming model for the optimal synthesis of thermally linked distillation columns. Industrial & Engineering Chemistry Research, 2001. 40(10): p. 2260-2274
3. Caballero, J.A. and I.E. Grossmann, Synthesis of complex thermally coupled distillation systems including divided wall columns. AIChE Journal, 2013. 59(4): p. 1139-1159
4. Underwood, A., Fractional distillation of multi-component mixtures. Chem. Eng. Prog., 1948. 44: p. 603-614
5. Shah, V.H. and R. Agrawal, A matrix method for multicomponent distillation sequences. AIChE journal, 2010. 56(7): p. 1759-1775