(184a) Flexible and Computationally Efficient Shortcut Distillation Column Models for Superstructure-Based Process Synthesis

Distillation is the most common unit process for separation in chemical/petrochemical facilities due to its capability to handle a wide range of feed flow rates/concentrations and to produce products with high purity¹. Several methods have been proposed to estimate the energy requirement for a specific distillation task, while the Underwood equations² have been adopted in many works because of their simplicity. The Underwood equations enable the calculation of minimum vapor flow rates in the distillation column, which can be used to calculate the minimum energy requirement. Also, the Underwood equations can be extended to calculate the minimum energy of an entire distillation network to separate a zeotropic mixture³. Notably, the Underwood equations require a given set of components in the feed to calculate roots, which are essential to calculate the minimum vapor flow rates.

However, when we consider the synthesis of a system (e.g., separation network or combined reactor-separation network), component flow rates in the feed of a distillation system can vary, and some flow rates can be even zero, depending on decisions in other subsystems (e.g., reaction selections in upstream processes⁴). Variability in the feed, especially the presence of zero flow rates, complicates the use of the Underwood equations because it affects the number/location of their roots⁵. This limitation prevents us from adopting process synthesis approaches using superstructure-based optimization and thus finding novel solutions. Hence, it is desirable to develop a more flexible method that can handle this variability in the feed while successfully calculating the minimum energy for distillation.

Accordingly, in this work, we propose two novel reformulations of the Underwood equations, where the number/location of the roots are constrained depending on the presence of zero flow rates. Based on these reformulated Underwood equations, we propose two shortcut distillation column models which can be readily used for superstructure-based process synthesis. The proposed models can automatically identify adequate key components and corresponding energy requirement of a desired separation task while considering a broad range of types of splits including non-sharp/sloppy splits. Also, they can be readily utilized as submodules for the columns in the distillation network synthesis superstructure.

The key difference between the two models are 1) whether inactive roots are calculated and 2) how the recoveries of the key components are bounded. In the first model, only active roots (i.e., roots between the relative volatilities of the key components) are calculated depending on the key selection. The recoveries of the key components are bounded by constraints inspired by the Fenske equation, which can guarantee the physical feasibility of solutions with finite reflux and finite number of trays. In the second model, both active and inactive roots are calculated, and the inactive roots are used to enforce bounds on the recoveries of the key components, thereby guaranteeing that the solution is achievable with the minimum vapor flow rates. Also, based on the second model, we propose a shortcut distillation network model, which can be used to calculate an energy target for the separation of a zeotropic mixture without finding detailed distillation network configurations. This shortcut network model is particularly useful for preliminary process synthesis, where we want to estimate the energy requirement rather than to obtain detailed configuration of the network.

We close with a number of examples illustrating how the proposed models can be used to formulate and solve interesting and challenging process synthesis problems.

Reference

1. King CJ. Separation Processes. Courier Corporation; 2013.
2. Underwood AJ V. Fractional distillation of multicomponent mixtures. Ind Eng Chem. 1949;41(12):2844-2847.
3. Halvorsen IJ, Skogestad S. Minimum energy consumption in multicomponent distillation. 3. More than three products and generalized Petlyuk arrangements. Ind Eng Chem Res. 2003;42(3):616-629.
4. Ryu J, Kong L, de Lima AEP, Maravelias CT. A Generalized Superstructure-based Framework for Process Synthesis. Comput Chem Eng. 2019:106653.
5. Kong L, Maravelias CT. Generalized short‐cut distillation column modeling for superstructure‐based process synthesis. AIChE J. 2020;66(2):e16809.