(180a) From Atom Groups to Molecules and Mixtures/Formulations: A Comprehensive Design Methodology with Generalized Disjunctive Programming
In view of these challenges, our work focuses on developing a comprehensive methodology within the computer-aided mixture/blend design framework by combining mathematical modelling, optimisation and chemical engineering insights to formulate the general mixture problem. Within this approach, the optimal number of components in a mixture, their identities and compositions are determined simultaneously3,4 and the desired molecules are designed from a large set of atom groups (UNIFAC groups). A logic-based methodology, Generalised Disjunctive Programming5,6 (GDP), is used to express the general mixture problem within a mathematical framework and formulate the discrete choices inherent in the problem (i.e., how many components are designed, which specific molecules should be used - what atom groups are required). In order to exploit existing MINLP algorithms, Big-M approach7 is employed to transform the disjunctive constraints into mixed-integer form.
The proposed framework has been applied successfully to two case studies where the design of solvent mixtures for separation processes is presented. The first case study involves the design of optimal solvent and antisolvent mixtures for cooling and drowning out crystallization, respectively. In the second case study, optimal solvent mixtures are determined to separate acetic acid from water in a single stage liquid extraction process. Finally, integer cuts are introduced to the general mixture formulations and a list of optimal solutions (i.e., list of mixtures with different number, identity and compositions of ingredients) is obtained for each problem. Significant benefits can accrue by employing the general framework (number of mixture constituents not fixed a priori and molecules designed from functional groups) in mixture and product design: avoid evaluating explicitly every choice of the number of components, which can be computationally or experimentally costly and time-consuming, especially as the number of desirable ingredients increases; consider larger design spaces where many molecules and mixtures are designed and not selected from a limited set of choices.
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