(180a) From Atom Groups to Molecules and Mixtures/Formulations: A Comprehensive Design Methodology with Generalized Disjunctive Programming

In the chemical industry, the design of mixtures and blends that meet a specified set of physical and chemical properties is an important and challenging activity across a wide range of applications. Several chemical examples with different functions and qualities, such as agrochemicals (pesticides, insecticides, etc.), functional chemicals (solvents, refrigerants, lubricants, etc.) and household products (cosmetics & personal care products, pharmaceuticals & drugs, etc.), come as formulations/mixtures and are used in most aspects of human life. Computer-Aided Molecular (CAMD) and Mixture/blend (CAM^bD) Design^1,2 is a promising approach for efficient and reliable design of promising molecules, mixtures or blends that meet predefined target properties and optimise a given performance measure. When formulating a mixture problem via optimisation, the main purpose is to identify innovative solutions, which can be a new molecular structure, an existing molecule for a new property function, or a new mixture of existing/new molecules. Mixture design, however, can be very challenging because it requires finding the optimal number, identities and compositions of mixture components, and using nonlinear property models, which results in complex nonlinear problems with a large combinatorial space. Thus, a reduced version of the general CAM^bD problem is usually posed: the number of mixture ingredients is fixed a priori and the identity of a compound (or of all compounds) that can participate in a mixture is selected from a restricted list of candidate compounds, leading to suboptimal solutions.

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 simultaneously^3,4 and the desired molecules are designed from a large set of atom groups (UNIFAC groups). A logic-based methodology, Generalised Disjunctive Programming^5,6 (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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4. Jonuzaj S, Adjiman CS. Designing optimal mixtures using Generalized Disjunctive Programming: Hull relaxations. Chemical Engineering Science. 2017;159:106–130.
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