| Summary: | The main focus of this thesis is on the development of new techniques for the rational design of mixtures, based on a computer-aided mixture/blend design (CAMbD) framework, with applications to the chemical industry. Systematic CAMbD approaches for the design of mixtures and blends have the potential to deliver better products and processes and they enhance innovation in a highly competitive environment. In many existing mixture design methodologies, a simplified reduced version of the CAMbD problem is posed and solved, where the number of mixture ingredients is fixed in advance (usually a binary mixture is designed) and the identity of at least one compound is chosen from a given set of candidate molecules. A key achievement of this work is the development of a novel comprehensive and systematic approach for the formulation and solution of the general mixture problem where the number, identity and composition of mixture constituents are optimized simultaneously. A logic-based method, generalized disjunctive programming (GDP), is integrated for the first time into the CAMbD framework to formulate the discrete choices of mixture problems. In working towards creating a general CAMbD model, the standard (restricted) CAMbD problem is first formulated for the design of multicomponent mixtures (without focusing only on the design of binary mixtures), where the number of mixture ingredients is fixed a priori. Next, the mixture formulation is generalized by making the number, N, of components in the mixture a variable and optimising at the same time the three main decision variables of the problem, i.e., the number, identity and composition of the compounds that participate in the mixture. In the restricted and general models, the components are selected from a given list of candidate molecules. The GDP formulations are converted into mixed-integer form using the big-M (BM) approach in order to exploit the existing MINLP algorithms. The design methodology is demonstrated through a case study involving solid-liquid equilibrium calculations, where optimal solvent mixtures are determined for maximising the solubility of a drug. Solving the mixed integer optimization problems derived using BM can be challenging due to nonconvexities in the space of the continuous variables and a large combinatorial solution space which may lead to several numerical difficulties. To address the difficulties arising from the complexity of the models and facilitate problem formulation, the use of different relaxation techniques, including the big-M approach and Hull reformulations (HR), is investigated to convert the disjunctive constraints into mixed-integer form. Both solution strategies (i.e., BM and HR) are applied successfully to two case studies where optimal solvent mixtures that dissolve ibuprofen and separate acetic acid from water in a single stage liquid extraction process, respectively, are defined. The concept of a truly general approach for mixture design, where the optimal components that participate in mixtures are not selected from restricted lists or databases, is considered. In this general formulation, the molecules are designed (built) from an extensive set of atom groups, leading to the design of countless new and/or existing molecules and mixtures. The general methodology is once again applied to the design of solvent mixtures for separation processes, including crystallization and liquid extraction. First, the design of optimal solvent and antisolvent mixtures for cooling and drowning out crystallization, respectively, is resented. Next, optimal solvent mixtures are designed to separate acetic acid from water in a single-stage liquid extraction process. 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. The overall proposed mixture design approach paves the way for identifying innovative solutions (e.g., new molecular structures, mixtures, property functions) which play an integral role in the development of process, chemical and biochemical technologies. Part of the work presented in this thesis has been published in Jonuzaj and Adjiman [2016, 2017] and Jonuzaj et al. [2016].
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