Designing optimal mixtures using generalized disjunctive programming: Hull relaxations

A general modeling framework for mixture design problems, which integrates Generalized Disjunctive Programming (GDP) into the Computer-Aided Mixture/blend Design (CAMbD) framework, was recently proposed (S. Jonuzaj, P.T. Akula, P.-M. Kleniati, C.S. Adjiman, 2016. AIChE Journal 62, 1616–1633). In this paper we derive Hull Relaxations (HR) of GDP mixture design problems as an alternative to the big-M (BM) approach presented in this earlier work. We show that in restricted mixture design problems, where the number of components is fixed and their identities and compositions are optimized, BM and HR formulations are identical. For general mixture design problems, where the optimal number of mixture components is also determined, a generic approach is employed to enable the derivation and solution of the HR formulation for problems involving functions that are not defined at zero (e.g., logarithms). The design methodology is applied successfully to two solvent design case studies: the maximization of the solubility of a drug and the separation of acetic acid from water in a liquid-liquid extraction process. Promising solvent mixtures are identified in both case studies. The HR and BM approaches are found to be effective for the formulation and solution of mixture design problems, especially via the general design problem

Computer-aided design of optimal environmentally benign solvent-based adhesive products

The manufacture of improved adhesive products that meet specified target properties has attracted increasing interest over the last decades. In this work, a general systematic methodology for the design of optimal adhesive products with low environmental impact is presented. The proposed approach integrates computer-aided design tools and Generalised Disjunctive Programming (GDP), a logic-based framework, to formulate and solve the product design problem. Key design decisions in product design (i.e., how many components should be included in the final product, which active ingredients and solvent compounds should be used and in what proportions) are optimised simultaneously. This methodology is applied to the design of solvent-based acrylic adhesives, which are commonly used in construction. First, optimal product formulations are determined with the aim to minimize toxicity. This reveals that number of components in the product formulation does not correlate with performance and that high performance can be achieved by investigating different number of components as well as by optimising all ingredients simultaneously rather than sequentially. The relation between two competing objectives (product toxicity and concentration of the active ingredient) is then explored by obtaining a set of Pareto optimal solutions. This leads to significant trade-offs and large areas of discontinuity driven by discrete changes in the list of optimal ingredients in the product

Computer aided design of solvent blends for hybrid cooling and antisolvent crystallization of active pharmaceutical ingredients

Choosing a solvent and an antisolvent for a new crystallization process is challenging due to the sheer number of possible solvent mixtures and the impact of solvent composition and crystallization temperature on process performance. To facilitate this choice, we present a general computer aided mixture/blend design (CAMbD) formulation for the design of optimal solvent mixtures for the crystallization of pharmaceutical products. The proposed methodology enables the simultaneous identification of the optimal process temperature, solvent, antisolvent, and composition of solvent mixture. The SAFT-γ Mie group-contribution approach is used in the design of crystallization solvents; based on an equilibrium model, both the crystal yield and solvent consumption are considered. The design formulation is implemented in gPROMS and applied to the crystallization of lovastatin and ibuprofen, where a hybrid approach combining cooling and antisolvent crystallization is compared to each method alone. For lovastatin, the use of a hybrid approach leads to an increase in crystal yield compared to antisolvent crystallization or cooling crystallization. Furthermore, it is seen that using less volatile but powerful crystallization solvents at lower temperatures can lead to better performance. When considering ibuprofen, the hybrid and antisolvent crystallization techniques provide a similar performance, but the use of solvent mixtures throughout the crystallization is critical in maximizing crystal yields and minimizing solvent consumption. We show that our more general approach to rational design of solvent blends brings significant benefits for the design of crystallization processes in pharmaceutical and chemical manufacturing

The formulation of optimal mixtures with generalized disjunctive programming: a solvent design case study

Systematic approaches for the design of mixtures, based on a computer‐aided mixture/blend design (CAMbD) framework, have the potential to deliver better products and processes. In most existing methodologies the number of mixture ingredients is fixed (usually a binary mixture) and the identity of at least one compound is chosen from a given set of candidate molecules. A novel CAMbD methodology is presented for formulating the general mixture design problem where the number, identity and composition of mixture constituents are optimized simultaneously. To this end, generalized disjunctive programming is integrated into the CAMbD framework to formulate the discrete choices. This generic methodology is applied to a case study to find an optimal solvent mixture that maximizes the solubility of ibuprofen. The best performance in this case study is obtained with a solvent mixture, showing the benefit of using mixtures instead of pure solvents to attain enhanced behavior

A Convex Hull Formulation for the Design of Optimal Mixtures

The files contain some of the formulations implemented in GAMS for this publication. All problems are solved in GAMS version 24.2.3 and are run on a single core of a dual 6 core Intel Xeon X5675 machine at 3.07 GHz.The files contain some of the formulations implemented in GAMS for this publication. All problems are solved in GAMS version 24.2.3 and are run on a single core of a dual 6 core Intel Xeon X5675 machine at 3.07 GHz

The design of optimal mixtures from atom groups using Generalized Disjunctive Programming

A comprehensive computer-aided mixture/blend design methodology for formulating a gen- eral mixture design problem where the number, identity and composition of mixture constituents are optimized simultaneously is presented in this work. Within this approach, Generalized Dis- junctive Programming (GDP) is employed to model the discrete decisions (number and identities of mixture ingredients) in the problems. The identities of the components are determined by designing molecules from UNIFAC groups. The sequential design of pure compounds and blends, and the arbitrary pre-selection of possible mixture ingredients can thus be avoided, making it possible to consider large design spaces with a broad variety of molecules and mixtures. The proposed methodology is first applied to the design of solvents and solvent mixtures for max- imising the solubility of ibuprofen, often sought in crystallization processes; next, antisolvents and antisolvent mixtures are generated for minimising the solubility of the drug in drowning out crystallization; and finally, solvent and solvent mixtures are designed for liquid-liquid extraction. The GDP problems are converted into mixed-integer form using the big-M approach. Integer cuts are included in the general models leading to lists of optimal solutions which often contain a combination of pure and mixed solvents

Computer-aided design of optimal environmentally benign solvent-based adhesive products

In this work, a general systematic methodology for the design of optimal adhesive products with low environmental impact is presented. The proposed approach integrates computer-aided design tools and Generalised Disjunctive Programming to formulate and solve the product design problem. Key design decisions in product design (number of ingredients, identity of compounds and their proportions) are optimised simultaneously. This methodology is applied to the design of solvent-based acrylic adhesives, which are commonly used in construction. First, optimal product formulations are determined with the aim to minimize toxicity. This reveals that that high performance can be achieved by investigating different number of components as well as by optimising all ingredients simultaneously rather than sequentially. The relation between two competing objectives is then explored by obtaining a set of Pareto optimal solutions. This leads to significant trade-offs and large areas of discontinuity driven by discrete changes in the list of optimal product ingredients.In this work, a general systematic methodology for the design of optimal adhesive products with low environmental impact is presented. The proposed approach integrates computer-aided design tools and Generalised Disjunctive Programming to formulate and solve the product design problem. Key design decisions in product design (number of ingredients, identity of compounds and their proportions) are optimised simultaneously. This methodology is applied to the design of solvent-based acrylic adhesives, which are commonly used in construction. First, optimal product formulations are determined with the aim to minimize toxicity. This reveals that that high performance can be achieved by investigating different number of components as well as by optimising all ingredients simultaneously rather than sequentially. The relation between two competing objectives is then explored by obtaining a set of Pareto optimal solutions. This leads to significant trade-offs and large areas of discontinuity driven by discrete changes in the list of optimal product ingredients.

A Comprehensive Approach for the Design of Solvent-based Adhesive Products using Generalized Disjunctive Programming

<p>The files contain all the product design problems implemented in GAMS for this publication.</p> <p>All models are solved in GAMS version 24.8.3 and are run on a single core of a dual 6 core Intel Xeon E5-1660 machine at<br> 3.30 GHz.</p