Rigorous Design of Complex Distillation Columns Using Process Simulators and the Particle Swarm Optimization Algorithm

We present a derivative-free optimization algorithm coupled with a chemical process simulator for the optimal design of individual and complex distillation processes using a rigorous tray-by-tray model. The proposed approach serves as an alternative tool to the various models based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) . This is accomplished by combining the advantages of using a commercial process simulator (Aspen Hysys), including especially suited numerical methods developed for the convergence of distillation columns, with the benefits of the particle swarm optimization (PSO) metaheuristic algorithm, which does not require gradient information and has the ability to escape from local optima. Our method inherits the superstructure developed in Yeomans, H.; Grossmann, I. E.Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res.2000, 39 (11), 4326–4335, in which the nonexisting trays are considered as simple bypasses of liquid and vapor flows. The implemented tool provides the optimal configuration of distillation column systems, which includes continuous and discrete variables, through the minimization of the total annual cost (TAC). The robustness and flexibility of the method is proven through the successful design and synthesis of three distillation systems of increasing complexity.

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.

1,2-Functionalized Imidazoles as Palladium Ligands: An Efficient and Robust Catalytic System for the Fluorine-Free Hiyama Reaction

A variety of hydroxy- and amino-functionalized imidazoles were prepared from 1-methyl- and 1-(diethoxymethyl)imidazole by means of isoprene-mediated lithiation followed by reaction with an electrophile. These compounds in combination with palladium acetate were screened as catalyst systems for the Hiyama reaction under fluorine-free conditions using microwave irradiation. The systematic study of the catalytic system showed 1-methyl-2-aminoalkylimidazole derivative L1 to be the best ligand, which was employed under solvent-free conditions with a 1:2 Pd/ligand ratio and TBAB (20 mol-%) as additive. The study has revealed an interaction between the Pd/ligand ratio and the amount of TBAB. The established catalytic system presented a certain degree of robustness, and it has been successfully employed in the coupling of a range of aryl bromides and chlorides with different aryl siloxanes. Furthermore, both reagents were employed in an equimolecular amount, without an excess of organosilane.