Integration of modular process simulators under the Generalized Disjunctive Programming framework for the structural flowsheet optimization

The optimization of chemical processes where the flowsheet topology is not kept fixed is a challenging discrete-continuous optimization problem. Usually, this task has been performed through equation based models. This approach presents several problems, as tedious and complicated component properties estimation or the handling of huge problems (with thousands of equations and variables). We propose a GDP approach as an alternative to the MINLP models coupled with a flowsheet program. The novelty of this approach relies on using a commercial modular process simulator where the superstructure is drawn directly on the graphical use interface of the simulator. This methodology takes advantage of modular process simulators (specially tailored numerical methods, reliability, and robustness) and the flexibility of the GDP formulation for the modeling and solution. The optimization tool proposed is successfully applied to the synthesis of a methanol plant where different alternatives are available for the streams, equipment and process conditions.

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.

Walking Through Cantor's Paradise and Escher's Garden: Epistemological Reflections on the Mathematical Infinite (II)

Infinity is not an easy concept. A number of difficulties that people cope with when dealing with problems related to infinity include its abstract nature, understanding infinity as an ongoing, never ending process, understanding infinity as a set of an infinite number of elements and appreciating well-known paradoxes. Infinity can be understood in several ways with often incompatible meanings, and can involve value judgments or assumptions that are neither explicit nor desired. To usher in its definition, we distinguish several aspects, teleological, artistic (Escher); some definitive, some potential, and others actual. This article also deals with some still unresolved aspects of the concept of infinity.