Rigorous design of distillation columns using surrogate models based on Kriging interpolation

The economic design of a distillation column or distillation sequences is a challenging problem that has been addressed by superstructure approaches. However, these methods have not been widely used because they lead to mixed-integer nonlinear programs that are hard to solve, and require complex initialization procedures. In this article, we propose to address this challenging problem by substituting the distillation columns by Kriging-based surrogate models generated via state of the art distillation models. We study different columns with increasing difficulty, and show that it is possible to get accurate Kriging-based surrogate models. The optimization strategy ensures that convergence to a local optimum is guaranteed for numerical noise-free models. For distillation columns (slightly noisy systems), Karush–Kuhn–Tucker optimality conditions cannot be tested directly on the actual model, but still we can guarantee a local minimum in a trust region of the surrogate model that contains the actual local minimum.

Optimization of Chemical Processes Using Surrogate Models Based on a Kriging Interpolation

Superstructure approaches are the solution to the difficult problem which involves the rigorous economic design of a distillation column. These methods require complex initialization procedures and they are hard to solve. For this reason, these methods have not been extensively used. In this work, we present a methodology for the rigorous optimization of chemical processes implemented on a commercial simulator using surrogate models based on a kriging interpolation. Several examples were studied, but in this paper, we perform the optimization of a superstructure for a non-sharp separation to show the efficiency and effectiveness of the method. Noteworthy that it is possible to get surrogate models accurate enough with up to seven degrees of freedom.

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.

Variación espacial de la exposición a contaminación atmosférica en la ciudad de Valencia y su relación con un índice de privación

Objetivo: Evaluar la variación espacial de la exposición a dióxido de nitrógeno (NO2) en la ciudad de Valencia y su relación con la privación socioeconómica y la edad. Métodos: La población por sección censal (SC) procede del Instituto Nacional de Estadística. Los niveles de NO2 se midieron en 100 puntos del área de estudio, mediante captadores pasivos, en tres campañas entre 2002 y 2004. Se utilizó regresión por usos del suelo (LUR) para obtener el mapa de los niveles de NO2. Las predicciones del LUR se compararon con las proporcionadas por: a) el captador más cercano de la red de vigilancia, b) el captador pasivo más cercano, c) el conjunto de captadores en un entorno y d) kriging. Se asignaron niveles de contaminación para cada SC. Se analizó la relación entre los niveles de NO2, un índice de privación con cinco categorías y la edad (≥65 años). Resultados: El modelo LUR resultó el método más preciso. Más del 99% de la población superó los niveles de seguridad propuestos por la Organización Mundial de la Salud. Se encontró una relación inversa entre los niveles de NO2 y el índice de privación (β = –2,01 μg/m3 en el quintil de mayor privación respecto al de menor, IC95%: –3,07 a –0,95), y una relación directa con la edad (β = 0,12 μg/m3 por incremento en unidad porcentual de población ≥65 años, IC95%: 0,08 a 0,16). Conclusiones: El método permitió obtener mapas de contaminación y describir la relación entre niveles de NO2 y características sociodemográficas.

Large scale optimization of a sour water stripping plant using surrogate models

In this work, we propose a new methodology for the large scale optimization and process integration of complex chemical processes that have been simulated using modular chemical process simulators. Units with significant numerical noise or large CPU times are substituted by surrogate models based on Kriging interpolation. Using a degree of freedom analysis, some of those units can be aggregated into a single unit to reduce the complexity of the resulting model. As a result, we solve a hybrid simulation-optimization model formed by units in the original flowsheet, Kriging models, and explicit equations. We present a case study of the optimization of a sour water stripping plant in which we simultaneously consider economics, heat integration and environmental impact using the ReCiPe indicator, which incorporates the recent advances made in Life Cycle Assessment (LCA). The optimization strategy guarantees the convergence to a local optimum inside the tolerance of the numerical noise.