Advanced Optimization Tools for the Design and Retrofit of Process Plants Water Networks

Water is extensively used in industry and due to its increasing cost and the continuous quality deterioration of the available freshwater sources; its use is becoming also a cost concern in industries. An alternative to reduce costs associate to water consumption is the integration of the water system through reuses and recycles. This problem is often called Water Allocation Problem (WAP) and has been studied in the past three decades and several approaches to solve it have been presented. A comprehensive review of methods presented up to 2000 is given by Bagajewicz (2000); additional overviews can be found in a few books (Mann and Liu, 1999; Sikdar and El-Halwagi, 2001). The methods to solve the WAP can be divided into two big classes: those based on mathematical programming, and those based on graphical, heuristic or algorithmic methods. The most promising class is the one based on mathematical programming, which is being increasingly used, especially because of the inability of graphical, heuristic or algorithmic procedures to effectively provide rigorous solutions to multiple contaminant problems. Additionally, more elaborate objective functions (cost, number of connections, etc.) are easier to handle using mathematical programming approaches. Although this problem has been studied for three decades, some conceptual issues have been overlooked. The WAP first defined by Takama et al.(1980) considered two water subsystems commonly seen in the industry, the water-using subsystem and the wastewater treating subsystem, but left the water pre-treatment subsystem out of the systems integration. This work proves that the absence of this third subsystem has a strong effect on freshwater consumption targets and, in many cases, the use of the former definition creates systems that are "impossible" to reach zero liquid discharge. In the mathematical optimization group, approaches using LP, NLP, MILP, and MINLP have been presented. Aside from the linear models presented, which are only able to find the optimum solution for particular situations, the biggest challenge on the mathematical procedures is to overcome the difficulties generated by the non-linear and non-convex terms that arise from the contaminants balance (mixers and splitters). Such problems require good start points to find a feasible solution and most of the available solvers cannot guarantee global optimality if a solution is found. On the other hand, methodologies based on mathematical optimization are much easier to describe the problem in more detail and thus more complex problems can be approached. Although the integrated water system problem has been solved by other authors for minimum freshwater consumption and cost (Takama et al., 1980; Alva-Argaez et al., 1998; Huang et al., 1999; Karuppiah and Grossmann, 2006; Bagajewicz and Faria, 2009; Faria and Bagajewicz, 2009), robust methods to find optimum and sub-optimum solutions, present the option of investigating alternative solutions and are able to analyze the problem from different perspectives are needed. To overcome this drawback, different global optimization methods to solve the WAP using the complete water system are presented. Additionally, a method to find several alternative solutions is described and a planning model is suggested

Diseño óptimo de un sistema de tratamiento para la remoción de cromo hexavalente usando reactores electroquímicos continuos

95 páginas. Maestría en Ingeniería de Procesos.En este trabajo se investiga el problema de síntesis y optimización de sistemas de tratamiento selectivo de corrientes efluentes. La motivación surge del hecho de que comúnmente en las industrias se da un tratamiento centralizado a sus residuos acuosos derivados de un proceso productivo, sin ofrecer alternativas que reduzcan el volumen de agua a tratar. Es decir, el diseño estructural y sus propiedades de flujo y remoción de contaminantes no se estudian de manera sistemática con el fin de producir un diseño eficiente que minimice la contaminación de los sumideros y reduzca simultáneamente los costos de tratamiento. Con este fin se desarrolló un modelo de programación matemática para la síntesis y optimización de sistemas de tratamiento selectivo de efluentes para la reducción electroquímica de cromo hexavalente (Cr(VI)) a cromo trivalente (Cr(III)). El modelo de programación no lineal (PNL) se desarrolló a partir de la superestructura básica propuesta por Hernández-Suárez (2004), la cual toma en cuenta tres unidades de tratamiento. Se utilizó un modelo cinético de orden variable obtenido por Rodríguez y col. (2009) para la tecnología electroquímica de reducción de Cr(VI). La función objetivo considera las variables de flujo, consumo eléctrico y volumen del reactor, lo cual permite diseñar la estructura particular de tratamiento y el cálculo de sus propiedades al menor costo total anualizado. Por otra parte, el modelo de PNL desarrollado involucra términos no convexos, por lo tanto, el problema puede contener mínimos locales los cuales dificultan la obtención de un óptimo global. La posibilidad de manejar múltiples corrientes residuales y unidades de tratamiento en el sistema, introduce complejidades adicionales y un gran número de posibles configuraciones topológicas. Éstas son algunas de las dificultades que fueron abordadas en este trabajo de investigación con el enfoque de programación matemática.The problem of synthesis and optimization of selective wastewater treatment systems was investigated in this work. The motivation arises from the fact that a centralized treatment of wastewaters derived from productive activities is a common practice in industry, with no alternatives to reduce the total treated volume. That is to say, the structural design, the flow properties and the contaminants removal are not studied systematically in order to generate an efficient design that minimizes the contamination of sinks reducing also the wastewater treatment costs. With this purpose, a mathematical programming model was developed for the synthesis and optimization of wastewater treatment networks in which hexavalent chromium (Cr(VI)) is electrochemically reduced to trivalent chromium (Cr(III)). The nonlinear programming model (NLP) is developed from the basic network superstructure proposed by Hernández-Suárez (2004), by taking into account three treatment units. The kinetic model with variable order developed by Rodríguez et al. (2009) for the electrochemical technology for the reduction of Cr(VI) is utilized. The objective function takes into account flow rate variables, the consumption of electrical power and the volume of the reactor, allowing the synthesis of a particular network design with a minimum total annual cost. On the other hand, the developed NLP model involves nonconvex terms, therefore the problem can exhibit local minima which cause difficulties to obtain a global optimum. The management of multiple wastewater streams and treatment units in the system, introduce additional complexities and a large number of possible topological configurations. These are some difficulties which were addressed in this study with the mathematical programming approach.Consejo Nacional de Ciencia y Tecnología (México)

Towards Macroscopic Water Integration for Zero Liquid Discharge in Industrial Complexes

The increasing environmental pressures to minimize wastewater discharge from industrial plants to the environment have led to the emergence of policies and regulations that promote Zero-Liquid Discharge (ZLD) solutions. These systems are typically associated with high capital and operating cost and pose a significant economic burden to implementing industries. ZLD solutions are explored as End-of-Pipe treatment options to eliminate liquid discharges. Instead, ZLD options should be explored in the context of overall water integration of industrial facilities to achieve desired reductions in water footprints through efficient reuse together whilst achieving ZLD. In this work, we propose a systematic approach to screen sustainable and low cost strategies that will assist in targeting water integration for Zero Liquid Discharge (ZLD) in industrial parks. The approach expands an Eco-Industrial Park (EIP) representation for water integration to include different possible ZLD options. A mixed integer non-linear programming (MINLP) model for water integration in industrial parks is developed to screen the representation. The optimization model represents a decision support tool that can help the designer in quickly evaluate potential reuse and recycle scenarios with ZLD. The model is formulated to allow streams to be reused internally and externally in each plant, recycled in a shared centralized and decentralized treatment and in ZLD systems, and utilized for a number of options that can constitute ZLD including beneficial usage and/or ZLD processing. The default objective is to achieve ZLD at minimum total annual cost. A case study of an industrial park with three plants has been solved and analyzed in a number of scenarios to illustrate the usefulness of the proposed model