روش ترکیبی بهینه سازی شبیه سازی برای طراحی سیستم های جذب خودآگاه محیطی

This work addresses the optimization of ammonia–water absorption cycles for cooling and refrigeration applications with economic and environmental concerns. Our approach combines the capabilities of process simulation, multi-objective optimization (MOO), cost analysis and life cycle assessment (LCA). The optimization task is posed in mathematical terms as a multi-objective mixed-integer nonlinear program (moMINLP) that seeks to minimize the total annualized cost and environmental impact of the cycle. This moMINLP is solved by an outer-approximation strategy that iterates between primal nonlinear programming (NLP) subproblems with fixed binaries and a tailored mixed-integer linear programming (MILP) model. The capabilities of our approach are illustrated through its application to an ammonia–water absorption cycle used in cooling and refrigeration applications.

The worldwide cooling demand has drastically increased over the last few years, which has led to the installation of a large number of air conditioning systems (Balaras et al., 2007 and Henning, 2007). This has resulted in a dramatic rise in electricity consumption, which is nowadays mostly generated from fossil fuels. This trend has caused important environmental problems such as ozone layer depletion and global warming. In this general context, there is a clear need to develop environmentally friendly and energy efficient technologies in order to minimize the environmental impact of cooling applications. Particularly, absorption systems have emerged as a promising alternative to conventional compression cycles (Florides et al., 2002, Herold et al., 1996 and McMullan, 2002), since they can use low grade energy sources that are environmentally friendlier. Absorption machines use a mixture of a refrigerant and an absorbent. The most widely employed mixtures are ammonia–water (ammonia as refrigerant) and water–lithium bromide (water as refrigerant). An important difference between absorption and compression refrigeration systems lies in the energy source. Compression systems require electrical energy for its operation, whereas absorption systems can use low grade heat sources as energy input. Thus solar energy or waste heat (Keil, Plura, Radspieler, & Schweigler, 2008), can be used for saving up to 50% of the primary energy required for the provision of useful heat (Ziegler, Kahn, Summerer, & Alefeld, 1993). Energy conservation via waste heat recovery has been the focus of an increasing interest in the literature (Erickson, Anand, & Kyung, 2004). These systems can reduce global warming emissions (Darwish, Al-Hashimi, & Al-Mansoori, 2008) and mitigate as well the ozone layer depletion. They show a high reliability and a silent and vibration free operation. Unfortunately, absorption cycles require more units than compression cycles, which leads to larger capital investments. Finding ways to improve the efficiency of absorption systems has recently attracted an increasing interest (Darwish et al., 2008). In order to promote the use of absorption systems and to ensure their competitiveness with respect to conventional compression systems, it is still necessary to further improve their performance and reduce their cost. This can be accomplished by developing systematic strategies to assist in their design. Thermoeconomic optimization is well suited to address this problem, since it allows performing energy and economic analysis for different configurations and operating conditions in a systematic and rigorous manner (Kizilkan et al., 2007, Misra et al., 2005, Misra et al., 2006 and Selbas et al., 2006). Particularly, methods based on mathematical programming have recently gained wider interest in the optimization of cooling systems. Most of these approaches have focused on optimizing the economic performance of ammonia–water absorption refrigeration systems (AWRS). One of the first optimization models for absorption cycles was the one introduced by Fernandez-Seara, Sieres, and Vazquez (2003). More recently, Chavez-Islas and Heard (2009a) and Chavez-Islas and Heard (2009b) presented an equation-oriented method and a mixed-integer nonlinear programming (MINLP) model for the economical optimization of these systems. The same authors introduced an MINLP that considers different types of heat exchangers (Chavez-Islas, Heard, & Grossmann, 2009). Gebreslassie, Guillén-Gosálbez, Jiménez, and Boer (2009a) addressed also the optimization of a simplified AWRS considering uncertainties in the economic parameters. These works focused on optimizing the economic performance as unique criterion. New trends have motivated the development of systematic strategies for optimizing the environmental impact of thermodynamic cycles along with their economic performance. Particularly, a promising strategy to accomplish this task relies on combining multi-objective optimization (MOO) tools with economic analysis and life cycle assessment (LCA) principles. This approach allows automating the search for alternatives leading to life cycle environmental savings (see Azapagic & Clift, 1999a). The overwhelming majority of this type of strategies that provide decision-support for environmentally conscious process designs have focused on the chemical sector. In contrast, these techniques have not been used to the same extent in energy applications. Some examples on the combined use of LCA and MOO can be found in the works by Azapagic and Clift (1999b) (production of boron compounds), Alexander, Barton, Petrie, and Romagnoli (2000) (design of a nitric acid plant), Carvalho, Gani, and Matos (2006) (design of a methyl tertiary butyl ether plant) and Guillen-Gosalbez, Caballero, and Jiménez (2008) (optimization of the hydrodealkylation of toluene), among some others. Hence, the optimization of energy systems, and in particular, of cooling and refrigeration cycles with environmental concerns has received little attention to date. To the best our knowledge, Gebreslassie, Guillén-Gosálbez, Jiménez, and Boer (2009b) were the first to address the multi-objective optimization of absorption cycles with economic and environmental concerns. The main limitation of this work is that it relies on “short-cut” models of the process units, that is, on simplified equations that avoid the numerical difficulties associated with the nonlinearities and nonconvexities of the detailed equations of the process units of the cycle. These simplified models work well within a given range of operating conditions, but may perform poorly outside these intervals. Particularly, the generator of the cycle is a key unit that requires the use of complex thermodynamic packages for predicting the liquid–vapor equilibrium and stream properties (e.g., enthalpies, vapor pressures, etc.). Attempting to model this unit by short-cut formulations may lead to poor predictions, especially when working under refrigeration conditions. This work introduces a systematic tool for the optimal design of absorption systems that aims to overcome the limitations mentioned above. Our approach is based on the combined use of process simulation and optimization tools (Brunet et al., 2012, Caballero et al., 2005, Diaz and Bandoni, 1996, Diwekar et al., 1992, Kim et al., 2010, Kravanja and Grossmann, 1996 and Reneaume et al., 1995). One of the main advantages of our strategy is the use of detailed process models of the cycle, including a rigorous tray-by-tray formulation of the rectification column, all of which are implemented in a commercial process simulator (i.e., Aspen Plus). This avoids the definition of the underlying equations of the process units in an explicit form, taking advantage of the customized unit operations models and tailored solution algorithms already implemented in the process simulator. Furthermore, our method improves the robustness and numerical performance of the optimization algorithm, which is likely to fail even in identifying an initial feasible solution when using a simultaneous (i.e., equation oriented) approach. The optimization task is posed in mathematical terms as a multi-objective mixed-integer nonlinear programming (moMINLP) problem that accounts for the simultaneous minimization of the total annualized cost (TAC) and environmental impact (EI). The environmental impact is quantified using LCA principles, an approach that leads to solutions in which the overall environmental damage is globally minimized. The methodology presented is intended to promote a more sustainable design of absorption cycles. Our method has been tested using an AWRS at cooling and refrigeration conditions. Numerical results demonstrate that the method presented can identify solutions in which the environmental impact is reduced at a marginal increase in cost. The remainder of this article is organized as follows. We first formally introduce the problem of interest. The model is then presented and the solution procedure is described afterwards. Some numerical results are then provided, and the conclusions of the work are finally drawn in the last section of the paper.

This work has introduced a systematic method to assist decision makers in the design of environmentally conscious ammonia–water absorption machines for cooling and refrigeration applications. The approach presented shows three main advantages compared to other methods available in the literature: (1) it uses detailed process models implemented in a process simulator that are optimized with an external solver, (2) it applies rigorous deterministic mathematical programming techniques that ensure the (at least local) optimality of the solutions found, and (3) it quantifies the environmental impact of the system over its entire life cycle by applying LCA principles. A rigorous solution approach has been presented that decomposes the model into two hierarchical levels between which the algorithm iterates. The capabilities of this method have been tested in an ammonia–water absorption machine at cooling and refrigeration conditions. Numerical results demonstrate that it is possible to significantly improve the environmental performance of thermodynamic cycles by compromising the cost to a certain extent. This is accomplished by properly adjusting the operating conditions and equipment sizes of all their units.