NLP modeling for the optimization of LiBr-H2O absorption refrigeration systems with exergy loss rate, heat transfer area, and cost as single objective functions

Abstract

Based on a nonlinear mathematical programming model, the sizes and operating conditions of the process units of single-effect absorption refrigeration systems operating with a LiBr–H2O solution are optimized for a specified cooling capacity by minimizing three single objective functions: the total exergy loss rate, the total heat transfer area, and the total annual cost of the system. It was found that the optimal solution obtained by minimization of the total exergy loss rate provides “theoretical” upper bounds not only for the total heat transfer area of the system but also for each process unit and all stream temperatures, while the optimal solution obtained by minimization of the total heat transfer area provides the lower bounds for these model variables, to solve a cost optimization problem. The minimization of the total exergy loss rate by varying parametrically the available total heat transfer area between these bounds was also performed, allowing to see how the optimal distribution of the available total heat transfer area among the system components, as well as the operating conditions (stream temperature, pressure, composition, and mass flow rate) and heat loads, vary qualitatively and quantitatively with increasing available total heat transfer area. These optimization results allowed to find a “practical” value of the total heat transfer area, i.e. no benefits can be obtained by increasing the available total heat transfer area above this value since the minimal total exergy loss value cannot be significantly improved by distributing additional heat transfer area among the process units. The optimal solution corresponding to this practical value significantly improves the upper bounds for an economic optimization problem with respect to the optimal solution corresponding to the theoretical value. The optimal solutions corresponding to the theoretical and the practical upper bound values for the total heat transfer area (100 m2 and 61 m2, respectively) as well as the optimal solution obtained by minimization of the total annual cost are discussed for a case study considering a cooling capacity of 50 kW, upon the model assumptions made and a given cost model. Around three-quarters of the minimal total annual cost correspond to capital expenditures and the rest to operating expenditures. The generator and evaporator represent together around 70% of the capital expenditures. The absorber is the largest contributor to both the total heat transfer area and the total exergy loss rate, with around 33.19 and 39.16%, respectively, when the total annual cost is minimized.