## 1 Introduction
(2011) analyzed solar-driven distillers and reported exergy efficiencies of 19%-26%, 17%-20%, and less than 4% for triple-effect, double-effect, and single-effect systems. [PERSON] and [PERSON] [PERSON] and [PERSON] (2013) analyzed exergetic efficiencies of a 14-cell multi-effect distillation (SOL-14 MED) plant in Plataforma Solar de Almeria, Spain. They developed a thermodynamic computer program in order to propose improvements. The reported results showed that exergy efficiency of the plant increases from 1.4% to 4.7% and from 14.3% to 25.7% because of the integration of a double-effect absorption heat pump and energy recovery, respectively. Thermal energy demands have been analyzed for membrane-based water desalination systems. Solar powered MD was reported to have a specific heat demand of 140-200 kWh/m\({}^{3}\)[PERSON] et al. (2010), whereas a solar thermal and PV integrating stand-alone MD plant was reported to have a heat demand of 200-300 kWh/m\({}^{3}\)[PERSON] et al. (2010). [PERSON] et al. analyzed exergy destructions in different components of a two-stage 553 m\({}^{3}\)/h capacity reverse osmosis unit in a thermal power plant. The reported contributions for exergy destructions showed a maximum exergy loss in throttling valves (57%) followed by RO modules (21%), with plant's overall second-law efficiency of 4.1% [PERSON] et al. (2010). Energy (first-law) analysis is widely used for assessing efficiencies of water desalination systems. However, as it does not account for the quality of energy considered, second-law analysis is required to decide how much of the available energy is destroyed, for example, in heat exchangers and MD modules. Exergy analysis also helps to identify components responsible for deterioration of the available energy in terms of exergy destruction and hence helps to suggest unit redesign. It is clear that MD modules are responsible for the majority of the exergy destruction in water purification or desalination systems employing this technology. The challenges to be achieved in this study that have not been addressed previously are summarized in the following questions: What is the exergy destruction contribution of each component of AGMD system? How would temperature difference across the module affect the exergy efficiency of the modules? What would the applications for water purification be It was believed that the answers to these questions would be useful for developing or redesigning large-scale MD modules with improved exergy performances. Indeed, temperature dependency on exergy efficiency and exergy destruction is a key parameter, since MD technology offers freedom in selecting heat source and heat sink temperatures when integrated with other processes. Such aspects have not been covered in sufficient detail in previous studies. Moreover, to the authors' knowledge, air gap membrane distillation (AGMD) has not been previously considered in this context. The main objective of this study was to evaluate the exergy efficiencies and destruction of AGMD systems. The analyses are based on two types of semi-commercial AGMD modules for a new application of water treatment where contaminants in the feed are at relatively low concentrations. The study covers calculations of the exergy destruction contributions of the components of each MD system considered. Additionally, effects of feed-coolant temperature differences are analyzed, and comparisons are made with other studies on similar and related water purification systems.