## 1 Introduction  
Exergy studies on membrane-based desalination and water purification technologies such as reverse osmosis (RO) and membrane distillation (MD) focus on evaluating the exergetic efficiencies of the components, mainly membrane modules. Unlike energy, exergy is destroyed and can only be conserved when all processes occurring in a system and its surrounding environment are reversible [1]. This thermodynamic irreversibility in a system can be quantified and referred to as exergy destruction. Therefore, the exergy efficiency of processes is a measure of their approach to ideality or reversibility [2]. The exergy rates in streams of processes associated with heat transfer such as MD depend mainly on the temperature at which the process occurs in relation to the temperature of the environment. The exergy efficiencies of such processes are dependent on heat recovered and heat losses through module surfaces to the surrounding atmosphere. Hence, exergy analysis provides unique insights into the types, locations, and causes of losses and aids in identifying improved thermal integration. Membrane distillation involves the separation of water from a preheated feed by subjecting it to phase change and the subsequent passage through a hydrophobic porous membrane to yield pure water upon condensation. Membrane distillation requires heat to evaporate the feed and electricity for the low pressure pumps. The heat sources used in MD include solar [3; 4; 5; 6; 7], district heat [8], or waste heat [9; 10]. Though low-grade heat is sufficient to drive the MD process, thermal energy demand is high, and this together with low permeate flux create challenges for the technology. The high heat demand is largely related to the substantial amount of heat transferred through the membrane, mainly as latent heat but partially also from conductive heat transfer. However, the ability to supply an ultra high-quality permeate together with the possibility to drive the MD process with low grade or waste heat are the opportunities gaining acceptance in large scale industrial applications. Exergy analyses of membrane-based desalination or water purification processes have been investigated by few researchers. [PERSON] [PERSON] and [PERSON] and [PERSON] (2010) conducted exergy destruction analyses for compact and large-scale solar-powered MD systems. They reported that most of the exergy destruction was in the MD modules with 98.8% and 55.14% for compact and large scale systems, respectively. Exergy efficiency of a 24,000 m\({}^{3}\)/day DCMD desalination plant operated with and without heat recovery system was reported as 28.3% and 25.6% for the desalination plant with and without heat recovery, respectively [PERSON] and [PERSON] (2011). They also reported energy consumptions of 39.7 kWh/m\({}^{3}\) and 45 kWh/m\({}^{3}\) for the same plant with and without heat recovery, respectively. Another study [PERSON] and [PERSON] (2011) on energetic and exergetic analysis of RO/MD and NF/RO/MD hybrid systems for production capacities of 904 and 836 m\({}^{3}\)/h, respectively, reported specific thermal energy demand ranging from 2.25 to 15 kWh/m\({}^{3}\). The exergy destructions due to entropy production for each hybrid system was reported in the range of 7300 to 15,100 MJ/h. [PERSON] and [PERSON] carried out an energetic, exergetic, and economic evaluation of seawater desalination [PERSON] and [PERSON] (2011). The integrated system consisted of microfiltration, nanofiltration, membrane crystallization (MCr), RO, and MD, where MCr was applied on NF reentate, and MD was applied on RO reentate. Without energy recovery, the specific energy demand (SED) was found to be 28 kWh/m\({}^{3}\). When a pressure exchanger is included as an energy recovery device, a slightly lower SED (27.5 kWh/m\({}^{3}\)) was obtained. The reported exergetic efficiencies ranged from 15.8% without energy recovery to 21.9% when including the pressure exchanger and internal heat recovery. [PERSON] et al. [PERSON] et al.