**4. Performance evaluation**

The MD performance metrics can be divided into two thermodynamic categories: local and system level. Local metrics are impacted by local properties such as porosity, pore size, thickness, membrane conductivity etc. These include permeate flux and thermal efficiency. On the other hand, the system-level metrics are impacted by the process parameters such as temperature, energy flow, etc. These can be divided into first law efficiencies (GOR, SEC) and second law efficiencies (thermal efficiency-II) [43]. In the context of MD, these can be described as follows:

1.*Permeate flux:* The permeate flux *<sup>J</sup>* (kg�m�<sup>2</sup> h�<sup>2</sup> ) is the amount of distillate transported through a unit membrane area. It is the most significant parameter to evaluate the performance of an MD system. It can be expressed as:

$$J = \frac{\dot{m}\_d}{A\_m} \tag{27}$$

Where *Am* is the active surface area (m<sup>2</sup> ) of the membrane, and *m*\_ *<sup>d</sup>* is the amount of distillate that passes through the membrane (kg�s�1).

2.*Gained output ratio:* Gained output ratio (GOR) is the first law efficiency of a thermal desalination system and is often used to quantify energy efficiency. It is defined as the ratio of thermal energy required to vaporize the distillate mass to actual heat input. Mathematically, it can be expressed as [44, 45]:

$$GOR = \frac{\dot{m}\_d \* h\_{\rm fg}}{Q\_{\rm in}} \tag{28}$$

Where

$$Q\_{in} = \dot{m}\_f \* c\_p \* \Delta T\_{12} \tag{29}$$

Where *cp* is the specific heat capacity of fluid (Jkg�<sup>1</sup> K�<sup>1</sup> ). For a system, with no heat energy recovery, GOR is simply a thermal efficiency without a heat exchanger. The GOR is a dimension-less quantity and its value lies between 0 and 1 for a single pass system without any heat recovery, and more than 1 if

the evaporation and condensation heat is reused. In other words, GOR tells how many times the enthalpy of evaporation is reused. For most of the commercial systems and large distillation units, the condensation heat is utilized, therefore, shows values greater than 1.

3.*Specific energy consumption:* Specific energy consumption (SEC) is the energy consumed to produce a unit amount of distillate volume [42, 44, 46]. It is expressed as:

$$\text{SECC} = \frac{Q\_{in}}{m\_d} = \frac{\dot{m}\_f \* c\_p \* \Delta T\_{12}}{m\_d} \tag{30}$$

Where *m*\_ *<sup>f</sup>* , *cp*, Δ*T*12, *Qin*, and *md* are the mass flow rate of feed solution (kg�s �1 ), specific heat of water (kJ�kg�<sup>1</sup> K�<sup>1</sup> ), the temperature difference of inlet and outlet feed streams (K), the total input energy (kWh) consumed by the circulating feed, and the total mass of distillate produced (m3 ), respectively.

4.*Thermal efficiency:* Thermal efficiency *ηth* in MD is the ratio of energy of distillate to that of actual energy used [44]. It is also called first law efficiency. It can be expressed as:

$$
\eta\_{th} = \frac{Q\_v}{Q\_v + Q\_c} \tag{31}
$$

$$\eta\_{th} = \frac{J \ast A\_m \ast h\_{\text{f\'g}}}{Q\_{in}} \tag{32}$$

Where *<sup>J</sup>*, *Am*, *hfg* , *Qm*, *Qv*, *and Qc* are distillate flux (kg�m�<sup>2</sup> h�<sup>1</sup> ), membrane active area (m), latent heat of vaporization (kJ�kg�<sup>1</sup> K�<sup>1</sup> ), heat flux through membrane (W�m�<sup>2</sup> ), heat energy of vaporization (kJ�kg�<sup>1</sup> K�<sup>1</sup> ) and heat of condensation (kJ�kg�<sup>1</sup> K�<sup>1</sup> ), respectively. The *Qin* can be expressed as shown in Eq. (29)

To improve the thermal efficiency, the heat conduction *Qc* should be minimized by using higher thickness membranes, an air gap etc. However, this may require optimizing other parameters as well. Thermal efficiency matches with the GOR if there is no heat recovery [43].

5.*Second law efficiency:* First law efficiency generally used to compare systems with same energy source. However, if the energy source is different, the two systems can not be compared fairly. Using second law efficiency, exergies are compared instead. Therefore, systems can be compared regardless of their energy source. Exergy is the maximum available work extracted from the system when the system moves from its initial state to equilibrium. **Figure 12** shows a representation of second law efficiency. The first law expression can be deduced as [47]:

$$
\dot{Q}\_H + (\dot{m}\cdot\dot{h})\_{\text{av}} = \dot{Q}\_0 + (\dot{m}\cdot\dot{h})\_d + (\dot{m}\cdot\dot{h})\_{br} \tag{33}
$$

$$
\dot{Q}\_H - \dot{Q}\_0 = (\dot{m}.h)\_d + (\dot{m}.h)\_{br} - (\dot{m}.h)\_{sw} \tag{34}
$$

The second law can be expressed as:

$$\frac{\dot{Q}\_H}{T\_0} - \frac{\dot{Q}\_0}{T\_0} = (\dot{m}\,s)\_d + (\dot{m}\,s)\_{br} - (\dot{m}\,s)\_{sw} + \dot{s}\_{gen} \tag{35}$$

*Desalination by Membrane Distillation DOI: http://dx.doi.org/10.5772/intechopen.101457*

**Figure 12.**

*A schematic diagram of a black-box desalination system with heat transfer occurring from an external heat source at temperature TH, and to the environment at temperature T*0*.*

Multiplying second law equation Eq. (35) by *T*<sup>0</sup> and subtracting from Eq. (34**)**:

$$\left(1-\frac{T\_0}{T\_H}\right)\frac{\dot{Q}\_H}{\dot{m}\_d} = \left(G\_d - G\_{br}\right) - \frac{1}{RR}\left(G\_{sw} - G\_{br}\right) + T\_0 \frac{\dot{S}\_{gen}}{\dot{m}\_d} = \frac{\dot{W}\_{sep}}{\dot{m}\_d} \tag{36}$$

Where *RR* is the recovery ratio *<sup>m</sup>*\_ *<sup>p</sup> <sup>m</sup>*\_ *sw*, G is the Gibbs free energy (*h* � *T:s*). The second law efficiency can be expressed as:

$$
\eta\_{II} = \frac{\dot{\mathcal{W}}\_{separation}}{\dot{\mathcal{W}}\_{used}} \tag{37}
$$

6.*Recovery ratio:* Recovery rate (RR) is the distillate production relative to the input feed stream flow in the MD system [48]. It is expressed as:

$$RR = \frac{\dot{m}\_d}{\dot{m}\_f} \ast \mathbf{100\%} \tag{38}$$

A high recovery means a high distillate flow rate is obtained by a given feed flow. In a single pass MD system, feed recovery is very low as compared to other membrane systems. It is reported that the maximum recovery attained in single pass MD reached 10% even if 100% thermal efficiency is attained [49].

In the latest developments, hybridization of MD with existing technologies is used to improve the energy efficiency of MD. The MD has been successfully integrated with other processes as hybrid such as RO, MED, and FO. MD unit has been successfully realized to treat RO brine and FO draw solution which is a challenging part of the process. A comprehensive review of different hybrid technologies with the MD is described by Ghaffour et al. [50]. Additionally, in-situ heating of the feed water inside the MD module, so-called localized heating, has been introduced recently. Localized heating has shown a decreased TP effect which ensures the delivery of heat energy at the site of the feed-membrane interface. It eliminates the circulation heat loss associated with the conventional bulk heating [17, 51]. Photothermal energy source is the prime consideration due to its renewable and ever-existing energy source where the heat is delivered directly to the MD membrane. Politano et al. introduced the photothermal concept in MD first time using surface plasmon effect of silver nanoparticles [52, 53]. Various organic, inorganic, and polymeric materials have also been investigated as photothermal materials in the MD system [6, 54–56].

Similarly, Joule heating elements and spacers have been used to deliver localized heating to the feed channel [57, 58]. Ahmed et al [17] recently demonstrated the TP reduction by using the electrothermal property of carbon nanostructure. They obtained a decrease of SEC by 58%. Hence, localized heating provides a relatively simple infrastructure for small-scale clean water generation in remote off-grid regions.

#### **5. Conclusions**

Membrane distillation (MD) is a promising technology for the separation and purification industry. It is a specific distillation process in which vapor molecules travel through a hydrophobic membrane. MD has several advantages, including low-grade heat input, less fouling propensity, ability to treat high saline water. Four typical membrane configurations, membrane characteristics, membrane modules, heat and mass transfer mechanisms, thermal efficiency, and operating parameters have been presented. The most important limitation that has to be considered with membrane distillation is temperature polarization, which reduces the transmembrane temperature difference, hence the performance. MD is found to be most suitable when the input energy source is solar or waste heat, due to energy intensive nature of distillation process. The recent development in membrane technology allows MD to run in compact modular configurations such as spiral module configurations. The performance of MD is expressed in terms of flux output and the specific energy. Although flux is an important but not the only factor to demonstrate the performance of an MD system, energy input also plays an important role. The recent advances in localized heating make the MD more promising to operate on a bigger scale.

#### **Acknowledgements**

The authors would like to acknowledge King Abdullah University of Science and Technology (KAUST) for supporting the authors in preparing this manuscript.

#### **Conflict of interest**

The authors declare no competing financial interests.

*Desalination by Membrane Distillation DOI: http://dx.doi.org/10.5772/intechopen.101457*
