**4. Thermodynamic framework**

The term exergy was devised by Zoran Rant [15] in 1956 by using two Greek words, i.e., "ex" and "ergon" meaning "from work". However, the main concept was first studied by Willard Gibbs in 1873 [16]. The term exergy is defined as "the available work" and it constitutes the maximum useful (shaft) work that could be extracted from of a cycle. Recently, many researchers published on exergoeconomic and thermoeconomic analysis of desalination process [17–20].

To provide any misconceptions across the various type of seawater desalination processes, the thermodynamics of heat engines, representing the desalination methods, are invoked. The amount of ideal or Carnot work (WC) that can be extracted from a flow of heat input QH, emanating from a higher temperature (TH) heat source to an engine, producing an ideal work WC, whilst rejecting heat QL into a low temperature (TL) reservoir, is depicted schematically in **Figure 3**.

Due to incipient dissipative losses, the actual useful work (*Wact*,*<sup>i</sup>*Þ produced by an engine is lower than the ideal or Carnot work and thus, the Second Law efficiency (*η*} *<sup>i</sup>* <sup>Þ</sup> of engine defines the work ratio, i.e., *<sup>η</sup>*} *<sup>i</sup>* <sup>=</sup>*Wact*,*<sup>i</sup> WC* . We invoke the derived corollary of Second |Law of Thermodynamics relationship, i.e.,

$$\frac{W}{T\_H - T\_L} = \frac{Q\_H}{T\_H} = \frac{Q\_L}{T\_L},\tag{1}$$

where TH and TL are the process average temperatures corresponding to any desalination methods. For a given Carnot work (WC,) output from a cycle, the corresponding amount of heat supply (QH at TH) to the engine is deemed as the primary energy input. This can be expressed as the product of Carnot work and the ratio of TH to the temperature difference (TH–TL) between the reservoirs:

$$Q\_H = W\_C \left(\frac{T\_H}{T\_H - T\_L}\right). \tag{2}$$

#### **Figure 3.**

*A heat engine driven by heat transfers at high and low temperature reservoirs and Carnot (ideal) work that can be emanated by it.*

Assuming the same work output were to be derived from an adiabatic flame (Tadia) of a fuel burned with ambient air and operating between maximum temperature difference across the reservoirs (Tadia-To), the heat supply to the engine is equivalent to the work potential (exergy) of heat engine. A common thermodynamic platform across the temperatures, Tadia and To, is proposed where an equivalent heat transfer (QSPE) at the referenced platform would deliver the same Carnot work, i.e.,

$$Q\_{\rm SPE} = W\_C \left(\frac{T\_{\rm adia}}{T\_{\rm adia} - T\_o}\right). \tag{3}$$

Given the temperature platform, i.e., ð Þ *Tadia* � *To* , Eq. (3) implies the input exergy, *QSPE*, is equivalent to a fraction of supplied fuel to generate the Carnot work. Should there be "n" number of engines operating synergistically across the same referenced temperature reservoirs, then the total standard primary energy consumption by all engines is given by the summation of the right hand terms of Eq. (3), i.e.,

$$\sum\_{i=1}^{n} \mathbf{Q}\_{p e, i} = \left(\frac{T\_{adia}}{T\_{adia} - T\_o}\right) \sum\_{i=1}^{n} \mathbf{W}\_{C, i} \tag{4}$$

where "*i*" refers to a process in a combined machine. Eq. (4) depicts an important observation of decomposition of total input exergy (work) into fractions as accrued by a host of sequential machines. This is similar to the equivalent primary energy input, i.e., Q\_spe, contributed by all processes in a CCGT plant. At known heat transfer rates corresponding to each set of inlet and outlet temperatures of a cycle, the total Carnot work can be cumulatively summed to yield the primary energy of the fuel burned as presented in case example in following sections. Equivalently, the apportionment of standard primary energy consumption incurred by the processes of CCGT, namely the generation of electricity and low-grade steam energy, can now be accurately determined using a conversion factor for ease of application.

Extending the Eq. (4) by taking the ratio of standard primary energy and the Carnot work of a process to their respective total in the cycle gives their equivalency. Also the temperature ratios (1-To/Tadia) are eliminated.

*Performance Evaluation of Desalination Technologies at Common Energy Platform DOI: http://dx.doi.org/10.5772/intechopen.104867*

$$\frac{\mathbf{Q}\_{\text{SPE}}}{\sum\_{i=1}^{n} \mathbf{Q}\_{\text{SPE},i}} = \frac{\mathbf{W}\_{\text{C}}}{\sum\_{i=1}^{n} \mathbf{W}\_{\text{C},i}} \tag{5}$$

Herein a conversion factor *CFi* is defined as the standard primary energy to the actual derived energy. It can be expressed as

$$\text{CF}\_{i} = \frac{\mathbf{Q}\_{SPE}}{\mathbf{W}\_{d}} = \left(\frac{\sum\_{i=1}^{n} \mathbf{W}\_{C,i} / \left(\mathbf{1} - \frac{T\_{o}}{T\_{adi}}\right)}{\sum\_{i=1}^{n} \left(\mathbf{W}\_{C,i} \boldsymbol{\eta}\_{i}^{\cdot}\right)}\right) = \frac{\mathbf{1}}{\left(\mathbf{1} - \frac{T\_{o}}{T\_{adi}}\right) \boldsymbol{\eta}^{\cdot}}\tag{6}$$

where the Second Law efficiency of a process is defined as *η*} *<sup>i</sup>* <sup>¼</sup> *Wa*,*<sup>i</sup> WC*,*<sup>i</sup>* , and *T*adia is the adiabatic flame temperature of fuel burning in air which characterizes the highest temperature difference (*T*adia–*T*o) across the reservoirs of the heat engine.

#### **5. Results and discussion**

For clarity, a typical CCGT plant of nominal primary energy input of 2000 MW is considered as presented in **Figure 2**. By analyzing the heat transfer rates at the respective temperature reservoirs for each of the cascaded processes, the ideal or Carnot work can be determined with a selected common temperature platform, defined by the adiabatic flame and ambient temperatures. By summing all the standard primary energy (Q\_SPE), as described by Eq. (4), it yields the equivalent primary energy of fuel or the fuel exergy supplied to the CCGT plant. In terms of the useful output, the total electricity generation from both turbines of CCGT amounts to 1094.37 MWelec and a steam-powered multi-effect distillation (integrated MED\_TVC) produces 5445 m<sup>3</sup> /h potable water. To sustain the dissimilar derived energy, a steady heat rate of 2000 MW is needed by burning a fossil fuel such as the natural gas at the combustor of gas turbines (GT) cycle. The detailed thermodynamic states and the mass flow rates of working fluids operating in key components of CCGT, either the products of combustion or steam at all state points of key components, are presented in Appendix 1.

This procedure offers a means of apportionment of the Qspe into fractions that generate all types of useful derived energy to power the assorted desalination plants, as summarized in **Figure 4**. Based on these fractions of primary energy dissipation, the appropriate conversion factors are derived which forms a basis for level platform to normalize the primary fuel to derived energy or vice versa. For example, the conversion factor for electricity is simply expressed as the ratio of Q\_SPE to the electricity generated or alternatively, it can also be determined from the Second Law and temperature ratios as shown below:

$$\text{CF}\_{\text{elec}} = \frac{\left(Q\_{\text{SPE\\_GT}} + Q\_{\text{SPE\\_ST}}\right)}{\left(W\_{\text{SPE\\_GT}} + W\_{\text{SPE\\_GT}}\right)} = \frac{1}{\left(1 - \frac{T\_o}{T\_{\text{dia}}}\right)\eta\_i^{\cdot}} = 1.7328 \tag{7}$$

Similarly, the conversion factor for low-grade steam input to MED\_TVC is expressed by the ratio Qspe to the thermal energy input or it can also be determined from the appropriate temperature ratios:

$$\text{CF}\_{\text{thermal}} = \frac{\left(Q\_{\text{SPE of bled steam}}\right)}{\left(Q\_{\text{actual blled steam at low pressure}}\right)} = \frac{\mathbf{1} - \frac{T\_o}{T\_{\text{MED}}}}{\left(\mathbf{1} - \frac{T\_o}{T\_{\text{adia}}}\right)} = \mathbf{0.1250} \tag{8}$$

#### **Figure 4.**

*The consumption of standard primary energy and the production of useful derived energy by the major components of a combined cycle gas turbines (CCGT) power plant. The units of accompanying table are in MW.*

The thermodynamic limit of 0.78 kWhspe/m<sup>3</sup> is engaged to determine the Carnot work and the temperature reservoirs of the ideal states. Thus, the above calculations demonstrated that a common standard primary energy platform could resolve the long-held implicit misconception of equivalency that were assumed between different types of derived energy, namely that between electrical and thermal energy. Such a thermodynamic fallacy has unfortunately persisted in the desalination industry for over 5 decades.

**Figure 4** present the standard primary energy consumptions and the production of useful derived energy by the major components of a CCGT power plant based on derived conversion factors.

It is noticed that at ideal conditions, the maximum potable water production per unit primary energy consumed is 1.282 m<sup>3</sup> /kWhspe or minimum specific energy consumption is 0.943 kWhspe/m<sup>3</sup> . Being an ideal process, no conversion of primary energy to derived energy is needed. However, a common misconception, often seen in literature where the graph of specific energy consumption for desalination processes is presented against the various recovery ratios. Conventionally, it showed a curve of gradual increase of the derived energy consumption with increasing recovery ratio (RR) from zero to more than 60%. This depiction of specific derived energy consumption has omitted the dissipative losses incurred by the conversion plants in producing the derived energy when the RR is other than zero. A similar concept is found in the Carnot efficiency of a heat engine when the actual work output is deemed zero at the ideal limit, although the available Carnot work from the cycle is at its highest. Using the proposed common platform of standard primary energy consumption for all desalination processes, the cross comparison of energy efficiency amongst all desalination methods can now be accurately resolved. **Figure 5** shows the energy efficacy from about 60 seawater desalination plants powered by assorted desalination methods, stretching from 1983 to the present [21].

For a fair comparison, all conventional specific derived energy consumption in these plants is transformed to their equivalent primary energy with the relevant conversion factors, where the embedded quantitative and qualitative aspects of the derived energy are now incorporated. It can be seen that SWRO is has a slightly better energy efficacy than MED and MSF, achieving around 13% of TL.

*Performance Evaluation of Desalination Technologies at Common Energy Platform DOI: http://dx.doi.org/10.5772/intechopen.104867*

**Figure 5.**

*Energy efficiency of seawater desalination processes based on standard primary energy. The MED-TVC shows a higher energy efficacy as compared to MSF and the SWRO.*

Nevertheless, all practical methods available hitherto are still far below the TL, hovering less than 10–13% of the ideal.

The authors have conducted an experimental study at KAUST of a hybrid approach involving the well-proven heat driven MED-TVC processes with an adsorption (AD) cycle, arranged in a back-to-back manner [12, 22–31]. A quantum jump in the energy efficiency is achieved through the thermodynamic integration of two thermally-driven cycles with two salient consequences, namely (i) an increase in the available temperature differences between the top to bottom brine temperatures and hence more MED stages could be inserted, and (ii) an opportunity to scavenge more enthalpy from the seawater feed by liquid flashing in the lower stages of MED where the corresponding stage temperatures were below ambient. The recent pilot-scale experiments, conducted with hybrid design of MED-AD plant at KAUST, have attained a lowest brine temperature of 5°C. The vapor generation in these MED stages maximized both the effects from the thermally-driven film evaporation and the liquid flashing from the excess enthalpy embedded available in the feed spray [32–35]. Consequently, the thermodynamic synergy between MED-TVC and AD cycles have boosted distillate production by more than two folds with the same energy input to the top brine stage, attaining a specific energy consumption level of 4.85 kWhspe/m<sup>3</sup> that shows a quantum jump in energy efficiency from current 13 to 20% of TL, as indicated in **Figure 5**.

#### **6. Summary**

In summary, the common platform of standard primary energy consumption is thermodynamically the most rigorous method for the cross comparison of energy efficiency of assorted desalination processes. The outward acceptance of equivalency between electricity and low-grade thermal energy has led to a long-held indifference to the quality of derived energy supply to utilize more optimally. This attitude has afflicted the desalination industry for more than 5 decades. The consequence from such a fallacy has led to some inferior decisions by leaders of desalination industry particularly regarding the adoption of less energy efficient

desalination processes and hence non-optimal energy consumption. Such poor selection has burdened the future economy of many water-stressed countries with higher unit water costs over the decade-long life-span of plants. In concluding it is noted, firstly that the energy efficiency of all practical desalination methods available hitherto have been shown, on a standard primary energy platform, to be far below the ideal limit, typically hovering between 10 and 13% of the TL. Secondly, the design experiences accrued by scientists and engineers have demonstrated, in some other disciplines, that a plausible energy efficiency target of an engine operating between 35 and 40% of ideal limit is tenable for the cascaded designs of assorted desalination plants. Only at these higher efficacy levels will the desalination processes be poised to meet the future goals of sustainable seawater desalination. Hence, there is motivation to strive for higher efficiency with better thermally-driven distillation techniques or thin-film composite membranes [36–40]. The caveat is that a common platform for energy efficacy comparison is desirable, and it is anchored to the best available conversion technology known. For example, in the past three decades, the CCGT has the highest conversion efficiency in the production of convenient derived energy that powers the desalination processes. In future when making appropriate comparison, the same thermodynamic-rigorous methodology of using a standard primary energy platform is equally valid.
