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In contrast to exergy analysis approach, a simpler and yet accurate approach of equivalent heat engines is proposed where only minimal input information of key processes or cycles of conversion plant are needed, namely the work (Wa) or heat input (QH), the process average of high (TH), and low (TL) temperatures of heat reservoirs. Presenting the example of a CCGT with a nominal fuel energy input of 2000 MW, the respective ideal or Carnot work of temperature-cascaded heat or reverse engines of CCGT are readily computed, for example, the work engines of gas and steam turbines, as well as the bled steam-powered desalination plants (zero physical work output) as shown in Fig. 3.With this approach, the Carnot work of respective heat engines of CCGT can be “decomposed” individually with respect to the maximum temperature difference between two physical limits predicated by the input fuel and the ambient states. Emulating the same Carnot work as per design of actual cycle, it is then normalized to the respective standard primary energy (QSPE) at the common temperature platform. The thermodynamic consistency of the framework could be confirmed by summing all QSPE of cascaded cycles to yield the primary fuel energy at input. It is envisaged that one of the most plausible and optimal co-generation designs of a hybrid power plant with proven seawater desalination processes is illustrated pictorially in Fig. 7. Here, both electricity and low-grade heat sources are produced in-situ, providing the optimal grid power and capacity of potable water. Such an integrated power and water system is designed with maximum temperature cascade (hence minimum dissipative losses) for power generation and low-grade heat utilization.Fig. 7: A pictorial representation of combined cycle gas turbines (CCGT) plant.A pictorial representation of combined cycle gas turbines (CCGT) plant.Full size imageTo recap, the decoupling framework requires two requisites. Firstly, the matching of Carnot work of each cascaded engine of CCGT, as per designed temperatures, to the ideal engines at the common temperature platform for the computation of standard primary energy (QSPE), as shown in Fig. 3. Secondly, by summing all the standard primary energy (QSPE) available from the decomposed engines, one obtains the equivalent calorific value of fuel supplied to the CCGT.Owing to the common temperature platform of decomposed engines, the ratio of Carnot work (Wc) to the standard primary energy (QSPE) is equally applicable to either a single individual engine or all decomposed engines of the CCGT plant, i.e.,$$frac{{mathop {sum}nolimits_{i = 1}^n {left( {W_{{mathrm{C}},,i}} right)} }}{{mathop {sum}nolimits_{i = 1}^n {left( {Q_{{mathrm{SPE}},,i}} right)} }} = frac{{left( {T_{{mathrm{adia}}} – T_{mathrm{o}}} right)}}{{T_{{mathrm{adia}}}}} = left( {frac{{W_{mathrm{c}}}}{{Q_{{mathrm{SPE}}}}}} right)_i$$
(1)
where “i” refers to a specific engines and “n” denotes the total number of engines. The temperatures, (T_{{mathrm{adia}}}) and (T_{mathrm{o}}), are process-average adiabatic flame and ambient temperatures, respectively. As the first and third terms of Eq. 1 are equivalent to the common temperature ratio, i.e., (frac{{left( {T_{{{{{{mathrm{adia}}}}}}} – T_{mathrm{o}}} right)}}{{T_{{{{mathrm{adia}}}}}}}), the terms can be equated to each other and re-arranged to give the fractional form of process heat or work to their respective total, i.e.,$$frac{{Q_{{mathrm{H}},,i}}}{{mathop {sum}nolimits_{i = 1}^n {left( {Q_{{mathrm{H}},,i}} right)} }} = frac{{W_{{mathrm{c}},,i}}}{{mathop {sum}nolimits_{i = 1}^n {left( {W_{{mathrm{C}},,i}} right)} }}$$
(2)
Before moving to illustrative examples, it is noted that those seeking thermodynamic details should consult Supplementary Table 1 supplied in the article where it will be seen that the framework adheres to the Second Law.Electricity-driven desalination processesAs electricity is one of the convenient forms of derived energy, it is used to power work-driven membrane-based reverse osmosis (RO) desalination processes. By defining the 2nd Law Efficiency as (eta ^{primeprime} = frac{{W_{mathrm{a}}}}{{W_{mathrm{C}}}}) for an engine, where the actual work input is normally known via electricity consumption of processes. From the decomposed gas and steam turbines that produced electricity of a CCGT plant, a conversion factor (CF) can now be defined, based on the consumption of the standard primary energy of these engines to the actual electricity output, i.e.,$${mathrm{CF}}_{{mathrm{elec}}} = frac{{mathop {sum}nolimits_{i = 1}^{n = 2} {Q_{{mathrm{SPE}},i}} }}{{mathop {sum}nolimits_{i = 1}^{n = 2} {W_{a,i}} }}$$
(3)
where the subscripts (i = 1) and (i = 2) refer to the contributions from gas and steam turbines of CCGT, respectively. Note that the denominator term is the actual work, Wa. The latter can be related to the Carnot work (WC) via the empirical 2nd Law Efficiency (left( {eta ^{primeprime}} right)) of the respective work producing cycle. Equation 3 can be further expressed as a function based on the common temperature platform ratio and the sum of work-weighted second law efficiency of the processes, i.e., (mathop {sum}nolimits_{i = 1}^{n = 2} {left( {frac{{W_{{mathrm{C}},i}}}{{W_{{mathrm{C}},T}}}eta _i^{primeprime} } right)}).$${mathrm{CF}}_{{mathrm{elec}}} = frac{{mathop {sum }nolimits_{i = 1}^{n = 2} Q_{{mathrm{SPE}},i}}}{{mathop {sum }nolimits_{i = 1}^{n = 2} W_{a,i}}} = left( {frac{{mathop {sum}nolimits_{i = 1}^{n = 2} {left( {frac{{W_{{mathrm{C}},i}}}{{1 – frac{{T_o}}{{T_{{mathrm{adia}}}}}}}} right)} }}{{mathop {sum }nolimits_{i = 1}^{n = 2} left( {W_{{mathrm{C}},i}eta _i^{primeprime} } right)}}} right) = frac{1}{{left( {1 – frac{{T_o}}{{T_{{mathrm{adia}}}}}} right)mathop {sum }nolimits_{i = 1}^{n = 2} left( {frac{{W_{{mathrm{C}},i}}}{{W_{{mathrm{C}},{mathrm{T}}}}}eta _i^{primeprime} } right)}},$$
(4)
Note that the subscripts “c” and “a” refer to the Carnot and actual work, respectively. (W_{{mathrm{C}},{mathrm{T}}}) refers to the total Carnot work of heat engines. The temperatures (T_{{mathrm{adia}}}) and (T_o) are the process-average adiabatic flame temperature (with due allowance for the excess-air combustion) and ambient temperature, respectively.Although Eq. 4 has generated an expression for the desired figure of merit, (frac{{mathop {sum }nolimits_{i = 1}^2 Q_{{mathrm{SPE}},i}}}{{mathop {sum }nolimits_{i = 1}^2 W_{{mathrm{a}},i}}}), this function is a combination of the common temperature ratio platform and the work-weighted second law efficiency, ({mathrm{i.e.}},,bar eta ^{primeprime} = mathop {sum }nolimits_{i = 1}^{n = 2} left( {frac{{W_{{mathrm{C}},i}}}{{W_{{mathrm{C}},{mathrm{T}}}}}eta _i^{primeprime} } right)).Superficially, the inverse of ({mathrm{CF}}_{{mathrm{elec}}}) may appear similar to the conventional energy efficiency of a power plant. However, a closer examination of its derivation reveals a fundamental difference where it employs the standardized QSPE, and not QH. The latter term expresses only the quantitative aspect and makes no allowance for the quality of energy consumed.Thermally driven desalination processesFor a thermally driven multi-effect desalination system (MED), the low-grade heat supplied yielded zero physical work output as of heat engines. Instead, it produces a finite rate of potable water via evaporation and condensation processes. The Carnot work potential of the low-grade steam entering the MED is computed and it is then decomposed to the equivalent standard primary energy (QSPE) at the common energy platform. Hence, the conversion factor (CFth) of MED desalination is defined as the ratio of standard primary energy consumption to the actual heat supply, Qa, i.e.,$$left( {{mathrm{CF}}_{{mathrm{th}}}} right) = left{ {frac{{left( {Q_{{mathrm{SPE}}}} right)}}{{Q_{mathrm{a}}}}} right} = frac{{left( {1 – frac{{T_o}}{{T_{mathrm{H}}}}} right)}}{{left( {1 – frac{{T_o}}{{T_{{mathrm{adia}}}}}} right)}}$$
(5)
QSPE is based on Carnot work which is defined at application temperatures. Whereas Qa is the actual energy supplied at bled steam temperature. Since the steam inlet temperatures to different thermally driven desalination processes are different, hence the CFthermal are determined separately for assorted plants.Using the physically meaningful conversion factors, namely CFelec and CFth, these factors transform the absolute values (quantity and quality) of derived energy consumed by diverse desalination methods to the common platform primary energy consumption, enabling a cross comparison of energy efficiency from all desalination methods. In brief, the thermodynamic framework provides the common energy platform that served two key roles: Firstly, the fractional apportionment of standardized primary energy consumption, conducted on the cascaded processes of CCGT to the respective electricity, low-grade thermal sources, etc., yielded the causal calibrated conversion factors for the derived energy to power all diverse processes in industry. This calibration of conversion factors is performed with the best power plant systems available hitherto. Secondly, the calibrated conversion factors enable the conversion of specific energy consumption of practical desalination plants, consuming either electricity or thermal sources, into a common energy platform of QSPE. The relative consumption of standardized QSPE for water produced from all types desalination methods can now be compared accurately.In conclusion, the common energy temperature platform has been used to evaluate and compare the consumption of standard primary energy (QSPE) by assorted seawater desalination methods. In co-generating electricity and thermal heat sources from the best conversion plant available hitherto, the apportionment of respective QSPE to the derived energy at a common platform embeds their absolute quantity and quality of input fossil fuels. Based on the thermodynamic framework presented here, the causal conversion factors (CFelec and CFth) are devised, enabling the direct conversion of kWhelec or kWhth into the common energy platform of QSPE:- An essential requisite needed for a just comparison of energy efficiency of multifarious desalination processes or methods.Since 1983 till now, the energy efficiency of SWRO methods were shown to be better than thermally driven methods of MSF and MED. Comprehensively, all existing desalination methods were relatively energy inefficient, at specific energy efficiencies spanning between 7 and 16% of the thermodynamic limit of 1.06 m3/kWhSPE. Recent hybrid designs of thermally driven processes have improved significantly with the twofold increase in energy efficiency, from More

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