#
Integration of Supercritical CO_{2} Recompression Brayton Cycle with Organic Rankine/Flash and Kalina Cycles: Thermoeconomic Comparison

^{1}

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## Abstract

**:**

_{2}recompression Brayton (SCRB) cycle. Novel comparisons of the SCRB/ORC, SCRB/OFC and SCRB/KC integrated plants from thermodynamic, exergoeconomic and sustainability perspectives are performed to choose the most appropriate bottoming cycle for waste heat recovery for the SCRB cycle. For comprehensiveness, the performance of the SCRB/OFC and SCRB/ORC layouts are examined using ten working fluids. The influence of design parameters such as pressure ratio in the supercritical CO

_{2}(S-CO

_{2}) cycle, pinch point temperature difference in heater and pre-cooler 1, turbine inlet temperature and pressure ratio for the ORC/OFC/Kalina cycles are examined for the main system indicators including the net output power, energy and exergy efficiencies, and unit cost of power production. The order of the exergy efficiencies for the proposed systems from highest to lowest is: SCRB/ORC, SCRB/OFC and SCRB/KC. The minimum unit cost of power production for the SCRB/ORC system is lower than that for the SCRB/KC and SCRB/OFC systems, by 1.97% and 0.75%, respectively. Additionally, the highest exergy efficiencies for the SCRB/OFC and SCRB/ORC systems are achieved when n-nonane and R134a are employed as working fluids for the OFC and ORC, respectively. According to thermodynamic optimization design, the SCRB/ORC, SCRB/OFC and SCRB/KC systems exhibit sustainability indexes of 3.55, 3.47 and 3.39, respectively.

## 1. Introduction

_{2}thermophysical properties occur that can significantly lower the compression work, which can raise the efficiency of the S-CO

_{2}cycle. This addresses one of the problems with classical Brayton cycles, namely, high compression work. Regarding working fluids for power cycles, among the various options, CO

_{2}has numerous advantages: non-toxic, low cost, compactness and non-flammability. From an environmental perspective, the ozone depletion potential for CO

_{2}is zero while its global warming potential is 1 [2]. Since the S-CO

_{2}cycle operates above the critical point, the fluid remains dense throughout the cycle, reducing the size of turbomachinery [3].

_{2}cycle layouts and concluded that the recompression S-CO

_{2}cycle attains the highest thermodynamic efficiency. Dostal [5] examined the effect of reheating on the efficiency of the cycle and determined that the use of one reheating step is preferable in the S-CO

_{2}cycle. Dostal et al. [6] compared the economics of the SCRB cycle and the helium Brayton cycle. They concluded that, by using an S-CO

_{2}cycle instead of a helium system, a 15% cost saving is achieved. In a second law analysis and optimization study of the S-CO

_{2}recompression cycle, Sarkar [1] found that, from the viewpoint of exergy analysis, irreversibilities are more significant in heat exchangers than turbo-machinery. He also indicated that the turbine isentropic efficiency affects the system exergy efficiency by 2.5 times more than do the exergy efficiencies of the compressors. Moreover, he showed that pressure drop in the reactor in the SCRB cycle notably affects the cycle second law efficiency. In the S-CO

_{2}cycle, there is a difference between the fluid specific heats of the cold and hot side flows in recuperators. Therefore, introducing a recompressing compressor as an extra compressor prior to the pre-cooler in the recompression S-CO

_{2}cycle allows the flow to be split to narrow the gap of specific heat for the low temperature recuperator, leading to a higher thermal efficiency by reducing waste heat.

_{2}cycle can be enhanced to use low-grade thermal energy as the heater of the S-CO

_{2}cycle. To date, numerous cycles have been suggested as bottoming cycles for the S-CO

_{2}cycle. The rejected heat from the heater of the SCRB can be used in an ORC. Recently, the ORC has attracted much attention for its ability to utilize low temperature heat sources [7]. This, in addition to its simplicity, high reliability and ease of maintenance, can make the ORC appropriate as a bottoming cycle [8]. Besarati et al. [9] proposed three configurations for a S-CO

_{2}cycle: simple S-CO

_{2}Brayton cycle, recompression S-CO

_{2}Brayton cycle and partial cooling S-CO

_{2}Brayton cycle. Then, they employed an ORC as bottoming cycle for each of the cycles. They found that the integrated recompression S-CO

_{2}Brayton cycle/ORC has the highest efficiency. Mahmoudi et al. [10] investigated thermodynamically and exergoeconomically a S-CO

_{2}recompression Brayton cycle with an ORC. They assessed 8 ORC working fluids and found that the best thermodynamic and economic performance is achieved using isobutane and RC318. Specifically, they showed that the second law efficiency is 11.7% higher for the SCRB/ORC cycle than the SCRB cycle, and that the total product unit cost is 5.7% less for the SCRB/ORC cycle than the SCRB cycle. Wang et al. [11] concluded via an exergoeconomic analysis of a SCRB/ORC cycle that its second law efficiency with an isobutane working fluid can exceed 62%. The SCRB/ORC cycle exhibits the lowest total product unit cost when isobutene is utilized as the organic working fluid in the ORC. Song et al. [12] carried out a thermoeconomic analysis for the S-CO

_{2}cycle combined with ORC for geothermal power generation. They revealed that the geothermal combined system with the ORC utilizing waste heat from the S-CO

_{2}cycle provides 2940 kW of net power output, which is 45% more than that of the S-CO

_{2}cycle. The thermoeconomic analysis showed that the specific cost of the combined cycle is 2880 $/kW, 22% less than for the S-CO

_{2}cycle. In another study, Song et al. [13] studied an S-CO

_{2}cycle combined with an ORC for waste heat recovery for an internal combustion engine (ICE). They determined the net power output to be 215 kW for the combined cycle, which is 58% greater than that of the standalone S-CO

_{2}cycle, and that the specific investment cost related to the integrated cycle is 4% higher than that of S-CO

_{2}cycle

_{.}Gutierrez et al. [14] also analyzed a S-CO

_{2}cycle integrated with an ORC thermodynamically and exergoeconomically, and concluded that cyclohexane is the best choice as the ORC working fluid and that the specific investment for the system is 2310 $/kW.

_{2}cycle, based on achieving optimal mass flow rate, supercritical pressure and superheated temperature. The supercritical temperatures of all thirty working fluids were varied from 50 to 225 °C. In a study of the S-CO

_{2}cycle combined with an ORC dual loop for waste heat recovery for a diesel engine, Liang et al. [17] obtained the maximum system power output as 40.9 MW, which is 6.7% more than that of the dual-fuel engine. In another paper, Chen et al. [18] performed a thermo-environmental analysis on the combined S-CO

_{2}/ORC system. For enhancing the efficiency of the S-CO

_{2}cycle combined with an ORC, both subcritical and transcritical ORC systems were considered. The results demonstrated that, compared to the original waste-to-energy plant, the turbine output power and waste-to-energy efficiency for the S-CO

_{2}/subcritical organic Rankine cycle system are increased by $9.50\times {10}^{6}$ W and 59.4%, respectively, while the power generation and waste-to-energy efficiency of S-CO

_{2}/transcritical organic Rankine cycle system are raised by $10.2\times {10}^{6}$ W and 63.7%, respectively. Moreover, they have found that, from the viewpoints of first law efficiency and environmental performance, the combined cycle comprised of the S-CO

_{2}/transcritical organic Rankine cycle is more efficient than the S-CO

_{2}/subcritical organic Rankine cycle. They also analyzed the system from an environmental perspective. The sustainable index of the S-CO

_{2}cycle/subcritical ORC is 1.54, while it is 1.57 for the S-CO

_{2}cycle/transcritical ORC. Wang et al. [19] contrasted three cycles for a nuclear hydrogen production (NHP) system: steam Rankine cycle (SRC), S-CO

_{2}and combined S-CO

_{2}/ORC. They showed that, when the inlet temperatures of the reactor in the S-CO

_{2}cycle are 400 °C and 587 °C, the first law efficiency of the S-CO

_{2}cycle varies from 27.5% to 31.0% and 27.5% to 36.5%, respectively. Ma et al. [20] utilized waste heat of the engine exhaust gas by combining the supercritical CO

_{2}Brayton cycle and transcritical ORC, and analyzed the cycle thermodynamically and economically. The greatest exergy destruction was observed to occur in the heater. In addition, they found that the highest exergy efficiency of the system is 54.63% and the lowest levelized cost of energy is 36.95 USD/MWh. Javanshir et al. [21] compared two combined cycles: Brayton/ORC and steam Rankine/ORC. They found that the best working fluids for the Brayton cycle are air and CO

_{2}, and that the highest efficiency is achieved when isobutane, R11 and ethanol are employed as working fluids for the ORC.

_{2}cycle thermodynamically and exergoeconomically. They considered seven working fluids in the combined cycles and found that the second law efficiency of the SCRB/OFC cycle is 6.57% greater than that of the SCRB cycle. The total product unit cost for the SCRB/OFC cycle was determined to be 3.75% lower than that of the SCRB cycle. They concluded that the maximum second law efficiency and minimum total product unit cost of the SCRB/OFC cycle are attained using n-nonane as the working fluid.

_{2}cycle is the Kalina cycle. Since the Kalina cycle boiling/condensing process is at a temperature that is not constant, irreversibilities in the evaporator and condenser are reduced, increasing the second law efficiency [23]. Mahmoudi et al. [24] assessed a SCRB/KC cycle exergoeconomically and found that the exergy efficiency of the SCRB/KC cycle exceeds that of the SCRB cycle by 10% and the total product unit cost for the SCRB/KC cycle is 4.9% less than that of the SCRB cycle. Li et al. [25] also compared SCRB/KC and SCRB cycles and determined the second law efficiency of the SCRB/KC cycle is 8.0% higher than that of the SCRB cycle; however, the total product unit cost for the SCRB/KC cycle is 5.5% lower than that of the SCRB cycle. In a study of a supercritical CO

_{2}Brayton cycle combined with a Kalina cycle, Feng et al. [26] showed that the average annual fuel consumption is decreased by 16.6% by using this combined system compared to marine power generation auxiliary engines.

_{2}cycle.

## 2. System Description and Assumptions

_{2}(state 5), after receiving heat from the reactor, expands and produces work in the S-CO

_{2}turbine (ST). Part of the expanded stream (state 6) transfers heat to the fluid at state 2 and the other part transfers heat to the fluid at state 3 in the low temperature recuperator (LTR) and high temperature recuperator (HTR), respectively. Then, the CO

_{2}stream splits into the CO

_{2}stream 8a entering the heater with a high mass flow rate and the CO

_{2}stream 8b entering the recompression compressor (RC) with a low mass flow rate. In the heater, CO

_{2}stream 8a transfers heat to the organic working fluid in the OFC; the stream is then cooled in the pre-cooler. Next, the stream (state 1) is compressed in the main compressor (MC). The compressed CO

_{2}(state 2) in the MC is mixed with the compressed stream in the RC after being heated in the LTR. The mixture enters the reactor used in the SCRB cycle after absorbing heat in the HTR. In the OFC, the saturated liquid organic working fluid (state 12) is conveyed to the heater where it absorbs heat from hot CO

_{2}. This stream (state 13) is a saturated liquid at higher temperature. The hot stream (state 14) expands in valve 1. The stream at the inlet of the flash separator (Fs) (state 15) is separated to a saturated vapor (state 16) and a saturated liquid (state 18). The stream at state 16 expands and produces work in the turbine, while the stream at state 18 expands in valve 2 to mix with the turbine outlet flow (state 17) in the mixer. Finally, the mixture stream is condensed in the condenser to a saturated liquid.

_{2}in the heater. The hot organic working fluid (state 14) expands and generates work in the turbine. The turbine outlet flow (state 15) becomes a saturated liquid in the condenser.

_{2.}Then, the stream is separated to saturated liquid (state 13) and saturated vapor (state 12) parts. The saturated vapor absorbs heat in the superheater, while the saturated liquid is cooled in the KCHTR and expands through the valve. The outlet flow of the superheater (state 14) expands and generates work in the turbine and mixes with the outlet flow of the expansion valve in the mixer. The mixture (state 18) is cooled in the KCLTR and then condensed to a saturated liquid in the condenser.

- Use of a dry working fluid is suggested for preventing turbine blade erosion [29]. This characteristic suggests having a superheated outflow from the turbine.
- A working fluid with high critical temperature and low critical pressure is recommended. A low critical pressure provides the opportunity for a superheated outflow from the turbine with low heat input.

- (1)
- The systems operate under steady state conditions.
- (2)
- Pressure drops in all heat exchangers and pipelines are negligible.
- (3)
- Turbines, pumps and compressors have constant isentropic efficiencies.
- (4)
- Changes in kinetic and potential energies are negligible.
- (5)
- The cooling water enters the pre-cooler and condenser at ambient temperature and pressure.
- (6)
- At the heater and condenser outlets, the working fluid is in a saturated liquid state [33].
- (7)
- The HTR and LTR have constant effectiveness values.
- (8)
- At the outlets of the separator and condenser, the ammonia-water mixture is in a saturated liquid state.

## 3. Modeling and Analysis

#### 3.1. Thermodynamic Analysis

_{2}and organic fluids used in the corresponding cycles are considered to be pure substances and their structures do not change during the cycle processes, their chemical exergies at different states are the same. Therefore, the exergy destruction rate of components in the mentioned cycles is affected just by the thermophysical exergy rates. In this regard, there is no necessity to evaluate the chemical exergy for analyzing the cycles. However, the ammonia concentration is continuously changing during the various processes in the Kalina cycle. Thus, it is required to define chemical exergy for the ammonia-water working fluid, and this is done as follows [37]:

#### 3.2. Thermoeconomic Analysis

#### 3.3. Sustainability Analysis

## 4. Results and Discussion

#### 4.1. Validation

_{2}/OFC, S-CO

_{2}/ORC and S-CO

_{2}/KC combined power generation systems are validated. The simulation results are presented and compared with the corresponding reference data in Table 6, Table 7 and Table 8. According to these tables and the calculated errors, it is perceived that the results obtained by the present work exhibit good agreement with the reference data.

#### 4.2. Working Fluid Selection

_{2}power plant, first it is essential to optimize the performance of the two former cycles via careful selection of an appropriate working fluid. To accomplish this and considering the significant effect of exhaust CO

_{2}temperature from the S-CO

_{2}plant on the waste heat recovery process for the OFC and ORC cycles, a working fluid selection strategy is implemented. The power produced by the bottoming OFC and ORC cycles is investigated for the condition of high temperature waste heat recovery from the S-CO

_{2}plant. Higher CO

_{2}turbine inlet temperature and pressure ratios permit this condition. The best thermodynamic and thermooeconomic performances of the SCRB/OFC and SCRB/ORC are obtained when the outlet temperature of the reactor is at its maximum value (750 °C). Therefore, the mentioned condition is employed for selecting the working fluid. Figure 4 and Figure 5 show the effects of the turbine inlet temperatures of the bottoming cycles (OFC and ORC) and the pressure ratios in the bottoming cycle for high temperature waste heat recovery on the total net output power of the SCRB/OFC and SCRB/ORC systems, respectively.

#### 4.3. Parametric Study

_{c}), pinch point temperature difference in heater (${{\displaystyle \Delta T}}_{He}$) for SCRB/OFC and SCRB/ORC and pre-cooler 1 (${{\displaystyle \Delta T}}_{\mathrm{Pr}e1}$) for SCRB/KC, maximum temperature of the cycle (T

_{5}) and pressure ratio of the bottoming cycle (Pr

_{T}). In the parametric study, the effects of these variables are assessed on the total net output power of cycle (${{\displaystyle \dot{W}}}_{net,tot}$), first law efficiency (${{\displaystyle \eta}}_{th}$), exergy efficiency (${{\displaystyle \eta}}_{ex}$) and the total product unit cost of the system (${{\displaystyle c}}_{P,tot}$). As a particular parameter is studied, other parameters stay unchanged.

_{2}cycle pressure ratio. In this figure, three diagrams present the effects of the S-CO

_{2}cycle pressure ratio on the thermodynamic indicators including the total net output power, first and second law efficiencies, and the fourth diagram illustrates the effects of S-CO

_{2}cycle pressure ratio on the unit cost of power production. It is observed that the first law and exergy efficiencies of the SCRB/OFC, SCRB/ORC and SCRB/KC cycles are greater than those of the stand alone SCRB cycle, and that the total product unit cost of the SCRB/OFC, SCRB/ORC and SCRB/KC cycles are lower than that of the SCRB cycle. In Figure 6, optimum values are observed for the S-CO

_{2}cycle pressure ratio, in which the first and second law efficiencies of systems are maximized and also the total product unit cost of systems is minimized. At first, increasing Pr

_{c}causes the S-CO

_{2}turbine output power and the consumption power of both compressors in the S-CO

_{2}cycle to increase, which results in increasing the total net output power of the topping cycle. So, the first and second law efficiencies increase and the total product unit cost of systems decreases. Then, as Pr

_{c}increases further, the S-CO

_{2}turbine outlet temperature decreases which lowers the heat recovery in the HTR. As a result, the inlet temperature of the reactor decreases. Since the outlet temperatures of reactor (T

_{5}) and ${\dot{Q}}_{R}$ are constant, the mass flow rate of CO

_{2}decreases in the reactor. Therefore, the first and second law efficiencies decrease. Moreover, according to Figure 6, for lower S-CO

_{2}cycle pressure ratios, the SCRB/KC system has the highest exergy efficiency and the lowest total product unit cost. When the S-CO

_{2}cycle pressure ratios are more than nearly 2.9, SCRB/ORC performs better than SCRB/OFC and SCRB/KC thermodynamically and economically. These statements illustrate that, for lower S-CO

_{2}cycle pressure ratios, SCRB/KC can be the best option. However, SCRB/ORC is the most preferred option for higher S-CO

_{2}cycle pressure ratios.

_{c}which results in low heat transfer in heater and pre-cooler 1. The low heat transfer results in a low mass flow rate in the bottoming cycle. Consequently, the total output power in bottoming cycles decreases with increasing ${{\displaystyle \Delta T}}_{He}$. Referring to Figure 7, it is seen that the best thermodynamic performance among three combined cycles is exhibited by the SCRB/KC cycle. Moreover, the three combined cycles demonstrate the same behavior as ${{\displaystyle \Delta T}}_{He}$ increases. Thus, by increasing ${{\displaystyle \Delta T}}_{He}$, the temperature difference between working fluids in Heater and Pre-cooler 1 increases, raising the exergy destruction rate and decreasing the second law efficiency. By decreasing the total net output power of the systems, the unit cost of power production increases.

_{5}on the performances of the systems are shown in Figure 8. There, it can be seen that, as T

_{5}increases, the values of ${{\displaystyle \eta}}_{th}$, ${{\displaystyle \eta}}_{ex}$ and ${{\displaystyle \dot{W}}}_{net,tot}$ for the SCRB/OFC, SCRB/ORC and SCRB/KC cycles increase and ${{\displaystyle c}}_{P,tot}$ decreases. However, there is a material limitation for T

_{5}that does not allow researchers to consider turbine inlet temperature more than 750 °C. Interestingly, the behaviors of the SCRB/OFC and SCRB/ORC cycles as T

_{5}changes are the same when n-nonane and R134a are utilized as working fluids for the SCRB/OFC and SCRB/ORC cycles, respectively. Moreover, the best thermodynamic performance is achieved when the Kalina cycle is utilized as bottoming cycle for the S-CO

_{2}cycle as T

_{5}varies.

_{T}increases, the energy and exergy efficiencies first increase and then decrease. However, the total product unit cost behaves opposite to the first and second law efficiencies. By comparing the changes in the total product unit cost and exergy efficiency as Pr

_{T}varies, it is observed that there is a specific point where the first and second law efficiencies are maximized and the total product unit cost is minimized. In Figure 9, the SCRB/OFC and SCRB/KC cycles are seen to have nearly same values for the optimized Pr

_{T}. However, the optimized value for Pr

_{T}of the SCRB/ORC cycle is lower than for the other two systems.

#### 4.4. Optimization

_{5}and Pr

_{c}. System optimization is done using EES.

_{c}. However, the minimum total product unit cost for all three cycles is obtained at lower Pr

_{c}values than 4.2. Another important indicator is the sustainability index (SI). It is seen in Table 10 that the values for SI are greater when systems are under thermodynamic optimization design than when they are under economic optimization design. The highest value for SI is achieved when the SCRB/ORC system is utilized (3.553). The highest SI for the SCRB/ORC system is 2.48% and 4.62% greater than the corresponding values for the SCRB/OFC and SCRB/KC systems, respectively.

#### 4.5. Sensitivity Analysis

_{c}= 2.8). This means, for example, that the compressor pressure ratio is 2.2 when the variation of compressor pressure ratio is −0.6. According to Figure 10, raising the pinch point temperature difference in the heater and pre-cooler 1 has a negative effect on the exergy efficiency and a positive effect on total product unit cost. Referring to Figure 11, by increasing variation of compressor pressure ratio, the exergy efficiency increases at first and then decreases. The exergy efficiency and total product unit cost trends behave opposite to one other. Therefore, increasing the compressor pressure ratio causes the total product unit cost to decrease at first and then to increase. Referring to Figure 10, the resulting variation in the exergy efficiency of the SCRB/ORC system is 1% when variation in pinch point temperature difference is −5 K, which is highest variation. Note that the resulting variations in the exergy efficiencies of SCRB/OFC and SCRB/KC are same and they exhibit almost the same behavior. It is observed in Figure 10b that the highest variation in the total product unit cost is achieved for R134a and is 0.8% when the pinch point temperature difference is 5 K. Again, the behaviors of SCRB/OFC and SCRB/KC are nearly the same. Referring to Figure 11, the lowest resulting exergy efficiency achieved for SCRB/ORC is −8% when the variation in the compressor pressure ratio is −0.6%. Comparing Figure 10 and Figure 11 illustrates that the variations in the compressor pressure ratio affect the resulting variation in the exergy efficiency and total product unit cost much more than the variation in the pinch point temperature in heater or pre-cooler 1.

## 5. Conclusions

- (1)
- The parametric studies show that the SCRB/OFC, SCRB/ORC and SCRB/KC systems perform thermodynamically and economically better when the pinch point temperature difference is at its own lowest value, which is 8 °C for this work. For achieving more desirable performances for the systems from the viewpoints of thermodynamics and economics, the turbine inlet temperature should be 750 °C, noting that this value is limited by material technology.
- (2)
- Under the thermodynamic condition of T
_{5}= 550 °C and ${{\displaystyle \Delta T}}_{He}$ or ${{\displaystyle \Delta T}}_{\mathrm{Pr}e1}$ = 8K, there is an optimum value for the compressor pressure ratio at which the exergy efficiency is maximized and C_{p, total}is minimized. - (3)
- Based on the working fluid selection strategy, the SCRB/OFC and SCRB/ORC cycles achieve their best performances from the viewpoints of exergy and economics, when n-nonane and R134a are used as the working fluid, respectively.
- (4)
- For operation at low pressure ratios, the SCRB/KC cycle exhibits better performance from the viewpoints of thermodynamic and exergoeconomic analyses; however, at high pressure ratios, the SCRB/ORC is the best system.
- (5)
- The optimization results show that the exergy efficiency of the SCRB/ORC cycle is higher than that of the SCRB/OFC and SCRB/KC cycles, by up to 1.3%. In addition, the unit cost of power production of the SCRB/ORC cycle is lower than those of the SCRB/KC and SCRB/OFC systems by up to 1.9% and 0.75%, respectively.
- (6)
- The optimization results indicate that the sustainability index for the SCRB/ORC system is 2.48% and 4.62% higher than those for the SCRB/OFC and SCRBB/KC systems, respectively.
- (7)
- From thermodynamic, exergoeconomic and sustainability perspectives, the SCRB/ORC system is the best option while the SCRB/OFC system can be a promising integrated cycle.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | Area (m^{2}) |

$\dot{\mathrm{C}}$ | Cost rate ($\frac{\$}{\mathrm{yr}}$) |

$\mathrm{c}$ | Average cost per unit exergy ($\frac{\$}{\mathrm{GJ}}$) |

${{\displaystyle c}}_{p,tot}$ | Total product unit cost ($/GJ) |

CRF | Capital recovery factor |

$\dot{E}$ | Exergy rate (kW) |

${\dot{E}}_{D}$ | Rate of exergy destruction (kW) |

f | Exergoeconomic factor (%) |

h | Specific enthalpy (kJ/kg) |

${{\displaystyle i}}_{r}$ | Interest rate (%) |

$\Delta {T}_{LMTD}$ | Logarithmic mean temperature difference (K) |

$\dot{m}$ | Mass flow rate (kg/s) |

n | Number of operating years |

P | Pressure (bar) |

${\mathrm{Pr}}_{c}$ | Compressor pressure ratio |

${\mathrm{Pr}}_{p}$ | Pump pressure ratio |

${\mathrm{Pr}}_{T}$ | Turbine pressure ratio of bottoming cycle |

$\dot{Q}$ | Heat transfer rate (kW) |

s | Specific entropy (kJ/kg·K) |

SI | Sustainability index |

T | Temperature (K) |

U | Overall heat transfer coefficient (kW/m^{2}K) |

$\dot{W}$ | Work rate (kW) |

x | Mass flow ratio of CO_{2} |

Z | Capital investment cost ($) |

$\dot{Z}$ | Capital investment cost rate ($/h) |

Subscripts | |

0 | Ambient state |

1,2, … | State points |

Bot | Bottoming cycle |

ch | Chemical exergy |

CI | Capital investment |

Cond | Condenser |

D | Destruction |

EOD | Economic optimal design |

ex | Exergy |

Fs | Flash separator |

He | Heater |

HTR | High temperature recuperator |

L | Loss |

LTR | Low temperature recuperator |

MC | Main compressor |

OM | Operation and maintenance |

P | Product |

Pre | Pre-cooler |

ph | Physical exergy |

pp | Pinch point |

R | Reactor |

RC | Recompression compressor |

ST | S-CO_{2} turbine |

sup | Superheat/Superheater |

T | Turbine |

th | Thermal |

TOD | Thermodynamic optimal design |

tot | Total |

V | Valve |

Greek symbols | |

$\eta $ | Efficiency (%) |

$\epsilon $ | Effectiveness (%) |

$\gamma $ | Maintenance factor |

$\tau $ | Annual plant operation hours |

$\Delta T$ | Temperature difference (K) |

## Appendix A

Component | Cost Function | Reference Year | CEPCI_{0} | Reference |
---|---|---|---|---|

Reactor | ${Z}_{R}={c}_{in}{\dot{Q}}_{R},{c}_{in}=283\$/K{W}_{th}$ | 2003 | 402.3 | [38] |

S-CO_{2} turbine | ${Z}_{ST}=479.34\times {\dot{m}}_{in}\times (\frac{1}{0.93-{\eta}_{ST}})\times Ln({\mathrm{Pr}}_{c})\times (1+\mathrm{exp}(0.036\times {T}_{in}-54.4))$ | 1994 | 368.1 | [39] |

Compressors | ${Z}_{MC\&RC}=71.1\times {\dot{m}}_{in}\times (\frac{1}{0.92-{\eta}_{c}})\times {\mathrm{Pr}}_{c}\times Ln({\mathrm{Pr}}_{c})$ | 1994 | 368.1 | [39] |

HTR, LTR, Pre-cooler 1, Heater and Superheater | ${Z}_{k}=2681\times {A}_{k}{}^{0.59}$ | 1986 | 318.4 | [50] |

KCLTR, KCHTR, Condenser, Pre-cooler, Pre-cooler 2 | ${Z}_{k}=2143\times {{{\displaystyle A}}_{k}}^{0.514}$ | 1986 | 318.4 | [50] |

Turbine | ${Z}_{T}=4405\times {({\dot{W}}_{T})}^{0.7}$ | 2005 | 468.2 | [51] |

Pump | ${Z}_{P}=1120\times {({\dot{W}}_{P})}^{0.8}$ | 2005 | 468.2 | [51] |

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**Figure 4.**Effects of OFC turbine inlet temperature (

**a**) and OFC turbine pressure ratio (

**b**) in bottoming cycle of SCRB/OFC for high temperature waste heat recovery condition on the total net output power of SCRB/OFC.

**Figure 5.**Effects of ORC turbine inlet temperature (

**a**) and ORC turbine pressure ratio (

**b**) in bottoming cycle of SCRB/ORC for high temperature waste heat recovery condition on the total net output power of SCRB/ORC.

**Figure 6.**Effects of compressor pressure ratio on first law efficiency (

**a**), total net output power (

**b**), second law efficiency (

**c**) and total product unit cost (

**d**) for three integrated cycles (T

_{5}= 550 °C and $\Delta {T}_{He}$ or $\Delta {T}_{\mathrm{Pr}e1}$ = 10 K).

**Figure 7.**Effects of the pinch point temperature difference in heater and pre-cooler 1 on first law efficiency (

**a**), total net output power (

**b**), second law efficiency (

**c**) and total product unit cost (

**d**) for three integrated cycles. (T

_{5}= 550 °C and Pr

_{c}= 2.8).

**Figure 8.**Effects of turbine inlet temperature on first law efficiency (

**a**), total net output power (

**b**), second law efficiency (

**c**) and total product unit cost (

**d**) for three integrated cycles (Pr

_{c}= 2.8 and ${{\displaystyle \Delta T}}_{He}$ or ${{\displaystyle \Delta T}}_{\mathrm{Pr}e1}$ = 10 K).

**Figure 9.**Effects of turbine pressure ratio of bottoming cycle on first law efficiency (

**a**), total net output power (

**b**), second law efficiency (

**c**) and total product unit cost (

**d**) for three integrated cycles (Pr

_{c}= 2.8, T

_{5}= 550 °C and $\Delta {T}_{He}$ or $\Delta {T}_{\mathrm{Pr}e1}$ = 10 K).

**Figure 10.**Sensitivity analysis results, showing effect of pinch point temperature difference in heater and pre-cooler 1 on exergy efficiency (

**a**) and total product unit cost (

**b**).

**Figure 11.**Sensitivity analysis results, showing effect of compressor ratio on exergy efficiency (

**a**) and total product unit cost (

**b**).

**Table 1.**Thermophysical and environmental properties of ten working fluidss utilized in SCRB/OFC and SCRB/ORC cycles.

Working Fluid | Thermophysical Properties | Environmental Properties | ||
---|---|---|---|---|

Critical Temperature (K) | Critical Pressure (kPa) | ODP | GWP (100 Year) (Relative to CO_{2}) | |

R245fa | 427.2 [30] | 3640 [30] | 0 [29] | 950 [29] |

n-Pentane | 469.7 [30] | 3370 [30] | 0 [31] | 0 [31] |

n-Hexane | 507.82 [30] | 3034 [30] | 0 [31] | 0 [31] |

n-Heptane | 540.13 [30] | 2736 [30] | 0 [32] | 3 [32] |

n-Octane | 569.32 [30] | 2497 [30] | ||

n-Nonane | 594.55 [30] | 2281 [30] | ||

R123 | 456.83 [29] | 3662 [29] | 0.012 [29] | 120 [29] |

R142b | 479.96 [29] | 4460 [29] | 0.086 [29] | 700 [29] |

R134a | 374.21 [29] | 4056 [29] | 0 [29] | 1300 [29] |

Isobutane | 425.12 [29] | 3796 [29] | 0.12 [29] | 725 [29] |

System | Parameter | Value Reference |
---|---|---|

S-CO_{2} Brayton cycle | Cycle minimum temperature (°C) | 32 [11,34] |

Cycle maximum temperature (°C) | 550 [11,34] | |

Main compressor inlet pressure (bar) | 74 [11,34] | |

Compressor pressure ratio, Pr_{c} | 2.2–4.2 [11,34] | |

LTR and HTR effectiveness, ${\epsilon}_{LTR}$ and ${\epsilon}_{HTR}$ (%) | 86 [1,5,35] | |

S-CO_{2} turbine isentropic efficiency, ${\eta}_{ST}$ (%) | 90 [1,5,35] | |

Main compressor isentropic efficiency, ${\eta}_{MC}$ (%) | 85 [1,5,35] | |

Recompression compressor isentropic efficiency, ${\eta}_{RC}$ (%) | 85 [1,5,35] | |

Pinch point temperature difference in Heater, $\Delta {T}_{He}$ (K) | 8–16 [22] | |

Pinch point temperature difference in Pre-cooler 1, $\Delta {T}_{\mathrm{Pr}e1}$ (K) | 8–16 [22] | |

Heat provided by Reactor, ${\dot{Q}}_{R}$ (MW) | 600 [1,5,35] | |

Bottoming cycle Organic flash cycle | Reactor core temperature, ${T}_{R}$ (°C) Turbine isentropic efficiency, ${\eta}_{T}$ (%) Pump isentropic efficiency, ${\eta}_{P}$ (%) Flash separator inlet temperature, ${T}_{15}$ (°C) Pinch point temperature difference in Condenser, $\Delta {T}_{Cond}$ (K) | 800 [1,5,35] 80 [36] 80 [36] 80 [36] 10 [22] |

Organic Rankine cycle | Turbine inlet temperature, ${T}_{14}$ (°C) Pinch point temperature difference in Condenser, $\Delta {T}_{Cond}$ (K) Degree of superheat, $\Delta {T}_{Sup}$ (K) | 90 [11] 10 [22] 0 [11] |

Kalina cycle | Separator inlet temperature,
${T}_{11}$ (°C) Ammonia concentration in ammonia-water mixture leaving the condenser, X _{20} (%)Pump pressure ratio, Pr _{pump}Minimum temperature difference in superheater, ${{\displaystyle \Delta T}}_{\mathrm{sup}}$ (K) Standard chemical exergy of ammonia, ${e}_{ch,NH3}^{0}(\mathrm{J}/\mathrm{mol})$ Standard chemical exergy of water, ${e}_{ch,H2O}^{0}(\mathrm{J}/\mathrm{mol})$ | 79.85 [24] 95 [24] 2.55–3.65 [24] 1 [11] 337,900 [37] 900 [37] |

Economic data | Interest rate, ${i}_{r}$ Number of operation year, n Annual plant operation hours, $\tau $ Maintenance factor, $\gamma $ Fuel cost, ${{\displaystyle c}}_{fuel}$($/MWh) | 0.12 [10] 20 [10] 8000 [10] 0.06 [10] 7.4 [38] |

Ambient condition | Ambient temperature, T_{0} (k) | 298.15 |

Ambient pressure, P_{0} (bar) | 1 |

**Table 3.**Energy, exergy and cost rate balances and auxiliary equations for each component of SCRB/OFC cycle.

Component | Energy Balance | Exergy Balance | Cost Rate Balance and Ancillary Equation |
---|---|---|---|

Main compressor | ${\dot{m}}_{1}{h}_{1}+{\dot{W}}_{MC}={\dot{m}}_{2}{h}_{2}$ ${\eta}_{MC}=({h}_{2s}-{h}_{1})/({h}_{2}-{h}_{1})$ | ${\dot{E}}_{1}+{\dot{W}}_{MC}={\dot{E}}_{2}+{\dot{E}}_{D,MC}$ | ${\dot{C}}_{1}+{\dot{C}}_{MC}+{\dot{Z}}_{MC}={\dot{C}}_{2}$ ${c}_{MC}={c}_{ST}$ |

Recompression compressor | ${\dot{m}}_{8b}{h}_{8b}+{\dot{W}}_{RC}={\dot{m}}_{3b}{h}_{3b}$ ${\eta}_{RC}=({h}_{3s}-{h}_{8})/({h}_{3}-{h}_{8})$ | ${\dot{E}}_{8b}+{\dot{W}}_{RC}={\dot{E}}_{3b}+{\dot{E}}_{D,RC}$ | ${\dot{C}}_{8b}+{\dot{C}}_{RC}+{\dot{Z}}_{RC}={\dot{C}}_{3b}$ ${c}_{RC}={c}_{ST},{c}_{8b}=x{c}_{8}$ |

S-CO_{2} turbine | ${\dot{m}}_{5}{h}_{5}={\dot{W}}_{ST}+{\dot{m}}_{6}{h}_{6}$ ${\eta}_{ST}=({h}_{5}-{h}_{6})/({h}_{5}-{h}_{6s})$ | ${\dot{E}}_{5}={\dot{W}}_{ST}+{\dot{E}}_{6}+{\dot{E}}_{D,ST}$ | ${\dot{C}}_{5}+{\dot{Z}}_{ST}={\dot{C}}_{6}+{\dot{C}}_{ST}$ ${c}_{5}={c}_{6}$ |

Reactor | ${\dot{m}}_{4}{h}_{4}+{\dot{Q}}_{R}={\dot{m}}_{5}{h}_{5}$ | ${\dot{E}}_{4}+{\dot{Q}}_{R}(1-\frac{{T}_{0}}{{T}_{R}})={\dot{E}}_{5}+{\dot{E}}_{D,R}$ | ${\dot{C}}_{4}+{\dot{C}}_{fuel}+{\dot{Z}}_{R}={\dot{C}}_{5}$ |

HTR | ${\dot{m}}_{3}{h}_{3}+{\dot{m}}_{6}{h}_{6}={\dot{m}}_{4}{h}_{4}+{\dot{m}}_{7}{h}_{7}$ ${{\displaystyle \epsilon}}_{HTR}=\frac{{{\displaystyle T}}_{6}-{{\displaystyle T}}_{7}}{{{\displaystyle T}}_{6}-{{\displaystyle T}}_{3}}$ | ${\dot{E}}_{3}+{\dot{E}}_{6}={\dot{E}}_{4}+{\dot{E}}_{7}+{\dot{E}}_{D,HTR}$ | ${\dot{C}}_{3}+{\dot{C}}_{6}+{\dot{Z}}_{HTR}={\dot{C}}_{4}+{\dot{C}}_{7}$ ${c}_{7}={c}_{6},{\dot{C}}_{3}={\dot{C}}_{3a}+{\dot{C}}_{3b}$ |

LTR | ${\dot{m}}_{2}{h}_{2}+{\dot{m}}_{7}{h}_{7}={\dot{m}}_{3a}{h}_{3a}+{\dot{m}}_{8}{h}_{8}$ ${{\displaystyle \epsilon}}_{LTR}=\frac{{{\displaystyle T}}_{7}-{{\displaystyle T}}_{8}}{{{\displaystyle T}}_{7}-{{\displaystyle T}}_{2}}$ | ${\dot{E}}_{2}+{\dot{E}}_{7}={\dot{E}}_{3a}+{\dot{E}}_{8}+{\dot{E}}_{D,LTR}$ | ${\dot{C}}_{2}+{\dot{C}}_{7}+{\dot{Z}}_{LTR}={\dot{C}}_{3a}+{\dot{C}}_{8}$ ${c}_{7}={c}_{8}$ |

Pre-cooler | ${\dot{m}}_{9}{h}_{9}-{\dot{m}}_{1}{h}_{1}={\dot{m}}_{11}{h}_{11}-{\dot{m}}_{10}{h}_{10}$ | ${\dot{E}}_{9}+{\dot{E}}_{10}={\dot{E}}_{1}+{\dot{E}}_{11}+{\dot{E}}_{D,pre}$ ${\dot{E}}_{11}={\dot{E}}_{10}+{\dot{E}}_{L,pre}$ | ${\dot{C}}_{9}+{\dot{C}}_{10}+{\dot{Z}}_{\mathrm{Pr}e}={\dot{C}}_{1}+{\dot{C}}_{11}$ ${c}_{1}={c}_{9},{\dot{C}}_{10}=0$ |

Heater | ${\dot{m}}_{9}{h}_{9}+{\dot{m}}_{14}{h}_{14}={\dot{m}}_{8a}{h}_{8a}+{\dot{m}}_{13}{h}_{13}$ | ${\dot{E}}_{8a}+{\dot{E}}_{13}={\dot{E}}_{9}+{\dot{E}}_{14}+{\dot{E}}_{D,Heater}$ | ${\dot{C}}_{8a}+{\dot{C}}_{13}+{\dot{Z}}_{Heater}={\dot{C}}_{9}+{\dot{C}}_{14}$ ${c}_{8a}={c}_{9},{\dot{C}}_{8a}=(1-x){\dot{C}}_{8}$ |

Valve 1 | ${\dot{m}}_{14}{h}_{14}={\dot{m}}_{15}{h}_{15}$ | ${\dot{E}}_{14}={\dot{E}}_{15}+{\dot{E}}_{D,V1}$ | ${\dot{C}}_{14}+{\dot{Z}}_{V1}={\dot{C}}_{15}$ |

Valve 2 | ${\dot{m}}_{18}{h}_{18}={\dot{m}}_{19}{h}_{19}$ | ${\dot{E}}_{18}={\dot{E}}_{19}+{\dot{E}}_{D,V2}$ | ${\dot{C}}_{18}+{\dot{Z}}_{V2}={\dot{C}}_{19}$ |

Flash separator | ${\dot{m}}_{15}{h}_{15}={\dot{m}}_{16}{h}_{16}+{\dot{m}}_{18}{h}_{18}$ | ${\dot{E}}_{15}={\dot{E}}_{16}+{\dot{E}}_{18}+{\dot{E}}_{D,Flash}$ | ${\dot{C}}_{15}+{\dot{Z}}_{Flash}={\dot{C}}_{16}+{\dot{C}}_{18}$ $\frac{({\dot{C}}_{16}-{\dot{C}}_{15})}{({\dot{E}}_{16}-{\dot{E}}_{15})}=\frac{({\dot{C}}_{18}-{\dot{C}}_{15})}{({\dot{E}}_{18}-{\dot{E}}_{15})}$ |

Mixer | ${\dot{m}}_{17}{h}_{17}+{\dot{m}}_{19}{h}_{19}={\dot{m}}_{20}{h}_{20}$ | ${\dot{E}}_{17}+{\dot{E}}_{19}={\dot{E}}_{20}+{\dot{E}}_{D,Mixer}$ | ${\dot{C}}_{17}+{\dot{C}}_{19}+{\dot{Z}}_{Mixer}={\dot{C}}_{20}$ |

Pump | ${\dot{m}}_{12}{h}_{12}+{\dot{W}}_{Pump}={\dot{m}}_{13}{h}_{13}$ ${\eta}_{P}=({h}_{13s}-{h}_{12})/({h}_{13}-{h}_{12})$ | ${\dot{E}}_{12}+{\dot{W}}_{Pump}={\dot{E}}_{13}+{\dot{E}}_{D,Pump}$ | ${\dot{C}}_{12}+{\dot{C}}_{Pump}+{\dot{Z}}_{Pump}={\dot{C}}_{13}$ ${c}_{Pump}={c}_{Turbine}$ |

Turbine | ${\dot{m}}_{16}{h}_{16}={\dot{W}}_{Turbine}+{\dot{m}}_{17}{h}_{17}$ ${\eta}_{T}=({h}_{16}-{h}_{17})/({h}_{16}-{h}_{17s})$ | ${\dot{E}}_{16}={\dot{W}}_{Turbine}+{\dot{E}}_{17}+{\dot{E}}_{D,Turbine}$ | ${\dot{C}}_{16}+{\dot{Z}}_{Turbine}={\dot{C}}_{17}+{\dot{C}}_{Turbine}$ ${c}_{16}={c}_{17}$ |

Condenser | ${\dot{m}}_{20}{h}_{20}+{\dot{m}}_{21}{h}_{21}={\dot{m}}_{12}{h}_{12}+{\dot{m}}_{22}{h}_{22}$ | ${\dot{E}}_{20}+{\dot{E}}_{21}={\dot{E}}_{12}+{\dot{E}}_{22}+{\dot{E}}_{D,Cond}$ ${\dot{E}}_{22}={\dot{E}}_{21}+{\dot{E}}_{L,Cond}$ | ${\dot{C}}_{20}+{\dot{C}}_{21}+{\dot{Z}}_{Cond}={\dot{C}}_{12}+{\dot{C}}_{22}$ ${c}_{12}={c}_{20},{\dot{C}}_{21}=0$ |

**Table 4.**Energy, exergy and cost rate balances and auxiliary equations for each component of SCRB/ORC cycle.

Component | Energy Balance | Exergy Balance | Cost Rate Balance and Ancillary Equation |
---|---|---|---|

Main compressor | ${\dot{m}}_{1}{h}_{1}+{\dot{W}}_{MC}={\dot{m}}_{2}{h}_{2}$ ${\eta}_{MC}=({h}_{2s}-{h}_{1})/({h}_{2}-{h}_{1})$ | ${\dot{E}}_{1}+{\dot{W}}_{MC}={\dot{E}}_{2}+{\dot{E}}_{D,MC}$ | ${\dot{C}}_{1}+{\dot{C}}_{MC}+{\dot{Z}}_{MC}={\dot{C}}_{2}$ ${c}_{MC}={c}_{ST}$ |

Recompression compressor | ${\dot{m}}_{8b}{h}_{8b}+{\dot{W}}_{RC}={\dot{m}}_{3b}{h}_{3b}$ ${\eta}_{RC}=({h}_{3s}-{h}_{8})/({h}_{3}-{h}_{8})$ | ${\dot{E}}_{8b}+{\dot{W}}_{RC}={\dot{E}}_{3b}+{\dot{E}}_{D,RC}$ | ${\dot{C}}_{8b}+{\dot{C}}_{RC}+{\dot{Z}}_{RC}={\dot{C}}_{3b}$ ${c}_{RC}={c}_{ST},{c}_{8b}=x{c}_{8}$ |

S-CO_{2} turbine | ${\dot{m}}_{5}{h}_{5}={\dot{W}}_{ST}+{\dot{m}}_{6}{h}_{6}$ ${\eta}_{ST}=({h}_{5}-{h}_{6})/({h}_{5}-{h}_{6s})$ | ${\dot{E}}_{5}={\dot{W}}_{ST}+{\dot{E}}_{6}+{\dot{E}}_{D,ST}$ | ${\dot{C}}_{5}+{\dot{Z}}_{ST}={\dot{C}}_{6}+{\dot{C}}_{ST}$ ${c}_{5}={c}_{6}$ |

Reactor | ${\dot{m}}_{4}{h}_{4}+{\dot{Q}}_{R}={\dot{m}}_{5}{h}_{5}$ | ${\dot{E}}_{4}+{\dot{Q}}_{R}(1-\frac{{T}_{0}}{{T}_{R}})={\dot{E}}_{5}+{\dot{E}}_{D,R}$ | ${\dot{C}}_{4}+{\dot{C}}_{fuel}+{\dot{Z}}_{R}={\dot{C}}_{5}$ |

HTR | ${\dot{m}}_{3}{h}_{3}+{\dot{m}}_{6}{h}_{6}={\dot{m}}_{4}{h}_{4}+{\dot{m}}_{7}{h}_{7}$ ${{\displaystyle \epsilon}}_{HTR}=\frac{{{\displaystyle T}}_{6}-{{\displaystyle T}}_{7}}{{{\displaystyle T}}_{6}-{{\displaystyle T}}_{3}}$ | ${\dot{E}}_{3}+{\dot{E}}_{6}={\dot{E}}_{4}+{\dot{E}}_{7}+{\dot{E}}_{D,HTR}$ | ${\dot{C}}_{3}+{\dot{C}}_{6}+{\dot{Z}}_{HTR}={\dot{C}}_{4}+{\dot{C}}_{7}$ ${c}_{7}={c}_{6},{\dot{C}}_{3}={\dot{C}}_{3a}+{\dot{C}}_{3b}$ |

LTR | ${\dot{m}}_{2}{h}_{2}+{\dot{m}}_{7}{h}_{7}={\dot{m}}_{3a}{h}_{3a}+{\dot{m}}_{8}{h}_{8}$ ${{\displaystyle \epsilon}}_{LTR}=\frac{{{\displaystyle T}}_{7}-{{\displaystyle T}}_{8}}{{{\displaystyle T}}_{7}-{{\displaystyle T}}_{2}}$ | ${\dot{E}}_{2}+{\dot{E}}_{7}={\dot{E}}_{3a}+{\dot{E}}_{8}+{\dot{E}}_{D,LTR}$ | ${\dot{C}}_{2}+{\dot{C}}_{7}+{\dot{Z}}_{LTR}={\dot{C}}_{3a}+{\dot{C}}_{8}$ ${c}_{7}={c}_{8}$ |

Pre-cooler | ${\dot{m}}_{9}{h}_{9}-{\dot{m}}_{1}{h}_{1}={\dot{m}}_{11}{h}_{11}-{\dot{m}}_{10}{h}_{10}$ | ${\dot{E}}_{9}+{\dot{E}}_{10}={\dot{E}}_{1}+{\dot{E}}_{11}+{\dot{E}}_{D,pre}$ ${\dot{E}}_{11}={\dot{E}}_{10}+{\dot{E}}_{L,pre}$ | ${\dot{C}}_{9}+{\dot{C}}_{10}+{\dot{Z}}_{\mathrm{Pr}e}={\dot{C}}_{1}+{\dot{C}}_{11}$ ${c}_{1}={c}_{9},{\dot{C}}_{10}=0$ |

Heater | ${\dot{m}}_{9}{h}_{9}+{\dot{m}}_{14}{h}_{14}={\dot{m}}_{8a}{h}_{8a}+{\dot{m}}_{13}{h}_{13}$ | ${\dot{E}}_{8a}+{\dot{E}}_{13}={\dot{E}}_{9}+{\dot{E}}_{14}+{\dot{E}}_{D,Heater}$ | ${\dot{C}}_{8a}+{\dot{C}}_{13}+{\dot{Z}}_{Heater}={\dot{C}}_{9}+{\dot{C}}_{14}$ ${c}_{8a}={c}_{9},{\dot{C}}_{8a}=(1-x){\dot{C}}_{8}$ |

Pump | ${\dot{m}}_{12}{h}_{12}+{\dot{W}}_{Pump}={\dot{m}}_{13}{h}_{13}$ ${\eta}_{P}=({h}_{13s}-{h}_{12})/({h}_{13}-{h}_{12})$ | ${\dot{E}}_{12}+{\dot{W}}_{Pump}={\dot{E}}_{13}+{\dot{E}}_{D,Pump}$ | ${\dot{C}}_{12}+{\dot{C}}_{Pump}+{\dot{Z}}_{Pump}={\dot{C}}_{13}$ ${c}_{Pump}={c}_{Turbine}$ |

Turbine | ${\dot{m}}_{14}{h}_{14}={\dot{W}}_{Turbine}+{\dot{m}}_{15}{h}_{15}$ ${\eta}_{T}=({h}_{14}-{h}_{15})/({h}_{14}-{h}_{15s})$ | ${\dot{E}}_{14}={\dot{W}}_{Turbine}+{\dot{E}}_{15}+{\dot{E}}_{D,Turbine}$ | ${\dot{C}}_{14}+{\dot{Z}}_{Turbine}={\dot{C}}_{15}+{\dot{C}}_{Turbine}$ ${c}_{14}={c}_{15}$ |

Condenser | ${\dot{m}}_{15}{h}_{15}+{\dot{m}}_{16}{h}_{16}={\dot{m}}_{12}{h}_{12}+{\dot{m}}_{17}{h}_{17}$ | ${\dot{E}}_{15}+{\dot{E}}_{16}={\dot{E}}_{12}+{\dot{E}}_{17}+{\dot{E}}_{D,Cond}$ ${\dot{E}}_{17}={\dot{E}}_{16}+{\dot{E}}_{L,Cond}$ | ${\dot{C}}_{15}+{\dot{C}}_{16}+{\dot{Z}}_{Cond}={\dot{C}}_{12}+{\dot{C}}_{17}$ ${c}_{12}={c}_{15},{\dot{C}}_{16}=0$ |

**Table 5.**Energy, exergy and cost rate balances and auxiliary equations applied for each component of SCRB/KC cycle.

Component | Energy Balance | Exergy Balance | Cost Rate Balance and Ancillary Equation |
---|---|---|---|

Main compressor | ${\dot{m}}_{1}{h}_{1}+{\dot{W}}_{MC}={\dot{m}}_{2}{h}_{2}$ ${\eta}_{MC}=({h}_{2s}-{h}_{1})/({h}_{2}-{h}_{1})$ | ${\dot{E}}_{1}+{\dot{W}}_{MC}={\dot{E}}_{2}+{\dot{E}}_{D,MC}$ | ${\dot{C}}_{1}+{\dot{C}}_{MC}+{\dot{Z}}_{MC}={\dot{C}}_{2}$ ${c}_{MC}={c}_{ST}$ |

Recompression compressor | ${\dot{m}}_{8b}{h}_{8b}+{\dot{W}}_{RC}={\dot{m}}_{3b}{h}_{3b}$ ${\eta}_{RC}=({h}_{3s}-{h}_{8})/({h}_{3}-{h}_{8})$ | ${\dot{E}}_{8b}+{\dot{W}}_{RC}={\dot{E}}_{3b}+{\dot{E}}_{D,RC}$ | ${\dot{C}}_{8b}+{\dot{C}}_{RC}+{\dot{Z}}_{RC}={\dot{C}}_{3b}$ ${c}_{RC}={c}_{ST},{c}_{8b}=x{c}_{8}$ |

S-CO_{2} turbine | ${\dot{m}}_{5}{h}_{5}={\dot{W}}_{ST}+{\dot{m}}_{6}{h}_{6}$ ${\eta}_{ST}=({h}_{5}-{h}_{6})/({h}_{5}-{h}_{6s})$ | ${\dot{E}}_{5}={\dot{W}}_{ST}+{\dot{E}}_{6}+{\dot{E}}_{D,ST}$ | ${\dot{C}}_{5}+{\dot{Z}}_{ST}={\dot{C}}_{6}+{\dot{C}}_{ST}$ ${c}_{5}={c}_{6}$ |

Reactor | ${\dot{m}}_{4}{h}_{4}+{\dot{Q}}_{R}={\dot{m}}_{5}{h}_{5}$ | ${\dot{E}}_{4}+{\dot{Q}}_{R}(1-\frac{{T}_{0}}{{T}_{R}})={\dot{E}}_{5}+{\dot{E}}_{D,R}$ | ${\dot{C}}_{4}+{\dot{C}}_{fuel}+{\dot{Z}}_{R}={\dot{C}}_{5}$ |

HTR | ${\dot{m}}_{3}{h}_{3}+{\dot{m}}_{6}{h}_{6}={\dot{m}}_{4}{h}_{4}+{\dot{m}}_{7}{h}_{7}$ ${{\displaystyle \epsilon}}_{HTR}=\frac{{{\displaystyle T}}_{6}-{{\displaystyle T}}_{7}}{{{\displaystyle T}}_{6}-{{\displaystyle T}}_{3}}$ | ${\dot{E}}_{3}+{\dot{E}}_{6}={\dot{E}}_{4}+{\dot{E}}_{7}+{\dot{E}}_{D,HTR}$ | ${\dot{C}}_{3}+{\dot{C}}_{6}+{\dot{Z}}_{HTR}={\dot{C}}_{4}+{\dot{C}}_{7}$ ${c}_{7}={c}_{6},{\dot{C}}_{3}={\dot{C}}_{3a}+{\dot{C}}_{3b}$ |

LTR | ${\dot{m}}_{2}{h}_{2}+{\dot{m}}_{7}{h}_{7}={\dot{m}}_{3a}{h}_{3a}+{\dot{m}}_{8}{h}_{8}$ ${{\displaystyle \epsilon}}_{LTR}=\frac{{{\displaystyle T}}_{7}-{{\displaystyle T}}_{8}}{{{\displaystyle T}}_{7}-{{\displaystyle T}}_{2}}$ | ${\dot{E}}_{2}+{\dot{E}}_{7}={\dot{E}}_{3a}+{\dot{E}}_{8}+{\dot{E}}_{D,LTR}$ | ${\dot{C}}_{2}+{\dot{C}}_{7}+{\dot{Z}}_{LTR}={\dot{C}}_{3a}+{\dot{C}}_{8}$ ${c}_{7}={c}_{8}$ |

Superheater | ${\dot{m}}_{8a}{h}_{8a}+{\dot{m}}_{12}{h}_{12}={\dot{m}}_{9}{h}_{9}+{\dot{m}}_{14}{h}_{14}$ | ${\dot{E}}_{8a}+{\dot{E}}_{12}={\dot{E}}_{9}+{\dot{E}}_{14}+{\dot{E}}_{D,Sup}$ | ${\dot{C}}_{8a}+{\dot{C}}_{12}+{\dot{Z}}_{Sup}={\dot{C}}_{9}+{\dot{C}}_{14}$ ${c}_{8a}={c}_{9}$ |

Pre-cooler 1 | ${\dot{m}}_{9}{h}_{9}+{\dot{m}}_{23}{h}_{23}={\dot{m}}_{11}{h}_{11}+{\dot{m}}_{10}{h}_{10}$ | ${\dot{E}}_{9}+{\dot{E}}_{23}={\dot{E}}_{10}+{\dot{E}}_{11}+{\dot{E}}_{D,\mathrm{Pr}e1}$ | ${\dot{C}}_{9}+{\dot{C}}_{23}+{\dot{Z}}_{\mathrm{Pr}e1}={\dot{C}}_{10}+{\dot{C}}_{11}$ ${c}_{9}={c}_{10}$ |

Pre-cooler 2 | ${\dot{m}}_{1}{h}_{1}+{\dot{m}}_{25a}{h}_{25a}={\dot{m}}_{10}{h}_{10}+{\dot{m}}_{24a}{h}_{24a}$ | ${\dot{E}}_{10}+{\dot{E}}_{24a}={\dot{E}}_{1}+{\dot{E}}_{25a}+{\dot{E}}_{D,\mathrm{Pr}e2}$ ${\dot{E}}_{25a}={\dot{E}}_{24a}+{\dot{E}}_{L,\mathrm{Pr}e2}$ | ${\dot{C}}_{10}+{\dot{C}}_{24a}+{\dot{Z}}_{\mathrm{Pr}e2}={\dot{C}}_{1}+{\dot{C}}_{25a}$ ${c}_{10}={c}_{1},{\dot{C}}_{24a}=0$ |

Separator | ${\dot{m}}_{11}{h}_{11}={\dot{m}}_{12}{h}_{12}+{\dot{m}}_{13}{h}_{13}$ ${\dot{m}}_{11}{x}_{11}={\dot{m}}_{12}{x}_{12}+{\dot{m}}_{13}{x}_{13}$ | ${\dot{E}}_{11}={\dot{E}}_{12}+{\dot{E}}_{13}+{\dot{E}}_{D,Sep}$ | ${\dot{C}}_{11}+{\dot{Z}}_{Sep}={\dot{C}}_{12}+{\dot{C}}_{13}$ ${c}_{12}={c}_{13}$ |

KCHTR | ${\dot{m}}_{13}{h}_{13}+{\dot{m}}_{22}{h}_{22}={\dot{m}}_{23}{h}_{23}+{\dot{m}}_{16}{h}_{16}$ | ${\dot{E}}_{13}+{\dot{E}}_{22}={\dot{E}}_{16}+{\dot{E}}_{23}+{\dot{E}}_{D,KCHTR}$ | ${\dot{C}}_{13}+{\dot{C}}_{22}+{\dot{Z}}_{KCHTR}={\dot{C}}_{16}+{\dot{C}}_{23}$ ${c}_{13}={c}_{16}$ |

KCLTR | ${\dot{m}}_{18}{h}_{18}+{\dot{m}}_{21}{h}_{21}={\dot{m}}_{19}{h}_{19}+{\dot{m}}_{22}{h}_{22}$ | ${\dot{E}}_{18}+{\dot{E}}_{21}={\dot{E}}_{19}+{\dot{E}}_{22}+{\dot{E}}_{D,KCLTR}$ | ${\dot{C}}_{18}+{\dot{C}}_{21}+{\dot{Z}}_{KCLTR}={\dot{C}}_{19}+{\dot{C}}_{22}$ ${c}_{18}={c}_{19}$ |

Mixer and Valve | ${\dot{m}}_{18}{h}_{18}={\dot{m}}_{15}{h}_{15}+{\dot{m}}_{16}{h}_{16}$ | ${\dot{E}}_{15}+{\dot{E}}_{16}={\dot{E}}_{18}+{\dot{E}}_{D,Mixer}+{\dot{E}}_{D,V}$ | ${\dot{C}}_{15}+{\dot{C}}_{16}+{\dot{Z}}_{Mixer}+{\dot{Z}}_{V}={\dot{C}}_{18}$ |

Pump | ${\dot{m}}_{20}{h}_{20}+{\dot{W}}_{Pump}={\dot{m}}_{21}{h}_{21}$ ${\eta}_{P}=({h}_{21s}-{h}_{20})/({h}_{21}-{h}_{20})$ | ${\dot{E}}_{20}+{\dot{W}}_{Pump}={\dot{E}}_{21}+{\dot{E}}_{D,Pump}$ | ${\dot{C}}_{20}+{\dot{C}}_{Pump}+{\dot{Z}}_{Pump}={\dot{C}}_{21}$ ${c}_{Pump}={c}_{Turbine}$ |

Turbine | ${\dot{m}}_{14}{h}_{14}={\dot{W}}_{Turbine}+{\dot{m}}_{15}{h}_{15}$ ${\eta}_{T}=({h}_{14}-{h}_{15})/({h}_{14}-{h}_{15s})$ | ${\dot{E}}_{14}={\dot{W}}_{Turbine}+{\dot{E}}_{15}+{\dot{E}}_{D,Turbine}$ | ${\dot{C}}_{14}+{\dot{Z}}_{Turbine}={\dot{C}}_{15}+{\dot{C}}_{Turbine}$ ${c}_{14}={c}_{15}$ |

Condenser | ${\dot{m}}_{20}{h}_{20}+{\dot{m}}_{25b}{h}_{25b}={\dot{m}}_{19}{h}_{19}+{\dot{m}}_{24b}{h}_{24b}$ | ${\dot{E}}_{19}+{\dot{E}}_{24b}={\dot{E}}_{20}+{\dot{E}}_{25b}+{\dot{E}}_{D,Cond}$ ${\dot{E}}_{25b}={\dot{E}}_{24b}+{\dot{E}}_{L,Cond}$ | ${\dot{C}}_{19}+{\dot{C}}_{24b}+{\dot{Z}}_{Cond}={\dot{C}}_{20}+{\dot{C}}_{25b}$ ${c}_{19}={c}_{20},{\dot{C}}_{24b}=0$ |

State | T (K) | P (bar) | $\dot{\mathit{m}}\left(\frac{\mathbf{kg}}{\mathbf{s}}\right)$ | ||||||
---|---|---|---|---|---|---|---|---|---|

Present Work Ref. [22] Error (%) | Present Work Ref. [22] Error (%) | Present Work Ref. [22] Error (%) | |||||||

1 | 305.2 | 305.2 | 0 | 74 | 74 | 0 | 2098 | 2096 | 0.095 |

2 | 370.2 | 370.0 | 0.054 | 207.2 | 207.2 | 0 | 2098 | 2096 | 0.095 |

3 | 503.1 | 502.9 | 0.039 | 207.2 | 207.2 | 0 | 2939 | 2938 | 0.034 |

4 | 657.6 | 657.5 | 0.015 | 207.2 | 207.2 | 0 | 2939 | 2938 | 0.034 |

5 | 823.2 | 823.2 | 0 | 207.2 | 207.2 | 0 | 2939 | 2938 | 0.034 |

6 | 701.2 | 701.2 | 0 | 74 | 74 | 0 | 2939 | 2938 | 0.034 |

7 | 530.8 | 530.6 | 0.037 | 74 | 74 | 0 | 2939 | 2938 | 0.034 |

8 | 392.7 | 392.5 | 0.050 | 74 | 74 | 0 | 2939 | 2938 | 0.034 |

9 | 323.8 | 323.8 | 0 | 74 | 74 | 0 | 2098 | 2096 | 0.095 |

12 | 313.2 | 313.2 | 0 | 2.496 | 2.5 | 0.160 | 2072 | 2071 | 0.048 |

13 | 313.9 | 313.9 | 0 | 15.58 | 15.49 | 0.581 | 2072 | 2071 | 0.048 |

14 | 382.7 | 382.5 | 0.052 | 15.58 | 15.49 | 0.581 | 2072 | 2071 | 0.048 |

15 | 353.2 | 353.2 | 0 | 7.908 | 7.89 | 0.228 | 2072 | 2071 | 0.048 |

16 | 353.2 | 353.2 | 0 | 7.908 | 7.89 | 0.228 | 622.4 | 618.8 | 0.581 |

17 | 324.2 | 324.3 | 0.031 | 2.496 | 2.5 | 0.160 | 622.4 | 618.8 | 0.581 |

18 | 353.2 | 353.2 | 0 | 7.908 | 7.89 | 0.228 | 1449 | 1452 | 0.207 |

19 | 313.2 | 313.2 | 0 | 2.496 | 2.5 | 0.160 | 1449 | 1452 | 0.207 |

20 | 313.2 | 313.2 | 0 | 2.496 | 2.5 | 0.160 | 2072 | 2071 | 0.048 |

State | T (K) | P (bar) | $\dot{\mathit{m}}\left(\frac{\mathbf{kg}}{\mathbf{s}}\right)$ | ||||||
---|---|---|---|---|---|---|---|---|---|

Present Work Ref. [22] Error (%) | Present Work Ref. [22] Error (%) | Present Work Ref. [22] Error (%) | |||||||

1 | 305.2 | 305.2 | 0 | 74 | 74 | 0 | 2084 | 2082 | 0.096 |

2 | 369.5 | 369.3 | 0.054 | 207.2 | 207.2 | 0 | 2084 | 2082 | 0.096 |

3 | 498.8 | 498.6 | 0.040 | 207.2 | 207.2 | 0 | 2917 | 2916 | 0.034 |

4 | 656.3 | 656.3 | 0 | 207.2 | 207.2 | 0 | 2917 | 2916 | 0.034 |

5 | 823.2 | 823.2 | 0 | 207.2 | 207.2 | 0 | 2917 | 2916 | 0.034 |

6 | 701.2 | 701.2 | 0 | 74 | 74 | 0 | 2917 | 2916 | 0.034 |

7 | 527.2 | 527.0 | 0.038 | 74 | 74 | 0 | 2917 | 2916 | 0.034 |

8 | 391.6 | 391.4 | 0.051 | 74 | 74 | 0 | 2917 | 2916 | 0.034 |

9 | 357.9 | 358.2 | 0.083 | 74 | 74 | 0 | 2084 | 2082 | 0.096 |

12 | 303.2 | 303.2 | 0 | 1.097 | 1.10 | 0.273 | 440 | 436.6 | 0.778 |

13 | 303.4 | 303.4 | 0 | 6.252 | 6.24 | 0.192 | 440 | 436.6 | 0.778 |

14 | 363.2 | 363.2 | 0 | 6.252 | 6.24 | 0.192 | 440 | 436.6 | 0.778 |

15 | 318.2 | 317.5 | 0.220 | 1.097 | 1.10 | 0.273 | 440 | 436.6 | 0.778 |

State | T (K) | P (bar) | $\dot{\mathit{m}}\left(\frac{\mathbf{kg}}{\mathbf{s}}\right)$ | ||||||
---|---|---|---|---|---|---|---|---|---|

Present Work Ref. [22] Error (%) | Present Work Ref. [22] Error (%) | Present Work Ref. [22] Error (%) | |||||||

1 | 308.2 | 308.2 | 0 | 74 | 74 | 0 | 2187 | 2187 | 0 |

2 | 385.9 | 385.9 | 0 | 214.6 | 214.6 | 0 | 2187 | 2187 | 0 |

3 | 526.5 | 526.5 | 0 | 214.6 | 214.6 | 0 | 2980 | 2980 | 0 |

4 | 660.2 | 660.2 | 0 | 214.6 | 214.6 | 0 | 2980 | 2980 | 0 |

5 | 823.2 | 823.2 | 0 | 214.6 | 214.6 | 0 | 2980 | 2980 | 0 |

6 | 697.2 | 697.2 | 0 | 74 | 74 | 0 | 2980 | 2980 | 0 |

7 | 550.4 | 550.4 | 0 | 74 | 74 | 0 | 2980 | 2980 | 0 |

8 | 409 | 408.9 | 0.024 | 74 | 74 | 0 | 2980 | 2980 | 0 |

9 | 398.3 | 398.3 | 0 | 74 | 74 | 0 | 2187 | 2187 | 0 |

12 | 338.9 | 338.9 | 0 | 74 | 74 | 0 | 2187 | 2187 | 0 |

13 | 353 | 353 | 0 | 32.47 | 32.47 | 0 | 191.4 | 191.4 | 0 |

14 | 353 | 353 | 0 | 32.47 | 32.47 | 0 | 146.3 | 146.3 | 0 |

15 | 353 | 353 | 0 | 32.47 | 32.47 | 0 | 45.13 | 45.13 | 0 |

16 | 407.9 | 407.9 | 0 | 32.47 | 32.47 | 0 | 146.3 | 146.3 | 0 |

17 | 323.8 | 323.8 | 0 | 10.47 | 10.47 | 0 | 146.3 | 146.3 | 0 |

18 | 309 | 309.1 | 0.032 | 32.47 | 32.47 | 0 | 45.13 | 45.13 | 0 |

19 | 307.1 | 307.2 | 0.032 | 10.47 | 10.47 | 0 | 45.13 | 45.13 | 0 |

20 | 309 | 309.1 | 0.032 | 10.47 | 10.47 | 0 | 191.4 | 191.4 | 0 |

21 | 308.5 | 308.6 | 0.032 | 10.47 | 10.47 | 0 | 191.4 | 191.4 | 0 |

22 | 301.2 | 301.2 | 0 | 10.47 | 10.47 | 0 | 191.4 | 191.4 | 0 |

23 | 301.8 | 301.8 | 0 | 32.47 | 32.47 | 0 | 191.4 | 191.4 | 0 |

24 | 304 | 304.1 | 0.033 | 32.47 | 32.47 | 0 | 191.4 | 191.4 | 0 |

25 | 314.5 | 314.6 | 0.031 | 32.47 | 32.47 | 0 | 191.4 | 191.4 | 0 |

**Table 9.**Comparison of results of present paper with previously published results from exergy, total product unit cost and sustainability perspectives with the same input data.

Cycle | Working Fluid | ${\mathit{\eta}}_{\mathit{e}\mathit{x}}(\mathit{\%})$ | ${\mathit{c}}_{\mathit{P},\mathit{t}\mathit{o}\mathit{t}}(\mathit{\$}/\mathit{G}\mathit{J})$ | Sustainability Index (SI) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Present work | Ref. | Error (%) | Present work | Ref. | Error (%) | Present work | Ref. | Error (%) | ||

SCRB/OFC | R245fa | 58.02 | 58.02 [22] | 0 | 13.08 | 12.64 [22] | 3.48 | 2.439 | -- | -- |

SCRB/ORC | R123 | 59.90 | 59.92 [11] | 0.03 | 13.04 | 9.7 [11] | 34.43 | 2.514 | 1.57 [18] | 60.12 |

SCRB/KC | Ammonia-water | 59.83 | 59.83 [24] | 0 | 12.97 | 12.02 [24] | 7.9 | 2.5 - | -- | -- |

**Table 10.**Results for thermodynamic and economic optimal design (TOD and EOD) cases for SCRB/OFC, SCRB/ORC and SCRB/KC cycles.

Parameter | SCRB/OFC | SCRB/ORC | SCRB/KC | |||
---|---|---|---|---|---|---|

TOD | EOD | TOD | EOD | TOD | EOD | |

Pr_{c} | 4.2 | 3.582 | 4.2 | 3.722 | 4.2 | 3.345 |

T_{5} (°C) | 750 | 750 | 750 | 750 | 750 | 750 |

$\Delta {T}_{He}or\Delta {T}_{\mathrm{Pr}e1}$ (K) | 8 | 8 | 8 | 8 | 8 | 8 |

${{\displaystyle \eta}}_{ex}$ (%) | 70.38 | 69.52 | 71.31 | 70.49 | 70.36 | 69.22 |

${{\displaystyle c}}_{P,tot}$ ($/GJ) | 10.76 | 10.70 | 10.65 | 10.62 | 10.96 | 10.83 |

${{\displaystyle \dot{W}}}_{net,tot}$ (MW) | 305.0 | 301.3 | 309.0 | 305.5 | 304.9 | 300.0 |

${{\displaystyle \dot{W}}}_{net,SCRBC}$ (MW) | 290.7 | 288.4 | 290.7 | 289.2 | 283.2 | 280.9 |

${{\displaystyle \dot{W}}}_{net,Bot}$ (MW) | 14.28 | 12.82 | 18.30 | 16.25 | 21.68 | 19.06 |

${{\displaystyle \dot{m}}}_{CO2}$ (kg/s) | 1944 | 2046 | 1944 | 2020 | 1987 | 2141 |

${{\displaystyle \dot{m}}}_{Bot}$ (kg/s) | 801.9 | 898.2 | 1241 | 1102 | 187.7 | 177.5 |

${{\displaystyle \dot{Z}}}_{tot}$ ($/h) | 8612 | 8399 | 8643 | 8469 | 8821 | 8488 |

${{\displaystyle \dot{E}}}_{D,tot}$ (MW) | 125.0 | 128.7 | 122.0 | 125.2 | 127.8 | 132.7 |

${{\displaystyle \dot{E}}}_{L,tot}$ (MW) | 3.348 | 3.444 | 2.349 | 2.697 | 0.640 | 0.651 |

x | 0.255 | 0.232 | 0.255 | 0.238 | 0.240 | 0.197 |

SI | 3.467 | 3.367 | 3.553 | 3.464 | 3.396 | 3.292 |

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## Share and Cite

**MDPI and ACS Style**

Seyed Mahmoudi, S.M.; Ghiami Sardroud, R.; Sadeghi, M.; Rosen, M.A.
Integration of Supercritical CO_{2} Recompression Brayton Cycle with Organic Rankine/Flash and Kalina Cycles: Thermoeconomic Comparison. *Sustainability* **2022**, *14*, 8769.
https://doi.org/10.3390/su14148769

**AMA Style**

Seyed Mahmoudi SM, Ghiami Sardroud R, Sadeghi M, Rosen MA.
Integration of Supercritical CO_{2} Recompression Brayton Cycle with Organic Rankine/Flash and Kalina Cycles: Thermoeconomic Comparison. *Sustainability*. 2022; 14(14):8769.
https://doi.org/10.3390/su14148769

**Chicago/Turabian Style**

Seyed Mahmoudi, Seyed Mohammad, Ramin Ghiami Sardroud, Mohsen Sadeghi, and Marc A. Rosen.
2022. "Integration of Supercritical CO_{2} Recompression Brayton Cycle with Organic Rankine/Flash and Kalina Cycles: Thermoeconomic Comparison" *Sustainability* 14, no. 14: 8769.
https://doi.org/10.3390/su14148769