# Thermoeconomic Analysis and Optimization of a New Combined Supercritical Carbon Dioxide Recompression Brayton/Kalina Cycle

^{1}

^{2}

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## Abstract

**:**

_{2}recompression Brayton/Kalina cycle (SCRB/KC) is proposed. In the proposed system, waste heat from a supercritical CO

_{2}recompression Brayton cycle (SCRBC) is recovered by a Kalina cycle (KC) to generate additional electrical power. The performances of the two cycles are simulated and compared using mass, energy and exergy balances of the overall systems and their components. Using the SPECO (Specific Exergy Costing) approach and employing selected cost balance equations for the components of each system, the total product unit costs of the cycles are obtained. Parametric studies are performed to investigate the effects on the SCRB/KC and SCRBC thermodynamic and thermoeconomic performances of key decision parameters. In addition, considering the exergy efficiency and total product unit cost as criteria, optimization is performed for the SCRBC and SCRB/KC using Engineering Equation Solver software. The results indicate that the maximum exergy efficiency of the SCRB/KC is higher than that of the SCRBC by up to 10%, and that the minimum total product unit cost of the SCRB/KC is lower than that of the SCRBC by up to 4.9%.

## 1. Introduction

_{2}(S-CO

_{2}) cycle is considered promising as it is simple, compact, secure and economic [2]. The cycle working fluid, carbon dioxide, is a non-toxic and non-combustible material [3]. Another advantage of CO

_{2}is the sudden change of its thermophysical properties at its near critical point. This characteristic brings about a lower value of compression work so that the efficiency of the S-CO

_{2}cycle is high [2]. The cycle was first proposed by Feher and Angelino in 1968 [4,5]. Dostal in 2004 compared the performances of a S-CO

_{2}Brayton cycle and a Rankine cycle of similar generation capacity and reported a significantly reduced size of turbomachinery and higher efficiencies for the S-CO

_{2}cycle [6]. Having used a low-grade heat source, Cayer et al. performed a detailed analysis for a carbon dioxide transcritical power cycle [7]. They reported the work in four steps: energy analysis, exergy analysis, finite size thermodynamics and heat exchanger surface calculation. They concluded that there exists an optimum high pressure for each of the mentioned steps. Angelino and Invernizzi used low-temperature liquefied natural gas (LNG) as a heat sink in proposing new configurations for the CO

_{2}power cycle in order to improve the system performance [8]. Sarkar performed an exergy analysis for the SCRBC and optimized its performance [9]. He reported that the irreversibilities in heat exchangers are higher than those in turbo-machinery and that the high temperature regenerator (HTR) is more effective than the low temperature regenerator (LTR) at raising the cycle efficiency. In another paper, Sarkar and Bhattacharyya examined the effect of reheating on SCRBC performance and studied the optimized condition of the cycle when the operating parameters and component performance are changed [10]. Wang et al. assessed the effects on the optimized condition of the S-CO

_{2}cycle of varying thermodynamic parameters. They used a genetic algorithm and an artificial neural network for the optimization [11]. Yari and Sirusazar combined the SCRBC with a transcritical CO

_{2}cycle for performance enhancement [12]. Jeong et al. optimized the performance of a S-CO

_{2}-based binary gas mixture Brayton cycle with a sodium-cooled fast reactor. They selected a mixture of CO

_{2}and some other gases as the working fluid so that the critical point of the working fluid is shifted [13]. Yoon et al. concluded that cycle simplicity, high efficiency and compact turbomachinery and heat exchangers are significant advantages for the S-CO

_{2}cycle [14]. They stated that the S-CO

_{2}cycle is appropriate for small and medium size water-cooled nuclear reactors. Thermodynamic analyses were performed by Kim et al. for a transcritical CO

_{2}cycle utilizing both low and high temperature heat sources [15]. Floyd et al. described the off-design response of a SCRBC coupled with a sodium fast reactor as the heat sink temperature changes [16]. Singh et al. proposed an extremum-seeking controller to enhance the performance of a direct heated S-CO

_{2}closed loop Brayton cycle for a fluctuating solar input energy and ambient temperature [17]. Moullec showed that an efficiency of 50% can be achieved for a coal power plant with a S-CO

_{2}Brayton cycle when the maximum cycle temperature and pressure are 893 K and 300 bar, respectively [18]. Nithyanandam and Pitchumani investigated the thermodynamic and economic performances of a concentrating solar power (CSP) power-tower system utilizing Rankine and S-CO

_{2}cycles integrated with encapsulated phase change material for thermal energy storage or thermal energy storage with embedded heat pipes [19].

_{2}and traditional working fluids, and pure CO

_{2}[20]. They reported that, when zeotropic mixtures are used, the pressure level in the cycle is reduced and the thermal efficiency is improved. Akbari and Mahmoudi optimized the thermodynamic and thermoeconomic performance of a combined cycle consisting of a SCRBC and an Organic Rankine cycle (ORC) [2]. Using the turbine bleed gas for regenerative heating, Mondal and De showed that a transcritical CO

_{2}power cycle results in higher 1st and 2nd law efficiencies [21]. Hu et al. compared the performance of a supercritical gas Brayton cycle for several types of working fluids such as CO

_{2}-based binary mixtures and pure carbon dioxide. They found higher efficiencies for both CO

_{2}-He and CO

_{2}-Kr mixtures [22]. Energy and exergy analyses were carried out for four different S-CO

_{2}Brayton cycle configurations integrated with solar central receivers by Padilla et al. [23]. They reported that the recompression cycle with primary compression intercooling attained the highest thermal efficiency. Gholamian et al. proposed and analyzed a new cogeneration system combining a biomass fuelled gas turbine and a S-CO

_{2}cycle coupled with a domestic water heater. They showed that the exergy efficiency and CO

_{2}emissions are higher for the cogeneration system, compared to the stand alone gas turbine and power generation systems [24].

_{2}recompression Brayton/Kalina cycle (SCRB/KC) in which waste heat from the pre-cooler of the SCRBC is utilized to drive a KC. The investigation is performed from the viewpoints of both thermodynamics and thermoeconomics. Through a parametric study, the influence of some important decision parameters on the second law efficiency and the product unit cost of the SCRBC and SCRB/KC are studied. Finally, the thermodynamic and thermoeconomic performances of the SCRBC and the SCRB/KC are optimized. The objective is to improve understanding of the new system and we expect that the obtained results will be useful in designing a more efficient heat recovery system for nuclear power plants.

## 2. System Description and Assumptions

_{2}exiting pre-cooler1 rejects additional heat in pre-cooler2 before being compressed in compressor1. The compressed CO

_{2}leaving compressor1 is heated in the LTR before mixing with the CO

_{2}stream exiting compressor2. The mixture (stream 10) flows to the HTR where it is heated before entering the reactor.

_{2}before passing to the separator. In the separator the working fluid is separated into a rich ammonia–water mixture saturated vapor (stream 12) and a poor ammonia–water mixture saturated liquid (stream 13). The saturated vapor is then superheated in the superheater by the CO

_{2}before entering turbine2. The saturated ammonia–water liquid mixture flows to the KCHTR where it is cooled before passing to the expansion valve. The stream exiting the expansion valve flows to the mixer and mixes with the stream exiting turbine2. The mixture then passes to the KCLTR, where it rejects heat, before flowing to the condenser, completing the Kalina cycle.

- The system operation is at steady state.
- Pressure drops in all components and connecting lines, except turbines, compressors and the pump, are negligible [2].
- The turbines, the pump and the compressors are taken to have specific isentropic efficiencies.
- No changes occur in kinetic and potential energies.
- The cooling water entering the pre-cooler and the condenser is at environmental conditions.
- The LTR and HTR have specific effectiveness values.
- The state of the ammonia–water solution is saturated at both the condenser and separator exits.

## 3. Thermodynamic Analysis

_{2}, however, the chemical exergy does not change from one point to another and, therefore, it is not taken into account.

## 4. Thermoeconomic Analysis

## 5. Results and Discussion

#### 5.1. Parametric Study

_{C}), pump pressure ratio (PR

_{p}), minimum temperature difference in the superheater ($\Delta {\mathrm{T}}_{\mathrm{s}\mathrm{u}\mathrm{p}}$), ammonia concentration in the ammonia–water mixture leaving the condenser (X

_{20}), pinch point temperature difference in pre-cooler1 ($\Delta {\mathrm{T}}_{\mathrm{Pinch}}$), and temperature of ammonia–water solution exiting pre-cooler1 (T

_{11}). For the SCRBC, the only decision parameter is taken to be the compressor pressure ratio (PR

_{C}).

_{C}) on the exergy efficiency (${\eta}_{ex,tot}$) and total product unit cost (c

_{p,tot}) of the SCRBC and the SCRB/KC.

_{C}at which the exergy efficiency of the SCRBC or SCRB/KC is maximized. This is justified if we consider that, as the PR

_{C}increases, the net specific work output for the SCRBC increases and the CO

_{2}mass flow rate decreases, due to the increase in the specific enthalpy difference across the reactor [2]. The increase in net specific work and the decrease in CO

_{2}mass flow rate lead to the maximization of the net produced power for the SCRBC as PR

_{C}increases. As the exergy input to the cycle is constant the variation of exergy efficiency with PR

_{C}is justified for the SCRBC. A similar discussion can be made for the SCRB/KC noting that the net specific work of the Kalina cycle increases steadily with increasing PR

_{C}. It is clear in Figure 2a that at higher PR

_{C}values the exergy efficiency of the SCRB/KC is flatter than that of the SCRBC. This can be explained if we consider that as the PR

_{C}increases the temperature at the inlets of the superheater and pre-cooler1 increase resulting in an increase in the KC exergy input and consequently a higher KC output power. In addition, the increase in the KC power output, because of an increase in PR

_{C}, leads to a higher optimum PR

_{C}for the SCRB/KC compared to the corresponding value for the SCRBC, as shown in Figure 2a.

_{C}for both the SCRBC and the SCRB/KC. This is expected based on Equation (15). However, for both cycles, the optimum PR

_{C}value at which c

_{p,tot}is minimized is less than the corresponding value at which the exergy efficiency is maximized. This can be explained considering the decrease of associated costs with decreasing PR

_{C}. It is seen in Figure 2 that the differences in optimum values of PR

_{C}for the SCRBC and the SCRB/KC, for maximum exergy efficiency, are higher than the corresponding values for minimum c

_{p,tot}.

_{p,tot}) with the pump pressure ratio (PR

_{P}) is shown in Figure 3, for the SCRB/KC. Although the range of variation for the two parameters is small, the trend is interesting. The value of PR

_{P}at which the exergy efficiency is maximized is seen in Figure 3 to be the same as that at which the total product unit cost is minimized. This point indicates that, at a given value of PR

_{P}, the changes in c

_{p,tot}are related only to the net produced power for the KC.

_{b}changes, is actually related to the KC performance. This can be explained by noting that an increase in the PR

_{P}causes a decrease in the pre-cooler1 outlet vapor mass fraction (q

_{11}). This decrease reduces the turbine2 inlet mass flow rate. On the other hand, the increase in PR

_{P}brings about a higher specific work for the KC so that the product of the specific work and the mass flow rate is maximized at a specific value of PR

_{P}. This maximization leads to the maximization for exergy efficiency and the minimization for the total product unit cost for the SCRB/KC.

_{p,tot}) of the temperature of the ammonia–water solution at the pre-cooler1 outlet (T

_{11}) for the SCRB/KC. Although Figure 4 shows that the exergy efficiency is maximized and the total product unit cost is minimized with changing T

_{11}, the variations in the objectives are small.

_{11}results in a lower ammonia–water mass flow rate in the KC, but a higher vapor mass fraction (${\mathrm{q}}_{11}={\dot{m}}_{vapor}/{\dot{m}}_{total}$) in the pre-cooler1 outlet, so that the turbine2 mass flow rate remains almost constant, i.e., the produced power in the KC is almost constant. Figure 5 shows the variations in the exergy efficiency and total product unit cost of the SCRB/KC as $\Delta {\mathrm{T}}_{\mathrm{sup}}$ changes.

_{sup}increases, the exergy efficiency increases and the total product unit cost is minimized. In fact an increase in the ΔT

_{sup}causes a decrease in the output power of the KC (because of lower heat recovery in the supeheater) and, consequently, the exergy efficiency of the SCRB/KC is reduced. However, the increase in ΔT

_{sup}, brings about a reduction in the superheater capital investment cost rate (${\dot{Z}}_{SH}$) due to the reduction in the required heat transfer area. Accordingly, as indicated in Figure 5, there exists an optimum value for ΔT

_{sup}at which the total product unit cost is minimized.

_{pinch}due to higher values of power generated by the KC. The justification for results in Figure 6 is similar to that for those in Figure 5. However the increase in the cost rate associated with the exergy destruction in pre-cooler1 is dominant so that no minimum value is observed for c

_{p,tot}.

_{20}) on the exergy efficiency and total product unit cost of the SCRB/KC. Figure 7 indicates that as X

_{20}increases the exergy efficiency increases and the total product unit cost decreases. This is justified if we consider that as X

_{20}increases the exergy destruction in pre-cooler1 and the superheater decreases because of the reduced value of the temperature difference in these two components. Although the reduced value of temperature difference is expected to increase the capital investment cost rate associated with the above-mentioned two components, the increase in produced power is dominant.

#### 5.2. Optimization

_{C}). Thus, the Quadratic Approximations method in the EES software is used to optimize the performance of the SCRBC. For the SCRB/KC, however, five decision parameters are identified, i.e., pump pressure ratio (PR

_{p}), output stream temperature (ammonia–water) of pre-cooler1 (T

_{11}), pinch point temperature difference in pre-cooler1 ($\Delta {\mathrm{T}}_{\mathrm{Pinch}}$), minimum temperature difference in the superheater ($\Delta {\mathrm{T}}_{sup}$), and ammonia concentration in the ammonia–water mixture leaving the condenser (X

_{20}). Therefore, the direct search method in the EES software is used to optimize the SCRB/KC performance. The optimization for both the SCRBC and SCRB/KC are performed from the viewpoints of either thermodynamics or thermoeconomics as follows:

#### Optimization Results

_{C}) lower than the value at which the exergy efficiency is maximized. In fact, the lower value of PR

_{C}brings about a lower value of $\dot{Z}$ and the lower value of $\dot{Z}$ results in a lower value of f. Therefore, the suggestion of reducing f for turbine1, as made in the discussion about the results in Table 7, is confirmed here. In addition, Table 8 indicates that the CO

_{2}mass flow rate is higher for the EOD case as expected because of the lower value of PR

_{C}for the EOD case [2]. Referring to Table 8 and comparing the EOD and TOD cases for the SCRBC, a reduction of about 3% in the total product unit cost is obtained at the expense of about a 3.3% reduction in the exergy efficiency. Table 8 also indicates that the total capital cost rate $({\dot{Z}}_{tot})$ for the SCRBC, when it is optimized for minimum total product unit cost, is reduced by 6.7% compared to the case when it is optimized for maximum exergy efficiency.

_{p,tot}values as the KC is coupled with the SCRBC. The comparison shows that the exergy efficiency is improved by 10% and 9.2% for the TOD and the EOD cases, respectively. Similarly, a reduction of 4.2% and 4.9% in c

_{p,tot}is observed for the TOD and the EOD cases, respectively. In fact, when the KC is combined with the SCRBC, ${\dot{Z}}_{tot}$ is increased by 6.7% and 4.6% for the TOD and EOD cases, respectively. However, the increases of 10% and 9.2% in the net output power (see Table 8) for the TOD and EOD cases, respectively, results in a reduction of c

_{p},

_{tot}.

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

## Nomenclature

A | heat transfer area (m^{2}) |

$\dot{\mathit{C}}$ | cost rate ($/h) |

c | cost per exergy unit ($/GJ) |

c_{p,tot} | total product unit cost ($/GJ) |

$\dot{\mathit{E}}$ | exergy rate (kW) |

e | specific exergy (kJ/kg) |

h | specific enthalpy (kJ/kg) |

i_{r} | interest rate |

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

P | pressure (bar) |

PR | pressure ratio |

PR_{c} | compressor pressure ratio |

PR_{p} | pump pressure ratio |

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

s | specific entropy (kJ/kg K) |

T | temperature (°C, K) |

T_{11} | pre-cooler1 outlet temperature (°C, K) |

${\dot{\mathit{W}}}_{\mathit{C}}$ | compressor power (kW) |

${\dot{\mathit{W}}}_{\mathit{P}}$ | pump power (kW) |

${\dot{\mathit{W}}}_{\mathit{T}}$ | turbine power (kW) |

x | recompressed mass fraction |

X | ammonia concentration |

Z | capital cost of a component ($) |

$\dot{\mathit{Z}}$ | capital cost rate ($/h) |

## Subscripts and Abbreviations

0 | dead (environmental) state |

1, 2, 3… | state points |

C | compressor |

ch | chemical |

CI | capital investment |

cond | condenser |

CRF | capital recovery factor |

D | destruction |

EOD | economic optimal design |

F | fuel |

HTR | high temperature recuperator |

LTR | low temperature recuperator |

OM | operation and maintenance |

p | pump, product |

pc | pre-cooler |

ph | physical |

R | reactor |

sup | superheater |

T | turbine |

TOD | thermodynamic optimal design |

## Greek Symbols

$\mathit{\u03f5}$ | effectiveness |

${\mathit{\eta}}_{\mathit{t}\mathit{h}}$ | thermal efficiency |

${\mathit{\eta}}_{\mathit{e}\mathit{x}}$ | exergy efficiency |

${\mathit{\eta}}_{\mathit{i}\mathit{s}}$ | isentropic efficiency |

ΔT | minimum temperature difference |

ΔT_{pinch} | pinch point temperature difference |

## Appendix A

Component | Capital Investment Cost Function |
---|---|

Reactor | ${Z}_{R}={C}_{1}\times {\dot{Q}}_{r}\text{},\text{}{C}_{1}=283\text{}\raisebox{1ex}{$\$$}\!\left/ \!\raisebox{-1ex}{$K{W}_{th}$}\right.$ [2] |

Turbine1 | ${Z}_{T1}=479.34\times {\dot{m}}_{in}\left[\frac{1}{0.93-{\eta}_{t1}}\right]\times \mathrm{ln}\left(P{R}_{c}\right)\times \left(1+{e}^{\left(0.036\times {T}_{2}-54.4\right)}\right)$ [2] |

Compressors | ${Z}_{C1\&2}=71.1\times {\dot{m}}_{in}\left[\frac{1}{0.92-{\eta}_{c}}\right]\times P{R}_{c}\times \mathrm{ln}\left(P{R}_{c}\right)$ [2] |

HTR, LTR, Pre-cooler1 | ${Z}_{k}=2681\times {{A}_{k}}^{0.59}$ [2] |

Condenser, Pre_cooler2 | ${Z}_{k}=2143\times {{A}_{k}}^{0.514}$ [2] |

KCHTR, KCLTR | ${Z}_{k}=2143\times {{A}_{k}}^{0.514}$ [29] |

Superheater | ${Z}_{k}=2681\times {{A}_{k}}^{0.59}$ [29] |

Turbine2 | ${Z}_{T2}=4405\times {{\dot{W}}_{T2}}^{0.7}$ [29] |

Pump | ${Z}_{P}=1120\times {{\dot{W}}_{p}}^{0.8}$ [29] |

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**Figure 1.**Schematic diagram for the proposed supercritical CO

_{2}recompression Brayton/Kalina cycle (SCRB/KC).

**Figure 2.**Effect of compressor pressure ratio (PR

_{C}) on: (

**a**) exergy efficiency; and (

**b**) total product unit cost for the SCRBC and the SCRB/KC with base case values.

**Figure 3.**Effect of pump pressure ratio (PR

_{P}) on exergy efficiency and total product unit cost for the SCRB/KC with base case values.

**Figure 4.**Effect of outlet stream temperature (ammonia–water) of pre-cooler1 (T

_{11}) on exergy efficiency and total product unit cost for the SCRB/KC with base case values.

**Figure 5.**Effect of minimum temperature difference in superheater (ΔT

_{sup}) on the exergy efficiency and total product unit cost for the SCRB/KC for the base case condition.

**Figure 6.**Effect of pinch point temperature difference in pre-cooler1 (ΔT

_{Pinch}) on exergy efficiency and total product unit cost for the SCRB/KC with base case values.

**Figure 7.**Effect of ammonia concentration in the ammonia–water mixture leaving the condenser (X

_{20}) on exergy efficiency and total product unit cost for the SCRB/KC with base case values.

Stream | Temperature (K) | Pressure (Bar) | Ammonia Concentration | Mass Flow Rate | ||||
---|---|---|---|---|---|---|---|---|

Present | Ref. [28] | Present | Ref. [28] | Present | Ref. [28] | Present | Ref. [28] | |

11 | 389.15 | 389.15 | 32.3 | 32.3 | 0.82 | 0.82 | 16.8 | 16.8 |

12 | 389.15 | 389.15 | 32.3 | 32.3 | 0.9718 | 0.97 | 11.27 | 11.4 |

13 | 389.15 | 389.15 | 32.3 | 32.3 | 0.5104 | 0.5 | 5.527 | 5.4 |

14 | 389.15 | - | 32.3 | - | 0.5104 | - | 5.527 | - |

15 | 314.45 | 316.15 | 6.6 | 6.6 | 0.9718 | 0.97 | 11.27 | 11.4 |

16 | 318.44 | 319.15 | 31.3 | 31.3 | 0.5104 | 0.5 | 5.527 | 5.4 |

17 | 318.85 | - | 6.6 | - | 0.5104 | - | 5.527 | - |

18 | 318.44 | 319.15 | 6.6 | 6.6 | 0.82 | 0.82 | 16.8 | 16.8 |

19 | 303.05 | 303.15 | 5.6 | 5.6 | 0.82 | 0.82 | 16.8 | 16.8 |

20 | 281.15 | 281.15 | 4.769 | 4.6 | 0.82 | 0.82 | 16.8 | 16.8 |

21 | 281.59 | 281.15 | 35.3 | 35.3 | 0.82 | 0.82 | 16.8 | 16.8 |

22 | 313.44 | 314.15 | 34.3 | 34.3 | 0.82 | 0.82 | 16.8 | 16.8 |

23 | 336.02 | 336.15 | 33.3 | 33.3 | 0.82 | 0.82 | 16.8 | 16.8 |

Present work | Ref. [28] | |||||||

Net power (kW) | 2201 | 2194.8 |

^{a}X

_{11}= 0.82, $\dot{m}=16.8$ kg/s.

**Table 2.**Economic data used in the simulation [2].

Parameter | Value |
---|---|

${i}_{r}(\%)$ | 12 |

$n\left(\mathrm{year}\right)$ | 20 |

$\tau \left(\mathrm{h}\right)$ | 8000 |

${\gamma}_{k}$ | 0.06 |

Component | Fuel Exergy | Product Exergy |
---|---|---|

Compressor1 | ${\dot{E}}_{29}({\dot{W}}_{C1})$ | ${\dot{E}}_{9}-{\dot{E}}_{8}$ |

LTR | ${\dot{E}}_{4}-{\dot{E}}_{5}$ | ${\dot{E}}_{10a}-{\dot{E}}_{9}$ |

HTR | ${\dot{E}}_{3}-{\dot{E}}_{4}$ | ${\dot{E}}_{1}-{\dot{E}}_{10}$ |

Reactor | ${\dot{E}}_{1}-{\dot{E}}_{core}$ | ${\dot{E}}_{2}$ |

Turbine1 | ${\dot{E}}_{2}-{\dot{E}}_{3}$ | ${\dot{E}}_{27}({\dot{W}}_{T1})$ |

Compressor2 | ${\dot{E}}_{28}({\dot{W}}_{C2})$ | ${\dot{E}}_{10b}-{\dot{E}}_{5b}$ |

Superheater | ${\dot{E}}_{5a}-{\dot{E}}_{6}$ | ${\dot{E}}_{14}-{\dot{E}}_{12}$ |

Pre-cooler1 | ${\dot{E}}_{6}-{\dot{E}}_{7}$ | ${\dot{E}}_{11}-{\dot{E}}_{23}$ |

Pre-cooler2 | ${\dot{E}}_{7}-{\dot{E}}_{8}$ | ${\dot{E}}_{25a}-{\dot{E}}_{24a}$ |

Separator | ${\dot{E}}_{11}$ | ${\dot{E}}_{12}+{\dot{E}}_{13}$ |

Turbine2 | ${\dot{E}}_{14}-{\dot{E}}_{15}$ | ${\dot{E}}_{30}({\dot{W}}_{T2})$ |

Mixer and throttling valve | ${\dot{E}}_{16}+{\dot{E}}_{18}$ | ${\dot{E}}_{20}$ |

KCLTR | ${\dot{E}}_{18}-{\dot{E}}_{19}$ | ${\dot{E}}_{22}-{\dot{E}}_{21}$ |

Condenser | ${\dot{E}}_{19}-{\dot{E}}_{20}$ | ${\dot{E}}_{25b}-{\dot{E}}_{24b}$ |

Pump | ${\dot{E}}_{31}({\dot{W}}_{p})$ | ${\dot{E}}_{21}-{\dot{E}}_{20}$ |

KCHTR | ${\dot{E}}_{13}-{\dot{E}}_{16}$ | ${\dot{E}}_{23}-{\dot{E}}_{22}$ |

Component | Cost Balance | Auxiliary Equations |
---|---|---|

Compressor1 | ${\dot{C}}_{9}={\dot{C}}_{29}+{\dot{C}}_{8}+{\dot{Z}}_{C1}$ | |

LTR | ${\dot{C}}_{5}+{\dot{C}}_{10a}={\dot{C}}_{9}+{\dot{C}}_{4}+{\dot{Z}}_{LTR}$ | $\frac{{\dot{C}}_{4}}{{\dot{E}}_{4}}=\frac{{\dot{C}}_{5}}{{\dot{E}}_{5}}$ or c_{4} = c_{5} |

HTR | ${\dot{C}}_{1}+{\dot{C}}_{4}={\dot{C}}_{10}+{\dot{C}}_{3}+{\dot{Z}}_{HTR}$ | $\frac{{\dot{C}}_{3}}{{\dot{E}}_{3}}=\frac{{\dot{C}}_{4}}{{\dot{E}}_{4}}$ or c_{3} = c_{4} |

Reactor | ${\dot{C}}_{2}={\dot{C}}_{fuel}+{\dot{C}}_{1}+{\dot{Z}}_{R}$ | |

Turbine1 | ${\dot{C}}_{3}+{\dot{C}}_{27}={\dot{C}}_{2}+{\dot{Z}}_{T1}$ | $\frac{{\dot{C}}_{3}}{{\dot{E}}_{3}}=\frac{{\dot{C}}_{2}}{{\dot{E}}_{2}}$ or c_{2} = c_{3} |

Compressor2 | ${\dot{C}}_{9b}={\dot{C}}_{28}+{\dot{C}}_{5b}+{\dot{Z}}_{C2}$ | $\frac{{\dot{C}}_{28}}{{\dot{E}}_{28}}=\frac{{\dot{C}}_{29}}{{\dot{E}}_{29}}$ or c_{28} = c_{29}$\frac{{\dot{C}}_{28}}{{\dot{E}}_{28}}=\frac{{\dot{C}}_{27}}{{\dot{E}}_{27}}$ or c _{28} = c_{27} |

Superheater | ${\dot{C}}_{6}+{\dot{C}}_{14}={\dot{C}}_{12}+{\dot{C}}_{5a}+{\dot{Z}}_{sh}$ | $\frac{{\dot{C}}_{6}}{{\dot{E}}_{6}}=\frac{{\dot{C}}_{5a}}{{\dot{E}}_{5a}}$ or c_{6} = c_{5a} |

Pre-cooler1 | ${\dot{C}}_{7}+{\dot{C}}_{11}={\dot{C}}_{23}+{\dot{C}}_{6}+{\dot{Z}}_{pc1}$ | $\frac{{\dot{C}}_{6}}{{\dot{E}}_{6}}=\frac{{\dot{C}}_{7}}{{\dot{E}}_{7}}$ or c_{6} = c_{7} |

Pre-cooler2 | ${\dot{C}}_{25a}+{\dot{C}}_{8}={\dot{C}}_{24a}+{\dot{C}}_{7}+{\dot{Z}}_{pc2}$ | ${\dot{C}}_{24a}=0$ |

Separator | ${\dot{C}}_{12}+{\dot{C}}_{13}={\dot{C}}_{11}+{\dot{Z}}_{sp}$ | $\frac{{\dot{C}}_{12}}{{\dot{E}}_{12}}=\frac{{\dot{C}}_{13}}{{\dot{E}}_{13}}$ or c_{12} = c_{13} |

Turbine2 | ${\dot{C}}_{30}+{\dot{C}}_{15}={\dot{C}}_{14}+{\dot{Z}}_{T2}$ | $\frac{{\dot{C}}_{14}}{{\dot{E}}_{14}}=\frac{{\dot{C}}_{15}}{{\dot{E}}_{15}}$ or c_{14} = c_{15} |

Mixer and throttling valve | ${\dot{C}}_{18}={\dot{C}}_{15}+{\dot{C}}_{16}+{\dot{Z}}_{valve}+{\dot{Z}}_{mix}$ | |

KCLTR | ${\dot{C}}_{22}+{\dot{C}}_{19}={\dot{C}}_{18}+{\dot{C}}_{21}+{\dot{Z}}_{LTRKC}$ | $\frac{{\dot{C}}_{18}}{{\dot{E}}_{18}}=\frac{{\dot{C}}_{19}}{{\dot{E}}_{19}}$ or c_{18} = c_{19} |

Condenser | ${\dot{C}}_{25a}+{\dot{C}}_{20}={\dot{C}}_{24a}+{\dot{C}}_{19}+{\dot{Z}}_{cond}$ | ${\dot{C}}_{24b}=0$ |

Pump | ${\dot{C}}_{21}={\dot{C}}_{20}+{\dot{C}}_{31}+{\dot{Z}}_{p}$ | $\frac{{\dot{C}}_{30}}{{\dot{E}}_{30}}=\frac{{\dot{C}}_{32}}{{\dot{E}}_{32}}$ or c_{30} = c_{32} |

KCHTR | ${\dot{C}}_{23}+{\dot{C}}_{16}={\dot{C}}_{13}+{\dot{C}}_{22}+{\dot{Z}}_{HTRKC}$ | $\frac{{\dot{C}}_{13}}{{\dot{E}}_{13}}=\frac{{\dot{C}}_{16}}{{\dot{E}}_{16}}$ or c_{13} = c_{16} |

Parameter | Value |
---|---|

${\mathrm{T}}_{\mathrm{o}}\text{}\left(\mathrm{K}\right)$ | 298.15 |

${\mathrm{P}}_{\mathrm{o}}\text{}\left(\mathrm{bar}\right)$ | 1.01 |

${\mathrm{P}}_{1}\text{}\left(\mathrm{bar}\right)$ | 74 ^{a} |

PR_{C} | 2.2–4.2 |

${\mathrm{T}}_{\mathrm{max}}\text{}\left(\mathrm{K}\right)$ | 823.15 ^{a} |

${\mathrm{T}}_{7}\text{}\left(\mathrm{K}\right)$ | 308.15 ^{a} |

${\mathrm{T}}_{\mathrm{r}}\text{}\left(\mathrm{K}\right)$ | 1073.15 ^{a} |

${\eta}_{t1\text{}}(\%)$ | 0.9 ^{a} |

${\eta}_{c}\text{}(\%)$ | 0.85 ^{a} |

${\u03f5}_{LTR}\text{}\mathrm{and}\text{}{\u03f5}_{HTR}$ | 0.86 ^{a} |

${\mathrm{T}}_{11}\text{}\left(\mathrm{K}\right)$ | 348–363 |

X_{20} (%) | 0.95 |

PR_{p} | 2.55–3.65 |

$\Delta {\mathrm{T}}_{\mathrm{pinch}}\text{}\left(\mathrm{K}\right)$ | 3–15 |

$\Delta {\mathrm{T}}_{\mathrm{pinch}\_\mathrm{sup}}\text{}\left(\mathrm{K}\right)$ | 0–15 |

${\eta}_{t2}\text{}(\%)$ | 0.87 |

${\eta}_{p}\text{}(\%)$ | 0.87 |

Fuel cost ($/MWh) | 7.4 ^{a} |

${\dot{\mathrm{Q}}}_{\mathrm{R}}\text{}\left(\mathrm{MW}\right)$ | 600 ^{a} |

^{a}Source [2].

Stream | Temperature (K) | Pressure (Bar) | $\dot{\mathit{m}}\mathbf{\left(}\mathbf{k}\mathbf{g}\mathbf{/}\mathbf{s}\mathbf{\right)}$ | X (%) | e_{ch} (kJ/kg) | e_{ph} (kJ/kg) | Costs | |
---|---|---|---|---|---|---|---|---|

$\dot{\mathit{C}}\text{}\mathbf{(}\frac{\mathbf{\$}}{h}\mathbf{)}$ | $\mathit{c}\text{}\mathbf{(}\frac{\mathbf{\$}}{GJ}\mathbf{)}$ | |||||||

1 | 660.19 | 214.6 | 2980 | - | - | 411.4 | 36,646 | 8.304 |

2 | 823.15 | 214.6 | 2980 | - | - | 531.5 | 43,456 | 7.622 |

3 | 697.15 | 74 | 2980 | - | - | 386.9 | 31,632 | 7.622 |

4 | 550.37 | 74 | 2980 | - | - | 299.7 | 24,503 | 7.622 |

5 | 408.91 | 74 | 2980 | - | - | 239.9 | 19,614 | 7.622 |

5a | 408.91 | 74 | 2187 | - | - | 239.9 | 14,395 | 7.622 |

5b | 408.91 | 74 | 793 | - | - | 239.9 | 5219 | 7.622 |

6 | 398.3 | 74 | 2187 | - | - | 236.6 | 14,197 | 7.622 |

7 | 338.91 | 74 | 2187 | - | - | 221.8 | 13,307 | 7.622 |

8 | 308.15 | 74 | 2187 | - | - | 216.6 | 12,998 | 7.622 |

9 | 385.88 | 214.6 | 2187 | - | - | 255.8 | 16,604 | 8.245 |

10 | 526.48 | 214.6 | 2980 | - | - | 328.4 | 29,480 | 8.368 |

10a | 526.48 | 214.6 | 2187 | - | - | 328.4 | 21,534 | 8.328 |

10b | 526.48 | 214.6 | 793 | - | - | 328.4 | 7947 | 8.477 |

11 | 353 | 32.47 | 191.4 | 0.95 | 18,800 | 392.6 | 130,285 | 9.85 |

12 | 353 | 32.47 | 146.3 | 0.9976 | 19,724 | 447.1 | 104,741 | 9.859 |

13 | 353 | 32.47 | 45.13 | 0.7957 | 15,731 | 216 | 25,544 | 9.859 |

14 | 407.91 | 32.47 | 146.3 | 0.9976 | 19,724 | 493.2 | 104,948 | 9.856 |

15 | 323.81 | 10.47 | 146.3 | 0.9976 | 19,724 | 317.5 | 104,036 | 9.856 |

16 | 309.14 | 32.47 | 45.13 | 0.7957 | 15,731 | 194.7 | 25,509 | 9.859 |

17 | 307.15 | 10.47 | 45.13 | 0.7957 | 15,732 | 191.6 | 25,509 | 9.86 |

18 | 309.14 | 10.47 | 191.4 | 0.95 | 18,801 | 286.6 | 129,545 | 9.848 |

19 | 308.6 | 10.47 | 191.4 | 0.95 | 18,800 | 286.1 | 129,541 | 9.848 |

20 | 301.15 | 10.47 | 191.4 | 0.95 | 18,782 | 267.7 | 129,289 | 9.848 |

21 | 301.83 | 32.47 | 191.4 | 0.95 | 18,782 | 271.2 | 129,338 | 9.85 |

22 | 304.14 | 32.47 | 191.4 | 0.95 | 18,782 | 271.4 | 129,343 | 9.85 |

23 | 314.6 | 32.47 | 191.4 | 0.95 | 18,782 | 273.2 | 129,380 | 9.852 |

24 | 298.15 | 1.013 | 43,018 | - | - | 0 | 0 | 0 |

25 | 299.15 | 1.013 | 43,018 | - | - | 0.006999 | 266.9 | 246.2 |

_{C}= 2.9, ${\mathrm{T}}_{11}=353\text{}\left(\mathrm{K}\right)$, $\Delta {\mathrm{T}}_{\mathrm{sup}}=1\text{}\mathrm{K}$, PR

_{p}= 3.1.

Component | SCRBC | SCRB/KC | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

${\dot{\mathit{E}}}_{\mathit{D}}\left(\mathbf{M}\mathbf{W}\right)$ | ${\dot{\mathit{C}}}_{\mathit{D}}\left(\mathbf{\$}/\mathbf{h}\right)$ | ${\dot{\mathit{Z}}}_{\mathit{k}}\left(\mathbf{\$}/\mathbf{h}\right)$ | ${\dot{\mathit{C}}}_{\mathit{D}}+{\dot{\mathit{Z}}}_{\mathit{k}}+{\dot{\mathit{C}}}_{\mathit{L}}\left(\mathbf{\$}/\mathbf{h}\right)$ | ${\mathit{f}}_{\mathbf{k}}(\%)$ | ${\mathit{r}}_{\mathit{k}}(\%)$ | ${\dot{\mathit{E}}}_{\mathit{D}}\left(\mathbf{M}\mathbf{W}\right)$ | ${\dot{\mathit{C}}}_{\mathit{D}}\left(\mathbf{\$}/\mathbf{h}\right)$ | ${\dot{\mathit{Z}}}_{\mathit{k}}\left(\mathbf{\$}/\mathbf{h}\right)$ | ${\dot{\mathit{C}}}_{\mathit{D}}+{\dot{\mathit{Z}}}_{\mathit{k}}+{\dot{\mathit{C}}}_{\mathit{L}}\left(\mathbf{\$}/\mathbf{h}\right)$ | ${\mathit{f}}_{\mathit{k}}(\%)$ | ${\mathit{r}}_{\mathit{k}}(\%)$ | |

Reactor | 75.43 | 1746 | 5053 | 6799 | 74.32 | 18.55 | 75.43 | 1746 | 5053 | 6799 | 74.32 | 18.55 |

Turbine1 | 19.73 | 541.3 | 2202 | 2743 | 80.27 | 24.31 | 19.73 | 541.3 | 2202 | 2743 | 80.27 | 24.31 |

Compressor1 | 11.28 | 384.9 | 297.9 | 682.8 | 43.63 | 23.36 | 11.28 | 384.9 | 297.9 | 682.8 | 43.63 | 23.36 |

Compressor2 | 6.593 | 224.9 | 108 | 332.9 | 32.45 | 13.9 | 6.593 | 224.9 | 108 | 332.9 | 32.45 | 13.9 |

Pre_cooler2 | 47.91 | 1315 | 8.541 | 1323.6 | 0.6454 | 32.14 | 10.99 | 301.5 | 7.786 | 309.3 | 2.517 | 4190 |

HTR | 12.61 | 346.1 | 37.2 | 383.3 | 9.706 | 5.651 | 12.61 | 346.1 | 37.2 | 383.3 | 9.706 | 5.651 |

LTR | 19.29 | 529.2 | 41.84 | 571.1 | 7.326 | 13.1 | 19.29 | 529.2 | 41.84 | 571.1 | 7.326 | 13.1 |

Pre_cooler1 | - | - | - | - | - | - | 6.097 | 167.3 | 14.66 | 182 | 8.058 | 25.17 |

KCHTR | - | - | - | - | - | - | 0.6144 | 21.81 | 1.905 | 23.71 | 8.034 | 189.7 |

KCLTR | - | - | - | - | - | - | 0.08839 | 3.134 | 1.481 | 4.615 | 32.09 | 384.2 |

Superheater | - | - | - | - | - | - | 0.4668 | 12.81 | 9.285 | 22.1 | 42.02 | 11.92 |

Turbine2 | - | - | - | - | - | - | 3.113 | 110.4 | 213.6 | 324.1 | 65.92 | 40.43 |

Mixer | - | - | - | - | - | - | 0.24 | - | - | - | - | - |

Valve | - | - | - | - | - | - | 0.051 | - | - | - | - | - |

Separator | - | - | - | - | - | - | 3.321 | - | - | - | - | - |

Pump | - | - | - | - | - | - | 0.1012 | 5.043 | 10.01 | 15.05 | 66.49 | 45.57 |

Condenser | - | - | - | - | - | - | 6.817 | 241.7 | 14.52 | 256.2 | 5.668 | 2400 |

Overall system | 192.85 | 5087 | 7749 | 12,836 | 86.21 | 47.37 | 176.8 | 4636 | 8013 | 12,650 | 87.58 | 53.08 |

Parameter | SCRBC | SCRB/KC | ||
---|---|---|---|---|

Optimal Cases | Optimal Cases | |||

TOD | EOD | TOD | EOD | |

PR_{c} | 3.01 | 2.27 | 3.39 | 2.39 |

PR_{p} | - | - | 3.45 | 2.718 |

${\mathrm{T}}_{11}\left(\mathrm{K}\right)$ | - | - | 357.66 | 349.5 |

ΔT_{sup} (K) | - | - | 0 | 1.5 |

ΔT_{pinch} (K) | - | - | 3 | 3 |

${\eta}_{ex}\text{}(\%)$ | 54.8 | 53.04 | 60.31 | 57.93 |

c_{p,tot} ($/GJ) | 11.2 | 10.87 | 10.73 | 10.34 |

${\dot{\mathrm{W}}}_{\mathrm{net}}\text{}\left(\mathrm{MW}\right)$ | 237.6 | 229.8 | 261.3 | 251 |

${\dot{\mathrm{W}}}_{\mathrm{net},\mathrm{SCRBC}}\text{}\left(\mathrm{MW}\right)$ | 237.6 | 229.8 | 236.4 | 232.5 |

${\dot{\mathrm{W}}}_{\mathrm{net},\mathrm{KC}}\text{}\left(\mathrm{MW}\right)$ | - | - | 24.9 | 18.5 |

${\dot{m}}_{{\mathrm{CO}}_{2}\text{}}\left(\mathrm{kg}/\mathrm{s}\right)$ | 2940 | 3307 | 2.824 | 3227 |

${\dot{m}}_{{\mathrm{NH}}_{3}/{\mathrm{H}}_{2}\mathrm{O}\text{}}\left(\mathrm{kg}/\mathrm{s}\right)$ | - | - | 196 | 181 |

${\dot{Z}}_{tot}\text{}\left(\$/\mathrm{h}\right)$ | 7819 | 7291 | 8344 | 7627 |

${\dot{C}}_{D,tot\text{}}\left(\$/\mathrm{h}\right)$ | 4569.5 | 4949.4 | 4331.5 | 4516.5 |

x | 0.273 | 0.198 | 0.294 | 0.216 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

S. Mahmoudi, S.M.; D. Akbari, A.; Rosen, M.A.
Thermoeconomic Analysis and Optimization of a New Combined Supercritical Carbon Dioxide Recompression Brayton/Kalina Cycle. *Sustainability* **2016**, *8*, 1079.
https://doi.org/10.3390/su8101079

**AMA Style**

S. Mahmoudi SM, D. Akbari A, Rosen MA.
Thermoeconomic Analysis and Optimization of a New Combined Supercritical Carbon Dioxide Recompression Brayton/Kalina Cycle. *Sustainability*. 2016; 8(10):1079.
https://doi.org/10.3390/su8101079

**Chicago/Turabian Style**

S. Mahmoudi, S. Mohammad, Ata D. Akbari, and Marc A. Rosen.
2016. "Thermoeconomic Analysis and Optimization of a New Combined Supercritical Carbon Dioxide Recompression Brayton/Kalina Cycle" *Sustainability* 8, no. 10: 1079.
https://doi.org/10.3390/su8101079