#
Exergetic and Economic Evaluation of a Transcritical Heat-Driven Compression Refrigeration System with CO_{2} as the Working Fluid under Hot Climatic Conditions

^{1}

^{2}

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## Abstract

**:**

_{2}as the working fluid from thermodynamic and economic viewpoints. Particular attention was paid to air-conditioning applications under hot climatic conditions. The system was simulated by Aspen HYSYS

^{®}(AspenTech, Bedford, MA, USA) and optimized by automation based on a genetic algorithm for achieving the highest exergetic efficiency. In the case of producing only refrigeration, the scenario with the ambient temperature of 35 °C and the evaporation temperature of 5 °C showed the best performance with 4.7% exergetic efficiency, while the exergetic efficiency can be improved to 22% by operating the system at the ambient temperature of 45 °C and the evaporation temperature of 5 °C if the available heating capacity within the gas cooler is utilized (cogeneration operation conditions). Besides, an economic analysis based on the total revenue requirement method was given in detail.

## 1. Introduction

_{2}(R744) as a natural working fluid is getting more and more attention and has been extensively researched since it is nontoxic, nonflammable, inexpensive, and environmentally benign. For example, Lorentzen and Pettersen [13], as well as Cavallini and Zilio [14], discussed deeply how promising CO

_{2}would be as a natural working fluid in the future. The low critical temperature (31.1 °C) and the high critical pressure (73.8 bar) of CO

_{2}in conjunction with its thermodynamic properties (slightly above critical point and near saturation lines) create a high potential for improving the thermodynamic and economic effectiveness of the refrigeration systems.

_{2}as a refrigerant focused mainly on the transcritical VCRC. For example, Rozhentsev and Wang [15] discussed the thermodynamic efficiency of the heat regeneration within the transcritical VCRC, while Shiferaw at al. [16] evaluated the economic potential for transcritical VCRC systems, and Fazelpour and Morosuk [17] proposed two optimal configurations of the transcritical VCRC with economizer from the exergoeconomic analysis point of view. The idea of implementing ejector technologies to a transcritical cascade refrigeration cycle was also reported [18,19]. The information reported for the transcritical heat-driven refrigeration cycle considering CO

_{2}as the working fluid was minimal. In general, compared to conventional vapor-compression refrigeration machines, it is advantageous to employ thermally-driven vapor compression refrigeration machines to ensure the stable refrigeration capacity (for food and vaccine preservation, and/or for air conditioning) for the areas without a secure power supply. Besides, driving the vapor-compression refrigeration machines by heat offers more system flexibility as it is possible to integrate the system into other systems by utilizing any kinds of heat sources, and the system can produce not only refrigeration capacity but also power and heating capacities based on the local requirements. Using CO

_{2}as the working fluid for a heat-driven VCRC provides additional potentials for reducing the size of the system, for improving the system efficiency and for reducing the system cost as well. This is appealing for waste heat recovery applications to improve the system efficiency, for ship and automotive applications due to the limited space, and for offices, hotels, and other buildings where refrigeration, power, and heating capacities are needed simultaneously.

_{2}as the working fluid has been discussed by authors [20]. The system was designed to utilize the low-grade waste heat, and four scenarios with various evaporation temperatures were evaluated and compared for storage of a wide range of food products and air conditioning applications. This work aimed to pay special attention to air conditioning applications for countries or regions having hot climates (for example, the Middle East, India, and South China) since these countries/regions are developing substantially and with massive populations, which leads to considerable energy consumption for air conditioning purpose.

## 2. System Description

- R744 is the only working fluid for both subsystems.
- The power cycle operates entirely in the supercritical region, and part of the refrigeration cycle is above the critical point.
- The shafts of the expander and two compressors are directly connected.
- The refrigeration capacity of the evaporator is the main product.
- The net shaft work (can be further converted to electricity), which is the difference between the power generation of the expander and the total power consumption of two compressors, can be produced as the second product of the system.
- The available heating capacity within the gas cooler can be considered as the third product depending on the local requirements.
- Any kinds of heat sources, in general, can be used for driving the system, for example, solar thermal energy, geothermal heat, heat from biomass and waste heat from chemical plants and internal combustion engines. The low-medium grade waste heat was focused in this study.

- the machine is used for air conditioning purposes (T
_{EVAP}= 5 and 15 °C [21]), and

- The refrigeration capacity is 100 kW.
- The shaft work generated from the expander is merely sufficient to power both compressors, ${\dot{\mathrm{W}}}_{\mathrm{net}}=0\text{}\mathrm{kW}$.
- The temperature of cooling water (stream 7) is equal to the assumed environmental temperature, T
_{7}= T_{0}. - The temperature of “heat source” (HS) for the heater is always 20 K higher than the turbine inlet temperature (TIT): T
_{HS}= T_{TIT}+ 20 K. Since the system in this work is considered to be driven by waste heat (for example, waste heat from flue gases), a gas–gas heat exchanger is assumed. - The outlet stream from the evaporator (stream 1) is saturated vapor (since it has been proved that the effect of the superheating process within the evaporator for transcritical refrigeration machines can be neglected [15]).
- The isentropic efficiency of both compressors, CM_P and CM_R (turbo-compressor), is equal to 0.85 [21].
- The isentropic efficiency of the expander (turbo-expander) is assumed to be equal to 0.9 [21].
- The gas cooler and the evaporator are considered to operate with the pinch temperature difference of 5 K.
- The simulation is completed under steady-state conditions. The pressure drops in pipes, heat exchangers, as well as within the mixer and the splitter are neglected.

## 3. Methods

^{®}Software (AspenTech, Bedford, MA, USA). Moreover, the exergy-based method was applied for optimizing, comparing, and investigating the system under various operation conditions. The Span–Wagner equation of state was selected for calculating the thermodynamic properties of CO

_{2}since it is one of the most accurate models to predict CO

_{2}behaviors in a wide range of temperature and pressure, including a high temperature, at high pressure and in the vicinity of its critical point [22]. To conduct the exergy-based method, the reference temperature T

_{0}varies when the assumption of the ambient temperature varies (T

_{0}= 35/45 °C), while the reference pressure p

_{0}in this study keeps constant (p

_{0}= 1.013 bar).

#### 3.1. Optimization

_{10}and p

_{10}. The pressure ratio within the compressors is PRc. The outlet stream of R744 from the GC is with T

_{3}and p

_{3}. The maximum pressure for operating the supercritical CO

_{2}power cycle is assumed to be 200 bar [21,26,27] because higher operating pressure will lead to thicker walls and more expensive materials, which increases the cost of the overall system.

#### 3.2. Analysis

#### 3.2.1. Energetic Analysis

#### 3.2.2. Exergetic Analysis

#### 3.2.3. Economic Analysis

^{3}, ${f}_{m}$ was needed, $Volum{e}_{metal}=Volum{e}_{PCHE}\ast {f}_{m}$. The size of the heat exchanger $Volum{e}_{PCHE}$ can be estimated by the area of the heat exchanger and the information of the typical area per unit volume, $Volum{e}_{PCHE}=\frac{{A}_{PCHE}}{\mathrm{typical}\text{}\mathrm{area}\text{}per\text{}\mathrm{unit}\text{}\mathrm{volume}}$. Depending on the operating pressure, the typical area per unit volume for PCHEs is around 1300 m

^{2}/m

^{3}at 100 bar and 650 m

^{2}/m

^{3}at 500 bar [32]. The heat-transfer area of the heat exchanger ${A}_{PCHE}$, was calculated by the equation Q = U A T

_{LMTD}. Q stands for the transferred heat within the heat exchanger; U is the overall heat-transfer coefficient; and T

_{LMTD}is the log mean temperature difference. The assumptions made for estimating the cost of PCHEs are summarized in Table 4.

^{2}K) [17]. In Table 5, the values used for the cost estimation of the compressor and evaporator are listed.

- For the refrigeration machine with the cooling capacity of 100 kW, the cost of the TV equals to 100 € [17];
- The costs of the mixer and the splitter are neglected.

_{2017}:

## 4. Results and Discussion

#### 4.1. Thermodynamic Investigations

_{EVAP}= 5 and 15 °C) under hot climatic conditions (T

_{0}= 35 and 45 °C) were simulated, optimized, and compared. Table 6 demonstrates the exergetic optimization results aiming at the highest exegetic efficiency of the overall system for each scenario.

_{10}but the highest p

_{10}were selected for each scenario, while the optimal T

_{3}and p

_{3}depended on the ambient temperature rather than the evaporation temperature. Hence, the closed power cycle, for various scenarios with the same ambient temperature, was suggested to operate at the same conditions. Only the ${\dot{\mathrm{m}}}_{\mathrm{P}}$ differed, but the energetic and exergetic efficiencies of the power cycle with the same ambient conditions were consistent. Meanwhile, for the transcritical refrigeration cycle, by changing the evaporation temperature from 5 to 15 °C, the pressure ratio ${\mathrm{PR}}_{\mathrm{R}}$ and the ${\dot{\mathrm{m}}}_{\mathrm{P}}$ varied simultaneously, which affected its energetic and exergetic efficiencies. With the higher evaporation temperature, the higher COP of the transcritical refrigeration cycle was achieved as well as the better energy performance of the overall system. While the exergetic efficiencies of the refrigeration cycle and the overall system decreased significantly by increasing the evaporation temperature.

- For different ambient operating conditions (ambient temperatures of 35 and 45 °C), the exergetic efficiency of the overall system (with and without available heating product) decreased with increasing the evaporation temperature. Therefore, the system was preferred to operate at a lower evaporation temperature.
- By varying the ambient temperature from 35 to 45 °C, the exergetic efficiency with the consideration of utilizing only refrigeration products reduced, while the efficiency was improved once the heating product was also taken into consideration. It revealed that the ambient temperature had a significant effect on the amount of the available heating capacity, and a large amount of heat, particularly at higher ambient temperature, should be utilized based on the local requirements to improve the performance of the overall system.

#### 4.2. Economic Investigations

_{0}= 45 °C and T

_{EVAP}= 5 °C. Moreover, the costs only associated with CM_R and the EX contributed more than half to the total PEC of the overall system for all the operating conditions, while the CM_P had a relatively low cost due to the low power consumption.

_{0}= 45 °C with T

_{EVAP}= 5 °C, the system operated with the highest pressure ratio of the transcritical refrigeration cycle, which resulted in the highest cost of the overall system. However, by increasing the evaporation temperature (pressure) and decreasing the operating pressure within the GC, the lowest cost needed to be paid for the scenario of T

_{0}= 35 °C and T

_{EVAP}= 15 °C. It can be concluded that, from an economic viewpoint, the system operating with lower environmental temperature and higher evaporation temperature was considered with a lower payment, and the pressure ratio of the transcritical refrigeration cycle should be paid attention in the system design phase.

## 5. Conclusions

_{2}as the working fluid was proposed. Compared to other vapor-compression refrigeration systems, the system, in general, can utilize any kinds of heat sources to produce refrigeration, heating, and power capacities simultaneously. This technology is beneficial to stabilize the refrigeration capacity for the areas without a secure power supply. Moreover, the system using CO

_{2}—a natural working fluid—as the refrigerant can be driven by renewable energies (for example, solar, geothermal, and biomass energies) and low to medium grade waste heat (for example, waste heat from chemical plants and internal combustion engines), which makes the system attractive from an environmental viewpoint. The low critical temperature (31.1 °C) and the high critical pressure (73.8 bar) of CO

_{2}in conjunction with its thermodynamic properties (slightly above critical point and near saturation lines) create a high potential for improving the thermodynamic and economic effectiveness of the refrigeration systems.

_{0}= 45 °C and T

_{EVAP}= 5 °C. The TV and the heat exchangers, especially the GC, had the lowest exergetic efficiency, while the HE, the GC, and the TV were the dominating contributors to the exergy destruction of the overall system. To further improve the performance of the overall system, great attention should be paid to the configurations that can minimize the irreversibilities within the TV and the heat exchangers.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | area [m^{2}] |

$\dot{C}$ | cost rate associated with an exergy stream [$ (h)^{−1}] |

c | cost per unit of exergy [$ (GJ)^{−1}] |

COP | coefficient of performance [-] |

$\dot{E}$ | exergy rate [W] |

e | specific exergy [kJ kg^{−1}] |

f | fraction of metal per m^{3} of the heat exchanger [m^{3} m^{−3}]/correction factor [-] |

i | interest rate [%] |

LMTD | log-mean temperature difference [K] |

$\dot{m}$ | mass flow rate [kg s^{−1}] |

n | economic life of the plant [year] |

p | pressure [bar] |

$\dot{Q}$ | heat rate [W] |

r | inflation rate [%] |

T | temperature [K, ºC] |

U | overall heat-transfer coefficient [W m^{−2} K^{−1}] |

V | volume [m^{3}] |

$\dot{W}$ | power [W] |

$\dot{Z}$ | cost rate [$ (h)^{−1}] |

## Greek Symbols

ε | exergy efficiency [%] |

$\rho $ | density [kg (m^{3})^{−1}] |

$\tau $ | annual operating hours [h (year)^{−1}] |

η | efficiency [-] |

## Abbreviations

CC | carrying charges |

CELF | constant escalation levelization factor |

CM_R | compressor of the refrigeration cycle |

CM_P | compressor of the power cycle |

CRF | capital recovery factor |

COM | component object model |

EVAP | evaporator |

EX | expander |

FC | fuel cost |

GA | genetic algorithm |

GC | gas cooler |

HE | heater |

HS | heat source |

MIX | mixer |

OMC | operating and maintenance cost |

ORC | organic Rankine cycle |

PCHE | printed circuit heat exchanger |

PEC | purchased equipment cost |

PRc | compressor pressure ratio |

SBC | supercritical Brayton cycle |

SCO_{2} | supercritical carbon dioxide |

SPLIT | splitter |

TCI | total capital investment |

TCO_{2} | transcritical carbon dioxide |

TIP | expander (=turbine) inlet pressure |

TIT | expander (=turbine) inlet temperature |

TRR | total revenue requirement |

TV | throttling valve |

VCRC | vapor-compression refrigeration cycle |

## Subscripts and Superscripts

0 | reference state (dead state)/ the first year |

a | average |

B | base case |

CI | capital investment |

Cooling | refrigeration capacity |

D | exergy destruction |

eff | effective |

EVAP | evaporator |

F | exergy of fuel |

Heating | heat capacity |

k | kth component |

L | levelized |

M | mechanical |

P | exergy of product/power cycle |

PH | physical |

R | refrigeration cycle |

T | thermal/temperature |

tot, overall | total |

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**Figure 1.**(

**a**) Schematic and (

**b**) thermodynamic cycle of a transcritical heat-driven compression refrigeration machine with R744.

**Figure 2.**${\epsilon}_{Overall}$ with and without available heating product for different environmental temperatures by varying evaporation temperatures (

**a**) T

_{0}= 35 °C and (

**b**) T

_{0}= 45 °C.

**Figure 5.**System exergy balance (exergy destruction of each component and potential product of the overall system in exergy) for each scenario.

Design Variable | Range |
---|---|

T10 (°C) | 220–500 [24,25] |

p_{10} (bar) | 150–200 [21,26,27] |

PRc | 1.7–3.0 |

T_{3} (°C) | ≥32 [25,28] |

p_{3} (bar) | ≥77 [25,28] |

Component/System | $\mathbf{Exergy}\text{}\mathbf{of}\text{}\mathbf{Fuel}\text{}\left({\dot{\mathit{E}}}_{\mathit{F}}\right)$ | $\mathbf{Exergy}\text{}\mathbf{of}\text{}\mathbf{Product}\text{}\left({\dot{\mathit{E}}}_{\mathit{P}}\right)$ | $\mathbf{Exergy}\text{}\mathbf{of}\text{}\mathbf{Loss}\text{}\left({\dot{\mathit{E}}}_{\mathit{L}}\right)$ |
---|---|---|---|

Evaporator (EVAP) | ${\dot{E}}_{4}-{\dot{E}}_{1}$ | ${\dot{E}}_{6}-{\dot{E}}_{5}$ | - |

Compressor for refrigeration cycle (CM_R) | ${\dot{W}}_{CM\_R}+{\dot{E}}_{1}^{T}$ | ${\dot{E}}_{2\_1}^{T}+{\dot{E}}_{2\_1}^{M}-{\dot{E}}_{1}^{M}$ | - |

Mixer (MIX) | - | - | - |

Gas cooler (GC) | ${\dot{E}}_{2}-{\dot{E}}_{3}$ | ${\dot{E}}_{8}-{\dot{E}}_{7}$ | - |

Throttling valve (TV) | ${\dot{E}}_{3\_1}^{M}-{\dot{E}}_{4}^{M}+{\dot{E}}_{3\_1}^{T}$ | ${\dot{E}}_{4}^{T}$ | - |

Compressor for power cycle (CM_P) | ${\dot{W}}_{CM\_P}$ | ${\dot{E}}_{9}-{\dot{E}}_{3\_2}$ | - |

Heater (HE) | ${\dot{Q}}_{HE}\left(1-\frac{{T}_{0}}{{T}_{HS}}\right)$ | ${\dot{E}}_{10}-{\dot{E}}_{9}$ | - |

Expander (EX) | ${\dot{E}}_{10}-{\dot{E}}_{2\_2}$ | ${\dot{W}}_{EX}$ | - |

Overall (only refrigeration) | ${\dot{Q}}_{HE}\left(1-\frac{{T}_{0}}{{T}_{HS}}\right)$ | ${\dot{E}}_{6}-{\dot{E}}_{5}$ | ${\dot{E}}_{8}-{\dot{E}}_{7}$ |

Overall (refrigeration and heat) | ${\dot{Q}}_{HE}\left(1-\frac{{T}_{0}}{{T}_{HS}}\right)$ | ${\dot{E}}_{6}-{\dot{E}}_{5}+{\dot{E}}_{8}-{\dot{E}}_{7}$ | $0$ |

Overall (refrigeration and power) | ${\dot{Q}}_{HE}\left(1-\frac{{T}_{0}}{{T}_{HS}}\right)$ | ${\dot{E}}_{6}-{\dot{E}}_{5}+{\dot{W}}_{net}$ | ${\dot{E}}_{8}-{\dot{E}}_{7}$ |

Overall (heat, refrigeration, and power) | ${\dot{Q}}_{HE}\left(1-\frac{{T}_{0}}{{T}_{HS}}\right)$ | ${\dot{E}}_{6}-{\dot{E}}_{5}+{\dot{W}}_{net}$+ ${\dot{E}}_{8}-{\dot{E}}_{7}$ | $0$ |

Variable | Nomenclature | Unit | Value |
---|---|---|---|

The economic lifetime of the power plant | n | a | 20 |

Annual full load hours | τ | h a^{−1} | 8000 |

Effective interest rate | i_{eff} | % | 10 |

Average general inflation rate | ${r}_{FC}$$,{r}_{OMC}$ | % | 2.5 |

Total Capital Investment | TCI | $ | 6.32 PEC [29] |

Fuel cost at the beginning of the first year | $F{C}_{0}$ | $ | 0 |

Operating and maintenance cost at the beginning of the first year | $OM{C}_{0}$ | $ | 0.05 TCI n^{−1} |

Item | Nomenclature | Value | Unit |
---|---|---|---|

Overall heat-transfer coefficient | U | 500 [32] | W m^{−}^{2}K^{−}^{1} |

The fraction of metal per m^{3} of the heat exchanger | ${f}_{m}$ | 0.564 [27] | m^{3} m^{−}^{3} |

The density of stainless steel | $Densit{y}_{SS}$ | 7800 | kg m^{−}^{3} |

Cost of stainless steel per unit mass | $Cost\text{}per\text{}unit\text{}mas{s}_{SS}$ | 50 [32] | $ kg^{−}^{1} |

**Table 5.**The values used for computing the costs of the compressor for refrigeration cycle (CM_R) and evaporator (EVAP) [33].

CM_R | |||||

${C}_{B}$ ($) | ${X}_{B}\text{}\left(\mathrm{kW}\right)$ | M | ${f}_{M}$ | ${f}_{P}$ | ${f}_{T}$ |

98,400 | 250 | 0.95 [29] | 1 | 1.5 | 1 |

EVAP | |||||

${C}_{B}$ ($) | ${X}_{B}$(m^{2}) | M | ${f}_{M}$ | ${f}_{P}$ | ${f}_{T}$ |

32,800 | 80 | 0.68 | 1 | 1.3 | 1 |

T_{0} = 35 °C | T_{0} = 45 °C | |||
---|---|---|---|---|

T_{EVAP} = 5 °C | T_{EVAP} = 15 °C | T_{EVAP} = 5 °C | T_{EVAP} = 15 °C | |

Operating parameters | ||||

T_{10} (°C) | 220 | 220 | 220 | 220 |

p_{10} (bar) | 200 | 200 | 200 | 200 |

T_{3} (°C) | 50 | 50 | 40 | 40 |

p_{3} (bar) | 95 | 95 | 112 | 112 |

${\mathrm{PR}}_{\mathrm{P}}$ (-) | 2.11 | 2.11 | 1.79 | 1.79 |

${\mathrm{PR}}_{\mathrm{R}}$ (-) | 2.48 | 1.92 | 2.91 | 2.27 |

${m}_{P}$(kg h^{−1}) | 4558.22 | 3267.43 | 10,289.66 | 8080.17 |

${m}_{R}$ (kg h^{−1}) | 3396.58 | 3776.06 | 4535.40 | 5138.80 |

${m}_{P}/{m}_{R}$ (-) | 1.34 | 0.87 | 2.27 | 1.57 |

Energetic results | ||||

$\text{}{\eta}_{P}$ (%) | 10.92 | 10.92 | 8.56 | 8.56 |

COP (-) | 2.56 | 3.57 | 1.59 | 2.03 |

$\text{}CO{P}_{overall}$ (-) | 0.28 | 0.39 | 0.14 | 0.17 |

Exergetic results | ||||

${\epsilon}_{P}$ (%) | 27.35 | 27.35 | 22.52 | 22.52 |

${\epsilon}_{R}$ (%) | 17.07 | 11.14 | 16.10 | 13.14 |

${\epsilon}_{Overall}$ (%) | 4.67 | 3.05 | 3.63 | 2.93 |

${\dot{E}}_{Heating}/{\dot{E}}_{Cooling}$ (-) | 2.73 | 3.95 | 5.08 | 5.90 |

Scenarios | T_{0} = 35 °C,T _{EVAP} = 5 °C | T_{0} = 35 °C,T _{EVAP} = 15 °C | T_{0} = 45 °C,T _{EVAP} = 5 °C | T_{0} = 45 °C,T _{EVAP} = 15 °C |
---|---|---|---|---|

Levelized Cost ($ year^{−1}) | 96,382 | 78,524 | 146,241 | 124,441 |

© 2019 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**

Luo, J.; Morosuk, T.; Tsatsaronis, G.; Tashtoush, B.
Exergetic and Economic Evaluation of a Transcritical Heat-Driven Compression Refrigeration System with CO_{2} as the Working Fluid under Hot Climatic Conditions. *Entropy* **2019**, *21*, 1164.
https://doi.org/10.3390/e21121164

**AMA Style**

Luo J, Morosuk T, Tsatsaronis G, Tashtoush B.
Exergetic and Economic Evaluation of a Transcritical Heat-Driven Compression Refrigeration System with CO_{2} as the Working Fluid under Hot Climatic Conditions. *Entropy*. 2019; 21(12):1164.
https://doi.org/10.3390/e21121164

**Chicago/Turabian Style**

Luo, Jing, Tatiana Morosuk, George Tsatsaronis, and Bourhan Tashtoush.
2019. "Exergetic and Economic Evaluation of a Transcritical Heat-Driven Compression Refrigeration System with CO_{2} as the Working Fluid under Hot Climatic Conditions" *Entropy* 21, no. 12: 1164.
https://doi.org/10.3390/e21121164