Advanced Exergy and Exergoeconomic Analysis of Cascade High-Temperature Heat Pump System for Recovery of Low-Temperature Waste Heat
Abstract
:1. Introduction
- Both conventional and advanced exergy and exergoeconomic analyses were utilized to explore the enhancement potential provided by the CHTHP system and its components, taking into account both thermodynamic and economic factors. This is expected to provide guidance for the engineering application of CHTHPs in low-temperature waste heat recovery.
- CHTHP systems improved through conventional and advanced exergy analyses can reduce carbon emissions, benefiting the environment.
2. Description of a CHTHP System
3. Modeling
3.1. Basic Hypotheses
- The system works in a steady state.
- The changes in the kinetic and potential energies of the working fluid are negligible.
- The heat dissipation of all components and the pressure drop of the heat exchangers and pipelines are negligible.
- The expansion processes in HTEV and LTEV are considered to be isenthalpic.
3.2. Exergy and Exergoeconomic Analyses’ Modeling
3.2.1. Conventional Exergy and Exergoeconomic Analyses
3.2.2. Advanced Exergy and Exergoeconomic Analyses
4. Results and Discussion
4.1. Conventional Exergy and Exergoeconomic Analyses
4.2. Advanced Exergy and Exergoeconomic Analyses
5. Conclusions
- (1)
- Conventional exergy analysis showed that the total exergy destruction of the CHTHP system is 2.639 kW, with a lower exergy efficiency of 48.24%, and its exergoeconomic factor is just 0.75%, indicating the high exergy destruction cost. All these values suggest the need for system improvement.
- (2)
- The avoidable endogenous exergy destruction in the system accounts for 62.26% of the total exergy destruction. This indicates that the exergy destruction mainly comes from the components, and the CHTHP system has significant potential for improvement.
- (3)
- The components with the highest endogenous avoidable exergy destruction are the LTC and HTC, accounting for 88.12% and 83.30% of the exergy destruction, respectively. They, along with the highest endogenous avoidable exergy destruction cost, should be prioritized for improvement.
- (4)
- In the comprehensive consideration of thermodynamic and economic performance, the priority for improvement should be given to the HTC, LTC, and CHE in CHTHP systems.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Symbols | |
e | Specific exergy flow rate (J/kg) |
E | Exergy (kW) |
f | Exergoeconomic coefficient (%) |
h | Specific enthalpy (kJ/kg) |
m | Mass flow rate (kg/s) |
p | Pressure (kPa) |
Q | Heat transfer rate (kW) |
s | Specific entropy (kJ/(kg·K)) |
t | Hour (h) |
U | Heat transfer coefficient (W/(m2·K)) |
y* | Exergy loss ratio (%) |
Z | Investment cost (USD/h) |
Z’ | Total cost (USD/h) |
ε | Exergy efficiency (%) |
i | Annual interest rate (%) |
φ | Maintenance cost coefficient |
Abbreviations | |
A | Heat exchange area (m2) |
CD | Condenser |
C | Exergy cost rate (USD/h) |
CHTHP | Cascade high-temperature heat pump |
CRF | Capital recovery coefficient |
EVP | Evaporator |
CHE | Cascade heat exchanger |
HTC | High-temperature compressor |
HTEV | High-temperature expansion valve |
HTWT | High-temperature water tank |
LTC | Low-temperature compressor |
LTEV | High-temperature expansion valve |
LTWT | Low-temperature water tank |
Subscripts | |
0 | Environmental state |
1~12 | State points |
D | Destruction |
F | Fuel |
i | Inlet |
k | Cycle component number |
o | Outlet |
OP | Annual operating |
P | Production |
tot | Total |
Superscripts | |
AV | Avoidable |
UN | Unavoidable |
EN | Endogenous |
EX | Exogenous |
CI | Initial investment |
OM | Operation and maintenance |
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Component | Energy Balance Equation |
---|---|
HTC | WH = (h6 − h5) mf |
LTC | WL = (h2 − h1) mf |
EVP | QEVP = (h1 − h4) mf |
CD | QCD = (h6 − h7) mf |
CHE | QCHE = (h5 − h8) mf = (h2 − h3) mf |
HTEV | h7 = h8 |
LTEV | h3 = h4 |
Component | Exergy Destruction | Exergy Efficiency |
---|---|---|
HTC | E6 − E5 − WH | WH/(E6 − E5) |
LTC | E2 − E1 − WL | WL/(E2 − E1) |
EVP | E9 − E1 + E4 − E10 | (E1 − E2)/(E9 − E10) |
CD | E6 + E11 − E7 − E12 | (E12 − E11)/(E6 − E7) |
CHE | E2 − E5 − E3 + E8 | (E5 − E8)/(E2 − E3) |
HTEV | E7 − E8 | E8/E7 |
LTEV | E3 − E4 | E4/E3 |
Component | Investment Cost Equation |
---|---|
HTC | Z = 1374.9 × W0.46 |
LTC | Z = 145.5 × W0.46 |
EVP | Z = 199.6 × A0.89 |
CD | Z = 199.6 × A0.89 |
CHE | Z = 54.79 × A0.65 |
HTEV | Z = 20.64 × m |
LTEV | Z = 20.64 × m |
Component | Parameter | Ideal | Unavoidable | Real |
---|---|---|---|---|
HTC | Isentropic efficiency (%) | 1 | 0.95 | 0.68 |
LTC | Isentropic efficiency (%) | 1 | 0.95 | 0.7 |
EVP | Pinch-point temperature difference (°C) | 0 | 0.5 | 4 |
CHE | Pinch-point temperature difference (°C) | 0 | 0.5 | 4 |
CD | Pinch-point temperature difference (°C) | 0 | 0.5 | 4 |
LTEV/HTEV | -- | Isentropic | Isentropic | Isenthalpic |
State Point | Working Fluid | Temperature (K) | Pressure (MPa) | Mass Flow Rate (kg/s) | Specific Enthalpy (kJ/kg) | Specific Entropy (kJ/(kg·K)) | Specific Exergy (kJ/kg) |
---|---|---|---|---|---|---|---|
1 | R134a | 308.23 | 0.800 | 0.048 | 419.45 | 1.73 | 44.46 |
2 | R134a | 367.68 | 2.540 | 0.048 | 454.52 | 1.76 | 70.67 |
3 | R134a | 349.86 | 2.540 | 0.048 | 316.05 | 1.37 | 43.33 |
4 | R134a | 305.52 | 0.800 | 0.048 | 316.05 | 1.39 | 37.19 |
5 | R245fa | 347.69 | 0.630 | 0.076 | 459.63 | 1.79 | 37.46 |
6 | R245fa | 399.07 | 2.090 | 0.076 | 489.07 | 1.81 | 60.59 |
7 | R245fa | 393.28 | 2.090 | 0.076 | 372.62 | 1.51 | 27.16 |
8 | R245fa | 345.87 | 0.630 | 0.076 | 372.62 | 1.53 | 21.98 |
9 | Water | 314.44 | 0.101 | 0.260 | 86.06 | 0.59 | 6.64 |
10 | Water | 309.85 | 0.101 | 0.260 | 71.49 | 0.53 | 4.86 |
11 | Water | 389.07 | 0.101 | 0.500 | 490.69 | 1.48 | 67.04 |
12 | Water | 393.25 | 0.101 | 0.500 | 504.24 | 1.53 | 71.96 |
State Point | Working Fluid | Temperature (K) | Pressure (MPa) | Mass Flow Rate (kg/s) | Specific Enthalpy (kJ/kg) | Specific Entropy (kJ/(kg·K)) | Specific Exergy (kJ/kg) |
---|---|---|---|---|---|---|---|
1 | R134a | 309.85 | 0.930 | 0.063 | 417.96 | 1.73 | 47.18 |
2 | R134a | 351.24 | 2.303 | 0.063 | 435.98 | 1.76 | 65.19 |
3 | R134a | 346.95 | 2.303 | 0.063 | 310.97 | 1.37 | 42.17 |
4 | R134a | 309.85 | 0.930 | 0.063 | 316.36 | 1.39 | 37.56 |
5 | R245fa | 346.95 | 0.674 | 0.087 | 459.63 | 1.79 | 38.08 |
6 | R245fa | 393.25 | 1.931 | 0.087 | 489.07 | 1.81 | 55.79 |
7 | R245fa | 393.25 | 1.931 | 0.087 | 372.62 | 1.51 | 27.16 |
8 | R245fa | 346.95 | 0.674 | 0.087 | 372.62 | 1.53 | 21.45 |
9 | Water | 314.44 | 0.101 | 0.364 | 86.06 | 0.59 | 6.73 |
10 | Water | 309.85 | 0.101 | 0.364 | 71.49 | 0.53 | 4.95 |
11 | Water | 389.07 | 0.101 | 0.500 | 490.69 | 1.48 | 67.04 |
12 | Water | 393.25 | 0.101 | 0.500 | 504.24 | 1.53 | 71.96 |
State Point | Working Fluid | Temperature (K) | Pressure (MPa) | Mass Flow Rate (kg/s) | Specific Enthalpy (kJ/kg) | Specific Entropy (kJ/(kg·K)) | Specific Exergy (kJ/kg) |
---|---|---|---|---|---|---|---|
1 | R134a | 309.35 | 0.917 | 0.058 | 417.73 | 1.73 | 46.95 |
2 | R134a | 352.20 | 2.316 | 0.058 | 437.11 | 1.76 | 65.50 |
3 | R134a | 347.20 | 2.316 | 0.058 | 311.41 | 1.37 | 42.26 |
4 | R134a | 309.35 | 0.917 | 0.058 | 311.41 | 1.39 | 37.90 |
5 | R245fa | 346.70 | 0.669 | 0.086 | 457.42 | 1.79 | 37.95 |
6 | R245fa | 393.75 | 1.951 | 0.086 | 476.34 | 1.81 | 56.19 |
7 | R245fa | 393.75 | 1.951 | 0.086 | 373.56 | 1.51 | 27.35 |
8 | R245fa | 346.70 | 0.669 | 0.086 | 373.56 | 1.53 | 22.60 |
9 | Water | 314.44 | 0.101 | 0.319 | 86.06 | 0.59 | 6.73 |
10 | Water | 309.85 | 0.101 | 0.319 | 71.49 | 0.53 | 4.95 |
11 | Water | 389.07 | 0.101 | 0.500 | 490.69 | 1.48 | 67.04 |
12 | Water | 393.25 | 0.101 | 0.500 | 504.24 | 1.53 | 71.96 |
Component | EF (kW) | EP (kW) | ED (kW) | CD (USD/h) | Ε (%) | fk (%) | y* (%) |
---|---|---|---|---|---|---|---|
EVP | 0.464 | 0.351 | 0.113 | 1.43 × 10−6 | 75.59 | 98.47 | 4.29 |
LTC | 2.166 | 1.265 | 0.901 | 0.09359 | 58.40 | 1.4 | 34.14 |
CHE | 1.319 | 1.180 | 0.139 | 7.71 × 10−5 | 89.44 | 27.59 | 5.28 |
LTEV | 2.090 | 1.794 | 0.296 | 6.42 × 10−5 | 85.84 | 0.53 | 11.21 |
HTC | 2.468 | 1.761 | 0.707 | 0.229705 | 71.36 | 0.59 | 26.79 |
CD | 2.546 | 2.459 | 0.087 | 0.00008 | 96.58 | 69.66 | 3.30 |
HTEV | 2.069 | 1.674 | 0.395 | 0.07561 | 80.90 | 0.001 | 14.98 |
System | 5.098 | 2.459 | 2.639 | 0.39914 | 48.24 | 0.75 | 100 |
Component | (kW) | (kW) | (kW) | (kW) | (kW) | (kW) | (kW) | (kW) |
---|---|---|---|---|---|---|---|---|
EVP | 0.155 | −0.042 | 0.079 | 0.034 | 0.109 | −0.029 | 0.047 | −0.013 |
LTC | 0.842 | 0.059 | 0.848 | 0.053 | 0.794 | 0.054 | 0.048 | 0.005 |
CHE | 0.130 | 0.009 | 0.129 | 0.010 | 0.119 | 0.011 | 0.012 | −0.002 |
LTEV | 0.264 | 0.032 | 0.089 | 0.207 | −0.010 | 0.099 | 0.274 | −0.067 |
HTC | 0.648 | 0.059 | 0.641 | 0.066 | 0.589 | 0.052 | 0.060 | 0.006 |
CD | 0.086 | 0.000 | 0.054 | 0.033 | 0.054 | 0.000 | 0.033 | 0.000 |
HTEV | 0.399 | −0.004 | 0.043 | 0.352 | −0.010 | 0.054 | 0.409 | −0.057 |
System | 2.525 | 0.114 | 1.885 | 0.754 | 1.643 | 0.242 | 0.882 | −0.128 |
Component | (USD/h) | (USD/h) | (USD/h) | (USD/h) | (USD/h) | (USD/h) | (USD/h) | (USD/h) |
---|---|---|---|---|---|---|---|---|
EVP | 2.85 × 10−5 | 0.1 × 10−8 | 1.42 × 10−6 | 1.42 × 10−6 | 1.42 × 10−6 | 1.42 × 10−6 | 0.1 × 10−8 | 0.1 × 10−8 |
LTC | 0.874585 | 0.00612 | 0.08808 | 0.005505 | 0.082472 | 0.005608 | 0.004985 | 0.00052 |
CHE | 0.0006 | 4.28 × 10−6 | 0.00006 | 4.28 × 10−6 | 5.57 × 10−5 | 5.71 × 10−6 | 5.71 × 10−6 | −1.42 × 10−6 |
LTEV | 0.000685 | 8.57 × 10−6 | 2.28 × 10−5 | 5.42 × 10−5 | −2.85 × 10−6 | 2.57 × 10−5 | 7.14 × 10−5 | −1.71 × 10−5 |
HTC | 2.105342 | 0.019168 | 0.20826 | 0.021442 | 0.191364 | 0.016894 | 0.019494 | 0.00195 |
CD | 0.0008 | 0 | 0.00005 | 0.00003 | 0.00005 | 0 | 0.00003 | 0 |
HTEV | 0.763757 | −0.00076 | 0.008231 | 0.067378 | −0.00191 | 0.010337 | 0.07829 | −0.01091 |
System | 3.745785 | 0.024544 | 0.304707 | 0.094417 | 0.272 | 0.032871 | 0.102877 | −0.00846 |
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Hu, X.; Shi, C.; Liu, Y.; Fu, X.; Ma, T.; Jin, M. Advanced Exergy and Exergoeconomic Analysis of Cascade High-Temperature Heat Pump System for Recovery of Low-Temperature Waste Heat. Energies 2024, 17, 1027. https://doi.org/10.3390/en17051027
Hu X, Shi C, Liu Y, Fu X, Ma T, Jin M. Advanced Exergy and Exergoeconomic Analysis of Cascade High-Temperature Heat Pump System for Recovery of Low-Temperature Waste Heat. Energies. 2024; 17(5):1027. https://doi.org/10.3390/en17051027
Chicago/Turabian StyleHu, Xiaowei, Chenyang Shi, Yong Liu, Xingyu Fu, Tianyao Ma, and Mingsen Jin. 2024. "Advanced Exergy and Exergoeconomic Analysis of Cascade High-Temperature Heat Pump System for Recovery of Low-Temperature Waste Heat" Energies 17, no. 5: 1027. https://doi.org/10.3390/en17051027
APA StyleHu, X., Shi, C., Liu, Y., Fu, X., Ma, T., & Jin, M. (2024). Advanced Exergy and Exergoeconomic Analysis of Cascade High-Temperature Heat Pump System for Recovery of Low-Temperature Waste Heat. Energies, 17(5), 1027. https://doi.org/10.3390/en17051027