Energy, Exergetic, and Thermoeconomic Analyses of Hydrogen-Fueled 1-kW Proton-Exchange Membrane Fuel Cell
Abstract
1. Introduction
2. Energy and Exergy Analyses of Thermal Systems
2.1. Energy Conservation
2.2. Exergy Balance Equation and the Second Law of Thermodynamics
2.3. Exergy Cost-Balance Equation
3. Hydrogen-Fueled 1-kW PEMFC System
3.1. Energy Conservation and Exergy Balance and Exergy Cost-Balance Equations for PEMFC System
- Air blower
- Humidifier
- Anode
- Cathode
- HTX in the FCS
- FCS
- HTX for DI
- DI water tank
- Pump 1
- HTX for coolant
- Coolant water tank
- Pump 2
3.2. Energy Conservation and Exergy Balance of the FCS
3.3. Exergy Cost-Balance Equation for the Overall System
4. Calculation Results and Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
unit cost | |
annualized cost | |
initial investment cost | |
unit cost of fuel | |
exergy per unit mass | |
exergy flow rate | |
enthalpy per unit mass | |
enthalpy flow rate | |
latent heat of water | |
electric current | |
irreversibility rate | |
mass flow rate | |
mole flow rate | |
number of stacks | |
heat flow rate | |
entropy per unit mass | |
entropy flow rate | |
entropy generation rate | |
temperature | |
ambient temperature | |
workflow rate | |
capital cost flow rate | |
Greek letters | |
annual operating hours | |
maintenance cost factor | |
Superscripts | |
chemical | |
fuel | |
exergy destruction | |
mechanical | |
thermal | |
work or electricity | |
Subscripts | |
chemical | |
control volume | |
reference point | |
mechanical | |
thermal reservoir | |
entropy | |
thermal | |
work or electricity |
Abbreviations
CCHP | combined cooling, heating, and power |
CHP | cooling, heating, and power |
CRF | capital recovery factor |
DI | deionized |
F | Faraday constant |
FCS | fuel cell stack |
HHV | higher heating value |
LHV | lower heating value |
PEMFC | proton-exchange membrane fuel cell |
HTX | heat exchanger |
PWF | present worth factor |
SV | salvage value |
Appendix A
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States | (kmol/h) | (kPa) | (K) | (kJ/h) | (kJ/h/K) | (kJ/h) |
---|---|---|---|---|---|---|
101 | 0.0846 | 100.90 | 299.40 | 3.0821 | 0.471 | −1.186 |
102 | 0.0846 | 113.36 | 305.99 | 19.340 | 0.443 | 23.461 |
103 | 0.0846 | 105.40 | 322.14 | 59.280 | 0.621 | 10.214 |
104 | 0.0748 | 102.28 | 332.99 | 76.067 | 0.540 | 35.345 |
105 | 0.0748 | 102.42 | 312.52 | 31.335 | 0.407 | 30.376 |
206 | 0.0275 | 103.98 | 299.97 | 1.443 | 0.005 | 0.0 |
207 | 0.0079 | 102.05 | 326.10 | 6.368 | 0.020 | 0.002 |
508 | 4.8295 | 99.80 | 325.69 | 19,136.736 | 64.053 | 435.754 |
509 | 4.8295 | 143.63 | 325.59 | 19,103.614 | 63.940 | 436.496 |
510 | 4.8295 | 122.48 | 333.13 | 21,846.193 | 72.273 | 694.585 |
511 | 4.8295 | 110.48 | 326.14 | 19,301.256 | 64.555 | 450.631 |
512 | 2.2926 | 102.35 | 303.10 | 5185.052 | 17.998 | 7.057 |
513 | 2.2926 | 114.85 | 303.03 | 5173.442 | 17.958 | 7.378 |
514 | 2.2926 | 105.72 | 331.47 | 10,082.861 | 33.445 | 299.545 |
515 | 2.2926 | 103.72 | 331.47 | 10,082.791 | 33.445 | 299.463 |
516 | 2.2926 | 101.75 | 303.05 | 5176.401 | 17.970 | 6.891 |
518 | 2.2926 | 100.75 | 302.05 | 5003.788 | 17.400 | 4.340 |
Enthalpy Inflow | Enthalpy Outflow | Workflow | Heat Flow | Irreversibility Rate | ||
---|---|---|---|---|---|---|
Air blower | −3.082 | 19.340 | −16.258 | 0.0 | −8.389 | −8.389 |
Anode | −1.443 | 6.368 | 0.0 | −4.925 | 4.648 | −0.277 |
Cathode | −59.280 | 76.067 | 0.0 | −16.787 | −24.097 | −40.884 |
Humidifier | −95.408 | 90.615 | 0.0 | 4.793 | 13.484 | 18.277 |
HTX for the FCS | −19,103.614 | 21,486.193 | −2742.579 | 2484.490 | −258.089 | |
HTXDI | −27,019.635 | 29,384.117 | 0.0 | −2364.482 | 2316.269 | −48.213 |
DIWT | −19,301.256 | 19,136.736 | 164.521 | −149.644 | 14.877 | |
Pump 1 | −19,136.736 | 19,103.614 | −5.503 | 38.625 | −33.864 | 4.762 |
HTXWC | −10,082.791 | 5176.401 | −18.000 | 4924.390 | −4613.819 | 310.572 |
Hot WT | −5003.788 | 5185.052 | 0.0 | −181.264 | 178.548 | −2.716 |
Pump 2 | −5185.052 | 5173.442 | −0.645 | 12.255 | −11.931 | 0.324 |
Component | Net Exergy Flow Rates (kJ/h) | Irreversibility | |||
---|---|---|---|---|---|
Rate (kJ/h) | |||||
Air blower | −16.258 | 0.0 | 0.244 | 24.403 | −8.389 |
Anode | 0.0 | 0.0 | 1.622 | −1.620 | −0.002 |
Cathode | 0.0 | 0.0 | 31.651 | −6.521 | −25.131 |
Humidifier | 0.0 | 0.0 | −1.381 | −16.834 | 18.215 |
HTX in the FCS | 0.0 | 0.0 | 259.935 | −1.845 | −258.090 |
FCS | 2923.596 | −5666.175 | (2642.475) | 0.0 | 100.104 |
HTX DI | 49.638 | −1.425 | −48.213 | ||
DIWT | 0.0 | 0.0 | −13.945 | −0.932 | 14.877 |
Pump 1 | −5.503 | 0.0 | −3.083 | 3.824 | 4.762 |
HTXWC | −18.0 | 0.0 | −292.490 | −0.082 | 310.572 |
Hot WT | 2.650 | 0.066 | −2.716 | ||
Pump 2 | −0.645 | −0.196 | 0.518 | 0.324 | |
Total | 2883.19 | −5666.175 | (2677.12) | −0.448 | 106.313 |
C1P | C2T | C3T | C4C | C5T | C6W | C7T |
−0.8955 | −230.52 | 102.99 | −86,238.0 | −4.173 | 0.2703 | −3.9587 |
C8T | C9P | C10T | C11T | C12P | CT | CP |
5.80 | 94.494 | −4.790 | 2.065 | 52.719 | 114.76 | 12.759 |
CC | CW | CS | ||||
−86,238.0 | 0.2703 | −4.483 |
Component | Electricity Cost Flow | Thermal Exergy Cost Flow | Mechanical Exergy Cost Flow | Lost Cost Flow | Invest Cost Flow | Investment (USD) |
---|---|---|---|---|---|---|
Air blower | −0.004 | 0.028 | −0.022 | 0.038 | −0.039 | 1431.5 |
Anode | 0.167 | −0.021 | −0.146 | 5332.4 | ||
Cathode | −3.515 * | 3.632 | −0.083 | 0.113 | −0.146 | 5332.4 |
Humidifier | 0.318 | −0.215 | −0.082 | −0.022 | 800.0 | |
HTX in the FCS | −1.085 | −0.024 | 1.157 | −0.049 | 1775.3 | |
FCS | 0.790 | −0.449 | −0.342 | 7856.6 | ||
HTX DI | −0.197 | −0.018 | 0.216 | −0.001 | 52.2 | |
DIWT | 0.081 | −0.012 | −0.067 | −0.002 | 84.2 | |
Pump 1 | −0.001 | −0.354 | 0.361 | −0.001 | −0.005 | 168.4 |
HTXWC | −0.005 | 1.401 | −0.001 | −1.392 | −0.003 | 111.1 |
Pump 2 | −0.022 | 0.027 | −0.0 | −0.005 | 168.4 | |
Hot WT | 0.005 | 0.001 | 0.012 | −0.018 | 673.7 | |
Total | −2.735 (0.78+) | 3.974 | −0.007 | −0.455 | −0.778 | 23,786.2 |
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Yoo, Y.; Lee, S.-Y.; Seo, S.-H.; Oh, S.-D.; Kwak, H.-Y. Energy, Exergetic, and Thermoeconomic Analyses of Hydrogen-Fueled 1-kW Proton-Exchange Membrane Fuel Cell. Entropy 2024, 26, 566. https://doi.org/10.3390/e26070566
Yoo Y, Lee S-Y, Seo S-H, Oh S-D, Kwak H-Y. Energy, Exergetic, and Thermoeconomic Analyses of Hydrogen-Fueled 1-kW Proton-Exchange Membrane Fuel Cell. Entropy. 2024; 26(7):566. https://doi.org/10.3390/e26070566
Chicago/Turabian StyleYoo, Yungpil, Sang-Yup Lee, Seok-Ho Seo, Si-Doek Oh, and Ho-Young Kwak. 2024. "Energy, Exergetic, and Thermoeconomic Analyses of Hydrogen-Fueled 1-kW Proton-Exchange Membrane Fuel Cell" Entropy 26, no. 7: 566. https://doi.org/10.3390/e26070566
APA StyleYoo, Y., Lee, S.-Y., Seo, S.-H., Oh, S.-D., & Kwak, H.-Y. (2024). Energy, Exergetic, and Thermoeconomic Analyses of Hydrogen-Fueled 1-kW Proton-Exchange Membrane Fuel Cell. Entropy, 26(7), 566. https://doi.org/10.3390/e26070566