Exergy and Exergoeconomic Analysis for the Proton Exchange Membrane Water Electrolysis under Various Operating Conditions and Design Parameters
Abstract
:1. Introduction
2. Numerical Simulation
2.1. System Description
2.2. Model Assumptions
- The system is modelled in a steady state condition.
- Flow is laminar and incompressible.
- Changes in kinetic and potential energy are discarded.
- The anode pressure is equal to 1 bar.
- The ideal gas behavior is applied to the gas mixture.
- The contact resistance between various layers has been overlooked.
- The GDL, catalyst layer, and membrane are treated as isotropic and homogeneous.
2.3. Modeling Definition
2.4. Gas Crossover through the Membrane
2.5. PEMWE Efficiency according to the Voltage and Exergy Analysis
2.6. Exergoeconomic Analysis for the PEMWE
2.7. Validation
3. Results and Discussion
3.1. Effect of the Current Density
3.2. Effect of the Operating Temperature
3.3. Effect of the Cathode Pressure
3.4. Effect of the Membrane Thickness
3.5. Electricity Price Effect
4. Conclusions
- The current density, operating temperature, membrane thickness, and cathode pressure have a tremendous effect on the exergy and exergoeconomic analysis for PEMWE.
- Both voltage and second law efficiency are favorably affected by increasing the operating temperature and decreasing the membrane thickness, minimizing the hydrogen exergy cost. When the gas leakage through the membrane increases, the trade-off between the ohmic overpotentials losses and hydrogen leakage for ideal overall cell performance and hydrogen cost becomes a critical issue and needs future research. The voltage and second law efficiency are reduced by nearly 9% and 7.3% at a current density of 15,000 A/m2 by increasing the membrane thickness from 0.05 to 0.25 mm. At the same time, the hydrogen exergy cost is increased from 36.5 to 39.3 USD/GJ.
- The increase in exergy destroyed and hydrogen exergy cost, as well as the decline in second law efficiency due to the gas crossover, are more noticeable at higher pressures. As the cathode pressure rises from 1 to 30 bar at a current density of 10,000 A/m2, the increase in energy destroyed and hydrogen exergy cost, as well as the decline in second law efficiency, increase from 0.9 kJ/mol, 0.11 USD/GJ, and 0.2% to 38.5 kJ/mol, 4.6 USD/GJ, and 7.3%, respectively. As a result, raising the cathode pressure not only significantly deteriorates the gas crossover performance but also raises the hazard of explosion. Therefore, further study is needed in the future to propose alternate solutions to the gas crossover and explosion issues.
- The effects of gas crossover and hydrogen leakage on the exergy and exergoeconomic analysis are prominent at low current densities and reduce gradually with increasing current densities, and finally become insignificant at high current densities. Furthermore, increasing the current density has a positive effect on the hydrogen exergy cost. The hydrogen exergy cost is reduced from 59.7 to 33.4 USD/GJ as the current density grows from 5000 to 20,000 A/m2. As a result, the PEMWE performance associated with the gas crossover phenomenon and the hydrogen cost is more optimal at high current density.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
Nomenclature | |
Flow cost rate, USD × h−1 | |
c | Flow cost rate per unit exergy, USD × GJ−1 |
CRF | Factor of capital recovery |
Effective diffusion coefficient, m2 × s−1 | |
Standard enthalpy of formation for liquid water, kJ × mol−1 | |
ir | Interest rate |
Total current density, A | |
n | Overall system’s operational period, year |
Reaction rate of species, mol × m−2 × s−1 | |
Diffusive hydrogen crossover flux, mol × m−2 × s−1 | |
Diffusive oxygen crossover flux, mol × m−2 × s−1 | |
Hydrogen crossover flux due to the differential pressure, mol × m−2 × s−1 | |
Total hydrogen crossover flux, mol × m−2 × s−1 | |
Total oxygen crossover flux, mol × m−2 × s−1 | |
Diffusive gas permeability coefficients, mol × m−1 × s−1 × bar −1 | |
Gas permeability coefficients due to the differential pressure, mol × m−1 × s−1 × bar −1 | |
Thickness of membrane, mm | |
Actual voltage, V | |
Energy consumed, W | |
Rate of exergy, W | |
Total investment cost, USD × s−1 | |
Capital cost, USD × s−1 | |
Operating cost, USD × s−1 | |
Greek symbols | |
Voltage efficiency | |
Specific exergy, J × kg−1 | |
Second−law efficiency | |
Faraday efficiency | |
Abbreviations | |
ABP | Anode bipolar plate |
CBP | Cathode bipolar plate |
CFD | Computational fluid dynamics |
PEM | Membrane |
PEMWE | Proton exchange membrane water electrolysis |
WE | water electrolysis |
References
- Singh, S.; Jain, S.; PSV; Tiwari, A.; Nouni, M.; Pandey, J.; Goel, S. Hydrogen: A sustainable fuel for future of the transport sector. Renew. Sustain. Energy Rev. 2015, 51, 623–633. [Google Scholar] [CrossRef]
- Barbir, F. PEM electrolysis for production of hydrogen from renewable energy sources. Sol. Energy 2005, 78, 661–669. [Google Scholar] [CrossRef]
- Atlam, O.; Kolhe, M. Equivalent electrical model for a proton exchange membrane (PEM) electrolyser. Energy Convers. Manag. 2011, 52, 2952–2957. [Google Scholar] [CrossRef]
- Ferrero, D.; Santarelli, M. Investigation of a novel concept for hydrogen production by PEM water electrolysis integrated with multi-junction solar cells. Energy Convers. Manag. 2017, 148, 16–29. [Google Scholar] [CrossRef]
- Li, Y.; Yang, G.; Yu, S.; Kang, Z.; Mo, J.; Han, B.; Talley, D.; Zhang, Y. In-situ investigation and modeling of electrochemical reactions with simultaneous oxygen and hydrogen microbubble evolutions in water electrolysis. Int. J. Hydrogen Energy 2019, 44, 28283–28293. [Google Scholar] [CrossRef]
- Sapountzi, M.; Gracia, M.; Weststrate, C.J.; Fredriksson, O.A.; Niemantsverdriet, J.W. Electrocatalysts for the generation of hydrogen, oxygen and synthesis gas. Prog. Energy Combust. Sci. 2016, 58, 1–35. [Google Scholar] [CrossRef] [Green Version]
- Li, Y.; Kang, Z.; Mo, J.; Yang, G.; Yu, S.; Talley, D.A.; Han, B.; Zhang, F.Y. In-situ investigation of bubble dynamics and two-phase flow in proton exchange membrane electrolyzer cells. Int. J. Hydrogen Energy 2018, 43, 11223–11233. [Google Scholar] [CrossRef]
- Lagadec, M.F.; Grimaud, A. Water electrolysers with closed and open electrochemical systems. Nat. Mater. 2020, 19, 1140–1150. [Google Scholar] [CrossRef]
- Laguna-Bercero, M.A. Recent advances in high temperature electrolysis using solid oxide fuel cells: A review. J. Power Sources 2012, 203, 4–16. [Google Scholar] [CrossRef] [Green Version]
- Kumar, S.S.; Ramakrishna, S.U.B.; Krishna, S.V.; Srilatha, K.; Devi, B.R.; Himabindu, V. Synthesis of titanium (IV) oxide composite membrane for hydrogen production through alkaline water electrolysis. S. Afr. J. Chem. Eng. 2018, 25, 54–61. [Google Scholar] [CrossRef]
- Kadier, A.; Simayi, Y.; Abdeshahian, P.; Azman, N.F.; Chandrasekhar, K.; Kalil, M.S. A comprehensive review of microbial electrolysis cells (MEC) reactor designs and configurations for sustainable hydrogen gas production. Alex. Eng. J. 2016, 55, 427–443. [Google Scholar] [CrossRef] [Green Version]
- Ju, H.K.; Badwal, S.; Giddey, S. A comprehensive review of carbon and hydrocarbon assisted water electrolysis for hydrogen production. Appl. Energy 2018, 231, 502–533. [Google Scholar] [CrossRef]
- Nikolaidis, P.; Poullikkas, A. A comparative overview of hydrogen production processes. Renew. Sustain. Energy 2017, 67, 597–611. [Google Scholar] [CrossRef]
- Cheng, J.; Zhang, H.; Chen, G.; Zhang, Y. Study of IrxRu1-xO2 oxides as anodic electrocatalysts for solid polymer electrolyte water electrolysis. Electrochim. Acta 2009, 54, 6250–6256. [Google Scholar] [CrossRef]
- Kumar, S.S.; Ramakrishna, S.U.B.; Devi, B.R.; Himabindu, V. Phosphorus-doped graphene supported palladium (Pd/PG) electrocatalyst for the hydrogen evolution reaction in PEM water electrolysis. Int. J. Green Energy 2018, 15, 558–567. [Google Scholar] [CrossRef]
- Yunus, A.Ç. Thermodynamics: An Engineering Approach; McGraw-Hill Education: New York, NY, USA, 2014; Chapter 8. [Google Scholar]
- Rosen, M.A. Energy and exergy analyses of electrolytic hydrogen production. Int. J. Hydrogen Energy 1995, 20, 547–553. [Google Scholar] [CrossRef]
- Ni, M.; Leung, H.; Leung, C. Energy and exergy analysis of hydrogen production by a proton exchange membrane (PEM) electrolyzer plant. Energy Convers. Manag. 2008, 49, 2748–2756. [Google Scholar] [CrossRef]
- Nafchi, F.M.; Afshari, E.; Baniasadi, E.; Javani, N. A parametric study of polymer membrane electrolyser performance, energy and exergy analyses. Int. J. Hydrogen Energy 2019, 44, 18662–18670. [Google Scholar] [CrossRef]
- Javadi, M.; Najafi, N.; Abhari, M.; Jabery, R.; Pourtaba, H. 4E analysis of three different configurations of a combined cycle power plant integrated with a solar power tower system. Sustain. Energy Technol. Assess. 2021, 48, 101599. [Google Scholar] [CrossRef]
- Javadi, M.; Khodabakhshi, S.; Ghasemiasl, R.; Jabery, R. Sensivity analysis of a multi-generation system based on a gas/hydrogen-fueled gas turbine for producing hydrogen, electricity and freshwater. Energy Convers. Manag. 2022, 252, 115085. [Google Scholar] [CrossRef]
- Ozden, E.; Tari, I. Energy-exergy and economic analyses of a hybrid solar-hydrogen renewable energy system in Ankara, Turkey. Appl. Therm. Eng. 2016, 99, 169–178. [Google Scholar] [CrossRef]
- Kazim, A.M. Exergoeconomic analysis of a PEM electrolyser at various operating temperatures and pressures. Int. J. Energy Res. 2005, 29, 539–548. [Google Scholar] [CrossRef]
- Toghyani, S.; Baniasadi, E.; Afshari, E. Numerical simulation and exergoeconomic analysis of a high temperature polymer exchange membrane electrolyzer. Int. J. Hydrogen Energy 2019, 44, 31731–31744. [Google Scholar] [CrossRef]
- Lee, B.; Heo, J.; Kim, S.; Sung, C.; Moon, C.; Moon, S.; Lim, H. Economic feasibility studies of high pressure PEM water electrolysis for distributed H2 refueling stations. Energy Convers. Manag. 2018, 162, 139–144. [Google Scholar] [CrossRef]
- Grigoriev, S.A.; Millet, P.; Korobtsev, S.V.; Porembskiy, V.I.; Pepic, M.; Etievant, C.; Puyenchet, C.; Fateev, V.N. Hydrogen safety aspects related to high-pressure polymer electrolyte membrane water electrolysis. Int. J. Hydrogen Energy 2009, 34, 5986–5991. [Google Scholar] [CrossRef]
- Schalenbach, M.; Carmo, M.; Fritz, D.L.; Mergel, J.; Stolten, D. Pressurized PEM water electrolysis: Efficiency and gas crossover. Int. J. Hydrogen Energy 2013, 38, 14921–14933. [Google Scholar] [CrossRef]
- Grigoriev, S.A.; Porembskiy, V.I.; Korobtsev, S.V.; Fateev, V.N.; Auprêtre, F.; Millet, P. High-pressure PEM water electrolysis and corresponding safety issues. Int. J. Hydrogen Energy 2011, 36, 2721–2728. [Google Scholar] [CrossRef]
- Truc, N.T.; Ito, S.; Fushinobu, K. Numerical and experimental investigation on the reactant gas crossover in a PEM fuel cell. Int. J. Heat Mass Transf. 2018, 127, 447–456. [Google Scholar] [CrossRef]
- Omrani, R.; Shabani, B. Hydrogen crossover in proton exchange membrane electrolysers: The effect of current density, pressure, temperature, and compression. Electrochim. Acta 2021, 377, 138085. [Google Scholar] [CrossRef]
- Afshari, E.; Khodabakhsh, S.; Jahantigh, N.; Toghyani, S. Performance assessment of gas crossover phenomenon and water transport mechanism in high pressure PEM electrolyzer. Int. J. Hydrogen Energy 2021, 46, 11029–11040. [Google Scholar] [CrossRef]
- Hassan, A.H.; Wang, X.; Liao, Z.; Xu, C. Numerical Investigation on the Effects of Design Parameters and Operating Conditions on the Electrochemical Performance of PEM Water Electrolysis. J. Therm. Sci. 2022, accepted. [Google Scholar]
- Toghyani, S.; Afshari, E.; Baniasadi, E.; Atyabi, S.A.; Naterer, G.F. Thermal and electrochemical performance assessment of a high temperature PEM electrolyzer. Energy 2018, 152, 237–246. [Google Scholar] [CrossRef]
- Olesen, A.C.; Rømer, C.; Kær, S.K. A numerical study of the gas-liquid, two-phase flow maldistribution in the anode of a high pressure PEM water electrolysis cell. Int. J. Hydrogen Energy 2016, 41, 52–68. [Google Scholar] [CrossRef] [Green Version]
- Rahim, A.H.A.; Tijani, A.S. Modeling and Analysis the Effects of Temperature and Pressure on the Gas-Crossover in Polymer Electrolyte Membrane Electrolyzer. Int. J. Energy Power Eng. 2016, 10, 1–7. [Google Scholar] [CrossRef]
- Zhang, H.; Su, S.; Lin, G.; Chen, J. Efficiency calculation and configuration design of a PEM electrolyzer system for hydrogen production. Int. J. Electrochem. Sci. 2012, 7, 4143–4157. [Google Scholar]
- Toghyani, S.; Afshari, E.; Baniasadi, E.; Atyabi, S.A. Thermal and electrochemical analysis of different flow field patterns in a PEM electrolyzer. Electrochim. Acta 2018, 267, 234–245. [Google Scholar] [CrossRef]
- Moulthrop, L.; Anderson, E.; Chow, O.; Friedland, R.; Maloney, T.; Schiller, M. Commercial Optimization of a 100 kg/day PEM Based Hydrogen Generator for Energy and Industrial Applications. In Proceedings of the 16th World Hydrogen Energy Conference (WHEC 16), Lyon, France, 13–16 June 2006. [Google Scholar]
- Wang, Z.M.; Xu, C.; Wang, X.Y.; Liao, Z.R.; Du, X.Z. Numerical investigation of water and temperature distributions in a proton exchange membrane electrolysis cell. Sci. China Technol. Sci. 2021, 64, 1555–1566. [Google Scholar] [CrossRef]
- Kaya, M.F.; Demir, N. Numerical Investigation of PEM Water Electrolysis Performance for Different Oxygen Evolution Electrocatalysts. Fuel Cells 2017, 17, 37–47. [Google Scholar] [CrossRef]
- Zinser, A.; Papakonstantinou, G.; Sundmacher, K. Analysis of mass transport processes in the anodic porous transport layer in PEM water electrolysers. Int. J. Hydrogen Energy 2019, 44, 28077–28087. [Google Scholar] [CrossRef]
- Han, B.; Mo, J.; Kang, Z.; Zhang, F.Y. Effects of membrane electrode assembly properties on two-phase transport and performance in proton exchange membrane electrolyzer cells. Electrochim. Acta 2016, 188, 317–326. [Google Scholar] [CrossRef] [Green Version]
- Ito, H.; Maeda, T.; Nakano, A.; Kato, A.; Yoshida, T. Influence of pore structural properties of current collectors on the performance of proton exchange membrane electrolyzer. Electrochim. Acta 2013, 100, 242–248. [Google Scholar] [CrossRef]
- Ruiz, D.; Sasmito, A.P.; Shamim, T. Numerical Investigation of the High Temperature PEM Electrolyzer: Effect of Flow Channel Configurations. ECS Trans. 2013, 58, 99–112. [Google Scholar] [CrossRef]
- Nguyen, T.; Fushinobu, K. Effect of operating conditions and geometric structure on the gas crossover in PEM fuel cell. Sustain. Energy Technol. Assess. 2020, 37, 100584. [Google Scholar] [CrossRef]
- Tsai, S.W.; Chen, Y.S. A mathematical model to study the energy efficiency of a proton exchange membrane fuel cell with a dead-ended anode. Appl. Energy 2017, 188, 151–159. [Google Scholar] [CrossRef]
- Baniasadi, E.; Toghyani, S.; Afshari, E. Exergetic and exergoeconomic evaluation of a trigeneration system based on natural gas-PEM fuel cell. Int. J. Hydrogen Energy 2017, 42, 5327–5339. [Google Scholar] [CrossRef]
- Szargut, J. Exergy Method: Technical and Ecological Applications; WIT Press: Southampton, UK, 2005. [Google Scholar]
- Fragiacomo, P.; Genovese, M. Modeling and energy demand analysis of a scalable green hydrogen production system. Int. J. Hydrogen Energy 2019, 44, 30237–30255. [Google Scholar] [CrossRef]
- Kocha, S.S.; Yang, J.D.; Yi, J.S. Characterization of Gas Crossover and Its Implications in PEM Fuel Cells. AICHE J. 2015, 61, 857–866. [Google Scholar] [CrossRef]
- Gurau, V.; Liu, H.; Kakaç, S. Two-dimensional model for proton exchange membrane fuel cells. AIChE J. 1998, 44, 2410–2422. [Google Scholar] [CrossRef]
- Harrison, K.W.; Martin, G.D.; Ramsden, T.G.; Kramer, W.E.; Novachek, F.J. The Wind-to-Hydrogen Project: Operational Experience, Performance Testing, and Systems Integration; National Renewable Energy Lab (NREL): Golden, CO, USA, 2011. [Google Scholar]
- Bejan, A.; Tsatsaronis, G.; Moran, M. Thermal Design and Optimization; John Wiley & Sons Canada Ltd.: Toronto, ON, Canada, 1996. [Google Scholar]
- Rosen, M.A.; Dincer, I. Exergoeconomic analysis of power plants operating on various fuels. Appl. Therm. Eng. 2003, 23, 643–658. [Google Scholar] [CrossRef]
- Ameri, M.; Ahmadi, P.; Hamidi, A. Energy, exergy and exergoeconomic analysis of a steam power plant: A case study. Int. J. Energy Res. 2002, 33, 499–512. [Google Scholar] [CrossRef]
- Millet, P. Water electrolysis using eme technology: Electric potential distribution inside a nafion membrane during electrolysis. Electrochim. Acta 1994, 39, 2501–2506. [Google Scholar] [CrossRef]
- Chiou, J.S.; Paul, D.R. Gas Permeation in a Dry Nafion Membrane. Ind. Eng. Chem. Res. 1988, 27, 2161–2164. [Google Scholar] [CrossRef]
- Lee, H.; Lee, B.; Byun, M.; Lim, H. Economic and environmental analysis for PEM water electrolysis based on replacement moment and renewable electricity resources. Energy Convers. Manag. 2020, 224, 113477. [Google Scholar] [CrossRef]
Parameters | Value | Unit | Source |
---|---|---|---|
Channel height | 1 | mm | [24] |
Channel width | 1 | mm | [24] |
Channel rib | 1 | mm | [24] |
Channel length | 50 | mm | [33] |
Thickness of GDL | 300 | µm | [34] |
Thickness of membrane, Nafion™ 212 | 50 | µm | [27,35,36] |
Thickness of CL | 10 | µm | [37] |
Area | 25 × 50 | cm2 | [38] |
Number of cells | 200 | - | [38] |
Number of stacks | 6 | - | - |
c | Value | Unit | Source |
---|---|---|---|
GDL porosity ( | 0.4 | - | [39] |
CL porosity () | 0.25 | - | [39] |
GDL Permeability | 1 × 10−11 | m2 | [40] |
Gas constant (R) | 8.3145 | J × mol−1 × K−1 | [41] |
Anode transfer coefficient () | 1 | - | - |
Cathode transfer coefficient () | 0.5 | - | - |
Anode reference exchange current density | 1 × 10−6 | A/cm2 | - |
Cathode reference exchange current density | 2 × 10−2 | A/cm2 | - |
Operating pressure (P) | 1 | bar | - |
Operating temperature (T) | 353 | K | - |
Diffusivity of oxygen | 3.2 × 10−5 | m2/s | [37,42,43,44] |
Diffusivity of hydrogen | 1.1 × 10−4 | m2/s | [37,42,43,44] |
Diffusivity of water | 7.35 × 10−5 | m2/s | [37,42,43,44] |
Reference temperature | 353 | K | [40] |
Reference pressure | 1.01325 | bar | [40] |
Activation energy | 53.99 | kJ/mol | [40] |
Membrane dry density, | 2000 | kg/m3 | [29,45] |
Membrane dry equivalent weight, Mm | 1.1 | kg/mol | [45] |
Activation energy of H2 and O2, | 1.8 × 104,2 × 104 | J/mol | [29,46] |
Permeability coefficient, | 2 × 10−9 | mol/(m × s × bar) | [27] |
Standard enthalpy of formation for liquid water, | 285,840 | J/mol | [27] |
Chemical exergy of hydrogen | 236.1 | kJ/mol | [24,47,48] |
Chemical exergy of oxygen | 3.97 | kJ/mol | [24,47,48] |
Chemical exergy of liquid water | 0.9 | kJ/mol | [48] |
Electricity cost | 0.06 | USD/kWh | [25] |
Oxygen cost | 0.011 | USD/kg | [24] |
Water cost | 1 | USD/m3 | [24] |
Thermo-neutral voltage | 1.48 | V | [49] |
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Hassan, A.H.; Liao, Z.; Wang, K.; Abdelsamie, M.M.; Xu, C.; Wang, Y. Exergy and Exergoeconomic Analysis for the Proton Exchange Membrane Water Electrolysis under Various Operating Conditions and Design Parameters. Energies 2022, 15, 8247. https://doi.org/10.3390/en15218247
Hassan AH, Liao Z, Wang K, Abdelsamie MM, Xu C, Wang Y. Exergy and Exergoeconomic Analysis for the Proton Exchange Membrane Water Electrolysis under Various Operating Conditions and Design Parameters. Energies. 2022; 15(21):8247. https://doi.org/10.3390/en15218247
Chicago/Turabian StyleHassan, Alamir H., Zhirong Liao, Kaichen Wang, Mostafa M. Abdelsamie, Chao Xu, and Yanhui Wang. 2022. "Exergy and Exergoeconomic Analysis for the Proton Exchange Membrane Water Electrolysis under Various Operating Conditions and Design Parameters" Energies 15, no. 21: 8247. https://doi.org/10.3390/en15218247