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Mathematical modeling of high-pressure PEM water electrolysis

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Abstract

This paper is devoted to the modeling and numerical optimization of proton-exchange membrane (PEM) water electrolysers for operation at elevated pressures (up to 130 bars). The model takes into account different geometrical parameters of the PEM cell, the kinetics of the hydrogen and oxygen evolution reactions, the electro-osmotic drag of water molecules, the permselectivity of the solid polymer electrolyte and associated gas cross-over phenomena. The role of various operating parameters (such as pressure, temperature, current density, flow rate of water) on cell efficiency, faradaic yield and heat produced during water electrolysis is evaluated and discussed. The model is also used for the purpose of optimizing the performances of PEM cells. In particular, optimal values of some critical operating parameters (current density, rate of water supplied to the anodes) are recommended.

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Abbreviations

Cg, Cl, CH, CO (mol m−3):

Molar density of gas, liquid, hydrogen, oxygen.

υg, υl (m s−1):

Velocity of gas and liquid.

υ0 (m s−1):

Velocity of cooling water

Pg, Pl, Pc (Pa):

Pressure of gas, liquid and capillary pressure

Kp (m2):

Permeability of porous current collector

Rp (m):

Average pore radius of porous current collector

krl, krg:

Relative permeabilities of liquid and water

s (adim.):

Saturation of porous current collector

sfc (adim.):

Saturation at the current collector–flow channel interface

scl (adim.):

Saturation at the current collector–catalytic layer interface

θc (deg.):

Wetting angle of porous current collector

ε (adim.):

Porosity of gas diffusion layer

Rbc (m):

Critical bubble radius

Ng, Nl, N (mol m−2 s−1):

Flux of gas, liquid, total flux

Nga, Nla (mol m−2 s−1):

Gas and liquid fluxes at current collector–anodic layer interface

Ngc, Nlc (mol m−2 s−1):

Gas and liquid fluxes at current collector–cathodic layer interface

CH (mol m−3):

Hydrogen concentration in the gas phase

Rp (m):

Effective pore radius

iΣ, i0, ip (A m−2):

Total, useful, and parasitic current densities

np (adim.):

Electro-osmotic drag coefficient

Ps (Pa):

Pressure of saturated water vapor

hm (m):

Membrane thickness

h (m):

Gas diffusion layer thickness

hfc (m):

Flow channel thickness

ΔT (°C):

Temperature difference along the membrane-electrode assembly (MEA)

SMEA (m2):

Active area of MEA

iex (A m−2):

Exchange current density

ρ m (Ohm−1 m−1):

Specific ionic conductivity of solid polymer electrolyte

Cpw = 4,217 (J kg−1 K−1):

Specific heat of liquid water at T = 100 °C

μl = 2.822 × 10−2 (Pa s):

Dynamic viscosity of liquid water at T = 100 °C and P = 13 MPa

μH = 1.09 × 10−5 (Pa s):

Dynamic viscosity of hydrogen at T = 100 °C and P = 13 MPa

μO = 2.47 × 10−5 (Pa s):

Dynamic viscosity of oxygen at T = 100 °C and P = 13 MPa

σ = 0.05884 (Pa m):

Surface tension of water at T = 100 °C and P = 13 MPa

ГH = 1.67 × 10−3 (mol mol−1):

Water solubility of hydrogen at T = 100 °C and P = 13 MPa

ГO = 1.85 × 10−3 (mol/mol):

Water solubility of oxygen at T = 100 °C and P = 13 MPa

Eeq = 1.29 (V):

Equilibrium cell voltage at T = 100 °C and P = 13.0 MPa

ΔH° = −285.0 (kJ/mol):

Enthalpy change for reaction \( {\text{H}}_{2} + {\frac{1}{2}}{\text{O}}_{2} \to {\text{H}}_{2} {\text{O}}\left( l \right) \) at T = 100 °C

np = 2.3 + 0.0212 · (T − 80):

Number of solvated water molecules associated with each proton (drag factor) in solid polymer electrolyte at full humidification versus temperature T in  °C (approximated from data in [1]).

\( D_{\text{OM}} = 2.44\, \times \,10^{ - 8} \exp \left( { - {\frac{2,100}{T}}} \right)\, \)(m2 s−1):

Diffusion coefficient of oxygen in solid polymer electrolyte at full humidification (approximated from data in [2]).

\( D_{\text{HM}} = 5.65\, \times \,10^{ - 8} \exp \left( { - {\frac{2,100}{T}}} \right)\,\, \)(m2 s−1):

Diffusion coefficient of hydrogen in solid polymer electrolyte at full humidification (approximated from data in [2]).

\( F_{\text{c}} (s) = \left( {\begin{array}{*{20}c} {1.417(1 - s) - 2.12(1 - s)^{2} + 1.263(1 - s)^{3} \quad } & {{\text{if}}\,\theta_{\text{c}} < 90^{^\circ } } \\ {1.417s - 2.12s^{2} + 1.263s^{3} } & {{\text{if}}\,\theta_{\text{c}} > 90^{^\circ } } \\ \end{array} } \right. \) :

Leverett function which is used to determine capillary pressure in porous media as a function of the wetting angle θ c (taken from [3]).

\( E_{\text{r}} = E^{(0)} - 8.5\, \times \,10^{ - 4} \left( {T - 298.15} \right) + 4.308\, \times \,10^{ - 5} T\ln \left( {P_{\text{H}} P_{\text{O}}^{0.5} } \right) \) (V):

Reversible voltage of electrolysis cell as a function of temperature T and gas pressures.

\( E_{\text{tn}} = - {\frac{{\Updelta H^{(0)} }}{2F}} - 8.5\, \times \,10^{ - 4} \left( {T - 298.15} \right) + 4.308\, \times \,10^{ - 5} T\ln \left( {P_{\text{H}} P_{\text{O}}^{0.5} } \right) \) (V):

Thermoneutral voltage of electrolysis cell as a function of temperature T and gas pressures.

References

  1. Ren X, Gottesfeld S (2001) J Electrochem Soc 148(1):A87

    Article  CAS  Google Scholar 

  2. Broka K, Ekdunge P (1997) J Appl Electrochem 27:117

    Article  CAS  Google Scholar 

  3. Pasaogullari U, Wang CY (2004) J Electrochem Soc 151:A399

    Article  CAS  Google Scholar 

  4. Millet P, Andolfatto F, Durand R (1996) Int J Hydrogen Energy 21:87

    Article  CAS  Google Scholar 

  5. Grigoriev SA, Porembsky VI, Fateev VN (2006) Int J Hydrogen Energy 31:171

    Article  CAS  Google Scholar 

  6. Ni M, Leung MKH, Leung DYC (2008) Energy Convers Manag 49:2748

    Article  CAS  Google Scholar 

  7. Onda K, Murakami T, Hikosaka T, Kobayashi M, Notu R, Ito K (2002) J Electrochem Soc 149:A1069

    Article  CAS  Google Scholar 

  8. Choi P, Bessarabov DG, Dattaa R (2004) Solid State Ion 175:535

    Article  CAS  Google Scholar 

  9. Springer TE, Zawodzinski TA, Gottesfeld S (1991) J Electrochem Soc 138:2334

    Article  CAS  Google Scholar 

  10. Springer TE, Wilson MS, Gottesfeld S (1993) J Electrochem Soc 140:3513

    Article  CAS  Google Scholar 

  11. Nguyen T, White RE (1993) J Electrochem Soc 140:2178

    Article  CAS  Google Scholar 

  12. He W, Yi JS, Nguyen TV (2000) AIChE J 46:2053

    Article  CAS  Google Scholar 

  13. Wang ZH, Wang CY, Chen KS (2001) J Power Sources 94:40

    Article  CAS  Google Scholar 

  14. You L, Liu H (2002) Int J Heat Mass Transfer 45:2277

    Article  CAS  Google Scholar 

  15. Natarajan D, Nguyen TV (2001) J Electrochem Soc 148:A1324

    Article  CAS  Google Scholar 

  16. Kaviany M (1999) Principles of heat transfer in porous media. Springer, New York

    Google Scholar 

  17. Wang CY, Cheng P (1997) Adv Heat Transfer 30:93

    CAS  Google Scholar 

  18. Grigoriev SA, Millet P, Korobtsev SV, Porembskiy VI, Pepic M, Etievant C, Puyenchet C, Fateev VN (2009) Int J Hydrogen Energy 34:5986

    Article  CAS  Google Scholar 

  19. Tsyganov IA, Pozdnyakov AI, Richter E, Majtts MF (2007) Solid State Phys. Bull Nizhniy Novgorod Univ N.I. Lobachevsky 1:52 (in Russian)

    Google Scholar 

  20. Vasilev VV, Luchaninov AA, Strelnitsky VE, Tolstolutskaja GD, Kopanets IE, Sevidova EK, Kononenko VI (2005) Quest Nucl Sci Tech 3(86):167 (in Russian)

    Google Scholar 

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Acknowledgments

This work has been supported by the Federal Agency for Science and Innovations of the Russian Federation within the framework of the Federal Principal Scientific-Technical Programme “Researches and development on priority directions in development of scientific technological complex of Russia for 2007–2012” and by the Commission of the European Communities (6th Framework Programme, STREP project GenHyPEM no 019802). Financial support from the Global Energy International Prize Non-Profit Foundation (Grant no MG-2008/04/3) is also gratefully acknowledged.

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Authors and Affiliations

  1. Hydrogen Energy and Plasma Technology Institute of Russian Research Center “Kurchatov Institute”, Kurchatov sq., 1, 123182, Moscow, Russia

    S. A. Grigoriev, A. A. Kalinnikov, V. I. Porembsky & V. N. Fateev

  2. Moscow Power Engineering Institute (Technical University), Krasnokazarmennaya 14, 111250, Moscow, Russia

    S. A. Grigoriev & V. N. Fateev

  3. Institut de Chimie Moléculaire et des Matériaux, UMR CNRS, n° 8182, Université Paris Sud, bât 420, 91405, Orsay Cedex, France

    P. Millet

Authors
  1. S. A. Grigoriev
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  2. A. A. Kalinnikov
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  3. P. Millet
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  4. V. I. Porembsky
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  5. V. N. Fateev
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Correspondence to S. A. Grigoriev.

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Grigoriev, S.A., Kalinnikov, A.A., Millet, P. et al. Mathematical modeling of high-pressure PEM water electrolysis. J Appl Electrochem 40, 921–932 (2010). https://doi.org/10.1007/s10800-009-0031-z

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