# Minimizing Specific Energy Consumption of Electrochemical Hydrogen Compressor at Various Operating Conditions Using Pseudo-2D Model Simulation

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

#### 2.1. Mass Balance

#### 2.2. Gas Diffusion Layer Modeling

#### 2.3. Overpotential Modeling

#### 2.4. Polymer Electrolyte Membrane Modeling

#### 2.5. Validation of Modeling

## 3. Results and Discussion

#### 3.1. Temperature Effects

#### 3.2. Membrane Thickness Effects

#### 3.3. Relative Humidity Effects

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

List of symbols | |

a | Activity/- |

ASR | Area-specific resistance/$\Omega {\mathrm{m}}^{2}$ |

$\mathrm{D}$ | Binary diffusivity/${\mathrm{m}}^{2}{\mathrm{s}}^{-1}$ |

${\mathrm{D}}_{\mathsf{\lambda}}$ | Water diffusivity/${\mathrm{m}}^{2}{\mathrm{s}}^{-1}$ |

E | Cell voltage/V |

F | Faraday constant/${\mathrm{A}\mathrm{s}\mathrm{mol}}^{-1}$ |

i | Current density/${\mathrm{A}\mathrm{m}}^{-2}$ |

J | Water flux considering electroosmotic drag and back diffusion/mol ${\mathrm{s}}^{-1}{\mathrm{m}}^{-2}$ |

K | Kinetic constant/${\mathrm{mol}\mathrm{s}}^{-1}{\mathrm{m}}^{-2}$ |

$\dot{\mathrm{m}}$ | Mass flow rate/${\mathrm{kg}\mathrm{s}}^{-1}$ |

M | Equivalent weight of membrane/${\mathrm{kg}\mathrm{mol}}^{-1}$ |

$\mathrm{n}$ | Number of electrons in hydrogen |

${\dot{\mathrm{n}}}_{\mathrm{x}}$ | Hydrogen crossover flux/mol ${\mathrm{s}}^{-1}{\mathrm{m}}^{-2}$ |

$\dot{\mathrm{N}}$ | Molar flux/${\mathrm{mol}\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$ |

$\mathrm{P}$ | Pressure/bar |

${\mathrm{P}}_{\mathrm{Cell}}$ | Power/$\mathrm{W}$ |

$\mathrm{R}$ | Ideal gas constant/${\mathrm{J}\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$ |

t | Thickness/mm |

$\mathrm{T}$ | Temperature/K |

$x$ | Mole fraction/- |

Greek letters | |

$\mathsf{\alpha}$ | Transfer coefficient/- |

$\mathsf{\epsilon}$ | Porosity/- |

$\mathsf{\rho}$ | Density/${\mathrm{kg}\mathrm{m}}^{-3}$ |

Subscripts and superscripts | |

act | Activation losses |

amb | Ambient |

$\mathrm{A}$ | Anode |

$\mathrm{A}\to \mathrm{C}$ | Anode to cathode |

$\mathrm{Back}$ | Back diffusion |

BP | Bipolar plate |

$\mathrm{C}$ | Cathode |

$\mathrm{C}\to \mathrm{A}$ | Cathode to anode |

Cons | Consumption |

drag | Drag coefficient |

evo | Evolution |

e | Electron |

GDL | Gas diffusion layer |

${\mathrm{H}}_{2}$ | Hydrogen |

${\mathrm{H}}_{2}\mathrm{O}$ | Water |

$\mathrm{in}$ | Inlet |

mem | Polymer electrolyte membrane |

Nernst | Nernst potential |

$\mathrm{out}$ | Outlet |

ohmic | Ohmic losses |

o | Oxidation of hydrogen |

Prod | Production |

r | Reduction of hydrogen |

sa | Chemical species of a |

sb | Chemical species of b |

s | Surface |

SAT | Saturation |

Total | Applied voltage to the EHC |

$\mathrm{x}-\mathrm{over}$ | Hydrogen crossover |

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**Figure 4.**Comparison of local current density/average current density according to the anode inlet distance analyzed by the pseudo-2D model and reference model.

**Figure 5.**Polarization curve of the pseudo-2D electrochemical hydrogen compressor with respect to temperature.

**Figure 6.**Polymer electrolyte membrane resistance and hydrogen crossover flux according to the temperature measured at 0.18 V.

**Figure 7.**Local current density measured along the channel length according to the temperature at 0.18 V.

**Figure 9.**Polarization curve of the pseudo-2D electrochemical hydrogen compressor according to the polymer electrolyte membrane thickness.

**Figure 10.**Polymer electrolyte membrane resistance and hydrogen crossover rate according to the thickness measured at 0.18 V.

**Figure 11.**Local current density measured along the channel length according to the polymer electrolyte membrane thickness at 0.18 V.

**Figure 13.**Polarization curve of the pseudo-2D electrochemical hydrogen compressor with respect to the relative humidity.

**Figure 14.**Polymer electrolyte membrane resistance and hydrogen crossover flux according to the thickness measured at 0.18 V.

**Figure 15.**Local current density measured along the channel length according to the relative humidity at 0.18 V.

Parameter | Units | Value |
---|---|---|

Faraday constant (F) | C/mol | 96,485.332 |

Gas constant (R) | J/mol∙K | 8.3144 |

Equivalent weight of membrane (${\mathrm{M}}_{\mathrm{mem}}$) | kg/kmol | 1100 [22] |

Dry density of membrane (${\mathsf{\rho}}_{\mathrm{dry}}$) | $\mathrm{kg}/{\mathrm{m}}^{3}$ | 1970 [22] |

Channel length (${\mathrm{l}}_{\mathrm{ch}}$) | mm | 300 [23] |

Thickness of bipolar plate (${\mathrm{t}}_{\mathrm{BP}}$) | mm | 1 |

Through-plane electrical conductivity of bipolar plate (${\mathsf{\sigma}}_{\mathrm{BP}}$) | S/m | 3.3 [24] |

Thickness of gas diffusion layer (${\mathrm{t}}_{\mathrm{GDL}}$) | $\mathsf{\mu}$m | 325 [25] |

Through-plane electrical conductivity of gas diffusion layer (${\mathsf{\sigma}}_{\mathrm{GDL}}$) | S/m | 220 [25] |

Gas diffusion layer porosity (${\mathsf{\epsilon}}_{\mathrm{GDL}}$) | - | 0.5 [25] |

Polymer electrolyte membrane thickness (${\mathrm{t}}_{\mathrm{mem}}$) | $\mathsf{\mu}$m | 25, 50, 127, 183 |

Parameter | Units | Value |
---|---|---|

Operating temperature (T) | °C | 30, 60, 80 |

Operating pressure (P) | bar | 100 |

Relative humidity (RH) | % | 100, 90, 80, 70 |

Flow rate | sccm | 41.4 |

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**MDPI and ACS Style**

Kim, C.; Gong, M.; Lee, J.; Na, Y.
Minimizing Specific Energy Consumption of Electrochemical Hydrogen Compressor at Various Operating Conditions Using Pseudo-2D Model Simulation. *Membranes* **2022**, *12*, 1214.
https://doi.org/10.3390/membranes12121214

**AMA Style**

Kim C, Gong M, Lee J, Na Y.
Minimizing Specific Energy Consumption of Electrochemical Hydrogen Compressor at Various Operating Conditions Using Pseudo-2D Model Simulation. *Membranes*. 2022; 12(12):1214.
https://doi.org/10.3390/membranes12121214

**Chicago/Turabian Style**

Kim, Changhyun, Myungkeun Gong, Jaewon Lee, and Youngseung Na.
2022. "Minimizing Specific Energy Consumption of Electrochemical Hydrogen Compressor at Various Operating Conditions Using Pseudo-2D Model Simulation" *Membranes* 12, no. 12: 1214.
https://doi.org/10.3390/membranes12121214