# Performance Analysis of a Proton Exchange Membrane Fuel Cell Based Syngas

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}can provide enough heat for the endothermic reaction. However, the new product CaCO

_{3}may cover the catalyst of the steam reforming reaction and thus limits the long-term durability. The high-temperature exhaust heat from a Stirling engine can be used for steam reforming [9], but the operation of the PEM fuel cell is dependent on the engine.

## 2. The Auxiliary Systems outside a PEM Fuel Cell

#### 2.1. The Heat Needed in HE1 and HE2

^{−1}) and the amount of water in the flow is twice of that needed for the steam reforming and water gas shift reactions, the steam reforming and water gas shift reactions are, respectively,

#### 2.2. The Molar Ratio of Syngas into the Burner and Steam Reformer

## 3. The Electric Power of a PEM Fuel Cell Based Syngas

^{−1}·m

^{−2}), the product of ${n}^{*}$ and ${u}_{{\mathrm{H}}_{2}}$ is always smaller than the optimum value, even though ${u}_{{\mathrm{H}}_{2}}$= 1 in Figure 5 and the electric power density of the PEM fuel cell is a monotonous increasing function of the molar flow rate of the syngas in Figure 4. When ${n}^{*}\ge $ 0.17 (mol·s

^{−1}·m

^{−2}), the hydrogen utilization factor is decreasing with the increase of the molar flow rate of syngas to reach the optimal product of them in Figure 5, and the electric power density is constant in Figure 4.

## 4. The Total Energy Conversion Efficiency

^{−1}·m

^{−2}), the working conditions of the maximum efficiency and the maximum power density are the same: The hydrogen should be reacted totally in the fuel cell, and the molar ratio of the syngas into the burner and steam reformer is 0.4. When $0.065\le {n}^{*}\le 0.14$ (mol·s

^{−1}·m

^{−2}), there should be residual hydrogen leaving the fuel cell and x is smaller than 0.4 for the maximum efficiency of the system. When ${n}^{*}$ is larger than 0.14 (mol·s

^{−1}·m

^{−2}), the hydrogen utilization factor is constant and about 0.61; there is no need to add syngas into the burner.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

${A}_{c}$ | Effective surface area of the bipolar plate |

${\alpha}_{a}$ | Charge transfer coefficient at anode |

${\alpha}_{c}$ | Charge transfer coefficient at cathode |

${\beta}_{1}$ | Parameter in the expression of overpotential |

${\beta}_{2}$ | Constant in the expression of overpotential |

${C}_{\mathrm{k},\mathrm{m}}$ | Molar heat capacity of k |

$\Delta h$ | Enthalpy change of gases |

$\Delta h(T)$ | Enthalpy change of gases |

$\Delta g(T)$ | Gibbs function change of gases |

$\Delta s(T)$ | Entropy change of gases |

${\delta}_{a}$ | Stoichiometry coefficient |

${\delta}_{c}$ | Stoichiometry coefficient |

${\delta}_{mem}$ | Membrane thickness |

$F$ | Faraday constant |

$\eta $ | Efficiency of the hybrid system |

${h}_{\mathrm{k}}$ | Molar enthalpy of k at 600 °C |

${h}_{\mathrm{k}}^{0}$ | Molar enthalpy of k at 25 °C |

${h}_{\mathrm{k}}(T)$ | Molar enthalpy of k at temperature T |

${\dot{H}}_{cell}$ | Enthalpy of gases leaving the fuel cell |

${\dot{H}}_{in}$ | Enthalpy of gases into burner |

${\dot{H}}_{out}$ | Enthalpy of gases leaving the burner |

$I$ | Electric current of a PEM fuel cell |

${i}_{0}$ | Exchange current density of the electrodes |

$i$ | Current density of a PEM fuel cell |

${i}_{L}$ | Limiting current density of a PEM fuel cell |

${L}_{{\mathrm{H}}_{2}\mathrm{O},\mathrm{m}}$ | Latent heat of one mole water |

${\mu}_{mem}$ | Water content |

$n$ | Mole flow rate of syngas into HE1 |

${n}_{{\mathrm{H}}_{2}\mathrm{O}}$ | Mole rate of water added into syngas |

${n}^{*}$ | Mole flow rate of syngas into HE1 unit area |

${n}_{e}$ | Number of electrons |

${P}_{e}^{*}$ | Electric power density of a PEM fuel cell |

${P}_{e}$ | Electric power of a PEM fuel cell |

${p}_{c}$ | Pressure at the cathode |

${p}_{a}$ | Pressure at the anode |

${p}_{s}$ | Saturation pressure of water |

${p}_{k}$ | Partial pressure of k at the electrode |

${\dot{Q}}_{2}$ | The heat needed in HE2 unit time |

${\dot{Q}}_{1}$ | The heat needed in HE1 unit time |

${q}_{LHV}(k)$ | Lower heating value of k per molar |

$R$ | Universal gas constant |

${s}_{\mathrm{k}}^{0}$ | Molar entropy of k at 25°C |

${\sigma}_{mem}$ | Membrane conductivity |

$T$ | Operating temperature of a PEM fuel cell |

${T}_{C}$ | Combustion temperature |

$t$ | Temperature |

${T}_{C}^{\prime}$ | Temperature of gases leaving HE1 |

${u}_{{\mathrm{H}}_{2}}$ | Hydrogen utilization factor in a fuel cell |

${V}_{act}$ | Activation overpotential |

${V}_{ohm}$ | Ohm overpotential |

${V}_{con}$ | Concentration overpotential |

${x}_{\mathrm{c}}$ | Dry gas molar ratio at cathode |

${x}_{\mathrm{a}}$ | Dry gas molar ratio at anode |

$x$ | The molar ratio |

${x}_{\mathrm{k}}$ | Molar fraction of k in syngas |

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**Figure 1.**The schematic diagram of a proton exchange membrane (PEM) fuel cell based syngas, where abbreviations of HE1, HE2, and HE3 are heat exchangers, SR is a steam reformer, HTS and LTS are water gas shift reactions, PROX is a preferential oxidizer, and AB is an auxiliary burner.

**Figure 3.**Curves of ${T}_{C}^{}$ varying with ${u}_{{\mathrm{H}}_{2}}$, where ${T}_{C}^{\prime}$ = 30 °C.

**Figure 4.**The power density varying with ${n}^{*}$, where $T$ = 70 °C and ${T}_{C}^{\prime}$ = 30 °C. The solid and dash curves are, respectively, the maximum power density and the power density under the maximum efficiency.

**Figure 5.**The hydrogen utilization factor varying with ${n}^{*}$, where $T$ = 70 °C and ${T}_{C}^{\prime}$ = 30 °C. The solid and dash curves are, respectively, the hydrogen utilization factor under the maximum power density and the maximum efficiency.

**Figure 6.**Curves of x varying with ${n}^{*}$, where $T$ = 70 °C and ${T}_{C}^{\prime}$ = 30 °C. The solid and dash curves are x under the maximum power density and the maximum efficiency, respectively.

**Figure 7.**The efficiency varying with ${n}^{*}$, where $T$ = 70 °C and ${T}_{C}^{\prime}$ = 30 °C. The dash and solid curves are, respectively, the maximum efficiency and the efficiency under the maximum power density.

**Table 1.**The composition of syngas [20].

Component k | ${\mathbf{H}}_{2}$ | ${\mathbf{CH}}_{4}$ | $\mathbf{CO}$ | ${\mathbf{CO}}_{2}$ | ${\mathbf{H}}_{2}\mathbf{O}$ | ${\mathbf{N}}_{2}$ |
---|---|---|---|---|---|---|

Mole fraction of k in syngas: x_{k} | 0.13 | 0.01 | 0.16 | 0.05 | 0.36 | 0.29 |

Component $\mathbf{k}$ | ${\mathit{h}}_{\mathbf{k}}^{0}$ (J·mol ^{−1}) | ${\mathit{s}}_{\mathbf{k}}^{0}$ (J·mol ^{−1}·K^{−1}) | ${\mathit{L}}_{{\mathbf{H}}_{2}\mathbf{O},\mathbf{m}}$ (J·mol ^{−1}) | Molar Heat Capacity ${\mathit{C}}_{\mathbf{k},\mathbf{m}}$ (J·mol ^{−1}·K^{−1}) |
---|---|---|---|---|

N_{2} | 0 | — | — | 29.12 |

O_{2} | 0 | 205.138 | — | 25.8911 + 0.0129874t − 0.0000038644t^{2} |

CH_{4} | −75,000 | — | — | 14.1555 + 0.0755466t − 0.0000180032t^{2} |

CO_{2} | −393,800 | — | — | 26.0167 + 0.0435259t − 0.0000148422t^{2} |

CO | −110,500 | — | — | 26.8742 + 0.006971t − 0.0000008206t^{2} |

H_{2} | 0 | 130.695 | — | 29.0856 − 0.0008373t + 0.0000020138t^{2} |

H_{2}O (g) | −241,800 | — | — | 30 + 0.01071t + 33000/t^{2} |

H_{2}O (l) | −285,800 | 69.940 | 40,700 | 75.44 |

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

Number of electrons, ${n}_{e}$ | 2 |

Faraday constant, F (C mol^{−1}) | 96485 |

Universal gas constant, R (J·mol·K^{−1}) | 8.314 |

Pressure at the anode, ${p}_{a}$ (atm) | 3 [13] |

Pressure at the cathode, ${p}_{c}$ (atm) | 5 [13] |

Anode stoichiometry, ${\delta}_{a}$ | 1.5 [20] |

Cathode stoichiometry, ${\delta}_{c}$ | 3 [20] |

Dry gas molar ratio at anode, ${x}_{a}$ | $({x}_{{\mathrm{N}}_{2}}+{x}_{{\mathrm{CO}}_{2}}+{x}_{{\mathrm{CH}}_{4}}+{x}_{\mathrm{CO}})/({x}_{{\mathrm{H}}_{2}}+{x}_{\mathrm{CO}}+4{x}_{{\mathrm{CH}}_{4}})$ [13] |

Dry gas molar ratio at cathode, ${x}_{c}$ | 3.762 (air) |

Charge transfer coefficient at the anode, ${\alpha}_{a}$ | 0.5 [20] |

Charge transfer coefficient at the cathode, ${\alpha}_{c}$ | 1 [20] |

Membrane thickness, ${\delta}_{mem}$ (cm) | 0.018 [13] |

${\mu}_{mem}$ | 14 [21] |

Constant, ${\beta}_{2}$ | 2 [20] |

Limiting current density, ${i}_{L}$ (A cm^{−2}) | 2 [20] |

T = 70 °C: ${p}_{\mathrm{s}}$ (atm); ${\beta}_{1}$ | 0.3071; 0.2048 |

${q}_{\mathrm{LHV}}(\mathrm{k})$ (kJ mol^{−1}): k = H_{2}; CO; CH_{4} | 241.9; 283.2; 803.7 |

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**MDPI and ACS Style**

Zhang, X.; Lin, Q.; Liu, H.; Chen, X.; Su, S.; Ni, M.
Performance Analysis of a Proton Exchange Membrane Fuel Cell Based Syngas. *Entropy* **2019**, *21*, 85.
https://doi.org/10.3390/e21010085

**AMA Style**

Zhang X, Lin Q, Liu H, Chen X, Su S, Ni M.
Performance Analysis of a Proton Exchange Membrane Fuel Cell Based Syngas. *Entropy*. 2019; 21(1):85.
https://doi.org/10.3390/e21010085

**Chicago/Turabian Style**

Zhang, Xiuqin, Qiubao Lin, Huiying Liu, Xiaowei Chen, Sunqing Su, and Meng Ni.
2019. "Performance Analysis of a Proton Exchange Membrane Fuel Cell Based Syngas" *Entropy* 21, no. 1: 85.
https://doi.org/10.3390/e21010085