# A Novel Emergency Gas-to-Power System Based on an Efficient and Long-Lasting Solid-State Hydride Storage System: Modeling and Experimental Validation

^{1}

^{2}

^{3}

^{*}

_{2}Conversion)

## Abstract

**:**

## 1. Introduction

## 2. The Experimental Setup

#### 2.1. Description of the Experimental Setup

^{3}made of 316 L Stainless Steel, from the company Swagelok, Soren, OH, USA), as illustrated in Figure 1a. This low-temperature hydride was able to operate at pressures below 50 bar and loaded hydrogen at room temperatures. The 1.6 kW PEM (proton exchange membrane) Fuel Cell was from the type “DBX2000 power backup module”, produced by Dantherm Power (Figure 1a). It delivered a maximum power of 1.6 kW and needed a hydrogen supply of Grade 3.0 (99.9%) or higher. The system was made to provide constant power during power outages (i.e., in emergency cases). For this purpose, the PEM stack had an integrated electrical system. Such an integrated electrical system in a scale-up size can be connected to the public grid. The PEM stacks also included an ultracapacitor for the initial provision of energy. Type K thermocouples from Thermocoax are able to measure in a range between −200 °C and 800 °C were used. These kinds of thermocouples were utilized to measure the temperature in every tank and the system.

#### 2.2. Operating Scenarios and Test Parameters: MH2-Powerbank System

#### 2.2.1. Operating Scenarios

_{2}based on the Supplementary Material) (ESI, Figure S1). Moreover, the mass of hydrogen in the gas phase under 40 bar and 25 °C was about 5.3 g. Thus, the total amount of hydrogen in the loaded system was 110.8 g.

#### 2.2.2. Experimental Parameters

## 3. Mathematical Model

#### 3.1. MH-Tanks and the Connections with the Network: Description of the 0D Model

- The hydrogen transport inside the porous medium’s free volume is neglected due to the fast hydrogen velocity.
- The local thermal equilibrium is assumed: temperatures in both fluid (hydrogen) and solid phases (alloy-hydride) are equal.
- Hydrogen is considered an ideal gas due to the low working pressures.
- The mass exchange caused by the chemical reaction occurs directly between the hydride-forming alloy and the connected gas network.
- The heat exchange between the gas network and the hydride material is neglected.
- The gas pressure in the porous bed (alloy-hydride) is assumed to be equal to that of the connected gas network. Therefore, the mass flow of hydrogen during the reaction occurs as part of the gas network.
- The temperature change of the gas phase due to gas transport between the gas phase and the solid hydride is neglected.

#### 3.1.1. Thermodynamics of the Metal Hydride: Determination of the Equilibrium Pressure through Pressure-Composition-Isotherms (PCIs) Modeling

_{2}. This correction factor ${f}_{kor,1}\left(w\right)$ was introduced, so it acts on the PCIs’ fitted of hydrogenation from about 1.4 wt.% H

_{2}. Therefore, from 0 wt.% H

_{2}to about 1.4 wt.%, the fitted PCI functions match very well with the measuring points without any correction factor.

#### 3.1.2. Kinetics of the Metal Hydride: Reaction Kinetic Model

#### 3.1.3. Heat Exchange Modeling: Dehydrogenation of MH-Tanks by Utilizing the Fuel Cell Waste Heat

#### 3.1.4. Model Implementations in Simscape

#### 3.1.5. Boundary Conditions

#### 3.1.6. Initial Condition and Simulation Parameters

## 4. Model Validation and Discussion of the Results

_{2}). However, depending on the experimental conditions upon hydrogen provision, supplied hydrogen capacity ranged between 0.5 and 1.0 wt.%. No deterioration of the hydrogen storage capacity of the system was noticed during cycling.

_{2}was desorbed.

_{4.6}Al

_{0.6}and MmNi

_{4.6}Fe

_{0.6}low-temperature hydrides. These tanks were individually desorbed from a 30–35 bar pressure to ambient pressure of 1 bar. The heat exchange was done using a liquid medium instead of air, as in this work. Despite the different hydrides, different kinds of configuration, and cooling medium, the experimental results of the temperature and pressure profiles demonstrate similar characteristics, as illustrated in Figure 7. However, the temperature drop behavior observed for tank 1 at 10 Ohm for the last measurement stage (Figure 7(B2)) represents a deviation from the behavior reported in [40].

## 5. Conclusions

## Supplementary Materials

^{−1}K

^{−1}] and thermal diffusivity a [m s

^{−2}]. ESI.3 Calculation of the heat transfer coefficient between the wall and the air ${\alpha}_{w-Air}$ for the tube bundle. ESI.4 Determination of the airspeed of the fuel cell exhaust air. ESI.5 Description of the “Pipe (G)” component in MATLAB/Simscape. Figure S3: Pipe (G) Simscape. ESI.6 Hydrogen consumption of the fuel cell used in the MH2-Powerbank. Figure S4: Hydrogen consumption of the fuel cell: experiments under constant resistance at 5.0, 7.5, 10.0, and 20.0 Ohm, dynamic daily profiles, and large power consumption variations. ESI.7 Interpolated velocity profiles from the fuel cell waste heat air stream obtained from the data measured with the anemometer. Figure S5: Interpolated velocity profiles from the fuel cell waste heat air stream: experiments under constant resistance at 5.0, 7.5, 10.0, and 20.0 Ohm, dynamic daily profiles, and large power consumption variations. ESI.8 Interpolated Temperature profiles from the fuel cell waste heat air stream obtained from the data measured in the anemometer. Figure S6: Interpolated Temperature profiles from the fuel cell waste heat air stream: experiments under constant resistance at 5.0, 7.5, 10.0, and 20.0 Ohm, dynamic daily profiles and large power consumption variations. ESI.9: Measured and simulated temperature profiles of tanks 1–5 from MH2-Powerbank. Figure S7: Experimental and modeled temperature profiles of the tanks under constant resistance at 5.0, 7.5, 10.0, and 20.0 Ohm, dynamic daily profiles, and large power consumption variations. ESI.10 Measured and simulated pressure profiles of MH2-Powerbank. Experimental and modeled pressure profiles of the tanks under constant resistance at 5.0, 7.5, 10.0, and 20.0 Ohm, dynamic daily profiles and large power consumption variations.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Comparison between the experimental (symbols) and fitted PCIs for TiFeMn hydride forming alloy (lines). Solid lines illustrate fits for the absorption (

**a**) and dotted lines, desorption (

**b**).

**Figure 4.**Heat transfer radial lengths in the internal cross-section of a tank (

**a**) and disposition of the cylinders bundle inside the heat exchange housing (

**b**).

**Figure 5.**Implementation of MH2-Powerbank in MATLAB Simulink/Simscape: regulation of the air velocity.

**Figure 6.**Experimental measurements to set the boundary conditions for the hydride storage and gas network models: (

**a**) Fuel cell consumption, (

**b**) Air velocity of the exhaust gas from the fuel cell, (

**c**) Air temperature, and (

**d**) Modified air temperature of the airflow coming from the fuel cell.

**Figure 7.**Simulated (Sim) and measured (Real) system pressure curves (1) and temperature curves of tanks 1 and 3 (2) at different condictions: (

**A**) 5.0 Ohm and (

**B**) 10.0 Ohm experiments.

**Figure 8.**Variable high load conditions: (

**a**) Simulated (Sim) and measured (Real) temperature development of tanks 1 and 3, (

**b**) Simulated (Sim) and measured (Real) system pressure, (

**c**) temperature of air stream from the fuel cell, and (

**d**) power of the fuel cell.

**Figure 9.**Variable dynamic load conditions: (

**a**) Simulated (Sim) and measured (Real) temperature development of tanks 1 and 3, (

**b**) Simulated (Sim) and measured (Real) system pressure (

**c**), temperature of the air stream coming from the fuel cell, and (

**d**) power of the fuel cell.

**Table 1.**Experimental parameters for the test performed with the MH2-Powerbank system, using scenario C.

Experiment | Resistance [Ohm] | Duration [h] | Power [W] |
---|---|---|---|

1 | 5.0 | 1.13 | 478 |

2 | 7.5 | 1.91 | 319 |

3 | 10.0 | 3.55 | 241 |

4 | 20.0 | 6.5 | 120 |

5 | Large variations of power consumption | 2.01 | 149–596 |

6 | Representative of the daily profile | 3.88 | 152–213 |

Coefficients | Absorption | Desorption | Coefficients | Absorption | Desorption |
---|---|---|---|---|---|

${a}_{0}$ | $-2.8724\times {10}^{3}$ | $-1.6692\times {10}^{3}$ | ${b}_{3}$ | $2.7672\times {10}^{-1}$ | $-6.2484$ |

${a}_{1}$ | $2.0849\times {10}^{-2}$ | $1.434\times {10}^{-2}$ | ${b}_{4}$ | $6.1852\times {10}^{-1}$ | $4.3904$ |

${a}_{2}$ | $-2.5888\times {10}^{-5}$ | $4.6251\times {10}^{-6}$ | ${b}_{5}$ | $1.7878$ | $1.5578$ |

${a}_{3}$ | $9.4389$ | $9.0343$ | $c$ | $0.1667$ | $0.2128$ |

${a}_{4}$ | $-9.7116$ | $-7.9554$ | ${k}_{1}$ | $8.5869\times {10}^{-12}$ | $1.2417\times {10}^{-69}$ |

${a}_{5}$ | $3.4163$ | $2.5782$ | ${k}_{2}$ | $1.8013\times {10}^{1}$ | $1.0428\times {10}^{2}$ |

${b}_{0}$ | $1.2467\times {10}^{-2}$ | $1.8402\times {10}^{-2}$ | ${k}_{3}$ | $2.9935\times {10}^{-3}$ | |

${b}_{1}$ | $-3.2360\times {10}^{-5}$ | $-5.181\times {10}^{-5}$ | ${k}_{4}$ | $3.8364$ | |

${b}_{2}$ | $3.6551\times {10}^{-3}$ | $4.2442\times {10}^{-3}$ |

Parameter | Value | Unit | Description |
---|---|---|---|

${T}_{m,0}$ | From 17 to 21 | °C | Range of initial measured temperature for the tanks |

${\rho}_{s,0}$ | 3250.04 | $\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}$ | Initial crystalline density full load (considering the experimental gravimetric capacity: 1.54 wt.%) |

${P}_{g,0}$ | 40 | bar | Initial gas pressure under hydrogenated state. |

Parameter | Value | Unit | Description | Parameter | Value | Unit | Description |
---|---|---|---|---|---|---|---|

${k}_{abs}$ | 2.6536 | $\frac{1}{\mathrm{s}}$ | Reaction kinetic constant of abs. | $\Delta {H}_{Abs}$ | From −33,638 to−28,211 | $\frac{\mathrm{J}}{{\mathrm{mol}\text{}\mathrm{H}}_{2}}$ | Enthalpy of abs. in the range of 0.2–1.3 wt.% |

${k}_{Des}$ | 0.8852 | $\frac{1}{\mathrm{s}}$ | Reaction kinetic constant of des. | $\Delta {H}_{Des}$ | From −34,917 to −29,969 | $\frac{\mathrm{J}}{{\mathrm{mol}\text{}\mathrm{H}}_{2}}$ | Enthalpy of des. in the range of 0.2–1.3 wt.% |

${E}_{Abs}$ | 17,500 | $\frac{\mathrm{J}}{{\mathrm{mol}\text{}\mathrm{H}}_{2}}$ | Activation energy of abs. | ${\rho}_{s,min}$ | 3200 | $\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}$ | Minimal bulk density |

${E}_{Des}$ | 13,750 | $\frac{\mathrm{J}}{{\mathrm{mol}\text{}\mathrm{H}}_{2}}$ | Activation energy of des. | ${\rho}_{s,max}$ | 3250.04 | $\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}$ | Maximal bulk density |

${c}_{s}$ | 682.4 | $\frac{\mathrm{J}}{\mathrm{kg}\text{}\mathrm{K}}$ | Heat capacity | $\epsilon $ | 0.5 | $-$ | Porosity |

${\lambda}_{s}\left(T\right)$ | 5–6.2 | $\frac{\mathrm{W}}{\mathrm{m}\text{}\mathrm{K}}$ | Thermal conductivity solid | ${\lambda}_{g}\left(p,T\right)$ | 0.163–0.227 | $\frac{\mathrm{W}}{\mathrm{m}\text{}\mathrm{K}}$ | Thermal conductivity gas [39] |

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**MDPI and ACS Style**

Dreistadt, D.M.; Puszkiel, J.; Bellosta von Colbe, J.M.; Capurso, G.; Steinebach, G.; Meilinger, S.; Le, T.-T.; Covarrubias Guarneros, M.; Klassen, T.; Jepsen, J.
A Novel Emergency Gas-to-Power System Based on an Efficient and Long-Lasting Solid-State Hydride Storage System: Modeling and Experimental Validation. *Energies* **2022**, *15*, 844.
https://doi.org/10.3390/en15030844

**AMA Style**

Dreistadt DM, Puszkiel J, Bellosta von Colbe JM, Capurso G, Steinebach G, Meilinger S, Le T-T, Covarrubias Guarneros M, Klassen T, Jepsen J.
A Novel Emergency Gas-to-Power System Based on an Efficient and Long-Lasting Solid-State Hydride Storage System: Modeling and Experimental Validation. *Energies*. 2022; 15(3):844.
https://doi.org/10.3390/en15030844

**Chicago/Turabian Style**

Dreistadt, David Michael, Julián Puszkiel, José Maria Bellosta von Colbe, Giovanni Capurso, Gerd Steinebach, Stefanie Meilinger, Thi-Thu Le, Myriam Covarrubias Guarneros, Thomas Klassen, and Julian Jepsen.
2022. "A Novel Emergency Gas-to-Power System Based on an Efficient and Long-Lasting Solid-State Hydride Storage System: Modeling and Experimental Validation" *Energies* 15, no. 3: 844.
https://doi.org/10.3390/en15030844