Designing Metal Hydride-Phase Change Material with Analytical and Numerical Method ^†

Abstract

This study examines the thermal characteristics of metal hydride systems comprised of MgH₂ and LaNi₅, paired with LiNO₃·3H₂O and NaNo₃ as a phase change material, through both analytical and computational approaches. Analytical methods were utilized to identify the most suitable volume and mass proportions of metal hydrides to PCM, whereas simulations calculated hydrogen absorption/desorption times and temperature distribution. The findings indicate that MgH₂ functions at a higher temperature and necessitates a greater volume of PCM on account of its high enthalpy. In comparison, LaNi₅ exhibits more rapid absorption and desorption reaction rates, rendering it beneficial for use in applications requiring quick hydrogen storage.

1. Introduction

Hydrogen, with its high energy density and zero carbon emissions, is a promising alternative fuel for enhancing renewable energy storage efficiency, offering solutions for transportation, energy storage, and industrial applications [1]. The key challenge is developing safe, efficient, and economical hydrogen storage technologies. Among gas, liquid, and solid storage methods, solid storage is particularly promising for its safety, high capacity, and hydrogen purification capabilities [2,3]. Metal-hydride hydrogen storage has become a prominent solution because of its ability to absorb hydrogen at low pressures and moderate temperatures [4]. Recent studies have emphasized the importance of improving thermal management in metal hydride reactors, including the use of high-conductivity materials and phase change materials (PCM), to enhance system efficiency [1]. Materials such as LaNi₅ also show advantages in terms of cycle stability and hydrogen storage capacity [5]. In recent years, magnesium hydride (MgH₂) has been identified as a potential solid metal hydride (MH) hydrogen storage material with a theoretical hydrogen storage capacity of 7.6 wt% [3]. To date, some work has been undertaken to improve the adsorption/desorption kinetics of MH through the creation of an ultra-fine microstructure and the intermixing of catalytically active species [3]. The current design primarily utilizes a cylindrical shape [3] because, with a cylinder design, the pressure has good distribution. Hydrating is an exothermic process, while dehydration is an endothermic reaction. This poses a challenge in hydrogen storage using metal hydrides. The release and absorption of heat during hydrating and dehydration are critical points in hydrogen storage design [5]. Effective thermal management is crucial in hydrogen storage tanks as it impacts absorption and release rates. PCM-based thermal management is gaining attention for its ability to store heat during absorption and reuse it during desorption. By absorbing and releasing latent thermal energy during phase changes, PCM stabilizes temperature profiles and reduces thermal loads on the system.

This study develops analytical and computational models for designing metal hydride-based hydrogen storage systems with PCM for thermal management, offering a preliminary guide to optimizing system efficiency and evaluating MgH₂ and LaNi₅ performance.

2. Method

2.1. Analytical Method

The metal hydride hydrogen storage system design in this study uses an analytical approach focusing on hydrogen storage capacity, metal hydride mass, and bed volume, as shown in Figure 1. This method evaluates the interplay between material properties and system requirements, enabling precise estimates of capacity, material use, and spatial efficiency. It balances storage performance with engineering constraints, addressing heat management during absorption and thermal reuse for desorption to enhance system performance.

To calculate the hydrogen capacity we use the following formula:

$$\mathit{Hydrogen} \mathit{amount}={\displaystyle \frac{P\times t\times 3600}{\eta \times \mathit{LHV}}}$$

(1)

Formula (1) is used to calculate hydrogen amount, where P is the power (Kw), t is time (second), $\eta$ is the efficiency of the design and LHV is the Low Heating Value (Kj/Kg).

Then, to calculate the mass of the metal hydride we use the formula below:

$$\mathit{Hydride} \mathit{mass}={\displaystyle \frac{\mathit{Hydrogen} \mathit{amount}}{\mathit{Hydrogen} \mathit{storage} \mathit{capacity}}}$$

(2)

In Formula (2), hydrogen amount is the amount of hydrogen that has been calculated before. Hydrogen storage capacity is the capacity of the material that can store hydrogen, and it is different from one material to another. Then, we calculate the metal hydride using the density of the metal hydride and the mass of the metal hydride. We followed the formula below:

$$\mathit{Volume}={\displaystyle \frac{m}{\rho }}\times 10\%$$

(3)

where 10% is the expansion when metal hydride absorbs hydrogen.

For the phase change material, we calculate using the heat transfer from metal hydride and phase change material. The heat transfer of MH-PCM is generally calculated using the diagram below.

For that, we use the following formula [5,6]:

$$Q_{m,a}-Q_{m,sen}=Q_{p,lat}+Q_{p,sen}$$

(4)

2.2. Computational Method

After conducting the calculations, we perform optimization with simulations of the design, below is the flowchart for performing the simulations. The simulations used ANSYS fluent 2D simulations. Figure 2 below is the flowchart for CFD simulations that are used for this research.

To develop a mathematical model for heat and mass transfer and the absorption reaction in the MH-PCM reactor, several assumptions are made [7,8]: hydrogen behaves as an ideal gas, natural convection in liquid PCM is neglected, PCM in the MH tank has good thermal insulation, thermophysical properties remain constant during absorption/desorption, and the gas and solid phases in the porous MH bed are in local equilibrium. The material properties are detailed in

Table 1. Material properties [9,10,11].

MH (LaNi5)	MH (MgH2)
${\rho }_{sat}=8527 \mathrm{kg}/{\mathrm{m}}^3$	${\rho }_{sat}=1450 \mathrm{k}\mathrm{g}/{\mathrm{m}}^3$
${\rho }_{emp}=8400 \mathrm{k}\mathrm{g}/{\mathrm{m}}^3$	${\rho }_{emp}=1800 \mathrm{k}\mathrm{g}/{\mathrm{m}}^3$
$$\begin{gathered} c_{p,m}=419 \mathrm{J}/(\mathrm{k}\mathrm{g}·\mathrm{K}) \\ {\lambda }_m=1.087 \mathrm{W}/(\mathrm{m}·\mathrm{K}) \end{gathered}$$	$$\begin{gathered} c_{p,m}=1545 \mathrm{J}/(\mathrm{k}\mathrm{g}·\mathrm{K}) \\ {\lambda }_m=2 \mathrm{W}/(\mathrm{m}·\mathrm{K}) \end{gathered}$$
$$\begin{gathered} \epsilon =0.5 \\ {k}_a=59.187 {\mathrm{s}}^{-1} \end{gathered}$$	$$\begin{gathered} \epsilon =0.3 \\ {k}_a={10}^{10} {\mathrm{s}}^{-1} \end{gathered}$$
$$\begin{gathered} E_a=21179.6 \mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l} \\ \mathsf{\Delta }H=30.1 \mathrm{k}\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l} \end{gathered}$$	$$\begin{gathered} E_a=130000 \mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l} \\ \mathsf{\Delta }H=75 \mathrm{k}\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l} \end{gathered}$$

. For the PCM we use LiNO₃·3H₂O and NaNo_3. Choosing material PCM is compared to the operational temperature range of the MH.

3. Result and Discussion

3.1. Volume and Design

The hydrogen storage capacity of LaNi5 is 2.07% [6], and for Mg/MgH₂ it is 7.06% [12]. So, the results of the volume are shown in

Table 2. Result volume of the metal hydride storage.

Material of MH	Hydrogen	Volume of MH	Volume of PCM
MgH2	0.3 kg	0.0023 m3	0.00032 m3
LaNi5	0.3 kg	0.0020 m3	0.00008 m3

. From the calculations, we obtain the volume of the metal hydride and PCM with different materials as shown below:

The hydrogen storage capacity of metal hydrides (MH) impacts the PCM required for thermal management as higher capacities release more heat during absorption. This heat depends on the absorbed hydrogen and reaction enthalpy. LaNi₅ stores ~1.4 wt.% hydrogen, releasing 30–40 kJ/mol, while MgH₂ stores ~7.6 wt.% hydrogen, producing 75 kJ/mol, necessitating more or higher-capacity PCM. High-capacity materials generate significant heat, requiring efficient PCM energy absorption to maintain stable temperatures within the phase change range. The PCM quantity depends on the heat produced by the metal hydride and the PCM's latent heat capacity. For instance, storing 0.5 moles of hydrogen in 1 kg of LaNi₅ releases ~15 kJ of heat, needing 0.075 kg of PCM with a 200 kJ/kg capacity. Higher-capacity materials like MgH₂ produce more heat, requiring larger PCM volumes. Research has also shown that the heat generated during absorption grows more quickly as the hydrogen storage capacity increases and the properties of the phase change material (PCM) improve, highlighting the need for more efficient phase change materials to manage thermal loads effectively [6]. Figure 3 is the design that used for this research Figure 3a,b is the isometric and top view, for Figure 3c is the design configuration between the MH and PCM.

3.2. Time and Temperature

Figure 4 is the compared time that is needed by both material for absorption and desorption. From that figure, MgH₂-NaNo₃ need more time to absorption and desorption. This is because it is highly stable and needs high temperatures (300–400 °C) to release hydrogen. Breaking the strong bonds between magnesium and hydrogen requires significant energy. Additionally, hydrogen moves slowly through magnesium, further slowing the absorption and desorption processes.

The reaction of these two materials is below [12,13]:

$$\mathrm{L}\mathrm{a}{\mathrm{N}\mathrm{i}}_5+3{\mathrm{H}}_2\leftrightarrow \mathrm{L}\mathrm{a}{\mathrm{N}\mathrm{i}}_5{\mathrm{H}}_6+30.1{\displaystyle \frac{\mathrm{k}\mathrm{j}}{\mathrm{m}\mathrm{o}\mathrm{l}}}$$

(5)

$$\mathrm{M}\mathrm{g}+{\mathrm{H}}_2\leftrightarrow {\mathrm{M}\mathrm{g}\mathrm{H}}_2+75{\displaystyle \frac{\mathrm{k}\mathrm{j}}{\mathrm{m}\mathrm{o}\mathrm{l}}}$$

(6)

Figure 5 highlights the significant kinetic differences between MgH₂ and LaNi₅, driven by their reaction enthalpy and activation energy. MgH₂, with a high decomposition enthalpy of ~75 kJ/mol, requires more energy to overcome its activation barrier, resulting in slower reaction rates: ~18,300 s for absorption and ~25,700 s for desorption. In contrast, LaNi₅, with a lower enthalpy of 30–40 kJ/mol, completes absorption in ~5400 s and desorption in ~2520 s, making it ideal for rapid hydrogen exchange. These differences underscore MgH₂’s need for higher temperatures or catalysts, while LaNi₅ is better suited for fast-response applications, emphasizing the importance of balancing storage capacity, kinetics, and thermal management in system design. The equilibrium and maximum temperature values for LaNi₅ and MgH₂ demonstrate the unique thermodynamic properties of these materials. LaNi₅ functions effectively at moderate temperatures, as evidenced by an equilibrium temperature of 326.01 K and a maximum temperature of 344.5 K, suggesting a low enthalpy of reaction. Its suitability lies in applications needing swift and low-energy thermal control. In contrast, MgH₂ has an equilibrium temperature of 610.7 K and a maximum temperature of 643.2 K, which underscores its high reaction enthalpy. Higher temperatures are characteristic of reduced rates of reaction and increased energy requirements during the absorption and release of hydrogen. Selecting materials for hydrogen storage systems depends on thermal needs and energy limitations.

MgH₂’s elevated operating temperature relative to LaNi₅ primarily stems from its increased reaction enthalpy and more robust hydrogen–metal interaction. This compound has a decomposition enthalpy of roughly 75 kJ/mol, necessitating substantial energy input to liberate hydrogen. In comparison to LaNi₅, the latter exhibits a lower reaction enthalpy of 30–40 kJ/mol, enabling it to function efficiently at moderate temperatures. The stronger chemical bonds in MgH₂ are responsible for its enhanced thermal stability, making it a suitable material for high-temperature applications and also leading to slower reaction rates compared to LaNi₅.

4. Conclusions

• MgH₂ necessitates a bigger volume of phase change material (PCM) because of its greater reaction enthalpy, resulting in the need for more effective thermal management compared to LaNi₅.
• Magnesium hydride, having slower reaction rates, is more suitable for systems focusing on greater storage capabilities. The operating temperature range for MgH₂ is between 610.7 and 643.2 K, which is significantly higher than the 326.01 to 344.5 K operating temperature of LaNi₅, indicating that MgH₂ is more suitable for applications requiring high temperatures, whereas LaNi₅ is more beneficial for moderate-temperature operations. In contrast, MgH₂, with slower kinetics, is better suited for systems prioritizing higher storage capacity.