Study of the Permeation Flowrate of an Innovative Way to Store Hydrogen in Vehicles

Abstract

With the global warming of the planet, new forms of energy are being sought as an alternative to fossil fuels. Currently, hydrogen (H₂) is seen as a strong alternative for fueling vehicles. However, the major challenge in the use of H₂ arises from its physical properties. An earlier study was conducted on the storage of H₂, used as fuel in road vehicles powered by spark ignition engines or stacks of fuel cells stored under high pressure inside small spheres randomly packed in an envelope tank. Additionally, the study evaluated the performance of this new storage system and compared it with other storage systems already applied by automakers in their vehicles. The current study aims to evaluate the H₂ leaks from the same storage system, when inserted in any road vehicle parked in conventional garages, and to show the compliance of these leaks with European Standards, provided that an appropriate choice of materials is made. The system’s compliance with safety standards was proved. Regarding the materials of each component of the storage system, the best option from the pool of materials chosen consists of aluminum for the liner of the spheres and the envelope tank, CFEP for the structural layer of the spheres, and Si for the microchip.

1. Introduction

Almost 87% of human CO₂ emissions worldwide are caused by fossil fuel use [1]. In the last few years, there has been great concern from the governments of several countries to provide a global and effective response to halt the increase of the global average temperature of the Earth and tackle the challenges related to climate change [2].

This effort was translated into the Paris Agreement, which aims to decarbonize world economies [3]. However, the targets for reducing carbon emissions imposed by the Paris Agreement have been questioned, concerning its suitability with the reduction of energy poverty [4]. Thus, in the search for decarbonization, it is expected that hydrogen (H₂) will soon be considered an important energy vector, either for propulsion or for energy storage [2,5,6,7].

The sustainable future involves the use of smart energy solutions and, consequently, the interests of many authors have been aroused to this topic [4,8,9]. Dincer and Acar [8] highlight that smart energy solutions are not possible without solutions that use hydrogen. They also reinforce the importance of sustainable methods of hydrogen production, which are still challenging, for a carbon-free economy. They concluded that requirements such as (i) energy conservation, (ii) the use of renewable energy, (iii) integration of clean energy, (iv) increase of valuable products from the same resources, (v) more efficient storage of energy carriers and chemicals, and (vi) the use of smart grids and control in renewable energy are the minimum and necessary requirements for a transition to a smart solution based on H₂, given a sustainable future [8].

The use of H₂ as fuel is still in its embryonic stage and it is necessary to create conditions to support its distribution and storage, including infrastructure (refueling stations), that are safe and fast to meet the necessary conditions for the common use of hydrogen [10,11].

The environmental impact of using H₂ as fuel in vehicles has been studied by comparing hydrogen-propelled vehicles with electric vehicles charged with electricity obtained from renewable sources [12,13]. Some studies include the production of H₂ from renewable energy (sun, wind, tides, among others), also known as green energy. These investigations show the great interest in H₂ storage since it is economically feasible to store large amounts of energy, in the form of H₂, according to the seasonal rhythms of the availability of green energy [14,15,16,17]. Indeed, to reduce the impact of obtaining H₂, the surplus production of renewable energies should be used to obtain H₂, which would be stored before being used [18]. Tarkowski [19] studied the feasibility of underground storage in different contexts, such as deep aquifers, depleted oil fields, salt caves, and depleted gas fields, and concluded that the differences between underground hydrogen storage and natural gas storage are not significant.

A competitive and ecological alternative to battery-powered electric vehicles is the use of vehicles propelled by stacks of fuel cells, which may become an economic reality. H₂ for fuel cells could achieve large-scale use in vehicles as renewable energy becomes more widespread [20,21,22]. One of the main challenges for this is a quick and safe supply of H₂ [23].

In line with the growing interest in the use of H₂ for vehicle propulsion, the concern for storing this fuel in vehicles has also grown. Thus, Fonseca et al. [18] state that almost 70% of publications on the H₂ topic focus on hydrogen storage. It should be noted that storage of hydrogen entails safety questions, and it should not compromise the useful space for passengers or cargo.

It is possible to distinguish two distinct ways of storing hydrogen [6]. The first one consists of storing it as (i) compressed gas (CGH₂), (ii) cryogenic liquid, (iii) adsorbed on carbon nanofibers, or (iv) adsorbed on metal or reversible metal hydride [6,24]. In a second way, H₂ is stored in the molecules of ammonia (NH₃) or methanol (CH₃OH), among others. The most widespread storage method for H₂, either in stationary applications or in vehicles, uses man-made pressurized containers, namely cylinders of various sizes; for stationary facilities, underground caves can be used. Larminie et al. [24] presented some advantages regarding the storage of H₂, taking CGH₂ as an example, namely the unlimited storage time, its simplicity, and no requirement of purity in H₂.

The current study is a follow-up to a previous paper [25], whose purpose was to assess a new system, proposed by Stenmark [26], to store H₂ in conventional vehicles. The investigation focused on the high-pressure H₂ storage system inside small spheres stowed randomly in a container, hereafter named the envelope tank, with dimensions similar to a conventional fuel tank used in current vehicles. Thus, such assessment was made based on: (i) the energy stored by weight of the system (GED), (ii) the energy stored by the volume of the system (VED), (iii) the leakage of H₂ from the system, through the comparison with other methods of H₂ storage and, finally, (iv) the compliance with current safety standards was checked. In the referred previous study, the main characteristics of the complete storage system (envelope tank and spheres) were studied, using spheres of 10 different materials, with an internal diameter of 10 to 70 mm. The following parameters were also considered: a packing factor between 52 and 74%, a safety factor of 1.41, a tank with an internal volume of 0.122 m³, and two types of microchip material were considered. From the study, the best combination of materials for the sphere composition was a structural layer in CFEP, a liner in aluminum, and a microchip in silicon. With this combination, the system achieved a VED between 0.61 and 0.87 kWh/L and a GED between 6.62 and 7.22 kWh/kg.

Figure 1 shows a comparison of the GED and VED of several fuels, including the spheres storage system of Stenmark [26], whereby it is possible to confirm the clear advantage of the new storage method, taken as new fuel, concerning the other systems.

H₂ materials for storage containers must be chosen carefully, always considering the limitations and requirements of the European Regulations [27]. An important parameter is the size of the H₂ molecule since it is the smallest, which results in its high average speed. Thus, the permeation of H₂ through the walls of a container cannot be neglected. Care must also be taken, for example, if the container is metallic because small H₂ bubbles will appear and create small cracks in the walls of the container. In the case that the container is made of metallic alloys with carbon, such as steel, it is likely there will be a reaction between the H₂ and carbon, resulting in CH₄ bubbles. As a result of this reaction, the walls will crack—a phenomenon known as H₂ embrittlement. According to the authors [24,28,29], a way to avoid this phenomenon is the addition of molybdenum and chromium to steel.

Another important point to consider is the danger associated with H₂ leakage, mostly for a container at very high pressure. Upon leakage, the H₂ self-ignites in a flammability range of 4 to 77% (v/v), and an invisible flame is generated. The solutions found to minimize the associated risks are the introduction of rupture discs, relief valves, and flame traps installed in the tanks.

According to Adams et al. [30], it seems that the H₂ flowing by permeation (typically low flowrates) from a container into a compartment such as a garage, spreads almost evenly across the available space, without noticeable stratification, in spite of its much lower density than the density of the air. The authors calculated the maximum allowable permeation flowrate from the H₂-polymer-containers for typical cars and city buses; this calculation took into account the initial mass/pressure of H₂ within the containers, the dimensions (ultimately the volume) of the compartment where the car is parked, the age of the polymer (which affects the permeability of the container), the temperature the polymer is subjected to (which also affects the permeability of the container), and the air change flowrate of the compartment, allowing a maximum percentage of H₂ in the compartment of 1% (v/v). For safety reasons, this is well below the lower flammability limit of H₂ in the air.

Crowl et al. [31] conducted a study where they distinguished the dangers and risks regarding the use of H₂. They defined the hazards linked to flammability, and the risks linked to the combination of the probability of an accident and the consequences of the accident. This question demands considering the minimum ignition energy of H₂, which is very low when compared to the homologous value for other gases, whereby it follows that the combustion of H₂ is easily activated. Another characteristic of H₂ to consider is its high range of flammability. It is necessary to limit the amount of H₂ in confined spaces. The high diffusivity of H₂ facilitates the aeration of spaces, and its low molecular weight promotes its upward dispersion.

The main purposes of the present study are, firstly, to assess the flowrate due to permeation of H₂ for a new storage system (envelope tank and spheres) when it is used in any road vehicle parked in a conventional garage, and, secondly, to show the compliance of these leaks with the European Regulations [27], provided a suitable choice of materials is made.

2. Methodology for Assessing the Performance of the System

As already stated, the current study addresses an innovative way of storing H₂ in common vehicles. The methodology followed to evaluate the performance of this storage system is described in

Table 1. Steps summary.

Step 1	Storage system description
Step 2	Time variation of pressure and mass in spheres and in tank
Step 3	Materials selection for the sphere, tank, and the values of permeation
Step 4	Regulation that must be complied
Step 5	Aim of calculations
Step 6	The packing factor (PF)

as a chain of steps.

2.1. Storage System Description: Step 1

The system consists of a set of small spheres randomly packed inside an envelope tank with any shape. In Figure 2, an example can be seen, with a “parallelepiped” envelope tank in the trunk of the vehicle. H₂ is inside the spheres at high pressure, say 700 bar, and at room temperature. All spheres have an embedded parallelepiped microchip, with dimensions of 0.5 × 0.5 × 2.5 mm³. Either the refilling of the empty spheres with H₂ or the release of H₂ from filled spheres are controlled through the microchip. If the internal pressure of the tank is below a chosen pressure threshold, say 5 bar, the spheres do not release H₂ into the tank, but if that pressure is above the said threshold, then the spheres release H₂ into the tank; in this study, the maximum operating pressure of H₂ in the tank was considered as 20 bar. The propeller, either a reciprocating spark-ignition engine or a stack of fuel cells, is fed by the tank.

2.2. Time Variation of Pressure and Mass in Spheres and in Tan: Step 2

The permeation flow of H₂ from the storage system occurs because of the permeability of the micro-spheres and of the envelope tank. It is important, for safety reasons, to determine if the flowrate of H₂, due to permeation during a prolonged stop of the vehicle, compromises the safety of the garage where the vehicle is parked. Thus, it is necessary to know the pressure, mass of H₂, permeation flowrate of H₂, and concentration of H₂ over time, for the micro-spheres, the envelope tank, and the garage.

This emptying of the storage system (spheres and envelope tank) is time-dependent. Yet, the calculations performed, and described below, assume a succession of time intervals, as small as required for the sake of accuracy, within which it is plausible to assume a steady state.

A description of the procedure used follows:

• Mass of H₂ within a sphere is given by (1),

  $${\mathrm{M}}_{{\mathrm{H}}_2-\mathrm{sph}}=\frac{P_{sph}·{\mathrm{V}}_{\mathrm{in} \mathrm{sph}}}{\mathrm{Z}·{\mathrm{R}}_{{\mathrm{H}}_2}·{\mathrm{T}}_{{\mathrm{H}}_2}}$$

  (1)
• Concentration of H₂ within a sphere is given by (2) since the mole fraction x_H₂ = 1 within the spheres.

  $${\left[H_2\right]}_{sph}=\frac{P_{sph}}{\mathrm{Z}·{\mathrm{R}}_{\mathrm{u}}·{\mathrm{T}}_{{\mathrm{H}}_2}}$$

  (2)
• Concentration of H₂ within the envelope tank is given by (3) since the mole fraction x_H2 = 1 within the envelope tank.

  $${\left[H_2\right]}_{tank}=\frac{P_{tank}}{\mathrm{Z}·{\mathrm{R}}_{\mathrm{u}}·{\mathrm{T}}_{{\mathrm{H}}_2}}$$

  (3)
• A part of the inner volume of the envelope tank is occupied by spheres, whose volume is given by (4),

  V_ts = PF × V_{int tank.}

  (4)
• Mass of H₂ contained in the part of the envelope tank free of spheres is given by (5),

  $${\mathrm{M}}_{{\mathrm{H}}_2-\mathrm{tank}}=\frac{P_{tank}·\left(1-PF\right){\mathrm{V}}_{\mathrm{int} \tan \mathrm{k}}}{\mathrm{Z}·{\mathrm{R}}_{{\mathrm{H}}_2}·{\mathrm{T}}_{{\mathrm{H}}_2}}.$$

  (5)
• The permeation coefficient, Φ, of H₂ was taken from tables [32]; its value is expressed either by mole/m/s/MPa, or mole/m/s/MPa^1/2, or mole/m²/s/MPa^1/2.
• The solubility, S, of H₂ was calculated as the quotient of H₂ by the partial pressure of H₂ if the permeation was expressed as mole/m/s/MPa, or as the quotient of H₂ by the root of the partial pressure of H₂, if the permeation was either expressed as mole/m/s/MPa^1/2 or mole/m²/s/MPa^1/2. The partial pressure of H₂ within the spheres equals the total pressure within the spheres; the partial pressure of H₂ within the envelope tank equals the total pressure within it; the H₂ in the atmosphere was considered zero.
• The diffusivity, D, of H₂ across each layer of the spheres and across the envelope tank was calculated with (6). In the case of the permeability being expressed in mole/m²/s/MPa^1/2, which was the case with Si for the microchip, to obtain the diffusivity in m²/s it was necessary to multiply the permeability by the thickness of the layer.

  Φ = DS.

  (6)
• Each micro-sphere is made of two concentric spheres, or layers, of different materials, and a parallelepipedal microchip embedded in both spheres; moreover, the outer diameter of the inner sphere equals the inner diameter of the outer sphere. The inner layer, named liner, is mostly intended to provide the necessary resistance to H₂ permeation and the outer layer, named structural, is mostly intended to provide structural strength. The permeation flow of H₂ from the micro-spheres must not be confounded with the intentional flow of H₂ from the spheres, controlled by the microchip, to fuel the propeller (engine or fuel cells). The former occurs in three different ways: by permeation through the spheric layers, by permeation through the microchip, and by the interface between the microchip and the sphere (which is unwanted). This latter flow is leakage and should be as small as possible; since it depends on the quality of the manufacture of the micro-spheres, it is human-controlled and will be neglected. Thus, the overall diffusivity for a micro-sphere is given by (7): it was calculated considering the flow across the series of the composite wall of two concentric spheres (liner and structural) in parallel with the flow across the microchip. As referred, r_{o liner} = r_{i strut}.

  $$D_{Total}=\left(\frac{1}{r_{i liner}}-\frac{1}{r_{o stru}}\right)\left[\frac{D_{microchip}{A}_{microchip}}{4\pi t_{microchip}}+\frac{1}{\frac{1}{D_{ liner}}\left(\frac{1}{r_{i liner}}-\frac{1}{r_{o liner}}\right)+\frac{1}{D_{stru}}\left(\frac{1}{r_{i stru}}-\frac{1}{r_{ o stru}}\right)}\right],$$

  (7)
• Total resistance to the diffusion of H₂ through a micro-sphere was calculated with Equation (8).

  $$R_{micro - sphere}=\frac{1}{4\pi D_{Total}}\left(\frac{1}{r_{i liner}}-\frac{1}{r_{o stru}}\right)$$

  (8)
• Mole flowrate of H₂ through a micro-sphere was calculated by (9); the concentrations of H₂ were considered at the inner face of the liner, and at the outer face of the structural layer.

  $${\dot{n}}_{H_2 micro - sphere}=\frac{{\left[H_2\right]}_{i liner}-{\left[H_2\right]}_{o stru}}{R_{micro - sphere}}$$

  (9)
• Masses of H₂ within a micro-sphere at the instant t, and at the instant t-Δt are related through (10).

  $$M_{H_2 micro - sphere} \left(t\right)=M_{H_2 micro - sphere}\left(t-\Delta t\right)-{\dot{n}}_{H_2 micro - sphere}\left(t\right)M{W}_{H_2}\Delta t$$

  (10)
• Concentration of H₂ within the envelope tank was obtained through (3) but was considered zero outside it, at the surrounding atmosphere.
• Solubilities of H₂ at the inner and outer surface of the envelope tank were calculated according to point 7. The diffusivity of H₂ through the envelope tank was calculated according to Equation (6).
• It was assumed a cylindrical enveloped tank, so the total resistance to the diffusion of H₂ through the envelope tank was calculated with Equation (11).

  $$R_{tank}=\frac{ln\left(\frac{r_{t o}}{r_{t i}}\right)}{2\pi L{D}_{tank}}$$

  (11)
• Mole flowrate of H₂ through the envelope tank to the atmosphere was calculated by (12), where the concentrations of H₂ were considered at the inner face of the envelope tank and at the outer face of the envelope tank; the value of the H₂ concentration in the envelope tank was assumed to be zero.

  $${\dot{n}}_{H_2 tank}=\frac{{\left[H_2\right]}_{i tank}-{\left[H_2\right]}_{o tank}}{R_{tank}}.$$

  (12)
• Masses of H₂ within the part of the envelope tank free of micro-spheres at the instant t, and at the instant t-Δt are related through Equation (13).

  $$M_{H_2 tank} \left(t\right)=M_{H_2 tank}\left(t-\Delta t\right)+M{W}_{H_2}\Delta t\left[N_{micro - spheres}{\dot{n}}_{H_2 micro-sphere}\left(t\right)-{\dot{n}}_{H_2 tank}\right]$$

  (13)
• At any instant t, the pressure within the micro-spheres or in the part of the envelope tank free of micro-spheres was calculated with the equation of perfect gases. The same was done regarding the H₂ concentrations.

R_H2 is the ideal gas H₂ constant, taken as 4124 Jkg⁻¹K⁻¹; Ru is the universal constant of perfect gases; MW_H₂ is the molecular weight of H₂ considered as 2.016 kg kmol⁻¹; T_H₂ is the temperature of H₂, assumed as 293.15 K; and Z is the compressibility factor of H₂ at 700 daNcm⁻² and 293.15 K, taken as 1.46 [33].

2.3. Materials Selection for the Sphere, Tank, and the Values of Permeation: Step 3

The studied materials, as well as their most relevant properties for the present study, are shown in

Table 2. Materials properties for the sphere and microchip.

Material	Φ		ρ (kgm−3)	σyield (MPa)	σult (MPa)	References
Al 5050-H38	4.34 × 10−20	mol/(msPa0.5)	2697	220	-	[34]
SS316	1.13 × 10−18	mol/(msPa0.5)	7990	290	-	[35]
Inconel 718	1.13 × 10−17	mol/(msPa0.5)	8190	1100	-	[35]
SS403	4.34 × 10−20	mol/(msPa0.5)	7800	310	-	[36]
PP	2.6 × 10−15	mol/(msPa)	870	-	17.4	[37,38]
HDPE	8.98 × 10−16	mol/(msPa)	1275	-	27	[39]
CFEP	1.9 × 10−16	mol/(msPa)	1790	-	4000	[39]
W	4.94 × 10−32	mol/(msPa0.5)	12,750	1045		[40]
Si	1 × 10−8	mol/(m2sPa0.5)	3220	-	-	[41]

. The silicon (Si), present in Table 2, was considered only for the microchip.

Since ensuring the safety of people is very important, it was necessary to assess the risks that are associated with permeation, namely the possibility of explosions. The permeability of H₂ through solid surfaces was studied for the materials of the spheres and of the envelope tank. According to the references [39,42], there are values of permeability with great uncertainties associated, and not always expressed in the same units. In Table 2, Φ represents the permeation value for the conditions at 293.15 K and 101.3 kPa. From this table, it can be concluded that the metal alloys (Al5050-H38, SS403, Inconel 718, W, and SS316) have lower permeation values, although they present higher strength values compared to polymeric materials (PP and HDPE). Composite materials (epoxy fiberglass and CFEP) have higher permeation values and identical or higher strength values compared to metal alloys.

At this juncture, the idea of coupling two materials in the construction of the micro-sphere came up. Such a combination was tested with two concentric spherical layers, the inner layer to provide the necessary resistance to H₂ permeation and the outer layer to provide structural strength.

Thus, the materials for the microchip, the inner and outer layer, as well as the material that constitutes the envelope tank were chosen according to

Table 3. Combinations of material for each part of the storage system studied.

Combinations	Lining	Structural Layer	Microchip	Envelope Tank
1	Al 5050-H38	CFEP	Si	Al 5050-H38
2	Al 5050-H38	CFEP	Si	SS316
3	Al 5050-H38	CFEP	Si	SS403
4	Al 5050-H38	CFEP	Si	Inconel 718
5	Al 5050-H38	CFEP	Si	PP
6	Al 5050-H38	CFEP	Si	HDPE
7	SS316	CFEP	Si	Al 5050-H38
8	SS316	CFEP	Si	SS316
9	SS316	CFEP	Si	SS403
10	SS316	CFEP	Si	Inconel 718
11	SS316	CFEP	Si	PP
12	SS316	CFEP	Si	HDPE
13	SS403	CFEP	Si	Al 5050-H38
14	SS403	CFEP	Si	SS316
15	SS403	CFEP	Si	SS403
16	SS403	CFEP	Si	Inconel 718
17	SS403	CFEP	Si	PP
18	SS403	CFEP	Si	HDPE
19	W	CFEP	Si	Al 5050-H38
20	W	CFEP	Si	SS316
21	W	CFEP	Si	SS403
22	W	CFEP	Si	Inconel 718
23	W	CFEP	Si	PP
24	W	CFEP	Si	HDPE
25	PP	CFEP	Si	Al 5050-H38
26	PP	CFEP	Si	SS316
27	PP	CFEP	Si	SS403
28	PP	CFEP	Si	Inconel 718
29	PP	CFEP	Si	PP
30	PP	CFEP	Si	HDPE

.

The Si was chosen for the micro-chip due to its easy tooling [31]; indeed, it is a material widely used in small electronic devices for this reason.

According to Dwivedi et al. [43], materials with high strength, such as steel, steel with a high magnesium content, titanium, and magnesium alloys are prone to embrittlement caused by H₂ when they are under conditions of high temperature, pressure, and exposure time.

Table 3 shows all the studied combinations of materials for each part of the storage system, from the set of materials referred on Table 2.

2.4. Regulations That Must Be Complied: Step 4

The European Regulations on the approval of future hydrogen-powered vehicles is called EU 406/2010 [27]. The standard requirements allow the permeation of metallic container materials to be neglected. However, polymeric materials must be submitted to suitable permeation tests. The research study meets this requirement [30], which concluded that the permeation of polymeric materials is higher than the permeation of metallics materials. At steady state, the maximum allowable permeation flow is 6 Ncm³h⁻¹L⁻¹, being this value per liter of the internal volume of the container and, for safety reasons, it is intended to avoid a possible mixture between H₂ and air in closed spaces, assuming a minimum air renewal per hour of 0.03 [44].

Another factor to consider, according to [45], is the temperature, since it affects the permeation of H₂ through the walls. In the current study, it is expected that temperatures during filling (in the case of rapid filling) are approximately 50 °C; however, it is assumed that there may be peaks of 85 °C. In the calculations performed in this study, a correction factor was added, considering that the tests were performed at temperatures below 55 °C [30,46].

The correction factor adopted was 2 [30], since the aging of the material causes an increase in the permeation of H₂, although this phenomenon has not yet been fully understood.

Thus, the value of C_% must be less than 1% (see Equation (14)), where C_% represents the volumetric flow of the H₂ ratio that leaves, by permeation, the envelope tank, Q_H2, and the sum of the flow of air in space due to air renewal, Qair with Q_H2. So,

$${\mathrm{C}}_{\%}=\frac{100·{\mathrm{Q}}_{\mathrm{H}2}}{{\mathrm{Q}}_{\mathrm{air}}{+\mathrm{Q}}_{\mathrm{H}2}},$$

(14)

Q_p-H₂, (see Equation (15)), is the maximum allowable flowrate of permeation of H₂, expressed in mL/h/L, i.e., the milliliters of H₂ leaked during one hour per liter of the inner volume of the storage vessel,

$${\mathrm{Q}}_{\mathrm{p}-{\mathrm{H}}_2}=\frac{{\mathrm{Q}}_{\mathrm{air}}·{\mathrm{C}}_{\%}}{{100-\mathrm{C}}_{\%}}·\frac{60·{10}^6}{{\mathrm{V}}_{\mathrm{int} \mathrm{all} \mathrm{sph}}·{\mathrm{f}}_{\mathrm{a}}·{\mathrm{f}}_{\mathrm{t}}}$$

(15)

with V_{int all sph} being the inner volume of the storage vessel (in the present case, the whole set of spheres in the envelope tank), f_a is the aging factor of 2, and f_t is the factor of correction for the temperature; V_{int all sph} is expressed in liters, Q_air and Q_H2 must be expressed in m³/min.

In short, the value of permeation varies during the emptying of spheres, either because of the decrease in the pressure within the spheres, or because of temperature or the aging of the spheres. Therefore, the flowrate of H₂ by permeation, across the wall of the sphere, must vary with time.

In the current study, Equations (14) and (15) were used considering the three following scenarios proposed by Adams et al. [30] for domestic garages and parked vehicles; see

Table 4. Scenarios for domestic garages and parked vehicles. Adapted from Adams et al. [30].

Features	Scenarios
	1	2	3
Garage volume (m3)	50	33	19
Garage free volume (m3)	46	31	18
Volume of impermeable material (m3)	4	2	1
Natural ventilation of the garage (ACH)	0.03	0.03	0.03
Natural ventilation of the garage (m3/h)	1.38	0.93	0.54

.

2.5. Aim of Calculations: Step 5

In the current study, the value of Q_H2 of Equation (14) was determined with the procedure described in step 2. Such values were determined over time, for a family vehicle parked inside a common garage for a long period of time; and at the beginning of such parking, the storage system was considered filled with H₂ at the highest pressure. The values of Q_air of Equations (14) and (15) were assumed as the air changes flowrates at the garage, taken from Table 4, for the referred three scenarios.

Ultimately, the aim is to see if for the new storage system, the value of C_%, according to Equation (14), is under 1%.

2.6. The Packing Factor (PF): Step 6

The PF indicates the proportion of usable space in the storage system. It must have the highest possible value.

Aigueperse et al. [47] studied the stowage of spheres randomly launched into a container. They concluded that the arrangement of the spheres is identical to the crystalline structures. The simplest combination of spheres is the body-centered cubic structure (BCC), with a packing factor of approximately 0.52.

Other authors also state that the closed hexagonal packing (HCP) [48,49] has the highest PF value, at approximately 0.74.

Regarding the storage of spheres, Dong et al. [50], Silbert et al. [51], and Onoda et al. [52] studied randomly compact packing (PRC) and randomly loose packing (PRL). According to the authors [50], after several studies, the best value achieved for Packing Factor (PF) was 0.64. The authors [51] concluded that PRC is the most efficient arrangement for randomly stowed spheres in a tank, surpassed only by an arrangement obtained through container vibration. Onoda et al. [52], in their experimental tests of glass spheres immersed in a liquid, disregarding the gravitational force, obtained a PF of 0.55.

3. Results and Discussion

All the combinations of materials shown in Table 3 were considered in calculations. The mass of H₂ in each sphere and the envelope tank were calculated along with the time, through Equations (10) and (13), respectively.

The time-step used in all the cases was 5000 s, and during each step, P_sph and P_tank were assumed constant. Furthermore, on one hand, the time-step was chosen in order to avoid needless time-consuming calculations because of too small time-steps without a noticeable increase of accuracy in the results, and, on the other hand, to avoid inaccurate results because of too large time-steps. So, the choice of 5000 s as the time-step results from a trade-off between the referred conflicting speed of calculations and accuracy of results but permits the obtaining of reasonably accurate results.

The pressure considered for calculating the permeation of the two layers of spheres was taken as the difference between the pressures within and without the spheres; similarly, the pressure considered for calculating the permeation of the envelope tank was taken as the difference between the pressures within the envelope tank and the atmospheric pressure.

The temperature of the atmosphere and the temperature of the H₂ within either the spheres or the envelope tank were considered to be 293.15 K. The atmospheric pressure was taken as 101,325 Pa. The initial pressure within the spheres was assumed as 71 MPa, whereas the initial pressure in the envelope tank in the space between spheres was taken as 0.5 MPa. The PF was taken as 0.52 because this is the value of PF normally found in the random stackings of spheres.

A first calculation was made to see which combinations of Table 3 correspond to less permeation losses from the spheres into the garage. To do this, a car was parked in a garage with a full H₂ storage system at 700 bar inside the spheres and 5 bar in the space of the envelope tank between spheres. In this situation, the H₂ will naturally permeate through the spheres into the envelope tank and from there, into the garage. The calculation aimed to obtain the time required for reaching 20 bar in the envelope tank between spheres, which obviously should be as long as possible, and at the same time to check if the value of C_%, see Equation (14), at that moment was below 1%, as required by regulations.

To obtain comparable results with those of Adams et al. [30], the storage system was assumed to be installed (i) in large cars, parked in garages with a volume of 50 m³, with a free volume of 46 m³ and 0.03 ACH (1.38 m³/h); (ii) in small cars, parked in garages with a volume of 33 m³, with a free volume of 31 m³ and 0.03 ACH (0.93 m³/h); and (iii) in micro cars, parked in garages with a volume of 19 m³, with a free volume of 46 m³ and 0.03 ACH (0.54 m³/h).

The results are shown in

Table 5. Time to obtain 20 bar in the envelope tank and values of C_% for the scenarios of Table 4.

Combinations	Elapsed Time (Days)	C% = 100 × QH2/(Qair + QH2) in Garage
		Scenarios
		1	2	3
1	79.6	2.8 × 10−10	4.1 × 10−10	7.1 × 10−10
2	79.6	1.1 × 10−8	1.6 × 10−8	2.7 × 10−8
3	79.6	1.4 × 10−5	2.1 × 10−5	3.6 × 10−5
4	79.6	3.8 × 10−7	5.6 × 10−7	9.7 × 10−7
5	82.6	3.1 × 10−3	4.7 × 10−3	8.0 × 10−3
6	80.4	8.3 × 10−4	1.2 × 10−3	2.1 × 10−3
7	79.6	2.8 × 10−10	4.1 × 10−10	7.1 × 10−10
8	79.6	1.1 × 10−8	1.6 × 10−8	2.7 × 10−8
9	79.6	1.4 × 10−5	2.1 × 10−5	3.6 × 10−5
10	79.6	3.8 × 10−7	5.6 × 10−7	9.7 × 10−7
11	82.6	3.1 × 10−3	4.7 × 10−3	8.0 × 10−3
12	80.4	8.3 × 10−4	1.2 × 10−3	2.1 × 10−3
13	69.4	2.8 × 10−10	4.1 × 10−10	7.1 × 10−10
14	69.4	1.1 × 10−8	1.6 × 10−8	2.7 × 10−8
15	69.4	1.4 × 10−5	2.1 × 10−5	3.6 × 10−5
16	69.4	3.8 × 10−7	5.6 × 10−7	9.7 × 10−7
17	71.8	3.1 × 10−3	4.7 × 10−3	8.0 × 10−3
18	70.0	8.3 × 10−4	1.2 × 10−3	2.1 × 10−3
19	79.6	2.8 × 10−10	4.1 × 10−10	7.1 × 10−10
20	79.6	1.1 × 10−8	1.6 × 10−8	2.7 × 10−8
21	79.6	1.4 × 10−5	2.1 × 10−5	3.6 × 10−5
22	79.6	3.8 × 10−7	5.6 × 10−7	9.7 × 10−7
23	82.6	3.1 × 10−3	4.7 × 10−3	8.0 × 10−3
24	80.4	8.3 × 10−4	1.2 × 10−3	2.1 × 10−3
25	0.8	2.7 × 10−10	4.0 × 10−10	6.8 × 10−10
26	0.8	1.0 × 10−8	1.5 × 10−8	2.6 × 10−8
27	0.8	1.4 × 10−5	2.0 × 10−5	3.5 × 10−5
28	0.8	3.7 × 10−7	5.4 × 10−7	9.4 × 10−7
29	0.8	3.0 × 10−3	4.5 × 10−3	7.8 × 10−3
30	0.8	8.1 × 10−4	1.2 × 10−3	2.1 × 10−3

and prove that, in all three scenarios, the value of C_% is well below 1% and that it takes about 2.5 months for the pressure in the envelope tank to rise from 5 to 20 bar, except for the cases of combinations 25 to 30, owing to the material of the lining being PP, whose permeation resistance is very low.

Further analysis was made for combinations 1, 7, and 19 since these combinations correspond to the lowest values of C_%. The evolution of H₂ pressure over time, in spheres and the envelope tank (since the car is parked until the pressure in the envelope tank reaches 20 bar), is shown for combinations 1, 7, and 19, respectively, in Figure 3, Figure 4 and Figure 5; moreover, the evolution of C_% over time is shown for combinations 1, 7, and 19, respectively, in Figure 6, Figure 7 and Figure 8.

From the graphs of Figure 3, Figure 4 and Figure 5, it can be seen that as the pressure inside the spheres decreases, the pressure in the envelope tank increases in spite of the permeation from the envelope tank to the garage. This is owing (i) to the fact that the permeation values of the envelope tank are much lower than the permeation values of the spheres and (ii) the pressure in the spheres is much higher than the pressure in the envelope tank.

Graphs of Figure 6, Figure 7 and Figure 8 show that for all the three scenarios considered, the storage system studied guarantees values of concentration of H₂, even for 1 year of parking, well below the 1% required by European Regulations [27]. Thus, this storage system is safe for the everyday use of hydrogen-propelled cars.

4. Conclusions

In this work, the best set of materials for the microchip, sphere, and envelope tank was studied, considering the permeation flowrate.

All the combinations of materials chosen to manufacture the parts of the storage system that exclude the PP allow the safe use of the currently studied storage system. The best option, among the pool of materials chosen, consists of aluminum for the liner of the spheres and the envelope tank, CFEP for the structural layer of the spheres, and Si for the microchip. Moreover, provided that European Regulations are adopted, and following the procedure of Adams et al. [30], if the user of the car leaves it parked in a garage for about 2.5 months, the H₂ storage system never creates a dangerous situation compromising the safety of persons or goods in the vicinity of the car.

Moreover, analytical [53,54] and experimental [54,55] studies over permeation flowrate from containers with CGH₂ provided results of the same order of magnitude obtained from the current study over concentration of H₂ in spaces such as garages.

Anyway, if there is an accident, such as the bursting of spheres, it is most likely that only a few spheres will be involved in it, which, at the outset, minimizes the disastrous consequences of the accident. Therefore, this storage system is intrinsically safer than other storage systems of compressed gaseous H₂.

Naturally, some of the results presented in this paper can be slightly corrected in the future, when more accurate values of permeation for materials are available. In any case, it is not likely that such corrections will entail conclusions that may fundamentally contradict the present ones.