Hydrogen Tutorial

by Arnold R. Miller, PhD


Arnold R. Miller, PhD

Preface: This tutorial is written at the level of a university student who has had at least one course each in chemistry and physics. I hope readers with less formal training can nonetheless take away the essential character of the monograph: intuitive insight into key physical phenomena - such as the idea that hydrogen is a gaseous metal and the analogy between electricity and hydrogen as energy carriers - but intuition confirmed by mathematical and physicochemical argument. The first section presents the potential benefits of hydrogen fuel, and the eighth reiterates the challenges. Six intervening sections link the promise and challenges. - ARM

(Note: The sections below are essentially complete, but the remaining sections are in progress.)



1. The Promise of Hydrogen

Hydrogen fuel, especially coupled with fuelcells, offers a solution to worldwide problems caused by the approaching scarcity of fossil fuels and ongoing atmospheric emissions of greenhouse gases. Hydrogen is sometimes termed the "forever fuel" and the "universal fuel" because, respectively, it is an energy carrier that is constantly recycled, and it can be produced from numerous primary energies. In several ways, hydrogen is analogous to electricity: (1) It is manufactured rather than recovered from geological deposits; (2) it is readily transmitted via pipelines that are analogous to electrical conductors; (3) when produced from clean primary energies, it is as clean in its applications as electricity, (4) in chemical processes, it often exists (up to being solvated) as a fundamental particle, the proton, and (5) electricity and hydrogen can always be interchanged, in a kind of yin-and-yang relationship, via electrolysis or fuelcells.

Below, I will provide the foundations of the above academic facts. However, practical widespread use of hydrogen is not yet a fait accompli, and I will also describe challenges that must be overcome before a hydrogen-based civilization can become reality.

2. Hydrogen in Nature

Hydrogen is the most abundant element in nature. About three-quarters of the ordinary matter of the universe is hydrogen. It and helium are the primary elements of the universe, and the heavier elements are derived from them though fusion processes in stars. On Earth, because hydrogen, like elemental metals, is a reductant - a substance having a tendency to donate electrons - it does not exist in elemental form but in chemical combination with oxidants. Hydrogen on Earth commonly exists in combination with oxygen, with the most abundant compound being water.

Periodic Table of the Elements
Figure 1. The position of hydrogen in the periodic table shows that it behaves chemically like a metal.

The unique position of hydrogen is shown by its position in the periodic table of the elements (see Fig. 1). As the table shows, most of the elements of nature are metals, and while most have the familiar metallic properties of hardness, reflectivity, electrical conductivity, and thermal conductivity, not all do. Mercury (Hg), a liquid, lacks hardness. Hydrogen, a gas, would seem to lack all metallic properties. Nonetheless, the most fundamental characteristic of a metal is its tendency to donate electrons in chemical reactions, and on this basis, hydrogen is classified as an alkali metal in the first column of the table. Moreover, solid hydrogen, at 14 K, has decidedly metallic properties, including electrical conductivity. Viewing hydrogen as a gaseous metal clarifies how fuelcells work (see "Fuelcell Tutorial" listed in the bibliography).

In some published periodic tables, hydrogen is also placed in the halogen family as a nonmetal. While it can accept electrons (e.g., in LiH), this is not its typical role in chemical reactions.

3. Properties

Several important properties of hydrogen are listed in Table 1. In comparison to air (see also Table 1), hydrogen exhibits 14-fold lower density, 3.8-fold higher speed of sound, and seven-fold higher thermal conductivity. These exceptional properties of hydrogen have useful applications: Its low density and high sonic speed are exploited in the supersonic tube vehicle (STV) concept, and its high thermal conductivity has been exploited by using hydrogen gas as a coolant for nuclear reactors so as to avoid radioactive contamination of the coolant.

Under conditions normally encountered, hydrogen exists as a diatomic molecule, H2, and unless otherwise stated, when we say “hydrogen,” we mean the diatomic molecule. With a mass of only 2.0 amu, compared to 4.0 for helium and 32 amu for oxygen, it is the lightest of all gases. Because the two atoms are held together by a covalent bond, and because of mirror-image molecular symmetry, the molecule has no permanent dipole moment. Low molecular mass and lack of charge separation are the main determinants of the properties in Table 1.

Table 1: Propertiesa of Hydrogen and Comparison with Properties of Air
Property Hydrogen Air Hydrogen Value/Air Value
Molecular mass, amu 2.016    
Boiling point, K 20    
Melting point, K 14    
Density (ρ ), g/L 0.082 1.16 0.071
Viscosity (µ), µPa-s 9.0 18.6 0.48
Speed of Sound, m/s (km/h) 1,310 (4,720) 346 (1,246) 3.8
Thermal Conductivity, mW/m-K 187 26.2 7.1
a At pressure P = 100 kPa and temperature T = 298-300 K

The invaluable ideal gas law can be derived from the kinetic theory of gases, in which gas molecules are treated as point masses exhibiting elastic collisions with the walls of their container (i.e., no kinetic energy is lost to the walls). The ideal gas law is stated as

P V = n R T (1)

where P is pressure in kPa, V is volume in m3, n is number of moles in mol, T is temperature in K, and R is the universal gas constant, with R = 0.008 314 m3 kPa / (K mol). By definition, one kilopascal equals 0.01 bar. Please note that this result is independent of the identity of the gas and applies to mixtures as well as pure gases. For example, methane, air, or hydrogen, or any of their mixtures, will equally obey the law if the assumptions of the kinetic theory are satisfactorily approximated.

We can easily derive an alternative, simpler but gas-specific form of the law as follows. From equation (1)

P = (n/V) R T (2)
P = ρ R* T (3)

where ρ is gas density in kg/m3 and constant R* = 4.124 m3 kPa / (K kg). Note that R*, distinct from the universal gas constant R in equation (1), converts molar concentration (mol/m3) into conventional density (kg/m3). Therefore, R* = R/M, in which M is the molar mass of the molecule in kg/mol, and constant R* is not universal but varies with the gas.

To intuitively understand the ideal gas law, it is useful to express equation (3) with gas density on the left-hand side:

ρ = P / (R*T) (4)

A gas more closely obeys the ideal gas law to the extent that it approximates the assumptions of the kinetic theory, in particular, that individual gas molecules do not interact, and they thus behave as point masses. Intuitively, therefore, the ideal gas law will be better obeyed when the gas density is lower. From equation (4), density will be low when either pressure P is low or temperature T is high. Because hydrogen in any case has the lowest density of any gas, it most easily approximates the assumptions of the kinetic theory and more widely obeys the ideal gas law.

Temperature is a direct measure of the mean speed (or other molecular motion, namely, vibration and rotation) of the molecules comprising a gas. To aid our understanding of the properties in Table 1, we will rewrite equation (3) as

T = P / (ρ R*) (5)

Thus, at a given pressure, hydrogen has the highest temperature of any gas because it has the lowest density. For hydrogen to exert a given pressure on a container, its molecules must collide with the container walls at higher speed to compensate for their smaller molecular mass.

We can sketch an explanation (using broad brush strokes) of several of the properties in Table 1 from what we now know about the molecular properties of hydrogen. The low melting and boiling points follow from the hydrogen molecule’s absence of a permanent dipole moment and its low volume, with consequent low surface area, which reduces intermolecular Van de Waals forces. Density has already been dealt with implicitly in deriving equation (3). Consider viscosity as the drag (force) on two opposing plates, closely-spaced on a macroscopic scale, when a gas flows through the gap between the plates. Low viscosity relative to other gases is expected because of hydrogen’s small molecular volume, which reduces interaction of the surfaces of the molecules with the plates, as well as interaction of the molecules themselves. Note, however, that the viscosity is only about half that of air (see Table 1). High thermal conductivity is related, in part, to hydrogen’s high molecular mean speed, which we discussed in connection with equation (5).

Infinitesimal volume element G with volume ΔV
Figure 2. Infinitesimal volume element G with volume ΔV

We will look more closely at the speed of sound s in a gas. Sound is a longitudinal mechanical wave and propagates through a gas via collisions between molecules. For wave propagation in a gas, in analogy to transverse wave propagation along a wire, the medium must exhibit both elasticity and inertia. Elasticity is provided by the fact that a gas can be compressed, and inertia is provided by the mass associated with gas density. Consider an infinitesimal rectangular prism of gas G, with volume ΔV and cross-sectional area ΔA, in the path of an advancing longitudinal pressure pulse. As the wave reaches G, the gas within increases in pressure by ΔP, but the pressure increase is resisted by the inertia of the mass of gas in G. It is the give-and-take of these two opposing forces – elasticity and inertia – that causes the sound wave to propagate at a finite and distinct value.

A formula for the speed of sound in a gas medium can be derived from Newton’s second law

ƒ = m a (6)

where ƒ is the compression force on the gas within G, m is the mass of the same gas, and a is acceleration that the mass experiences. Total force ƒ on the volume of gas in G is given by the formula ƒ = ΔP ΔA. The mass of gas m in G is m = ρ ΔV = ρ ΔA (s Δt), where ρ is gas density in g m-3, s is the wave propagation speed in m/s, or speed of sound, and Δd = s Δt is the length in meters of volume element G in the direction of wave propagation for time increment Δt (see Fig. 2). By definition of acceleration, a = – Δs / Δt, in which the sign is negative because the wave is decelerated by the inertia of the mass within G. Substituting these results for ƒ, m, and a in equation (6) gives

ΔP ΔA = – (ρ ΔA s Δt) (Δs / Δt) (7)

Simplifying and solving this for quantity ρ s gives

ρ s = – ΔP / Δs (8)

We will write equation (8) in terms of Δs / s because it allows three factors to be combined as a constant for ideal gases. Accordingly, multiplying both sides of the equation by s, and solving for s, gives the following equation for the speed of sound in an ideal gas

s = [ΔP / ρs / s)]1/2 (9)

Although it is beyond the scope of this article to prove it, for a given ideal gas, quantity ΔP / (Δs / s) is directly proportional to P and we have

ΔP / (Δs / s) = s ΔPs (10)
s lim Δs → 0 ΔPs = s dp/ds = γ P (11)

where γ is a proportionality constant for ideal gases and P is the gas pressure. Constant γ is equal to the adiabatic index.

We can therefore write equation (9) as

s = [γ P / ρ]1/2 (12)

which is our final form for an equation for the speed of sound in an ideal gas.

I have estimated for you the mean value of γ ideal diatomic gases, such as hydrogen. From the empirical speed of sound at 298-300 K for four gases – hydrogen, nitrogen, oxygen, and air (nitrogen plus oxygen) – the mean value of the constant was computed as γdiatomic = 1.41375 x 103 kg / (m s2 kPa).

We see that the final equation for the speed of sound, equation (12), contains the two factors always required for wave propagation: an elasticity factor, P, and an inertial factor, ρ. Because hydrogen has the lowest density of any gas, the equation shows that it has the highest speed of sound of any gas.

To test equation (12) against experiment, we will compute the speed of sound for hydrogen. Using pressure P = 100 kPa, ρ = 0.0824 kg/m3, shown in Table 1, and γdiatomic = 1.41375 x 103 kg / (m s2 kPa), equation (11) gives s = 1310 m/s, which agrees with the value in Table 1 to three significant figures. Please compute for yourself the speed of sound in oxygen at P = 100 kPa, given that ρ = 1.3080 kg/m3. (The empirical value is s = 330 m/s.)

Despite its reputation to the contrary, hydrogen is not very reactive under ambient conditions, at least with respect to oxygen or air. In principle, one could take hydrogen and oxygen in the stoichiometric ratio of two volumes (moles) of hydrogen and one volume (mole) of oxygen, place them in a sealed container, and the mixture would remain essentially unchanged for decades. Exposing the mixture, however, to a spark or a catalyst such as metallic platinum could result in an immediate conflagration. (Because of the possibility of a spark from static electricity, the reader should not attempt this experiment.)

The chemical equation describing the reaction, along with its associated free-energy values ΔG and ΔG, are given by

H2 + ½ O2→ H2O (gas), ΔG = -229 kJ/mol, ΔG = 42 kJ/mol (13)

The Gibbs free energy ΔG for the reaction is the energy difference between initial and final thermodynamic states of the reaction and describes the maximum energy, in any form, that can be extracted from the reaction. The activation energy ΔG, a quasi-thermodynamic variable, is the energy of a loosely bound complex of hydrogen and oxygen atoms, termed the activated complex, that lies between the initial and final states and is unstable with respect to both reactants and products. The relationships among ΔG, ΔG‡, and the initial and final states of the reaction are shown schematically by the reaction profile in Figure 3.

Equation (13) and Fig. 3 explain why hydrogen and oxygen can result in a conflagration if exposed to heat or a catalyst, yet remain quiescent for a long period of time if undisturbed. The negative free-energy difference of ΔG = -229 kJ/mol shows that the reaction can release large amounts of energy in the form of heat, light, or electricity; however, being a thermodynamic state-variable, it does not determine the rate of the reaction.

Figure 3. The reaction profile describes the free-energy changes as the reaction progresses from initial state to final state.
Figure 3. The reaction profile describes the free-energy changes as the reaction progresses from initial state to final state.

Activation energy ΔG = 42 kJ/mol represents an energy barrier (see Fig. 3) to the progress of the reaction, and for reaction to occur, the reactants must scale the energy barrier. An even higher barrier exists for reaction of hydrogen with air. The activation energy, by determining the concentration of the fleeting, quasi-thermodynamic activated complex, does indeed determine the reaction rate. A catalyst accelerates the reaction by lowering the energy of the activated complex; heat accelerates the reaction by increasing the energy of the initial state. In either case, the result is lowering of the energy difference between initial state and activated complex. An activation energy of ΔG‡ = 42 kJ/mol, a consequence of the covalent bonds in hydrogen and oxygen, makes the reaction so slow in the absence of heat or a catalyst that the reactants may take decades to react to a detectible degree.

Hydrogen is physiologically inert. Some other fuels, such as methane, have a low degree of physiological activity but are not as inert as hydrogen. Nonetheless, hydrogen can result in suffocation by displacing air in the respiratory system (see section 7 below).

4. Production and Distribution

In terms of moles, hydrogen rivals all chemicals in annual quantity produced, but since it has an atomic mass of unity, the annual mass produced is not so large. Annual worldwide hydrogen production is estimated as 45 million tonne (metric ton). Most of this is used for the frontend of large-scale chemical processes such as anhydrous ammonia synthesis and gasoline refining, and little is sold as hydrogen per se to consumers, i.e., as “merchant hydrogen”.

Hydrogen is produced commercially by two broad methods of synthesis: (a) production from feedstocks such as natural gas and (b) splitting of water by a variety of primary energies.

The most important method of production from a feedstock is steam reforming of natural gas, which is predominantly methane. About 95% of hydrogen today is produced by this method. The chemical equation for the reaction is

CH4 + 2 H2O→ CO2 + 4 H2, ΔG = 64 kJ/mol (14)

where all species are gases. Because the free-energy is positive, the reaction is not spontaneous but must absorb energy (heat) from a primary energy. To drive the reaction uphill and to maintain a useable rate, the reaction temperature is maintained as high as 1000 °C. Natural gas serves as both feedstock and the primary energy. This reaction may analogously utilize other carbon-containing feedstocks, for instance, liquid fossil fuels such as gasoline, alcohols, and coal. All such reactions are related by the fact that the carbon-containing substance, in part, chemically reduces water to hydrogen. For long-term production of hydrogen, equation (14) is problematic: (a) Carbon dioxide, a green-house gas, is produced as a byproduct and (b) the supplies of natural gas are limited. Methane produces the least carbon dioxide per kilogram of feedstock because the ratio of hydrogen to carbon is four; the ratio is approximately two for liquid fossil fuels and alcohols and close to unity for coal. The reaction will also proceed with pure carbon, in which case the hydrogen-carbon ratio is zero – the entire hydrogen product is derived from chemical reduction of water. In the case of pure carbon, the method becomes an instance of water splitting.

A distinct method of producing hydrogen from a precursor chemical is to dissociate anhydrous ammonia, as shown by the equation

2 NH3→ N2 + 3 H2, ΔG = 17 kJ/mol (15)

To afford sufficient rate and, because the reaction is endothermic, to increase the conversion of ammonia to hydrogen (recall Le Chatelier’s principle), the reaction is maintained at temperatures up to 1000 °C. Technology for onsite production of hydrogen from anhydrous ammonia according to Eq. (15) is commercially available. A typical application produces hydrogen at a factory for heat-treating metals in a reducing atmosphere. Being a thermo-catalytic dissociation (vis-à-vis a chemical reaction between feedstock and water), the process is cleaner than Eq. (14) and the processor is more compact. An obvious problem with this method is that ammonia is generally produced from hydrogen, along with nitrogen from the air. Thus, rather than being a true feedstock, ammonia serves as a hydrogen carrier. The method requires a processor to make ammonia from hydrogen and a coupled processor to remake hydrogen from ammonia.

Splitting of water by a primary energy to produce hydrogen and oxygen is, in principle, an ideal method of hydrogen production: (a) Because fuelcells produce water, the coupling of fuelcells with a water-splitting process recycles water, and water becomes an endless source of hydrogen for power production. (b) Depending on the primary energy, the energy cycle may be free of greenhouse gases. The chemical equation for splitting of liquid water is

H2O (liquid) → H2 + ½ O2, ΔG = 237 kJ/mol (16)

Gaseous water (steam) is used in some instances, and the required energy will differ some from the value given in Eq. (16).

A commercially mature water-splitting method is electrolysis of water. Unlike the reverse chemical process, the fuelcell, electrolysis of water is simple to accomplish. Place tap water in a coffee cup; add a drop of acid so as to allow H+ migration in the water; and place two carbon-rod electrodes in the cup. When an electric potential is applied, hydrogen will evolve as bubbles from one electrode (cathode) and oxygen from the other (anode). For commercial, large-scale applications, the electrical-energy input is derived from various energy conversion devices and a primary energy such as coal, wind, solar, or nuclear. If the primary energy is renewable or nuclear, there will be no greenhouse gases in the energy cycle.

Low energy-efficiency is often claimed as a deficiency of water electrolysis. The efficiency of the electrolyzer itself – hydrogen chemical energy divided by electrical energy input – is a decreasing function of the power of the electrolyzer. As the power approaches zero, the efficiency of the electrolyzer approaches a theoretical limit of 0.83. This limit is termed the intrinsic maximum efficiency and is given by the equation

η = ΔG / ΔH (17)

where ΔG and ΔH are, respectively, the free energy and enthalpy for the reaction of Eq. (16). Intrinsic maximum efficiency η is analogous to the Carnot limit for heat engines, and like the Carnot limit, is a theoretical quantity. Practical electrolyzers, which operate at some finite power, have lower efficiencies. A reasonable value for the practical efficiency of an electrolyzer is 0.75. This is an acceptable efficiency for energy conversion devices, and for comparison, it is similar to the efficiency of electric motors of a few kilowatts power.

The claim may be valid if one defines efficiency as the hydrogen chemical energy divided by the primary-energy input. For instance, if coal is the primary energy and the following steps are required to produce hydrogen,

coal → heat engine → alternator → transmission → rectifier → electrolyzer → hydrogen (18)

then the overall efficiency of hydrogen production is low (in the range 0.3 – 0.4). However, the same can be said for electricity itself. As we saw above, the efficiency of practical hydrogen production from electrolyzers is about 75% of the efficiency of electricity production. Because electricity offers so many benefits through its applications, hardly anyone criticizes electricity because its production from coal primary energy is a low-efficiency process. One of the points of this tutorial, emphasized in the section Hydrogen as an Energy Carrier, is that hydrogen is properly viewed as an analog of electricity. In any case, from an efficiency perspective, generating either electricity or hydrogen from sequence (18) is not a good idea. (If we must start with coal to produce hydrogen, one can more efficiently use a direct chemical conversion such as the variation of Eq. (14) with coal replacing methane.)

A promising method of hydrogen production is thermolytic water splitting. The objective of the method, still in the experimental stage, is to dissociate water to its elements by thermo-catalytic decomposition utilizing the heat from a nuclear reactor. The overall reaction is analogous to ammonia dissociation given by Eq. (15). Several thousand reaction sequences, illustrated by the sequence comprised of equations (19) through (22), have been proposed for achieving such dissociation at achievable temperatures:

CaBr2 + H2O → 2 HBr + CaO 750 °C (19)
Hg + 2 HBr → HgBr2 + H2 100 °C (20)
HgBr2 + CaO → HgO + CaBr2 25 °C (21)
HgO → Hg + ½ O2 500 °C (22)
Net: H2O + heat → H2 + ½ O2 (23)

All reactants other than water are not consumed and therefore formally serve as catalysts. Each step is normally an isolated process, requires separation of products, and requires transfer of products to one or more other steps in the sequence. A challenge of such methods is that the yield of the net reaction is the product of the yields of the individual steps.

Hydrogen may be distributed to large-scale applications as the compressed gas, as the liquid, or by gas pipeline. Compressed hydrogen, at around 180 bar, is routinely transported in tube trailers, each of which consists of a cluster of large steel tubes, sometimes wrapped with carbon-fiber material, running longitudinal on a truck-trailer chassis (see Fig. 4). Liquid hydrogen, used extensively by the US space program, is shipped via vacuum-insulated tank trucks. Despite high capital cost, hydrogen pipelines represent the ultimate solution in hydrogen distribution. A 26-km pipeline in the Los Angeles metro area supplies 400 thousand kilos per day to seven gasoline refineries. Underground pipelines can provide exceptional safety within a traffic-dense city and require less maintenance than trucks.

Hydrogen tube trailer
Figure 4.Hydrogen tube trailer manufactured by Air Products (Source: Vehicle Projects Inc)

5. Storage

Storage of hydrogen onboard a vehicle is a greater technical challenge than producing power from a fuelcell. Methods of hydrogen storage appropriate for high-power vehicles include (a) compressed-gas storage, (b) liquid storage, (c) reversible metal-hydride storage, (d) onboard reforming of a carbon-based fuel as described by Eq. (14), and (e) onboard physical dissociation of liquid ammonia fuel as shown by Eq. (15).

Compressed-gas storage is a widely used, simple, and relatively energy-efficient technology. Modern gas tanks are produced by wrapping an impervious aluminum or polypropylene liner with carbon-fiber cloth, which is held in place by an epoxy resin. The lightweight tanks can be placed at the roofline of large vehicles, such as buses and locomotives (see Fig. 5), without adversely affecting the vehicle’s center of gravity. This location places the tanks out of harms way, and because of the low density of hydrogen, any release of hydrogen harmlessly dissipates above the vehicle. Pressure-volume work comprises a parasitic loss associated with compressed-hydrogen storage. The loss depends strongly on whether the compression is adiabatic or isothermal. Adiabatic compression to 700 bar costs about 16% of the energy of the fuel as heat of compression. In contrast, isothermal compression loses costs about 5%. The loss for adiabatic compression is higher because the gas temperature in the tank rises as compression commences. Hence, to achieve, say, 700 bar pressure in the tank after it thermally equilibrates, one must first compress the gas to perhaps 850 bar. The energy required for compression from 700 bar to 850 bars is an extra loss for adiabatic compression vis-à-vis isothermal compression. Isothermal compression in a real tank can be approximated by very slow compression or multi-stage compression with intercoolers between stages.

Hydrogen fuelcell switch locomotive
Figure 5. Hydrogen fuelcell switch locomotive with carbon-fiber composite compressed-gas storage tanks at the roofline. (Source: Vehicle Projects Inc)

Liquid-hydrogen vehicular storage is well established. The second and third stages of the Saturn V rocket, the most powerful vehicle so far developed, used liquid hydrogen fuel. I estimate that the power of the second stage was 28 GW, the combined power of 200 Boeing 747 airplanes or 150 Nimitz-class nuclear aircraft carriers. A liquid-hydrogen internal-combustion engine automobile, the Hydrogen 7, was recently put into limited production by BMW. Two problems of liquid-hydrogen storage are (a) the high parasitic losses of liquefaction and (b) unavoidable boil-off of the liquid because of hydrogen’s 14 K boiling point, which makes refrigeration infeasible. Production of liquid hydrogen suffers the parasitic loss discussed above for gaseous hydrogen, plus a large additional loss associated with low-temperature condensation. Overall, the parasitic loses are about four times those for isothermal compression. Because liquid hydrogen boils at 14 K (see Table 1), it can only be maintained as a liquid by allowing it to boil in its storage tank. Tanks employ vacuum insulation, and the quality of the insulation determines the rate of evaporation. Two-percent per day is a practical value. Thus, if a vehicle were parked for two weeks, about a quarter of its fuel would evaporate. This creates a problem with storage inside of buildings, and garages would require ventilation at the rooftop.

Hydrogen fuelcell switch locomotive
Figure 6. Metal crystal lattice. Spheres (atoms or canon balls) cannot pack perfectly and leave interstices, or holes, between the spheres.

We will look at reversible metal-hydride storage in more depth. Reversible metal hydrides are low-flammability, solid materials – consisting of a bed of metal powder – that uses metal-hydrogen chemical bonds to store hydrogen safely and compactly. Metals, crystalline solids, consist of a regular array or lattice of spherical atoms. Spheres cannot pack perfectly, and the lattice of atoms also forms a superimposed lattice of holes or interstices (see Fig. 6). The interstices interconnect to form a three-dimensional network of channels. Because hydrgen has the smallest atom, it chemically bonds to the metal atoms while occupying the interstices. As we saw in Fig. 1, hydrogen is a metal, and the metal hydride, a compound of a metal and hydrogen, can be thought of as an alloy. Transition metals form hydrides that are readily reversible and constitute a safe, solid storage medium for hydrogen. By removing low-temperature heat from the crystal, hydrogen atoms enter the interstices throughout the crystal and charge the metal. Conversely, by providing low-temperature heat (60 - 70 °C) to a charged crystal, the process is reversed and the metal is discharged. The gas pressure is approximately constant during the process and can be very low, even below atmospheric.

Unlike liquid or gaseous fuels, metal hydrides are of low flammability. This is because hydrogen is trapped in the metal matrix or lattice, and the rate at which hydrogen atoms can file through the channels, recombine into hydrogen molecules, and be released is limited by the rate of heat transfer into the crystal. Rupture of a hydride system is self-limiting: As hydrogen escapes, the bed automatically cools because chemical bonds are being broken, and the colder bed has a lower rate of atom migration.

The metal matrix, moreover, forces the hydrogen atoms close together, as close as in liquid hydrogen, and is responsible for high volumetric energy density. Being a metallic fuel, metal-hydride storage is heavy and typically stores only 1-2% of its weight as hydrogen. This is often not a problem for industrial or transport vehicles such as locomotives. Metal-hydride storage exhibits effectively 100% energy efficiency because the low-temperature heat required to move hydrogen in or out of the system is provided by waste heat from the vehicle’s powerplant.

Metal-hydride storage was used in the world’s first hydrogen-fuelcell locomotive, an underground mine locomotive developed by Vehicle Projects Inc in 2002 and successfully demonstrated in a working gold mine in Ontario. This method of storage is unequaled for underground vehicles because of its compactness and high level of safety.

While reforming of hydrocarbons or alcohols (methanol), as described for methane in Eq. (14), has been strongly pursued by the auto industry as an onboard storage technology, it suffers the disadvantages of high volume, complexity, and low thermodynamic efficiency. Its large potential advantage is that a vehicular fueling infrastructure is already in place. Being a miniature chemical plant, the reformer is bulky and consumes energy to drive the reaction. As a rule of thumb, the volume of the reformer equals the volume of a car’s fuelcell system. This is like having the fuel-injection system of an internal-combustion engine equal to the size of the engine. Because of losses in the process and because the products are energetically uphill of the reactants, only about 80% of the chemical energy of the feedstock is converted into chemical energy of hydrogen. In comparison, isothermal compressed-hydrogen storage is up to 95% efficient and metal-hydride storage is effectively 100% efficient.

Liquid ammonia, as feedstock for thermo-catalytic dissociation to hydrogen (Eq. 15), is a non-carbon-based, renewable commodity that is typically transported by rail tank car or pipeline. Because ammonia dissociation does not involve a chemical reaction with another reactant (water, in the case of reforming), it is easier than reforming hydrocarbons or alcohols and cleanly produces a mixture of 75% hydrogen and 25% nitrogen. The nitrogen is separated and harmlessly exhausted to the atmosphere. Although ammonia has the disadvantage of being a strong tissue irritant, it offers the unusual advantage for a fuel of being nonflammable under the conditions of intended use.

Table 2: Theoretical Hydrogen Volumetric Densities1
Fuel System Conditions of Storage H2 Density, kg/m3
Compressed Hydrogen 350 bar (5100 psi) 25
Liquid Hydrogen ρ = .070 kg/m3 (P = 1 bar, T = bp) 70
Methanol ρ = .79 kg/m3, (T = 298 K) 99
Liquid Ammonia ρ = 0.62 kg/m3, (P = 7.2 bar, T = 288 K) 110
Reversible Metal Hydride AB5 alloy (LaNi5), ρ = 8.3 kg/m3, wt % = 1.5, 10 bar 125
1 From Miller et al, 2007 (see Bibliography)

For industrial and transport vehicles, minimum volume of the fuel storage system (or powerplant) is generally more important than minimum weight. That is, a high hydrogen volumetric density is more important than a high gravimetric density. Table 2 displays the limits or theoretical values of hydrogen volumetric density, as kg/m3, for five fuels abovementioned. These limits are a theoretical construct – they provide a measure of the best possible volumetric density that a given fuel can attain. They omit the volume of the container, associated hardware, and chemical processor. For example, if one had a cubic meter of hydrogen at a pressure of 350 bar, stored in tank, with piping, etc, of infinitesimal volume, the cubic meter would store 25 kg of hydrogen, corresponding to a volumetric density of 25 kg/m3. In the case of methanol, which requires thermo-catalytic reaction of the alcohol with water, with an equation analogous to equation (14), the limiting volumetric density also omits the volume of the reactant water (in principle, water can be obtained from the fuelcell). The results show that, in the limiting case, the reversible metal hydride is capable of the highest hydrogen volumetric density, namely, 125 kg/m3, and compressed hydrogen, the lowest.

A measure of the energy content of these masses of hydrogen is provided by the fact that the chemical energy in one kilogram of hydrogen is approximately equal to the energy in one gallon, or four liters, of gasoline.

Real systems require volume for their hardware (e.g., tank, piping, and valves, as well as chemical reactors for methanol and ammonia), and thus the practical hydrogen volumetric densities shown in Table 3 are smaller than the theoretical values of Table 2. The practical densities were computed from the volumes of actual systems. For example, based on scale-up of the liquid-hydrogen storage system of the commercially available BMW Hydrogen 7TM automobile, the hydrogen volumetric density of a real liquid hydrogen system is 26 kg/m3 rather than the 70 kg/m3 for the theoretical system. The volume of systems using a chemical processor, a methanol reformer or ammonia dissociator, depends on power. Greater power of the vehicle, and thus greater hydrogen flow, requires a larger chemical reactor. Because contemporary industrial and transport vehicles store hydrogen mass on the order of 100 kg and produce power on the order of 300 kW gross, we computed the densities of Table 3 for a system storing 100 kg of hydrogen and sustaining a power of 300 kW. The density of the practical methanol system includes the reactant water, as well as the reformer hardware.

Table 3: Practical Volumetric Hydrogen Densities1
100 kg of stored hydrogen sustaining 300 kW power
Fuel System Practical H2 Density, kg/m3 Storage Efficiency, %
Compressed Hydrogen 10 40
Liquid Hydrogen 26 37
Methanol (reformer) 23 23
Liquid Ammonia (dissociator) 44 40
Reversible Metal Hydride 20 16
1 From Miller et al, 2007 (see Bibliography)

“Storage Efficiency” is defined as the Practical Density / Theoretical Density x 100%. For example, liquid hydrogen has a storage efficiency of 26 kg m-3 / 70 kg m-3 x 100% = 37%. Storage Efficiency is a measure of how closely a storage system approaches its volumetric density limit or theoretical density; it is a measure of how well a storage system lives up to its potential, the limits of Table 2.

In conclusion, with today’s technology, liquid ammonia, at 44 kg/m3, has the highest practical hydrogen volumetric density. Compressed hydrogen, at 10 kg/m3, has the lowest. Compressed hydrogen and liquid ammonia, at 40% each, have the highest storage efficiency, and reversible metal hydride storage, at 16%, has the lowest. Although we have focused here on minimizing storage volume, other factors may also be important, for example, weight, safety, cost, and thermodynamic efficiency.

6. Safety

The odorless characteristic of hydrogen can be dealt with using a handheld or permanently installed (in vehicle or buildings) hydrogen detector. Detectors can identify hydrogen at levels far below dangerous flammability limits and provide adequate time for response. The buoyancy of hydrogen is an advantage, as hydrogen will very quickly dissipate upward and be reduced below its lower flammability level. However, care must be taken in design and service not to allow hydrogen fuel to accumulate in areas lacking adequate ventilation or dispersion volume because of the potential of detonation. It is a requirement for all those who work with hydrogen equipment, and who are first responders for emergencies, to be educated about and be aware of the invisibility of hydrogen flames. In addition to the hydrogen itself, the high pressure of 350 bar (5100 psi) of the hydrogen fuel storage system demands proper training and procedures for safe interaction. Whether high gas pressure poses a risk depends on the strength of the container, and the carbon-fiber containers are exceptionally strong. Commonplace compressed natural-gas vehicles use the same tanks that the locomotive uses.

Hydrogen is physiologically inert. Some other fuels, such as methane, have a low degree of physiological activity but are not as inert as hydrogen. Nonetheless, hydrogen can result in suffocation by displacing air in the respiratory system (see section 7, "Hydrogen as an Energy Carrier").




A. R. Miller, “Fuelcell Tutorial,” www.fuelcellpropulsion.org

A. R. Miller, K. S. Hess, and D. L. Barnes, Comparison of Practical Hydrogen-Storage Volumetric Densities. Proceeding of the National Hydrogen Association Annual Hydrogen Conference, San Antonio, 21 March 2007.



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