The Reality of Fuel Cell Vehicles

Daniel Lee
November 10, 2023

Submitted as coursework for PH240, Stanford University, Fall 2023

Introduction

Fig. 1: Audi A7 h-tron. (Source: Wikimedia Commons)

Hydrogen fuel cell vehicles are electric vehicles that use hydrogen fuel to generate electricity, producing zero harmful emissions. [1] Fuel cell vehicles work by combining hydrogen stored in a tank on the vehicle with oxygen from the air in a fuel cell. [2] This process produces electricity, water, and heat as byproducts. [2] The electricity is then used to power the vehicle's electric motor. Fig. 1 shows an example of a hydrogen-powered drive system. In today's world where governments constantly call for decarbonization, it should be apparent that a move towards fuel cell vehicles is a natural step that must be taken. Since passenger vehicles account for about 45.1% of the total CO2 emissions, replacing traditional carbon emission vehicles with fuel cell vehicles will approximately halve the global CO2 emissions, assuming perfectly clean hydrogen production and energy generation. [3] However, multiple practical limits prevent the spread of fuel cell vehicles, including density, energy efficiency, and economics. We must therefore better understand the science behind fuel cell vehicles and their limitations compared to other vehicles to make correct decisions on which path to take.

Hydrogen Fuel Cells

The hydrogen fuel cell is composed of three main pieces: anode, cathode, and electrolyte. [2] These pieces convert chemical energy into electricity. [2] As hydrogen is fed to the anode, oxygen is supplied to the cathode. [2] The electrolyte membrane acts as a filter to separate electrons from hydrogen, which are used to power the fuel cell as can be seen in Fig. 2. [2] The remaining hydrogen ions combine with the oxygen and produce water and heat as byproducts: [2]

2H2 + O2 → 2H2O + energy

Because no fuel is combusted during this process, no harmful emissions are generated, meaning that hydrogen fuel cells, at least on their own, are 100% green. [1]

Density and Efficiency

Fig. 2: Proton exchange membrane fuel cell diagram. (Source: Wikimedia Commons)

A problem with hydrogen compared to traditional gasoline is its extremely low mass density. While it has the highest energy density of any fuel by weight (143 MJ kg-1), it also has a very low density of 0.07 kg L-1, even when in its liquid form. [4,5] This is in comparison with gasoline, which has an energy density of 46.4 MJ kg-1 and a density of 0.74 kg L-1. [4,5] Therefore, liquid hydrogen has an energy density of

143 MJ kg-1 × 0.07 kg L-1 = 10.0 MJ L-1

and gasoline has an energy density of

46.4 MJ kg-1 × 0.74 kg L-1 = 34.3 MJ L-1.

This means that more than triple the volume of hydrogen is needed to equal the same amount of energy given by gasoline. This is a major issue in vehicles, as the amount of space for fuel is limited. This is the current limit of hydrogen's energy density, as metal hydride technology that uses metallic alloys to absorb hydrogen and release it when needed, further requires a heat-generating system and weighs much more than the weight of compressed hydrogen tanks, even though it can achieve higher densities than liquid hydrogen. [4]

Even if this volume problem is solved, we must also consider the energy efficiency of going from hydrogen-producing sources to electricity that can be used in vehicles. Assuming that we desire minimum carbon production, we can safely get rid of the steam reforming reaction, an industrial process that produces hydrogen from natural gas while also generating hydrocarbons. [6] We must therefore first consider the efficiency of electrolysis, the process of generating hydrogen from water, which can use energy generated by renewable means. [4] The efficiency of electrolysis is 60-90%. We take the midpoint of 75%. [6] Next, there is also the problem of hydrogen transportation. It is currently estimated that delivering liquid hydrogen by road is 75% efficient, with a 1% loss per 100 km. [4] Finally, there is energy loss directly inside fuel cells, with an efficiency of 47%. [7] This means that ignoring engine efficiency, using hydrogen for fuel cell vehicles will result in

100% input energy × 75% efficiency × 75% efficiency × 47% efficiency = 26.4% output energy

This means that for every 100 J of energy that goes into powering fuel cell vehicles, only about 26 J is actually usable by the vehicle. Even ignoring the motor efficiency, this value is much lower than the ~67% overall efficiency (energy to movement) of regular electric vehicles (gasoline engine vehicles are left out due to the difficulty of measuring the efficiency of acquiring gasoline). [8]

Economics of Hydrogen

An important factor to keep in mind while discussing hydrogen power is its cost. First, for comparison, we calculate the cost of 1J of pure energy delivered to the vehicle motor if using electric vehicles. Assuming a cost of $0.10/kWh of electricity, we get

$0.10 kWh-1
3.6 × 106 J kWh-1
= $2.80 × 10-8 J-1

meaning that it costs $2.80 × 10-8 for 1 J of pure energy delivered to the vehicle motor. [9] Assuming the same electricity price, the 75% efficiency of electrolysis, and hydrogen's energy density of 143 MJ/kg, we can calculate the cost floor of hydrogen produced with electrolysis, as the cost cannot be less than the cost of the electricity from which it was made. [4,6]

$0.10 kWh-1 × 143 MJ kg-1
3.6 MJ kWh-1 × 75% efficiency
= $5.30 kg-1

From this we can calculate the cost of 1 J of pure energy delivered to the vehicle motor if using fuel cell vehicles, assuming 47% efficiency of fuel cells. [7]

$5.30 kg-1
143 MJ kg-1 × 75% efficiency × 47% efficiency
= $5.30 kg-1
50.4 MJ kg-1
= $1.05 × 10-7 J-1

meaning that it costs $1.05 × 10-7 for 1 J of pure energy delivered to the vehicle motor. This is about 4 times the cost of electric vehicles' equivalent.

Conclusion

In conclusion, hydrogen fuel cell vehicles of today are inferior in density, energy efficiency, and economics to existing vehicles. While fuel cell vehicles offer perfectly clean operation compared to gasoline vehicles and offer much easier refueling than electric vehicles, their low energy density, low energy efficiency, as well as very high costs make it hard to convince the world that hydrogen is the future. [1] Therefore, advancements in hydrogen storage technology, hydrogen transportation technology, and hydrogen production technology will need to be made for the widespread use of fuel cell vehicles.

© Daniel Lee. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

References

[1] Y. Manoharan et al., "Hydrogen Fuel Cell Vehicles; Current Status and Future Prospect," Appl. Sci 9, 2296 (2019).

[2] R.-A. Felseghi et al., "Hydrogen Fuel Cell Technology for the Sustainable Future of Stationary Applications," Energies 12, 4593 (2019).

[3] Y. Huang et al., "Impacts of Built-Environment on Carbon Dioxide Emissions from Traffic: A Systematic Literature Review," Int. J. Environ. Res. Public Health 19, 16898 (2022).

[4] B. C. Tashie-Lewis and S. G. Nnabuife, "Hydrogen Production, Distribution, Storage and Power Conversion in a Hydrogen Economy - A Technology Review," Chem. Eng. J. Adv. 8, 100172 (2021).

[5] N. Wiberg, A. F. Holleman and E. Wiberg, eds., Hollman-Wiberg's Inorganic Chemistry, 1st Ed. (Academic Press, 2001).

[6] M. Nasser et al., "A Review of Water Electrolysis-Based Wystems For Hydrogen Production Using Hybrid/Solar/Wind Energy Systems," Environ Sci. Polut. Res. 29, 86994 (2022).

[7] M. A. Pellow et al., "Hydrogen or Batteries For Grid Storage? A Net Energy Analysis," Energy Environ. Sci. 8, 1938 (2015).

[8] R. T. Yadlapalli et al., "A Review on Energy Efficient Technologies For Electric Vehicle Applications," J. Energy Storage 50, 104212 (2022).

[9] M. Muratori, E. Kontou and J. Eichman, "Electricity Rates For Electric Vehicle Direct Current Fast Charging in the United States," Renew. Sustain. Energy Rev. 113, 109235 (2019).