# Can we extract work from atmospheric hydrogen?

In a discussion about future passenger aircraft which aren't powered by fossil fuels, my friend suggested that powered flight may be possible using hydrogen harvested from the atmosphere. I claimed that this was impossible, because an engine like this would be analogous to Maxwell's demon. That was based on my belief that the trace amount of hydrogen in the atmosphere comes from the equilibrium $\mathrm{2\ H_2 + O_2 ⇌ 2\ H_2O + 572\ kJ}$, which strongly favours $\mathrm{H_2O}$. Trying to power a fuel cell with collected $\mathrm{H_2}$ would be like trying to power a heat engine by collecting the hottest air particles.

# Proton conductivity in graphene monolayers

I began to doubt my claim after reading this University of Manchester story from November 2014:

The Manchester group also demonstrated that their one-atom-thick membranes can be used to extract hydrogen from a humid atmosphere. They hypothesise that such harvesting can be combined together with fuel cells to create a mobile electric generator that is fuelled simply by hydrogen present in air. Marcelo Lozada-Hidalgo, a PhD student and corresponding author of this paper, said: “When you know how it should work, it is a very simple setup. You put a hydrogen-containing gas on one side, apply small electric current and collect pure hydrogen on the other side. This hydrogen can then be burned in a fuel cell."

The paper is Hu, Lozada-Hidalgo et al, Proton transport through one-atom-thick crystals (2014) Nature 516, 227–230, which concludes:

... our observations establish that monolayers of graphene and hBN constitute a class of proton conductors that raise intriguing questions about the transfer of subatomic particles through atomically thin electron clouds. Moreover, the high proton conductivity, chemical and thermal stability, and impermeability to $\mathrm{H_2}$, water and methanol make these membranes attractive candidates for use in various hydrogen technologies. For example ... [the] ability of these membranes to act as a current-controlled source of hydrogen is also appealing for its simplicity and, once large-area graphene and hBN films become commercially available, might be used to extract hydrogen from gas mixtures or air.

The experiment shows that the proton current produced by $\mathrm{PdH_x}$, 'a proton-injecting material that converts an electron flow into a proton one', is conducted by monolayers of graphene and hBN. However, I cannot understand how this would make it possible to 'extract hydrogen from gas mixtures or air'. The article notes that the monolayer is impermeable to $\mathrm{H_2}$, but can carry a proton current (composed of $\mathrm{H^+}$). This may enable the construction of more efficient fuel cells, but it does not seem to allow the separation of $\mathrm{H_2}$ from a mixture of gases.

# Energy density of atmospheric hydrogen

Assuming that it is possible to extract $\mathrm{H_2}$ from a large volume of air and burn it (or convert chemical energy into electrical energy in a fuel cell), I estimated the volume of air required to produce $1\ \mathrm{kJ}$ by extracting and burning $\mathrm{H_2}$ at cruising altitude.

• The pressure in the tropopause of the International Standard Atmosphere is $22.6\ \mathrm{kPa} \sim 22\%$ of sea level pressure.

• The temperature is $−56.5°\mathrm{C}=217\ \mathrm{K}$.

• By the ideal gas law, we have $\frac{22.6⋅10^3}{8.31⋅217} = 12.5\ \mathrm{mol/m^3}$ of air.

• The measured global average $\mathrm{H_2}$ mixing ratio is 531 ppb (Novelli et al 1999). This may be a significant underestimate, if the partial pressure of $\mathrm{{H_2}}$ falls much more slowly than the air pressure as altitude increases, due to the low density of $\mathrm{H_2}$.

• The enthalpy of combustion of $\mathrm{H_2}$ in air is $286⋅10^3⋅12.5⋅531⋅10^{-9}=1.90\ \mathrm{J/m^3}$.

• The volume of air required to extract $1\ \mathrm{kJ}$ from the combustion of atmospheric $\mathrm{H_2}$ is $\frac{10^3}{1.9} \sim 526\ \mathrm{m^3}$.

• To match the power of the Boeing 777's GE90-115B engine, $110\ 000\ \mathrm{hp}$ (The Atlantic), the airflow required would be $4.31⋅10^7\ \mathrm{m^3/\,s}$, or $2.59\ \mathrm{km^3/\,min}$.

Even assuming that the heat of combustion can be converted to work with perfect efficiency, this seems to be a few orders of magnitude beyond what would be required to use atmospheric hydrogen as a viable power source.

# Sources of atmospheric hydrogen

In the above analysis, even the small amount of work that can be extracted depletes the stock of atmospheric $\mathrm{H_2}$. As well as measuring the concentration of atmospheric hydrogen, Novelli et al shows that my assumption that atmospheric hydrogen comes from the decomposition of water vapour is wrong, so my analogy to Maxwell's demon goes nowhere. The paper concludes:

[We] find that the oxidation of $\mathrm{CH_4}$ is the largest source of $\mathrm{H_2}$ to the atmosphere (30%), with production from the oxidation of natural [nonmethane hydrocarbons], technological processes, and biomass burning each ~20% of the global source. Surface deposition accounts for about 75% of the tropospheric sink, with the remainder due to reaction with $\mathrm{OH}$. Total sources are balanced, within error, by total sinks. With an annual turnover of $\sim 75\ \mathrm{Tg/yr}$ and an average tropospheric burden of $155\ \mathrm{Tg}$, the lifetime of $\mathrm{H_2}$ is about 2 years. Last, we note that the error associated with any particular term in the $\mathrm{H_2}$ budget is between +30% and +60%.

The annual turnover of $75\ \mathrm{Tg/yr}$ suggests that a maximum of $\frac{75⋅10^{12}⋅286⋅10^3}{1.008⋅365⋅12⋅24⋅60^2} \sim 674\ \mathrm{GW}$ of power could be produced if all sources of atmospheric hydrogen were immediately consumed as fuel. This is about 8,000 times the power consumed by the 777 engine, so it is probably within the ball park of the total power consumption of all aircraft flying at any point in time.

Again, given that perfect efficiency is assumed, we seem to be a few orders of magnitude away from the possibility that atmospheric hydrogen could power flight or make a significant dent in average global power consumption of $12.3\ \mathrm{TW}$. Further, because a major source of atmospheric hydrogen is the combustion of hydrocarbons, it may not have any advantage over fossil fuels.

# Questions

• Does the study by Hu et al provide evidence that it is possible to extract hydrogen from gas mixtures or air using graphene monolayers?

• Are my calculations correct and my assumptions reasonable? Is there any reason for believing that atmospheric hydrogen may be viable as a significant energy source?

• Whether your suggestion is technically feasible is an engineering question and off topic here. Checking the correctness and reasonableness of calculations is not something we do. Why don't you ask colleagues, or email the authors of the papers you cite? – sammy gerbil Nov 26 '16 at 15:50