I can't include emissions for building infrastructure or natural gas leaks, but I think it's a fair assumption that those costs are the same order of magnitude whether you use the gas directly or convert it to hydrogen + CO2, and then use the hydrogen. I mention transportation a bit further down.

Someone do the math on the net CO2 impact between jet fuel and natural gas reforming

Ask and thou shalt receive.

When we burn hydrocarbons, the overall reaction going on (neglecting byproducts) is

2 C~n~H~2n~ ~+~ ~2~ + (3n + 1) O~2~ => 2nCO~2~ + (2n + 2)H~2~O

When we steam-reform hydrocarbons, we use the reaction

4n H~2~O + 2 C~n~H~2n~~+~~2~ => 2 nCO~2~ + 2 (3n + 1)H~2~

Such that the CO~2~ emissions from the consumption of the hydrocarbons is exactly equal. Now, the question is about efficiency. Steam reforming has an efficiency of about 65-75 %, which means we need (very roughly) 253 kJ of energy as input per mol steam-reformed hydrocarbon (assuming 65 % efficiency).

The (ideal) energy output from the corresponding consumption of 4 moles of hydrogen is approximately 1140 kJ. Hydrogen fuel cells typically have an efficiency of about 40-60%, so the true output is about 456 kJ (assuming efficiency of 40 %). This gives a net energy output of 203 kJ per mole gas consumed by steam reforming, and consecutive hydrogen consumption.

For comparison: Internal combustion engines typically have efficiencies around 20-35%. If the same gas is consumed in a gas turbine, we thus get an energy output of about 280 kJ (assuming efficiency of 35%).

The comparison in total:

• Assuming lower end efficiencies for steam reforming + fuel cell: 203 kJ / mol gas
• Assuming higher end efficiencies for steam reforming + fuel cell: 464 kJ / mol gas
• Assuming lower end efficiency for gas turbine: 160 kJ / mol gas
• Assuming higher end efficiency for gas turbine: 280 kJ / mol gas

So, the only case in which the gas turbine beats steam reforming + hydrogen on efficiency is when we assume higher-end efficiency for gas turbines, and lower-end efficiencies for steam reforming and fuel cells.

It should also be added that combustion engines have a theoretical maximum efficiency of about 58 %, while hydrogen fuel cells have a theoretical maximum close to 100 %. In addition, combustion engines have a huge head start on fuel cells regarding development. We can expect steam-reforming + fuel cells to improve a lot in efficiency the coming years, the same is not the case for combustion.

I have also not mentioned yet that hydrogen has a higher energy density (by mass) than gas, making the transportation cost and emissions (per joule transported fuel) lower.

Shortly speaking: The numbers say that steam-reforming + fuel cells is already a competitive option when looking at energy waste and emissions per joule produced. It can be expected to get even better in coming years.

Now for some more points I haven't mentioned yet:

Using steam-reformed hydrogen makes hydrogen cheap, which helps incentivise building things that use hydrogen, rather than combustion, which further increases demand for hydrogen. This helps lay the ground work for future, green, hydrogen infrastructure.

Maybe most importantly of all: When hydrogen is produced by steam reforming, all the CO~2~ is produced in one place, which can make CO~2~-capture viable. When the gas is burned as fuel in a bunch of different places, CO~2~-capture becomes less viable, as current technology heavily favours large, centralised capture operations.