> how much would it cost to develop significant PV-powered electrolysis-and-Sabatier-process plant in any of the big coastal deserts, for exporting methane?

What are you thinking about as the carbon source? If coal, then this has been commercially viable for decades. In North Dakota there is a 1.5 gigawatt installation running since 1984. That one uses electricity from coal power IIUC, but today PV is cheaper than coal for electricity.

If you are talking about CO2 from direct air capture, the optimistic cost estimates of your CO2 feedstock are around $600/tonne. 1 tonne of CO2 gives ~137 kg of methane at 100% reaction yield, due to the molar weight ratio of CO2 to CH4.

So per tonne of methane produced, the CO2 cost alone is above $4000. For comparison a tonne of natural gas in the US today costs between $500 and $1000 for the end user.

This means that CO2 capture from air needs to become two orders of magnitude cheaper than today before this scheme works out.

I would say hydrogen electrolysis and then liquefaction for large scale distribution/export is way more realistic. This is what the EU seems to be going for together with Northern Africa.

Thanks! While this does not fully change your conclusion for air-capture CO₂, I am confused by this:

> 1 tonne of CO2 gives ~137 kg of methane at 100% reaction yield, due to the molar weight ratio of CO2 to CH4.

I think it’s more like 363 kg given the ratio of molar weights: http://www.wolframalpha.com/input/?i=co2%20molar%20weight%2F...

(Looks like an extra factor of two, but I can’t figure out why, everything I play with in WolframAlpha is a factor of two in the wrong direction)

To add to that: I'm not convinced that exporting even renewably-sourced methane is particularly renewable - methane has fugitive emissions when piped etc that are far worse pound-for-pound than CO2.

> Unfortunately, even a very small amount of noise in the data makes is basically impossible to know where you are in an S-curve.

While true, my point is that when combined with the fact that we are pre-inflection point, and the economics now stand on their own (renewables, Electric Vehcile TCO and various Energy Storage applications being already cheapest, competitive or very close too) it is not unreasonable when mapping out the 5-15 year future to bet on an acceleration of cost declines over a deceleration. Particularly because the actual driver of unit cost declines (Wrights Law/Moore's Law) is the doubling / magnitude of units manufactured and put through the system, for which with all the factories being ramped up and planned - point to the positive in my view on it.

Regarding your PV-powered and electrolysis-Sabatier (electrofuel) methane, I think there are two important considerations. In order for methane (or other e-fuels like hydrogen or longer chain hydrocarbons) to be made economically, the capital cost of the equipment needs to be utilized as close to 100% of the time as possible. We already know that PV excess will be centered around the daytime peak (5-7 hours per day) meaning that there would also need to be plenty of excess wind to balance this out to get anywhere close to 100% utilization of the excess energy. Until the electricity grids get sufficiently saturated with renewables broadly, most e-fuel applications will continue to not be competitive, particularly as things like energy storage applications (possibly run off an e-fuel) are likely to be economical prior there being an opportunity for the export of excess e-fuels. That's more at the a end of the S-Curve as far as I can tell.

Build enough PV to generate 24 hours worth of power for the reactor in daylight hours, and store the excess in batteries to power the reactor overnight.

At that point, just use battery storage and bypass the reactor entirely.

For domestic day-to-day consumption, absolutely.

The main argument for hydrogen AFAICT is that it can be exported overseas or stored for inter-seasonal use.

Batteries can't do that, as 1) when compared to literal rocket fuel, they're impractically heavy to put on a cargo ship for bulk transport, and 2) batteries trickle-discharge so after a month or two the battery will be flat.

In fairness, pure hydrogen is also leaky and hard to work with. That’s why I was asking about the economics of turning it into methane… and yet, one of the other replies I got pointed out that methane is also a bit leaky, so we might want to reform it (or whatever the word for “opposite of cracking” is) all the way up to a room temperature liquid.

I barely remember the process from school, something like this rings a bell: https://en.wikipedia.org/wiki/Catalytic_reforming

The largest energy draw is making the hydrogen. Store that and operate the reactor 24/7.