Cheap synthetic fuel

Hydrocarbon fuels are just too useful as portable energy sources not to mention being the basis for plastics and lubricants. All serious energy proposals (such as StratoSolar or power satellites) include making synthetic hydrocarbons. Even without considering climate problems, natural oil will eventually run out. The problem is to make synthetic fuel for close to the current price of oil.

Making synthetic fuel via the Fischer–Tropsch reaction is simple enough. Sasol has a plant in Qatar that makes 34,000 bbl/day from reformed natural gas. It has been running since 2007. World consumption of oil is around 100 million bbl/day so it would take around 3000 of these plants to replace natural oil. That's a large number, but not impossible.

Carbon

The Sasol plant uses reformed natural gas as a feedstock, made into CO and hydrogen. Synthetic fuel is roughly CH2. If you incorporate the step of reducing CO2 to CO, the overall reaction is:

CO2 + 3H2 yields CH2 + 2H2O 44 + 6 -> 14 + 36

It's not obvious this is the best way to go. It's possible to electrolyze CO2 into oxygen and carbon monoxide. If this is less costly (energy and capital) than making the extra hydrogen, that's the way to go.

34,000 bbl/day is 1417 bbl/hr. At 7.33 bbl/ton, 193 tons of carbon per hour. The CO2 input for a Sasol size plant would be 44/14 times this figure or 607 tons per hour. Air is about 1.2 kg/m^3 at 20 deg C and about 400 ppm CO2. A cubic meter would contain close to half a gram of CO2, 1000 cubic meters about half a kg, a million half a ton, a billion 500 tons. Depending on the separation efficiency, upwards of 1.26 cubic km of air will have to be processed to feed a Sasol-sized plant.

A problem is that combining CO and H2 is seriously exothermic.

There are two recent news stories that started this line of thinking.

First is the recent MIT release on a method to inexpensively capture CO2.

https://news.mit.edu/2019/mit-engineers-develop-new-way-remove-carbon-dioxide-air-1025

The second is the story about the world's lowest PV bid.

https://www.utilities-me.com/news/14081-dewa-receives-worlds-lowest-bid-of-usd-169-cents-per-kwh-for-900mw-5th-phase-of-the-mohammed-bin-rashid-al-maktoum

One much larger is being planned.

[and the cost is now down to 1.35 cents per kWh.]

https://www.utilities-me.com/article-5367-japans-softbank-to-build-worlds-largest-solar-power-plant-in-saudi-arabia

The first article says the capture method will work in the air. It takes about one GJ to capture a ton of CO2. A GJ is 278 kWh. At 1.69 cents per kWh, it will cost about $4.70 per ton of CO2. Or $17.23 per ton of carbon. 14 tons of oil has 12 tons of carbon at a cost of $206. Per bbl, the carbon would cost about $2.00

Oil is approximately CH2. Making hydrocarbons is scaled off the 34,000 bbl/day plant Sasol built 12 years ago in Qatar, it would take about 30,000 plants. 10,000 if the plant size was moved up to 100,000 bbl/day, but that may take too large a PV farm.

It may take reverse water gas shift to make the CO2 into CO. It is also possible that the CO2 might be electrolyzed to CO and O2 at a lower energy cost than making the extra hydrogen.

https://dioxidematerials.com/technology/co2-electrolysis/

https://en.wikipedia.org/wiki/Water-gas_shift_reaction#Reverse_water-gas_shift

https://en.wikipedia.org/wiki/Sabatier_reaction

https://en.wikipedia.org/wiki/Hydrogen_production

At 50 MWh/ton, 6 tons of hydrogen would take 300 MWh. That makes 14 tons of oil or 21 MWh/ton of oil. At 7.33 bbl/ton the energy required for a bbl of oil is about 3 MWh. For an energy cost of $16.90/MWh, the hydrogen energy cost is very close to $50/bbl.

[Oil runs about 1.7 MWh/bbl so the energy efficiency of making oil this way is about 1.7/3 or about 57%. It might be possible to increase the efficiency by electrolyzing CO2 to CO. Some of the energy released by the combination of hydrogen and CO can be captured in the steam used to cool the exothermic reaction.]

Add $2/bbl for carbon, and ~$10/bbl for the capital cost of the F/T plant. Carbon-neutral synthetic oil (fuel actually) would cost ~$62/bbl, possibly less with more process optimization. For example, there is no reason for inverters, the PV DC output can directly power the electrolysis cells. This should reduce the cost of energy in hydrogen below 1.69 cents per kWh.

The take-home is that in some places PV has gotten so inexpensive that it would be possible to make carbon-neutral synthetic hydrocarbons to replace natural oil for about the same price.

The area needed for the PV is huge, 120% of Saudia Arabia or about 28% of the Sahara Desert. (check these numbers, 100 million bbls/day/34,000 bbl.day, ~30,000 plants at ~90 square km/plant.)

[There is an factor of ten error here, it would only take 12% of SA or 3 percent of the Sahara]

34,000 bbl per day is a rate of around 1466 bbl/hr. At 3 MWh/bbl for the hydrogen, the average input to the hydrogen cells would be 4.25 GW and the peak about 4 times higher.

Sunlight comes down at a ~GW/km^2. Between the peak to average and the PV efficiency, a factor of about ~20 needs to need to be applied. This takes the PV area per plant up to 85-90 square km.

It could be done over a number of years, but the cost is going to be a problem. If we built the plants at 3000 a year, that alone would be $3 T. I am not sure what the capital cost for the PV would be, probably 4-5 times the billion-dollar plant cost.

I don't believe this option has been considered in the context of the global effects of CO2.

After checking the math and finding I had the area off by a factor of ten, I am not so sure it is something that could be considered. The Sasol plant cost a billion dollars. 30,000 would be $3 T a year for ten years. Also, the area needed is so large that much black PV might cause serious weather problems.

Sigh, it's not easy to make use of renewables, especially PV.