I figured out about how much methane/lox could be produced ( in theory ) from the plutonium energy source on the Curiosity rover. Assuming no errors, which could be a bit optimistic, I came up with 2852 kgs of reaction mass per Earth year. A brief guess indicates this wouldn't be nearly enough to get a capsule back into Mars orbit.
Since plutonium can last for a long time, it could run for several years as long as there were no malfunctions.
Now, back on Earth, the amount of methane that can be produced from carbon dioxide might be calculated assuming that the reactor had 10 megawatts of thermal energy.
I assumed 100 watts from the rover. Ten megawatts is ten million watts. It can produce theoretically 100k times more methane lox. But you won't need the lox on Earth. Looks like 57 million kgs or 57k metric tons of methane, or more since you don't need to produce the lox.
The significance of this I have not be figured out yet.
Double checking this math.
Here's the equation that is of particular interest in the case of the LFTR:
CO2 (g) + 2H2 (g) <-----> CH4 (g) + O2 (g) delta H = +318.6 kJ (4)Since this is not for a Mars liftoff, we aren't particularly interested in making the liquid oxygen. That part of the discussion can be dropped. This saves considerable energy, by the way.
A kilojoule is
So, every kilowatt hr has 3.6 million joules divided by 318,600 joules per reaction giving 11.3 reactions per kwh. That would yield 11.3 reactions times 16 grams per reaction giving 181 grams of methane per hour. Multiplying that by 24 hours in a day gives 4339 grams per day or 4.34 kgs. Multiply that by 365 days giving 1584 kgs. That's considerably less than before. Probably made a mistake. A ten megawatt LFTR is equivalent to 10,000 kwh, so multiply this by 10,000 giving 15,837,288 kgs! Divide by 1000 gives metric tons which is 15837 metric tons. Looks like a significant discrepancy, but still quite a bit of methane. These may be ideal numbers, which we won't account for inefficiencies. But we'll overlook that for now.
What made me want to recheck these numbers is the market value of methane. How much would this amount of methane be worth?
This chart quotes price in thousands of cubic feet of LNG , which would be at the most recent date of 7.82.
This chart does the conversions from metric tons to cubic feet.
1 metric ton liquefied natural gas (LNG) = 48,700 cubic feet of natural gas
Then we multiply 15837 metric tons derived above times 48700 giving 771275932 cubic feet. Divide this by 1000 since that how the price is quoted and this gives 771275 units which sell for 7.82 per thousand cubic feet. So multiply this by 7.82 and this gives $6,031,378 worth of methane.
The cost of the carbon dioxide is 8 bucks a ton. Add 10% for a metric ton. Say 9 bucks a metric ton.
You lose mass in the reaction. In order to produce 15,837 metric tons of methane, we will need 391,966 dollars worth of carbon dioxide. That's because each ton of methane takes 2.75 tons of carbon dioxide. The atomic weight of methane is 16, the atomic weight of carbon dioxide is 44. The ratio is multiplied by the methane output giving the required carbon dioxide and multiply that by 9 bucks per metric ton.
Looks like room for profit.
Perhaps I will look at this again in order to see if there are no mistakes.
I can't see any mistakes. Not like there couldn't be, but I don't see any thus far.
Taking the analysis a bit further, if Thorium is really cheaper than coal, then it should be able to produce the energy for 4 cents per kwh. At that price, this system could produce methane at a competitive price.