It is true that we must heat that shale oil in the Green River formation to release the Kerogen oil. If we used coal or petroleum fuels to do this it would be a no go economically. Nuclear reactors are great at making heat, a lot of heat! Nuclear reactors should be for making electricity and heat for this. Colocate them and they can do both. Oddly we have a uranium shortage in our nation thanks to policy and not availability. Only a small percentage of the potential power from uranium is used. We should go to breeder reactors to make fissionable plutonium to use in reactors and also bombs, but we have enough bombs today. Use it all for power. We suffer from poor policy not resources.
I have been singing the song of fast breed reactors for years. Thanks to Jimmy dang Carter the.USA lacks the critical reprocessing technology and the legal ability to do so. Without reprocessing you cannot recover the PU isotopes needed to start and perpetuate the breed cycle. So instead with PWR we burn less than 1% of the fissile material then throw it into fuel ponds and then into dry cask storage. They want to bury those wastes in a geological repository where it’s all wasted it should be a crime against humanity to do that.
Sodium reactors are just enough to make the process heat needed for kerogen cooking. The new Natrium reactor is 550C at the outlet of the primary heat exchanger then to the secondary then to the molten salt loop. You need 370C at minimum to cook shale so in theory you could use the heat from the tertiary loop directly. Electric joule heating from well casing to well casing string would be better since it penetrates the whole formation between the electrodes not just the immediate area around the well bores.
The idea is run the reactor flat out putting power to the grid during peak times and off peak send that electricity down the well bores using the thermal inertia of the whole formation to smooth out the 12 hour on off cycle. It would work but there is no will to put modular fast reactors all over the Green River Shale basin. You could just as easily use off peak wind power which tends to howl all night across the Great Plains.