So no, you can't do the math for how many nuclear plants you would need to get off oil.
So no, you can't do the math for how many nuclear plants you would need to get off oil.
Alternately, you could make enough nuclear capacity to provide your peak power levels all the time, and dump excess energy into some energy-hungry industrial process, like aluminum smelting, or synthetic fuel production, or ammonia synthesis.
So yes, you can do the math. It's just that there are a bunch of different ways to do that math, and most of them involve a lot of cleverness, large budgets, careful engineering, and a fair dose of uncertainty.
Heck, you don't have to do anything with it, just disconnect your turbines from your generators.
Liquid-Fluoride Thorium Reactors can be started and stopped without incident, in a few hours. I believe their output can also be adjusted in operation. They're safe and efficient enough to build one into a 40-foot trailer that can be started, stopped, and moved on a moment's notice.
Here's where it gets really fun: you can use the waste heat for desalination. There are a lot of places that sit next to a coastline but are short on electricity and fresh water. Russia is trying to make a lot of money from this, using a variant of the reactors they've been using on their nuclear ice-breaker ships.
And if you're using something like a LFTR that's compact enough to fit in a submarine, the water will protect you from hurricanes, earthquakes, aerial attack, and so on. It's a pretty clever scheme. Here's a thread on the Energy From Thorium forums discussing it:
It's true some 'burst' capacity is important, but can you not get a lot closer to 'average load' than the baseline by using the energy? Pumping water into a reservoir at night, and getting the power back with a small hydro plant during the day comes to mind. We smooth out an even worse problem with wind and solar, which is spiky AND out of sync with demand sometimes. I believe flywheels are used to store energy in the short term sometimes. You did mention 'really big batteries', implying that we would need too many, but we aren't limited to chemical forms of energy storage.
I think this is a solved problem, or at least a fairly solvable problem, and nuke plants can provide not only the 'baseline' but close to the bulk average needs for power. We can decouple the power generation and the need for "something adjustable" and benefit.
http://www.nationalgrid.com/uk/Electricity/Data/Realtime/Dem...
Electricity demand during the night is about half of what it is during the day. If you were to have nuclear baseline production that covers peak consumption, you would have to find a way to store about 100000MWh of energy that gets produced during the night and then distribute that during the following day, or you would just waste it, somewhere, somehow.
(Disclaimer: Back-of-the-envelope math, I'm assuming the scale on that graph is in MW, it's only for the UK, not the US)
Yes, it's not an impossible problem. Yes, you can even out the peaks by changing behaviour. Yes, you could perhaps figure out a way to store and release that much energy each day.
But my point still stands, replacing fossil-based electricity production with nuclear is not trivial, it's a lot more complicated than summing up the total output of all fossil-based plants and dividing it by the average output of a new nuclear plant as DanielBMarkham argues.
I'm also a big fan of nuclear. Many countries would probably benefit from having their baseline production completely covered by nuclear plants. But how to deal with peak demand of electricity without fossil-based production and in an economically viable way, that is not a solved problem yet.
Actually, thorium reactors have a natural load-following capability due to their negative thermal coefficient of reactivity. You suck power out of them too fast, they cool, get denser, and the reaction rate increases, increasing power output.
In addition, shutting down a liquid salt reactor is literally a matter of pulling, actually melting, a plug. Simply overheat the core, melting the freeze plug, and the fuel falls into a subcritically shaped catchment tray. Reheat and reload and the reactor is up again. They're very easy to start and stop.
There's a wealth of information on the Net about these guys. I hope they get built!