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Just did a bunch of my own math before realizing those numbers were already out there. We would need to add 3960 nuclear plants to match current energy demand for the world (440 power 10% of the world).
That would require at least 5 years of construction per plant. It takes about 7000 workers to produce a nuclear plant. To produce them concurrently would require about 27.7 million construction workers dedicated to this project for at least 5 years. So on one hand, perhaps you're right, since there are 100M construction workers in the world. I can't, however, find numbers about how much heavy equipment exists to facilitate a product requiring 1/4 the world's construction workers concurrently. You might be right that if all other construction were ground to a halt, we might be able to manage a 5-year plan of nuclear at the cost of about $20T (I had done the math before realizing this reply were about workers, not cost stupidity). I concede it seems "10x increase world construction capacity" was wrong, and the real number is somewhere around 1.5-2x, so long as we stay conservative with nuclear figures and ignore extra costs of building or transporting nuclear energy to countries incapable of building their own plants.
Interestingly, at those construction numbers, you could provide small-project rooftop solar to the world. I can't find construction numbers for power farm solar, except that it's dramatically more efficient than rooftop solar. Unlike nuclear, it appears we could easily squeeze full-world solar with our current world construction capacity.
I won't bore you with the cost math, but since I calculated them I'm still going to summarize them. Going full nuclear would cost us about a $20T down payment. Going full solar (with storage) down payment is about $4T (only about $1T without storage costs factored). And while nuclear would be cheaper than solar per year after that $20T down, solar power and storage would STILL be cheaper in a 100 year outlook, but would also benefit from rolling efficiency increases as we add new solar plants/capacitors and tear down older ones..
Not all 7,000 construction workers would be working on the site concurrently. Different trades come and go depending on the phase of the project. So at first you'll have the civil engineering earth movers come in, who clears the site and excavates the foundations. Then you'll have the concrete crews come in who pour the foundations and do all of the concrete work. Obviously on a nuclear power plant there is a lot of foundation work, as well as a lot of above ground concrete so probably a good chunk of the construction workers will fall into this category.
Power plants also have a lot of structural steel work, electrical and special equipment that would likey fall under the piping category but each of these uses a separate set of skilled labor that does not overlap.
If you were going to actually try to build 3,300 nuclear power plants, you would rotate crews from project to project which would increase efficiency rather than hiring 27 million separate workers.
In any case, I don't think converting the world's total electrical power generation to 100% nuclear is by any stretch of the imagination a good idea. Personally I think maybe 15 to 25% nuclear power generation would be a more realistic mix, similar to the US electrical power generation. The rest of the power should be solar, wind, hydro, wave and geothermal as they are absolutely cheaper to build.
I'm not sure I agree with how you'd be able to execute on that level or organized construction safely, but I think we're also reaching the "impossible-to-be-sure hypothetical" territory, so I'll concede the point for now.
I think my problems of cost and time still stand. It looks like adding rooftop solar with batteries to every building is still cheaper (on startup, and likely per MW) than nuclear plants. Regions that cannot support solar, onland wind, geo, or hydro can justify nuclear (at least unless shipping batteries or hydrogen conversion becomes cheap enough to compete), but I don't think they amount to nearly 15% of the power needs in the world since they represent fairly distinctive regions with low energy demand.
We do it all the time in the construction industry.
For instance, Bechtel has 55,000 people in the US.
So just hire them. Too bad they lost almost all of their institutional knowledge about nuclear construction compared to what they used to have.