There are countless ways to store energy: hydrogen, artificial hydroeletric, batteries, etc. Solar energy is practically unlimited. Nuclear still requires fuel, and it's a very limited resource unless you start considering things like extracting fuel from the ocean where costs just skyrocket.
And it's likely that our global energy usage will skyrocket in the future for a variety of reasons. The first level is that many places are still undeveloped and have not yet hit their 'China' phase. But beyond that we can also just do some really cool sci-fi soundings things if we massively ramped up our energy production. Fossil fuels, and fuels in general, were never really fit for these sort of ideas - but solar certainly is.
This [1] article goes into detail on the remaining nuclear material. Keep in mind that this is at current consumption rates. Energy usage rates are going to increase in the future, and right now only 4% of global energy production is nuclear. In other words, you can shave orders of magnitudes off the numbers they give in that article to give a ballpark for how long nuclear would last. It's just not a great fit for the longterm future.
Scientific American is flat out wrong, compare[1]. (Someone who states that "a breeder creates more fuel than it consumes" has to be wrong about many things.) Common rocks contain about 13ppm uranium and thorium, which gives them a 50x higher energy density than coal[2]. We will never run out of rocks. As a bonus, if we actually "burn the rocks", we end up with a lot of sand to be spread on fields, which counters soil erosion, serves as fertilizer, and captures CO2 through accelerated weathering. In other words, solar power uses land, nuclear power restores land.
It's a misleading, but technically accurate marketing point for breeders. More specifically it's fissile material, which is converted from larger amounts of fertile material used in the reactor. There's no violation of conservation principles, just some fast talk. Read your own links - as at least the first mentions this.
The second link is junk. The average distribution of elements in the Earth's crust does not mean each every and every chunk of earth contains exactly that distribution. And while many types of rocks do contain trace amounts of uranium, it's nowhere near 13 ppm. Though so far as I can see even that site didn't state that.
> It's a misleading, but technically accurate marketing point for breeders
That's the point, it's not technically accurate. A breeder makes more fissile material than it consumes. Fissile material is the fuel in light water reactors, but breeders use a different, more abundant fuel. I know that, you know that, and we both know that we both know that. But inaccuracies like this lead to the likes of Helen Caldicott dismissing the whole technology with a sneer such as "a breeder that magically makes more fuel than it consumes".
> trace amounts of uranium, it's nowhere near 13 ppm
It's about 13ppm uranium and thorium, in fact about 10ppm thorium and 2-4ppm uranium. And while energyfromthorium doesn't state these numbers explicitly, it clearly uses them in the energy density calculations.
> does not mean each every and every chunk of earth contains exactly that distribution
So "burning the rocks" will never work, because there are a few rocks that don't burn? It works even better, because some rocks burn better, e.g. Conway Granites at 56ppm thorium.
I'd expect we'd need either fast reactors or thorium reactors to cover that much usage. Either would be about 100x more fuel-efficient. There are two fast reactors operating commercially in Russia.
Extracting uranium from the oceans is about 5x more expensive than mining it. Since fuel is a small component of nuclear cost, that's not a big deal; we don't do it right now because mining covers our needs. With fast reactors, it wouldn't be a problem at all, and would cover our needs for many millions of years, even at much higher consumption rates.
Storage adds quite a bit of cost to solar (other than hydro, which is geographically limited). If we get storage technology that makes storage+solar cheaper than nuclear, then sure, that might be better.
However, we're already nearing a planetary limit on land usage, after which we seriously impact biodiversity. The vast solar arrays this would require wouldn't exactly help.
Fuel, at least according to Wiki [1], runs about 28% the cost of a nuclear plant's operating expenses. And our current nuclear tech was chosen largely because it was cheap. You're also looking at much greater expenses in running breeder plants. Those are already pretty substantial costs. And now on top of the cost extracting/refining/enriching fuel from saltwater would cost, you also have to keep basic economics in mind as well. Right now there's little demand for nuclear material, and so this is reflect in its cost. However, should this change you'd expect to see the cost change in turn, and likely quite sharply. That's a lot of stuff piling up pretty fast!
I'm not sure where you're getting he millions of years for breeders. The article mentions the value I've seen pretty much everywhere which saltwater extraction could theoretically provide enough material for about 60k years of nuclear operation. And breeders could ideally reduce consumption to a bit less than 1% of current usage. So that'd be 6 million years, but that's at current consumption rates. If we replaced our energy with nuclear that'd be a 25 fold increase in usage so we're down to 240k years at current rates. And that's in the scenario where we're extracting all the material we can from ocean water, using every single resource we have on the planet, and doing it all with perfectly functioning breeder reactors.
Just seems we should be targeting something that isn't a numbers game, though granted you can probably make some argument that cobalt will be a limiter on solar but solar also comes with many other perks - decentralization, minimal danger from failure, much cheaper, practically infinite energy availability, and so on. The only issue is storing energy, but this can be done affordably in numerous ways even with present day tech - and decentralization can also remove lots of the burden here.
So only, say 100K years before we have to figure out fusion or something? I'm thinking we could live with that.
However, uranium in seawater is actually in an equilibrium, so the more we extract, the more gets dissolved from rocks. Effectively it's a renewable resource:
Whether breeders would be more expensive depends on their design. One that looks quite economical, according to independent engineers who evaluated it, is Moltex:
And it's likely that our global energy usage will skyrocket in the future for a variety of reasons. The first level is that many places are still undeveloped and have not yet hit their 'China' phase. But beyond that we can also just do some really cool sci-fi soundings things if we massively ramped up our energy production. Fossil fuels, and fuels in general, were never really fit for these sort of ideas - but solar certainly is.
This [1] article goes into detail on the remaining nuclear material. Keep in mind that this is at current consumption rates. Energy usage rates are going to increase in the future, and right now only 4% of global energy production is nuclear. In other words, you can shave orders of magnitudes off the numbers they give in that article to give a ballpark for how long nuclear would last. It's just not a great fit for the longterm future.
[1] - https://www.scientificamerican.com/article/how-long-will-glo...