Sure but if we succeed at mitigating cimate change effects to a reasonable degree, civilization will survive for centuries, during which a reactor that uses itmight become available. It's a minor problem blown out of proportion, as opposed to CO₂ emissions, which are the opposite.
Even if this were true this doesn't help with the very real issue that we can't build the nuclear capacity fast enough whereas renewable energy can be built fast, is already being built, and doesn't have that problem that needs wishful thinking for it's solution.
Because batteries aren't as dangerous as reactors, are still making massive improvements on energy density and seem feasible to me. Doing anything useful with nuclear waste has been discussed for decades and no-one has come forward with any really promising results. The waste has been around for long enough if anyone could have done something productive with it it likely would have happened already.
It's just an example number. No matter what if you are building a grid that has 0 baseload power generation, you need some amount of storage capacity for each KWh of consumption. We can argue how much you actually need, but the fact remains that when you start storing large amounts of power, which you would need in-order to keep a city running during times of reduced generation, it takes a large amount of space.
In order to demonstrate that, I chose a pretty straight-forward scenario of a city of 1million for just one day. Let's assume that this amount of stored energy would be sufficient for a 100% renewable grid for say New York City.
So how much energy storage would be needed and how much space would such a storage facility take up?
The premise of powering a complete city just from one singular facility is a false one. It's unnecessary to build such a facility. You can build multiple smaller ones to supply sectors of a city according to the needs of that sector. The answer also depends on how smart the usage of the power is. Are people using power when it's available? Are people trying to use a lot of power when it's not available but must come from storage? There are so many factors your scenario doesn't take into account. The answer has to be: it depends.
This also feels a lot like a gotcha question not posed in good faith. Because again: you won't need to power anything solely from storage. Wind and sun will always supply a base level of energy.
Wind and sun will always supply a base level of energy.
That is objectively false. The sun doesn't shine at night, and wind doesn't blow 100% of the time. So logically there is some amount of time that you do not get a base load provided only by sun and wind. Hence the need for storage at all. And yes it is a gotcha question, because it's something that anti-nuclear people hand-wave away as if the significant storage infrastructure to support a 100% renewable is just a rounding error, and not worth thinking about.
For the fun of it I did do the calculation. Berlin uses about 12TWh per year. That's about 33GWh per day.
Assuming an energy density of 450Wh/l (a number car batteries apparently were able to reach 2020) that's about 80.000 m³.
A soccer field is about 4000 m². So a space of 10 soccer fields with 20m high battery stacks would do that.
Now assume that energy density will have improved in the last 4,5 years and that maybe storage batteries can be different from batteries in cars and that can go down by a lot. Seems reasonable enough for the biggest city in Germany.
That is a currently realized grid storage facility, the largest and really only one of it's kind. Today's renewables do not do storage at all, they rely on fossil fuels to make up the baseload.
Some numbers. This facility stores 1400MWh, on 2,000 acres or (~8,000,000 sq meters) Much greater then your 40,000sq meter estimate. Plus you said about 33GWh for a day. Well you'd need ~24 of these facilities to cover just Berlin.
Yes it wouldn't have to be monolithic like that facility is, but regardless of how you distribute it, it's a non-trivial amount of space taken up. Totally ignoring the costs, and sourcing the materials for the batteries of such facilities.
But just for fun that facility was ~$550M So you'd need to spend about $2.3T for the initial building of that storage.
Okay so your comparison has a few flaws there. The square meters I calculated were just a reference. The important thing is the volume taken up. If you stack your batteries only 1m high that's gonna cover a lot of ground. You also completely failed to take into account that energy density has apparently 4x since 2020 which shrinks the required volume significantly.
I'm gonna argue that 4000 of these facilities distributed around the whole USA isn't that much. Spacewise the USA is in a very comfortable position compared to European countries.
As for the price: taking the price for a pilot project and assuming that every facility is going to cost that is very wrong. If you're going to build 4000 of them, cost is going to go way down.
But if we are talking numbers here I too have a question. How much land would nuclear plants (and the intermediary storage and final storage for the waste) use to fulfill those 12TWh per year? And how much would those cost to build and maintain? I imagine that a battery facility is way cheaper to operate than a nuclear plant.
Yeah I'm not convinced that just burying the stuff deep in a hole will do what I think is responsible. That shit stays dangerous for multiple thousands of years. That's such a long timeframe that we cannot predict what's going to happen to our society. It is very realistic that we lose the knowledge of the location or even the dangerousness of that stuff. Imagine future people stumbling into this and actually getting something like a curse from an old pharao by weird invisible forces that make you sick.
Another thing about this is that locations that are "good" candidates for this kind of storage are extremely rare. Germany has been looking for a suitable place for the last few decades and didn't find any yet afaik. And the few places we might have are booked to be filled with all the old waste still sitting in intermediary storage.
Unless we have a reliable way of finding suitable storage places before we start producing more waste it will put us in the same situation we are in now, just worse.