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It’s basically impossible to make a closed loop hydro system with practical capacity. You need constant water replenishment. You’ll be losing 10-30 cm of water per month to evaporation and seepage, depending on weather and soil condition. Without plentiful source of water, this is not viable.
This one is extremely impractical, which you’d see if you even did a back of a napkin estimate. The fact that you mention this implies that you did zero legwork to verify if your ideas have even modicum of practicality.
Even absent the replenishment concerns, the amount of height and/or volume for gravitational storage just isn't practical. A kilogram of hydrocarbon fuel has ~40MJ of contained energy. To store the same amount of gravitational potential energy in a kilo of (water, but really anything) requires lifting it 4000km.
I'm not familiar with the state of the art in biochemistry, but the energy density of hydrocarbon fuels would plausibly make them excellent storage if we could produce them (from non-fossil sources) with even moderate efficiency. Not to mention the existing infrastructure. That said, that is a nontrivial synthesis problem.
Gravity storage with water as a medium is actually quite practical, and there are plenty of operational sites already, some with GWhs worth of capacity. You don’t have to lift 1 kg of water 4000 kms, you can instead lift 40 000 kg of water by 1000 meters.
This is practical and done in production, the problem is that you need a lot of water, and a lot of space to store this water in two separate reservoirs, which also need substantial difference in altitude. Because of this, it simply doesn’t scale: good sites are already mostly used, and we can’t build many more.
Synthetic hydrocarbons would make excellent store of energy, being very dense and already integrated in existing economy. The problem with those, though, is that the round-trip efficiency is really bad.
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We already can do something similar to this by producing hydrogen gas from water. Hydrogen has an energy density of about 33MJ/kg, which is comparable to hydrocarbons, and production is relatively trivial. The problem comes in converting it back to usable energy, which requires complicated fuel cells that are relatively expensive, which is, I believe, the biggest reason why the simpler but inferior EVs got the edge on hydrogen as the "green" vehicle solution.
Hydrogen isn't currently a panacea: it's difficult to store long term: it isn't very dense at room temperature and liquefies at a difficultly-low temperature. It also likes to leak really easily.
I don't know that it can be made practical for vehicular applications, but if you're thinking about fixed energy storage infrastructure it's probably worth considering.
Converting it to methane, if you could do so scalably and efficiently, would make the longer-term storage problem (months) much easier.
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Source. They've tested successfully, physically, to 1/10 scale. I haven't gone and found the paper, I'll admit; I'll give it a shot ASAP so we can argue productively.
In the meantime, if the napkin math is so easy, share it with the class?
I've casually found:
https://www.researchgate.net/profile/Jochen-Bard/publication/272318141_STENSEA_-_Stored_energy_in_the_Sea/links/54e1b2df0cf2953c22bb0fa2/STENSEA-Stored-energy-in-the-Sea.pdf?origin=publication_detail
https://www.researchgate.net/profile/Jochen-Bard/publication/308750542_DEVELOPMENT_AND_TESTING_OF_A_NOVEL_OFFSHORE_PUMPED_STORAGE_CONCEPT_FOR_STORING_ENERGY_AT_SEA/links/57ee6b9808ae280dd0ad588b/DEVELOPMENT-AND-TESTING-OF-A-NOVEL-OFFSHORE-PUMPED-STORAGE-CONCEPT-FOR-STORING-ENERGY-AT-SEA.pdf?origin=publication_detail
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This is not a “water tower at sea”. This is something different, actually quite smarter. I read their paper, and it doesn’t seem as immediately impractical as “water tower at sea” would, though it is still very much impractical.
According to their own analysis, the construction cost is something like 2-3x the cost of LiIon batteries per kWh. It’s something like $8M for storage equivalent to 2 minutes of operation of a single coal power plant. To build enough storage to replace one coal power plant for base load for half a day, you would need to build 400 of these, at a cost of $3.2B dollars. Coincidentally, this is about as much as it costs to build a nuclear power plant reactor of a similar size, which will keep generating the energy after the deep sea storage solution runs out of juice in 12 hours.
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I'm not seeing estimates on the price to build and maintain that per kWh. Without that, yes, you've failed to do the basic napkin math on practicality.
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