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How would you calculate the gravimetric & volumetric energy density of a gravity based system like Energy Vault ?

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  • Just as a side note: gravity based energy storage is already used for more than a century on large scale: en.wikipedia.org/wiki/Pumped-storage_hydroelectricity . Some factors that make them energetically favorable are relevant for the solid-based gravity batteries as well: We put them where geography is favorable so no supporting tower needs to be built. We put them where the storage material (water) is cheaply available. And we basically build them where the volume is of no concern (stone/concrete has a density of ≈ 2.5 t/m³ - that's only a factor 2.5 compared to water). May 24, 2023 at 10:02

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Let's look at the specifications of EnergyVault.

Firstly, the tower height is claimed to be "nearly 500 feet" or nearly 150 meters. However, since the tower consists of bricks, an average brick has half this height or 75 meters.

One kilogram at 75 meter height stores 75*9.81 = 736 joules or 0.2 watt-hours. Compare that to batteries that store 200 watt-hours per kilogram. Three orders of magnitude difference!

Most likely the bricks are made out of concrete since that's the only cheap reasonable heavy material out of which you can make bricks with flat top and bottom (so that you can stack them). It has density 2400 kg/m^3 or 2.4 kg / liter. However, batteries have about the same density so EnergyVault stores about 0.5 watt-hours per liter whereas batteries store 500 watt-hours per liter.

Looking pretty bad, right?

The claimed EnergyVault system can store 20, 35 or 80 MWh and discharge at rates of 4-8 MW for 8-16 hour discharge.

You need a tower crane to lift these. A tower crane has rental cost of about 160 000 euros per year. Therefore, if the 20 MWh system uses a single crane and the larger systems require multiple cranes, the cost per year is 8 EUR / kWh / year.

If lithium ion batteries cost 100 EUR / kWh and last for 25 years at interest rate of 4%, that's 6.4 EUR / kWh / year. Less than EnergyVault already and that didn't even include the price of the bricks!

Also crane costs are not exponentially decreasing contrary to battery costs that are. Therefore, the balance that slightly favors batteries will even more strongly favor batteries over EnergyVault in the future.

If one crane can discharge at 4 MW, and costs 160 000 euros per year, the cost per year is 40 EUR / kW / year. Wind turbines cost 1000 EUR / kW, so for 25-year lifetime and 4% interest rate, they cost 64 EUR / kW / year. So while a crane might look like slightly cheaper, you have to remember that a crane can produce energy only if you have enough bricks stacked, whereas wind turbine can produce energy out of "thin air" (wind).

Inverters cost 180 EUR / kW, so for 25-year lifetime and 4% interest rate that's 11.5 EUR / kW / year. So if you have batteries, converting their energy into grid voltages is cheaper than operating the tower crane in an EnergyVault system.

About the bricks. Concrete costs 100 EUR/m3. Density is 2400 kg/m3 so to store 480 watt hours or 0.48 kWh, you need 100 EUR. Therefore, the bricks cost 208 EUR / kWh. Compare that to lithium ion batteries (100 EUR / kWh). So if you want to increase the storage capacity of an EnergyVault installation while using the same number of cranes, you are paying 208 EUR for every kilowatt hour of extra capacity. With lithium ion batteries, you would be paying only 100 EUR for every extra kilowatt hour.

Now probably everyone agrees that EnergyVault is an extraordinarily poor idea. With lithium ion batteries connected to an inverter, you get cheaper per-kW and per-kWh costs if you compare them to a tower crane near a brick stack (which EnergyVault is).

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  • Thank you very much ! I can see how the stored energy is calculated, and definitely can see the incredible costs associated with it. With regards to energy density (energy/unit volume), how would you calculate that ? Apr 12, 2022 at 20:06
  • It's always nice to have a link.... energyvault.com Sep 26, 2022 at 10:51
  • BTW, energyvault are giving a cost- point of $150/kWh (no details of how they get to this price point on their website) Sep 26, 2022 at 11:02
  • juhist, The brick average height statement doesn't make sense to me. In the case of the EVx, the 24 ton block has dimensions of 11x9x4 feet and is raised to a height of "over 300 feet". So, the delta h certainly is much larger than 150 feet....
    – vronp
    May 10, 2023 at 14:03
  • +1 for crunching numbers even though I do not agree with all your assumptions (e.g. @vronp's comment). While I understand your calculations for the given system. a bunch of improvements both wrt. energy and costs IMHO fairly jump to the eye. Wrt. cost: yes, tower cranes are expensive. That's why they are typically only used where their particular advantages are needed: mobility (can be brought from one construction site to another) and adaptability (to the particular construction site). But when the lifting needs are not temporary, much simpler hoists are put in place (e.g. in mining shafts). May 24, 2023 at 9:50

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