A box of rocks?

I've blogged on a few occasions regarding energy storage, most recently a "LightSail Energy redux" (though I'll be updating that in the near future to revise an inaccuracy with respect to LightSail's ability to produce commercially in their existing Berkeley facility). But there are lots of ideas for storage out there, from molten salt to bags of air beneath the sea and many others. But a new one caught my eye not too long ago that seemed out of cloud cuckoo land.

The firm touting this technology is Heindl Energy and their concept is to cut an annulus around rock and space beneath the rock, thereby creating a rock mass piston in a rock mass cylinder. Water would be pumped in to lift the rock when excess energy (or cheap energy if arbitrage is the name of the game) is available and let the rock descend, pumping the water through turbines when energy is needed or expensive.

The idea is that the piston diameter is equal to its length, and it would be raised and lowered a length equal to its radius, so half or more of the piston would always be beneath the ground surface.

One claimed advantage is that, unlike pumped hydro or underground compressed air energy storage, the geological feature necessary for the storage is more easily found (though, obviously, they can't be built just any old place).

Another is that the density of rock is greater than that of water and so a smaller volume of rock is needed for a given potential energy availability (though the factor is only about 2.5 or so).

It's easy to show that the available energy, ignoring efficiency losses of various kinds, is ~E=(2\rho_{r}+\frac{3}{2}\rho_w)\pi gr^{4}~  where ~\rho_r~ is rock density, ~\rho_w~ is water density, ~\pi~ is, well, ~\pi~, ~g~ is the acceleration of gravity, and ~r~ is the radius of the rock piston. Note that the length of the piston is ~2r~ and the height to which it's raised is ~r~. Thus, the storage available scales with the fourth power of the radius. But, since construction is really all about the surface of the piston, construction time and cost scales approximately with the square of the radius. So, in this case, size truly matters! Doubling the radius gives approximately 16 times the capacity for "only" four times the construction cost and difficulty.

A bit of an issue is that the Heidl site "Idea & Function" page gives the energy as ~(2\rho_r\frac{3}{2}\rho_w)\pi gr^{4}~. I'm sure it's a typo and I've emailed them to mention it but still, it doesn't lend confidence. Nevertheless, I used Wolfram Mathematica to check on the validity of the table shown on that page and it's actually conservative. They claim efficiency of 85% but I have to reduce efficiency to 57% or so to hit their numbers. Update: I received an email from Dr. Eduard Heindl recognizing the typo and stating that it has now been fixed. Dr. Heindl agreed that such an error on the technical page should not have taken place.

Unlike many storage scheme sites and descriptions, Heidl limits their discussion to quantity (gigawatt hours) and doesn't, as far as I could find, discuss power (the rate at which energy can be delivered by such a system). Both metrics are, of course, crucial and this site has the opposite of my typical frustration. They also provide no discussion of any load following capabilities.

We're talking here about a very large project. Using their numbers, 8 gigawatt hours of storage requires a 125 meter radius piston (250 meters or over 2 1/2 football fields across). Such a piston would weigh about 35.2 million (short) tons! To lift it would require water pressure of about 64 bar (though their table shows 52 bar).

Such pressures would demand a lot from the seals between the piston and cylinder walls, otherwise, the system would act as a 250 meter diameter circular fountain! Heidl discusses the seal system here and it appears to be quite innovative (a rolling seal against, apparently, a steel cylinder sleeve) but I see no indication that a pilot plant has confirmed that it will work. The devil, as always, is in the details.

Finally, how many? If a single 250 meter diameter rock piston can store 8 gigawatt hours, what is required to provide stable delivery from renewable sources so that the need for fossil fuel burning base load, spinning reserve, and peaker plants can be minimized with increasing penetration of intermittent renewable sources? According to Heidl's site, Germany currently needs 1,600 gigawatt hours of storage, of which only 40 have so far been provided. Therefore, Germany currently needs 195 such storage facilities!

In the Q & A, Heidl estimates that the system is of comparable cost to pumped hydro storage at a radius of 100 meters, and less expensive above that due to the scaling factors mentioned above. They also estimate a minimum of 2 years of planning and 3 to 4 years of construction per facility. And my experience is that the grander the scale of the project, the less likely it is to meet budget and schedule estimates. And this has never been tried.

While I think that it's a long shot that this type of system will ever see widespread use, the bigger picture is the scale of the undertaking needed to provide sufficient storage for deep grid scale intermittent penetration regardless of the system used. I think that distributed generation and local storage are key to providing a sustainable energy future through renewable sources.

Note: R.I.P. BB King.