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.

While I procrastinate in writing about more important things...

Physicists (one of which I am not) are quite concerned about units and dimensions and use dimensional analysis for a variety of purposes. And if the units in an equation don't match in all terms and across the equals sign, you've erred.

But sometimes this can lead to confusion. For example, torque (exerting a force about an axis) is measured in dimensions of [force]*[length]. It could be pound feet or newton meters or, for the matter of that, dyne centimeters or ton furlongs. But work and energy are also measured in such units. A joule is a newton meter.

Thus, in thinking about my fuel economy as a U.S. resident, I'm accustomed to thinking of miles/gallon but in countries who've adopted the SI (metric) system, people make a very sensible inversion of this and, rather than distance/volume, they use volume/distance, typically liters/100 kilometers. While this isn't an SI unit, it is metric.

But it's also a volume divided by a length or [length]^3/[length] which is [length]^2 or an area. So I converted my 50 m.p.g. to an area to note that my fuel economy is 4.704*10*10^(-8) m^2 or 0.04704 mm^2. Next time someone asks about my fuel economy, I'm going to say "a bit over 47 thousandths of a square millimeter."

It's not surprising to note that Randall Munroe*, of xkcd fame, has beat me to it. I will state, for the record, that I noted his post after composing all but this portion of this one.



*This is the first time I've noticed a photo of Munroe. It always amazes me how little resemblance there is between what I picture someone to look like in my mind and what they actually look like when I see them or their photo. And I always picture them.

Kunstler gets serious

Typically, I ignore James Kunstler and, in fact, I posted the reasons for this. And this is despite that fact that I agree with many of his positions, particularly with respect to the exigency of our energy situation. But his bombastic prose, his need to reuse the same symbols of his disdain for modern U.S. culture (tatoo parlors and tatooed people, suburbs, cars, etc.) to the point of exhaustion, and his extreme repetitiveness finally caused me to stop reading him except on an occasional basis. And, on these occasions, it was the "same old same old."

But Kunstler's most recent post  in his "Clusterfuck Nation-Blog" is different. He doesn't rail on about tatoos, cars, suburbs, salad shooters, cheez doodles, banker boyz, etc. He states without bombast the things that he believes a sitting and any future U.S. President should do and the reasons why. I find it to be compelling and accurate.

I'm sure that I'm far to the conservative side in comparison to Kunstler, but as I've posted repeatedly, the idiocy, ignorance, obstinacy, and intransigence that passes for conservative thought these days disgusts me. The positions taken by Kunstler should be celebrated by true conservative thinkers. He deplores the security state, the militarization of police forces, the thievery engaged in by the financial sector, the revolving door in Washington, DC for lobbyists, cabinet members, congresspersons, etc. between government and private interests, Citizens United, the state of perpetual war and foreign adventurism, etc. A true conservative should applaud every one of these and I do.

Further, Kunstler points out that not one candidate, announced or otherwise, has adopted any significant fraction of these positions, from the buffoonish Trump and the supercilious slime-ball Cruz on the right to the self-appointed rightful heir Clinton and the daft Sanders on the left.

Do I think that Kunstler's post, let alone mine, will move the populace to demand better? No, even though I believe that most would agree with the grievances that Kunstler suggests be "nailed to the White House gate" (though I suspect that anyone approaching the White House with a hammer and nails would be whisked off to Guantanamo at best and shot at worst, particularly were that person to not have the attribute of being caucasian - full disclosure, I'm caucasian).

Kunstler typically generates several hundred comments to each of his posts, this one is no different. Reading them is a somewhat sadder experience, there's a lot of "eat the rich," "burn it down" comments which serve no purpose. But I understand the frustration exemplified by such sentiments.

I don't guess that this deviation from his usual smug, self-satisfied, and precious cleverness indicates a new seriousness, but I'll check tomorrow (his posts come out on Mondays). It's well worth the five minutes it takes to read.