Tuesday, January 03, 2012

Geothermal is not renewable

You can group geothermal plants into two types:
  • The kind that pump water underground and take steam or hot high pressure water out.
  • The kind that drill holes in the ground and use conduction to get heat out.
Admittedly, I don't know a great deal about geothermal systems, but I do understand heat flow reasonably well. And geothermal systems are all about heat flow. Here are the problems that I see:

Conduction is an impractical way to move utility-scale amounts of heat through anything but the thin walls of a heat exchanger. For instance, ground temperatures typically rise about 3 C for every 100 meters you go underground. Ground conductivity is about 1.5 watts/meter/kelvin. Multiply those two and get 45 kW/km^2. Remember that utility-scale power means you need hundreds of megawatts of heat. Bottom line: geothermal isn't renewable. It works by cooling down some chunk of rock in place, rather than by converting heat that rises from the earth's core.

You might think that a big hunk of rock can provide a lot of heat for a very long time. For instance, a cubic kilometer of granite, cooling 30 C, provides 2 gigawatt-years of heat. Figure 20% of that gets converted to electricity. Over 30 years, that cubic kilometer of granite will run a 13 megawatt power plant. We're going to need dozens of cubic kilometers.

You might think that dozens of cubic kilometers would be cheap. Ranch land out in Idaho goes for $360,000/km^2. Assuming you can suck the heat out of a vertical kilometer of rock, the 13 megawatts from that ground are going to bring you a present value of $90 million. Sounds great!

But wait... before you get started, you are going to have to shatter that cubic kilometer of rock so you can pump water through it to pick up the heat. The hydrofracking folks have learned quite a lot about getting fluid out of tight underground formations. I think the useful comparison to make is the value of the fluid extracted. Oil is worth $100/barrel right now, which is $850/m^3. Water from which we will extract 30 C of heat to make electricity at 4 cents a kilowatt-hour at 20% efficiency is worth 28 cents/m^3, ignoring the cost of capital to convert the heat to electricity. There is a factor of 3000 difference in the value of that fluid. Now hydrofracking rocks for heat doesn't have to be as thorough as hydrofracking them for oil, since you can count on ground conduction to do some work for you. But I don't think the difference is going to save a factor of 3000 in the fracking cost.

So, that means geothermal is going to be confined to places where the rock is already porous enough to pump water through. Like the Geysers in Northern California, which is a set of successful gigawatt geothermal plants. I think it's interesting that the output has been declining since 1987.

The problem is thought to be partial depletion of the local aquifer that supplies the steam, because steam temperatures have gone up as steam pressures have dropped. This sounds right to me, but I'll point out that the water in the aquifer is probably sitting in a zone of relatively cool rock which has hotter rock above it. As the aquifer has drained, the steam has to travel through more rock, causing more pressure drop, and thus less steam transport. Where water used to contact rock, steam does now, pulling less heat from the rock, so that the rock face heats up from conduction from hotter impermeable areas.

Wait... how did cool rock end up under hotter rock? The 150 or so gigawatt-years of heat that have been pulled out of the 78 km^2 area over the last 50 years have probably cooled a kilometer stack of rock by about 30 C (or maybe a thinner layer of rock by a larger temperature swing). I'm not at all convinced by the USGS claim that the heat source is the magma chamber 7km down. Assuming the magma surface is at 1250 C (the melting point of granite) and the permeable greywacke is at 230 C, a 78 km^2 area 6 km thick will conduct about 20 megawatts, an insignificant fraction of the energy being taken out.

Refilling the aquifer will help pull heat out of the shallower rock, but that's not going to last decades. To keep going longer they'll need to pull heat from deeper rock, and that's going to require hydrofracking the deeper greywacke.

And that's expensive.


  1. "It works by cooling down some chunk of rock in place, rather than by converting heat that rises from the earth's core." - That is exactly why I think is much more beneficial and reliable. Not to mention that its more environment friendly. Thanks for sharing this post!

  2. A lot of these alternative energy plans seem a bit hard to realize from the top level (material and energy flows. Usually you can for example just look at the carbon flow to find large scale biofuels improbable).

    What about going 7 kilometers down? Can you use just enough heat from the magma that it still stays molten and hopefully flows / convects so you don't have to drill more?

  3. Chad,

    Cooling down a chunk of rock in place means the rock gets cold, at which point your geothermal plant doesn't work any more. At The Geysers, the rock is porous, so every well they drill cools a large enough amount of rock. But places like The Geysers are rare. In most places, you can't get enough hot water out of a well to pay for the well, and thus geothermal doesn't work most places.

  4. Gravityloss,

    Go down 7 kilometers in rock that is 2.7 grams/cm^3, and you will find the pressure is 185 megapascals. At that pressure, some portion of most rock would be plastic even at room temperature. At the 1000 C temperatures down there, quite a lot of the rock will be plastic. Thus the rock will not be permeable, and you will not be able to fracture the rock and make it permeable. And so, you will not be able to push water through it.

    What would be really interesting to find would be a place where the composition of the magma is much different than the composition of the rock above it. If the magma carries a large amount of dissolved volatiles, it might be very fluid at low enough temperatures that the rock above might be fairly strong. And that might enable drilling, fracturing and backfilling with something like alumina sand which should be porous and very strong (3 GPa compressive strength at room temp and a melting point of 2072 C).

    But even so, things look pretty hopeless. If you were to drill and fracture within 200 meters of the e.g. 1100 C magma, and extract heat at 500 C, you are still only looking at 4.5 megawatts per square kilometer! That's just not utility grade. Worse still, if you get a little too close to that magma, or cut into a rock defect, you will get a blowout, and say hello to (remember those volatiles?) a career ending supersonic jet of molten rock. After blowing through your metallic equipment, my guess is the jet will erode the ground until it becomes a full-blown eruption, at which point you have a man-made volcano and angry residents.

  5. After 100 years of technology development, and tens of billions of subsidies, all the world's geothermal powerplants generate 0.3% of the world's electricity.


    That pretty much summarizes the situation.