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.