A geology question

I’m reading a science fiction novel that talks about using ‘core taps’ to provide energy and it got me to thinking. I know the deeper you get into the earth, the higher the temperature gets. Does anyone know how deep you have to get before, say, water boils? Is it approximately uniform or extremely variable? Is there a calculation for the change in temperature to the depth? Is there a theoretical and practical limit to how deep we can currently drill?


From Engines of Our Ingenuity: Drilling for Heat:

Temperature at depth can be affected by subsurface water flow and radiation, so it’s not uniform. In the outer core it’s as high as 3000° C.

The temperature gradient below the surface depends on many variables. Some of these are as simple as different sources of heat. There is the heat from when the earth first solidified and cooled, and the heat generated by the decay of radioactive isotopes.

Also, different materials conduct heat differently. I don’t know how technical you want this answer to be, but heat is transferred from hotter to colder regions by radiation, conduction, convection, and advection. These are limited by the physical structures of the rocks (molten, rigid, etc.).

If you’re just talking about the near surface, the crust of the earth, the geothermal gradient is loosely about 100degrees C for every 5 km below the surface. (“Igneous and Metamorphic Petrology”, J.D. Winter)

I don’t have a cite for this one, but I remember someone saying that the deepest we’ve ever drilled was 8km. Practically, there is a limit that we can drill. The heat would be very intense (not rock melting at 8km yet), but if you drill a hole that far down, the release of pressure would cause the hole to collapse in on itself. This happens in mines if they don’t build structures to support the walls. They call it rock burst, but it is an effect of the release of pressure when they drill the mine.

Theoretically, I have no idea how far they think we can drill. I’d like to go see “The Core” and see how they explain the science of that.

The Earth’s geothermal gradient (i.e. chang of temperature vs. depth) varies from one place to another. For example, the temperature increase vs. depth beneath Kansas City , KS or Duluth, MN (ca. 15 C per km) is less than in, say, the Cascade Mts., Yellowstone, or Japan ( ca. 40 C per km). So, in Kansas, you’d have to dig to about 6.7 km to reach the boiling point of water.

There are man-made “Geothermal” wells that provide heat energy for steam driven electric generators. In one design, two wells are drilled near each other, the region between them is fractured, and water is pumped down into one well and recovered from the other, having been heated by the interim rock. These have mainly been developed in volcanic complexes where there is a batch of magma only a few kms below the surface. Iceland exploits a natural geyser system by capturing high pressure steam from the ground into piping systems. For more, search for ‘geothermal energy’.

As for calculation, the simplest is to just assume the gradient is uniform (for most everyday purposes, this is an adequate approximation), i.e. x deg C per km. The value of x is “high” in areas of recent (<20 million years) volcanic activity and low in continental interior fars away from volcanic fields. If you insist on the gory details, go to your local university library and check out a book on solid earth geophysics.

There are a number of limitations on drilling depth. One of the most significant is the mechanical failure of a string of drill pipe that’s longer than about 10 km length. (For the deepest well yet, check your Guiness book.) Another problem, especially where down hole temperatures are high, is having the metal tools or rocks deform ductilely, but if all you’re interested in is a big heat reservoir, this kind of depth isn’t necessary.

Equilibrium geotherms (temperature-depth profiles) are controlled by a number of factors: conductivity, specific heat, density and radioactive heat generation of the rock column you’re examining, as well as heat flow into the rock column, the surface temperature and the rate at which material is added or removed from the top of the column. To put it more simply and with more practical purposes in mind, the geothermal heat gradient (i.e., the rate at which temperature changes with increasing depth) does vary with location and proximity to a heat source (like magma).

If you’re thinking about using geothermal heat as an energy source given current technology, you can really only make use of it in volcanically active areas (such as Iceland, or parts of the Pacific Northwest), where the gradient would be shallow. For other continental locations on the Earth’s crust, it just wouldn’t be practical, because the crust is thick enough to shield the surface from a lot of the heat produced in the mantle. I can’t find a reference just now, but I seem to recall an average geothermal gradient in continental crust of about 25 deg. C per kilometer, which means you would have to pump water down at least 4 kilometers to heat it up, and then find a way to keep the water hot while bringing it back up. On preview I see that Ringo cites some people who want to do this, but it doesn’t make much sense to me. (How much energy would we use to pump the water through a cycle in the first place?)

As for how deep we can drill with present technology… I think the super-deep hole drilled in Germany about 10 years ago reached a depth of around 9-10 km before the drill team called it quits. At that depth, temperature and pressure combine to make rock behave plastically (i.e., it flows), and the bottom of the hole kept getting pinched off by flowing rock whenever they had to pull up the drill string to replace the drill bit.

If the gradient is forty degrees per km, then why bother with
Why not just use turbines driven by the airflow that results from the temperature differential?

From this company’s website in Australia, there’s quite a good description of the processes and depths involved. They quote 3 kilometres (slightly less than 2 miles) as the depth needed to reach temperatures of 200ºC in one location.

geology rocks

Because gas turbines don’t work that way :). They require high temperatures/pressures to work practically.

Lookup geothermal energy for more info on earth’s power.