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At what power output would we be using so much geothermal energy that we cool the core enough to endanger the Earth's magnetic field and have to stop using it? Is this a conceivable concern for a future energy crisis?

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2 Answers 2

No, this seems highly unlikely.

According to online sources:

Average human power consumption in 2008 was estimated at 15 TW.

Total annual heat loss from the Earth due to the surface heat flux is estimated at 44.2 TW.

Estimates of the electricity generating potential of geothermal energy around the world are consistently less than 2 TW.

So although the average power consumption is a surprisingly large fraction of the total geothermal heat flux, the part that might possibly be extracted for power is quite small.

There are much more concerning environmental impacts to geothermal power development than freezing the core and destroying the Earth's Magnetic field. These include increased rates of release of carbon and sulfur into the atmosphere and land use issues.

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However unlikely, commercially invalid, or otherwise infeasible with today's technology there is a number of watts that if removed from the earth's core will solidify it. +1 for other 'more concerning environmental impacts'. –  Mazura Aug 1 at 0:54
    
@Mazura, a key point though is you cannot draw an arbitrary wattage from the core with geothermal energy. You can only get some fraction of the heat flux that is already conducting up to the surface anyway. So you aren't really affecting the core cooling rate. –  ZSG Nov 19 at 5:56
    
Mark, not sure what you mean by increased rates of carbon and sulphur released, can you say more? –  a different ben Nov 25 at 22:45
    
Regarding land use issues, footprints per kW of current geothermal power plants are amongst the smallest of all electricity-producing industries. –  a different ben Nov 25 at 22:47
    
@a different ben - Because C & S gas species are in volcanic/geothermal emissions, there are measurable emissions of these from a geothermal power plant. Should this be regulated in the same way as a carbon emission from an coal-fired plant. It is measured at a 'stack'. On the other hand it may be 'natural' in the sense that it was going to be emitted from a fumarole anyway. My understanding is that this is treated by regulatory agencies as the same. Perhaps this is a confusion, but I believe this has in fact had an impact on the licensing of geothermal power plants in places such as Hawaii. –  Mark Rovetta Nov 27 at 2:00

This is a bit of a what-if kind of answer, with some rough estimates. Just considering the cooling aspect - let's pretend that Earth is solid for a momnet.

The time-dependent heat equation tells us how long it will take for a change in temperature to travel a certain distance by conduction (the 'characteristic timescale'). The distance to the outer core, where the magnetic field is generated, is about 3000 km.

Assume that the geothermal installation is at the surface, and that it loses its heat instantaneously. Then, the 'characteristic timescale' is given by $$ \tau = \frac{l^2}{\kappa} $$ Taking $ l=3 \times 10^{6} $m as the distance to travel, and $ \kappa = 1 \times 10^{-6} $m2/s as the mean thermal diffusivity of the rocks, then it would take $ 2.85 \times 10^{11} $ years for the change in temperature due to extracting geothermal heat at Earth's surface to propagate to the outer core. The sun would have transitioned to a red giant by then.

The problem being of course that it's not all solid. Convection in the mantle would obliterate the temperature signal. I don't know how you'd go about calculating that.

More practically, a deep geothermal project of the EGS flavour would be managed as a mining project. The reservoir would be used up within 20 years or so, then either abandoned or mothballed (until perhaps it reheated?). The maximum temperature drawdown for economic feasibility might be of the order of 50°C or less, depending on a boatload of factors.

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