Calculate heat transfer in stone and from stone liquid heat carrier (water ++++)

Calculate heat transfer in stone and from stone liquid heat carrier (water ++++)


Job Description

This job is about calculating how heat flow in different types of rock with different temperatures.

Who different tasks

1. Geoology /gephysics / mathematics
Heat flow through rock at.

Deep under the surface rock is getting increasingly warmer. At 10.000 meter under the earth's surface the temperature is about 400 degrees Celcius.

If the rock at this depth is exposed for cooler water (via a well), the rock will slowly cool down.
The diameter if the well is about 5 meter (giving a circle of 16 m).
Assuming 200 meter is hot, the exposure surface is about 3100 sqm.

How fast will the rock be cooled of down in the shaft?

When will there be a equilibruim (heat escaping up, heat beeing transported from the surroundings of the shaft) ?

How much energy can be taken from a shaft?
How will shaft depth and the shaft wideness incluence the energy «harvest». (make some graphs illustrating these parameters)

Assuming the energy taken from the well is enought to produce 10 Twh elecrticity.

How deep, wide and what speed does the energy carrier liquid (water) need to move up the shaft?
(show the parametres in a graph).

At 10 km depth, we have roughly 3000 bar pressure.
If the hole is empty (air), the pressure difference is 3000 bar. If it is full of water, it’s 2000 bar.
This is far above the unconfined elastic strength of most rocks, so the hole will collapse.

That’s why they use these high density drilling muds to support the walls of the hole. The problem is that we do not have muds with such high densities (3000 kg/m3), at least not easily available.

Of course what makes the hole collapse is not pressure, but the stress tensor.
If I remember correctly, the stress distribution around a circular inclusion (or hole) looks like a 4-leaved clover. And the intensity of these differential stresses does not scale linearly with the radius of the hole.
So that’s why larger holes can support less pressure/stresses than small holes.

Certain Geopolymers has the strength of 20 mpa,
We need to build a vertcal shaft 5 meter wide and 10000 meter deep
As supporting walls to prevent collaps of the rock, we need to make a supporting circular pipe wall inside the shaft.
How thick must the walls of circular pipes be to withtand the pressure of 3000 bar.

Skills: mathematics, physics