The geothermal energy is produced in 3 main ways: When the Earth is formed eons ago, the kinetic energy of the mass that rammed into the surface of the earth turned into heat. Earth gravity force further compressed the materials that also generated some heat, element natural decay caused nuclear fission energy be produced.
Also, the Moon, the Sun’s gravity caused periodical (very slightly) distortions on Earth that also generate some heat though very little.
In these sources of heat: The Earth forming process stopped and the kinetic energy turned into heat no longer have supply. The gravity compress effect that generate heat no longer significant because matter already dense enough in Earth. Radioactive elements on Earth only can be consumed but no further supply from space; the heat they produced will be weaker and weaker when time elapse along. The tidal movement caused heat is too little on the Earth to compensate the loss of heat through natural dissipation.
The heat produced from the core (20×〖10〗^12W) cannot compensate the heat that being conducted to surface and dissipated out into space (44×〖10〗^12W).
So as an observed fact, the Earth’s total mass is cooling all the time. When there is no supply (or not enough supply) while there is a constant loss (natural energy dissipation) or accelerated loss (manmade energy dissipation by tapping into geothermal energy), it is a simple mathematical logic: the Earth’s geothermal energy is not sustainable --- don’t even mention renewable.
Someone argue: the Earth is so big and we are so small, we use a little bit of geothermal energy, it doesn’t matter. OK, if this proportional difference can allow human to use the geothermal energy long enough to the time the Sun’s life span is going to end and start to swell and scorch the Earth, then it makes sense. Otherwise it is non-sense.
Then how long it can last if we use geothermal energy?
Here is some rough calculation (because in this case we only need some qualitative analysis to decide sustainability issue on geothermal energy):
In 2006, human use 16 trillion w /s;
Earth total mass: 5.9763×〖10〗^24kg;
Mean density: 5517kg/M^3;
Estimated average heat capacity: 700 J/kg ℃;
16 trillion w/s = 〖16×10〗^9kw×〖60〗^2s= 〖57.6×10〗^12kw/h;
1℃ down for Earth total mass:
5.9763×〖10〗^24kg×700 J/kg÷ (3.6 ×〖10〗^6Joule)
How many years human use can cause 1℃ down for Earth total mass?
1162×〖10〗^18kw/h÷〖57.6×10〗^12kw/h×24h×7d×52w = 2309year
How many years human use can cause 200℃ down for Earth total mass?
2309year×200℃ = 461,800year
How many years we taking off our descendants by using geothermal energy for one year by this rate?
2 billion year/461,800year≈4331year
The heat inside the Earth is the living force that keeps the Earth alive --- the heat inside the Earth resist water be sipped into the Earth, keep the molten core flowing that maintain the magnetic fields of the Earth that protect all lives on it and that also protect the atmosphere not been blown away by solar wind, keep continental plates moving that make mountains which keep the Earth uneven to maintain weather and prevent all Earth surface be submerged into 50 meters of water…
Earth with weakened geothermal energy will become another Mars.