How long will geothermal energy last? Is it possible for it to run out; if so, when?
Geothermal energy is predicted to last over a billion years, but before it runs out, the sun will become a red dwarf and annihilate the earth.
Geothermal energy has its source in the intensely hot inner core of the earth. The heat reaches levels that we can observe through massive convection currents within the inner core and the mantle. These currents in the mantle keep changing the face of the earth as we have seen in earthquakes and volcanoes both on land and sea.
The other heat process is thermal conduction of heat directly from the inner core. The conduction takes a long time to reach the surface, as it has to pass through the outer core, then the inner and outer mantle, before reaching the earth's crust. It's like the core is wrapped up in a blanket.
Then there is the heat generated by ongoing nuclear reactions as several long lasting radioactive materials within the earth decay in an exothermic process to add to the heat.
Relative to these events, human's limited use of geothermal energy will certainly never cause it to run out soon.
There is a picture here: