Mines have what is called a cut off grade. Ore is prospected by Geologist. The geologist than make up 3d maps with blocks of ore in them, the Gold grade in this ore is known (estimated). The grade being Gold content of the block often given in grams per tonne or whatever strange system the USA uses.
Depending on how deep down or how much earth needs to be moved to get at the block a cut off grade determines if it is to be mined or not. The cut of grade is the lowest amount of gold per tonne that is economic to mine. It is worth noting that this cut off grade also varies with the gold price too.
A mine will have a mining plan normally a long and a short term plan. A well run mine will know well in advance that it is running out of economically viable ore and will slowly start to shut down according to a well planned schedule.
It is true to say the gold never runs out it just becomes un economic. Sea water contains gold in minute amounts as there is so much sea water most of the worlds gold is in the sea just not economic to recover.
I am a mining Engineer with over 20 years experience in Gold mining. The above explination is far from exhustive but is aimed at a 5 year old before hundreds of correction appear below.
Happy to answer more detailed questions if you have them.
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