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population itself isn't the limit, it starts to crash when the cost of extracting and using fossil carbon liquid fuels crosses an unkown EROI (energy return on investment) threshold.
the EROI of light sweet crude petroleum is about 20 to one, if I recall correctly. You get 20 barrels worth of oil energy out for every barrels worth of oil energy you spend.
if the oil is heavier or more contaminated or in a difficult to extract location, the EROI drops to something between 10 to 16 to one.
tar sands oil has an EROI of 5 to 1. corn based ethanol has an EROI of between 1.1 to 2-something. It doesnt work economically. Coal turned to liquid fuels has a complex EROI, the old methods had an EROI of .5 (you use twice as much energy producing the fuel as you get out of it), but people think it can be improved to the tar sands level.
as a side point, people argue that the tar sands are only economical because you can pay for the fuel needed to run the trucks and system using energy purchased at the world market rates, and that the real EROI would be lower if you had to use tar sands fuel to operate the system. Eventually we will find out.
So, if we guess, and say the EROI threshold of tar sands is the collapse limit...
then we have about 30 years maybe. thats when 3/4ths of the existing "known" ("known" includes projected, it's a complex estimate that companies have motivation to inflate) petroleum reseves will have been used up, if use continues at the present rate.
if we are lucky enough to have plague, and use drops, the lifespan of our oil-based civilization gets a bit longer.
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