The concept of “peak oil” means different things to different people. Some people use it as a general term to describe the eventual slowdown and then dwindling of oil production. I get the feeling that most people use it in Hubbert’s sense: that production over time rises, reaches some high point, maybe plateaus there for a while, and then inexorably declines. A lot of people take that behavior as a given, where the only unknowns are when the peak occurs, how high it is, and how fast or slow the rate of decline is.
I think it’s important to realize that there are a number of implicit assumptions being made in that case. These assumptions include: the amount of demand, rate of discovery, and efficiency of extraction. For example, take the graph of US production. There are two peaks here; the second one occurring when the Alaskan oilfields hit their stride. You could argue that the curve has an overall bell-shape, but note that the “plateau” was relatively long-lasting – about fifteen years between the first peak (1970) and the second (1985).

Source: http://www.eia.doe.gov/emeu/aer/txt/ptb0502.html.
One thing you can assert with confidence: if you assume that the amount of oil in the ground is fixed, then eventually production will near zero. But when will that happen?
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