Any of these "peak oil" or "running out of oil" (or any other commodity) are flawed for a simple reason: there is almost always more oil (or whatever) at a higher cost of extraction. One can imagine an unknown supply curve of oil available in 1700. The E&P (exploration and production) side of oil companies first reveal a part of that hidden supply curve, and then remove it (if it's cheap enough to do so) or add it to reserves (if it's not). Over time, more and more of the supply curve is revealed. Because today we generally know what to look for, and where to look for it, there's a fairly high degree of confidence of what the "unknown supply curve" now looks like below, say, $70/barrel. As prices continue to stay above $70, companies continue to look for more oil at these higher price points, and almost surely they'll find more.
Long story short: we won't run out of oil before we run out of money to pay for it.