How much oil is there? 3 trillion barrels? 4 trillion? How do we know?
There is no single answer to that question, because the answer depends upon price. At $80/barrel, there is a certain amount of oil remaining. At $150/barrel, there is far more oil remaining. And so on. The reason is because we leave most oil in the ground, since it's uneconomical to extract at current prices. As prices increase, the amount of economically extractable oil increases also. So there is no single "amount" of oil remaining. The amount depends upon price.
The Supply of Oil
Most resources are distributed according to a "resource pyramid." A "resource pyramid" is divided into layers, with small amounts of easily-extracted resource at the top, and larger amounts of harder-to-extract resource in the middle, and vast amounts of difficult-to-extract resource at the bottom. At the very bottom of the pyramid is a very diffuse resource, which is availabile in massive amounts, but which costs a lot to extract because it requires so much energy and money to "filter" it out of some substrate.
Oil supplies are distributed according to a resource pyramid. At the top of the pyramid was a small amount of easily-accessible oil. When we started drilling for oil, it would sometimes "gush" out of the ground with great force after drilling only a shallow well. That oil was easily extracted and inexpensive, and it was all used up within a few years. After that, we had to move down the resource pyramid to more difficult (and far more plentiful) resources.
At the bottom of the oil pyramid are resources like shale oil and tar sands, which are very diffuse and difficult to extract. (In fact the lower strata of the resource pyramid aren't really oil at all but are hydrocarbons which are converted into oil using chemical processes, for example, coal-to-liquids). At the very bottom of the resource pyramid is manufactured hydrocarbons using (for example) nuclear power, gasification, and the fischer-tropsch chemical method to convert any carbon source into hydrocarbons. This technique could supply oil indefinitely at an EROI of about 5:1.
As oil becomes harder to extract, it also becomes more expensive, which opens up vast amounts of oil that were previously uneconomic. When we start to run out of oil, we take a step down the "resource pyramid" and start using the far larger (and more expensive) oil at the lower stratum. The result is that supply of oil increases, as price increases.
For this reason, oil production worldwide will not follow a bell curve or anything similar. Instead, oil will peak and then prices will gradually increase, thereby allowing us to extract previously uneconomic resources, and thereby preventing any decline. We'll know when we're transitioning to a lower stratum on the pyramid because prices will increase permanently by some amount. However this doesn't imply any kind of decline, because more oil may be available at that price.
Take the USA as an example. Oil production peaked in 1970 in the USA, as per Hubbert's prediction, and then declined for several years thereafter. Then something funny happened. In 1976, prices increased because of a cartel, and production started increasing again in the USA, years after it had peaked. When the cartel failed, and prices for oil started delining, production in the USA started declining again. Now, decades later, prices for oil are high again, and production in the USA is increasing again, decades after the peak! Clearly, production depends upon price and does not necessarily follow a bell-shaped curve.1
Of course, as oil prices increase, alternatives become relatively cheaper. Trains become cheaper than trucks, since trains use about 1/8th the energy per pound-mile. Hybrids become cheaper than convetional cars, since they cost only slightly more and use far less fuel. This trend will reduce demand, and further attenuate the decline.
Because of these facts, the very idea of "peak oil" as it's commonly understood (where we have a fixed amount of oil and it will follow a bell-shaped curve) is mistaken. Instead, we face a plateau or oil, or perhaps very gradual declines, for many years after the peak. Oil will not follow a bell curve or anything similar.
The doomer idea of applying a "bell curve" to worldwide production probably stems from their graphs of individual oil wells, which do in fact follow such a curve, roughly. But that doesn't mean that all oil wells in aggregate will follow a similar curve. It would be a tremendous mistake to assume that all oil wells will follow a bell-shaped curve because any one oil well has historically done so. Whereas an individual oil well doesn't increase prices as it depletes, the sum of all wells depleting will increase prices, and thereby increase supply and prevent subsequent decline.
As we deplete the cheaper oil, we will move down the resource pyramid, thereby increasing the price and the supply, and thereby attenuating any decline. We will never face an abrupt drop-off in supplies as a result of depleted resources, nor will we face anything like the 3% annual declines which doomers assume.2
If anything, we face a greater threat from China out-bidding us for oil than from declining production.
None of this implies a perfect future. We will face higher prices for oil in the future, particularly because of competition from developing nations, and this may force unwelcome changes to the American lifestyle, like driving hybrids instead of SUVs. However, we do not face rapid declines of oil, nor do we face any kind of interruption of industrial civilization.
2 I'm referring to abrupt declines caused by depletion of resources. Of course, it's possible there will be abrupt declines caused by war, disruption, severe economic downturn, etc. It's also possible there will be brief abrupt declines of a few percent based upon miscalculations because oil production does not follow a smooth curve. It's also possible there will be fairly rapid declines caused by peak demand. For example, it's possible that prices for oil would increase greatly, and the prices of batteries would decrease, to the point that plug-in hybrids became cheaper to operate than conventional cars. In that case there could be a rapid transition over the course of 15 years or so to alternative propulsion for cars, leading to a 5% annual decline or greater. That would mean that oil wasn't crucial anymore.