Of course there is a date for peak oil. The Earth has a finite mass, and even if it was totally made of hydrocarbons we will eventually use them all up. There are Malthusian overtones in some peak oil commentaries - the rest of the world has expectations of a better standard of living and the population of the world continues to grow exponentially. If you assume an exponential growth of population at the current rate, and a planet made of nothing but hydrocarbons, we reach peak oil remarkably soon. But that is just simple Malthus.
Where the peak oil doomsayers get it a bit wrong is in two parts, two discussed earlier.
One, new technology of extraction. Fracking is just the latest, and has extended estimates out past our current lifetime. But other technologies were already causing some extension.
Two, rising prices causes an increase in economically recoverable reserves.
Three, estimates of recoverable reserves are not reliable due to second order effects.
The last of these is an effect you see in all mining industries, as well as oil and gas. The listed quantities of recoverable resource only ever seems to cover a few decades of production (except for resources that are so large that a single discovery contains massive reserves.) We see this in oil and gas, and many rare minerals. Part of the reason is simply that oil, gas, and mining companies don’t go looking for resources past a decade or two of need. They don’t need to, it costs money (sometimes big money) to do so, the exploration technology is constantly improving so it will cost less to do so in the future anyway, and finally - once they find it, it costs more money, even if they leave the resource in the ground. Once they find it - everyone will know where it is. Resource companies don’t own the land, they get leases on the land that allow recovery. These cost money, usually big money, related to the value of what is there. Different governments have different ideas about how leases are valued and paid for, but no matter what, discovering a big deposit means you are in for some big expenses, even if you don’t exploit it right away.
There are many areas of the world where only the most basic, or even no, exploration has been done. The most astounding to me was Saudi Arabia. The oil bearing geology runs in a diagonal across the lower part of the country. The wells, including the massive Ghawar Field, are at the Eastern end. Most of this area has never been surveyed. There could easily be another few Ghawar Fields in there. (My source - the head of exploration of Saudi Aramco.)
The place where the peak oil doomsayers get the economics wrong is in forgetting the elasticity in recovery as the price varies. The simple models seems to assume that once peak oil is reached it is a single event, and once it has occurred the laws of supply and demand will drive a huge and irreversible rise in prices. But as pointed out above, this isn’t what happens. If the price rises, more oil becomes economically recoverable. We will still run out, and it may be that peak oil is reached, but you will be hard pressed to nail down the date it happens. The term “peak oil” seems to imply a summit. The reality is that we will have a very slow slope, with a few wiggles as different technologies affect the market, and it will be very very difficult to identify a peak. It will still be there. And in hindsight analysis might be able to come up with an estimate of its location. What we are not going to see is a situation where we reach a peak production and wake up the next day to see oil prices have tripled and still rising. That only happens when external forces such as massive speculation drives the market in unintelligent ways. A lot poeple made a lot of money speculating on oil prices. Even more people lost even more money. Many were the same people.
A single well in the Gulf of Mexico costs about $100 million to drill. And there is a lot of oil to be found if you are prepared to go to these lengths.