I'm copying an entire essay taken from [http://ergobalance.blogspot.com/2007/10/hubbert-peak-oil.html] by Chris Rhodes. If he objects, I will remove it.
In 1956 a paper was published which will be of greater significance to the future of humankind than those reporting on the structure of DNA or the Theory of Relativity. Its title was "Nuclear Energy and the Fossil Fuels", and it was written and presented by M. King Hubbert at an oil-industry conference in Houston, Texas, while he was in the employ of the Shell Development Company. At first Hubbert was not taken seriously in his conclusions that the peak in oil production would follow the peak in oil discovery by about forty years, and so the best year for US oil output would be around 1965 - 1970, roughly 40 years after the most successful year of oil finds, in 1930. He was right, and thenceforth US home oil production has fallen to the extent that the nation now imports two thirds of all the oil it uses, a colossal 20 million or so barrels a day, or one quarter of the world's requirement of oil.
In days before computers, Hubbert would have drawn the graph by hand (probably with the aid of a flexy-curve, or simply freehand as I used to find best, before PC's were available routinely, and mathematical analysis packages such as the Origin programme, which is installed on this machine). The Hubbert peak is based on a logistic function, which is a restricted exponential, and the first derivative of it corresponds to a peak. The derivative of this (i.e. the second derivative of the logistic function) gives an inflexion, where the point at which the curve crosses the baseline corresponds to the peak maximum. The logistic function includes the familiar S-shaped curves that relate to the growth of bacteria and to enzyme kinetics such as those of Michaelis and Menton.
The Hubbert curve (peak) may be defined as:
Q(t) = Q(max)/(1 + ae^bt),
where Q(max) is the total recoverable amount of crude oil in the ground to start off with, Q(t) is the cumulative production (i.e. how much oil has been pulled out of the ground to date) and a and b are constants. Accordingly, the year of maximum production (peak oil) is given by:
t(max) = (1/b)ln(1/a),
and for the world altogether, with a peak discovery year of 1965, this appears as 2005. There is much speculation and analysis that oil production has already peaked, and it is my suggestion that enhanced recovery methods alone have maintained the present output of oil, much of it from the giant fields in the Middle East. It is obvious that the resource is concentrated in only a few particular regions of the Earth, vide supra, and also Russia, South America and Indonesia. Countries such as Iraq and Iran may become swing-producers, i.e. that produce more oil than they use, and I have read opinions to the effect that the Iraq war if not started in the interests of obtaining oil for the West, might become a worthy swing-producer, thus averting economic starvation at least for a few years. Iraq has about 140 billion barrels of oil, and Iran about the same, and so at a level consumption of 30 billion barrels a year for the world in total, we might get almost 10 years worth of supply from there. It is significant that Western companies such as BP and ExxonMobil have been granted 30 year contracts to exploit the Iraqi oil.
Not everybody agrees with the Hubbert analysis and some argue that we will be able to access around four times as much oil as there is present under the Earth in the form of crude-oil, by which they mean the Canadian tar-sands, oil shale, oil made from coal or from gas, biomass and so on. However, this does Hubbert a considerable disservice because he was talking explicitly about cheap oil, and it is this that will inexorably run out, most likely during the next 5 - 10 years. Hence there is no consolation to be found in any putative 3.7 trillion barrels of oil figure, because bringing that into reality will be extremely expensive both financially (to take an economist's standpoint) and more precisely in terms of the energy and other resources such as water that are mandatory in those actions necessary to do so.
We are not about to run out of oil. We will be able to produce hydrocarbons (oil) for decades to come, but not at the cheap prices we are used to. I am working on a rough figure of assuming that everything (and I mean everything - food, clothes, and all else) will cost about twice what it does now in that 5 - 10 year period. That would correspond to a $200 barrel. This will be uncomfortable especially for those who already bear considerable debts, particularly in the UK, which is the most indebted nation in Europe. We also drink more than anyone else apparently, and have a greater incidence of sexually transmitted diseases, which makes me think that the era of the "stiff upper lip" has rather passed for the English. Many of these problems may well be "cured" by a huge hiking-up of general costs in terms of booze, travel and the overused "plastic friend" - the credit card which often proves less than amicable.
Another feature of Britain is that we have "lost" most of our manufacturing industry, and so we buy cheap imports from e.g. China and therefore fuel the economic enterprise of that nation. Without imports to the West of washing machines, TV's and so on, the Chinese economy will grind onto the hard shoulder, and our own economy, based as it is around the "service sector" will crash too meaning that less service-businesses will survive if people have less cash in their pockets to buy their services, and an according loss of jobs in that industry.
The mathematics of Hubbert's theory is very interesting but as I have pointed out before, there were only so many squares on that sheet of graph paper in reflection that there is only so much cheap oil that can be drawn up from the Earth, [i.e. Q(max) in the above equation], hence no matter what values we chose for the constants (a) and (b) or whether we use a Gaussian or Lorenzian distribution or some other mathematical device, the future of humanity will unfold, in ways that will be only evident to later history, upon a world devoid of cheap oil, and to kid ourselves otherwise is an act of addicted denial. We need to plan a society based on localised communities and less dependent on apparently limitless cheap transport, and cheap products made from oil.
(3) "The Hubbert Curve: Its strengths and weaknesses" By, J.H.Laherrere: http://dieoff.org/page191.ht,m
(4) "Hubbert's Peak - the mathematics behind it", By Luis de Sousa: http://wolf.readinglitho.co.uk/hubbertmaths