It's a simple model, I know, but sometimes simplicity is best when capturing the essence of price behavior.

If you look at the historical chart for oil prices you'll find that they went down exponentially for most of the twentieth century, ignoring price spikes like the Iran Crisis and the like. This agrees with the last model, where pop growth < oil extraction, which suggests that the price of oil will skyrocket in the coming decades, ignoring price spikes and collapses, of course.

Check the Verhulst thread .. we have done the exercise
How did you do the fitting with Mathematica?
I used Mathematica for the same application (- humans) ... hope you understand Nonlinear regression

Yeah Mathematica is awesome wrt statistical curve fitting. I used it on historical prices to find the correct logistic model (exponential decline followed by skyrocketing prices) which I obtained by graphing a simple division:

Plot[PDF[LogisticDistribution[humanpeak,humancoeff],t]/PDF[LogisticDistribution[oilpeak,oilcoeff],t],{t,tmin,tmax}]

The humanpeak, humancoeff, oilpeak, oilcoeff parameters were found using a nonlinear fit on historical data. The tmin and tmax parameters are of your choosing. Happy datamining!

Be careful with the Levenberg Marquadt and check the curvature measures of nonlinearity. Curve fitting these equations can be bitch

Are you talking about skewness? (∫(x-m)^3 f(x)dx)

Nope ... the Verhulst or logistic growth equation estimation problem is extremely difficult if one does not have data after or at least after the peak. I'm not talking about the moment of the distribution, but about the subtleties of fitting nastily behaved curves ...
Link to curtosis (the measure suggested by Ratwovski is http://old-www.math.luc.edu/~tobrien/research/HOC.pdf)

What data? What source? What reliability? What effect does changing
technology have in the data? Can that even be modelled?

Data = crap
Source = sucks
Which means one has to rely on smoothing (at least that's what I did) of the production from BP review.
Changing technology is very interesting ... if one believes Simmons, it will not alter the URR . At first approximation (a very first approx) one may use the logistic growth understanding that the extraction rate will be an average.
But even when one uses simulated dataset, depletion of a resource following the curve is an absolute nightmare. Hence the various contradictory claims. Let the algorithm run one extra iteration and a whone new universe is revelaed before your eyes. So the solution is to assume that peak is about to happen and change lifestyle at the individual / societal level. With any luck the real peak will be in 2013 (as the French suggest) and not in 2006.
For the record I believe the peak will be between 2007-20010

It sounds like you're curve fitting, not modeling. If you were proposing a model then you would be discussing the complex interactions between the price of oil, supply, demand and the economy.

Since extrapolating without a sound understanding of the underlying mechanisms is an inherently dangerous thing to do I rather think the curve fitting exercise is pretty bogus. Just my opinion, but go ahead have fun.

Interesting, hats off to you for attempting some mathematical model.

At this point though I do not think population is a key factor pre peak for determining oil price. Consumption rate per capita is the key one. Rate of growth of consumption by nation could be calculated from the EIA spreadsheets. For pre-peak make an assumption that supply has peaked or has 1-2Mbbl more capacity.

Post peak there just isn't enough data to predict price. Also there are so many geopolitical and economic factors that will come into play that it will be just a guess.

i.e. Consumption approx numbers based on EIA spreadsheets (2005 Q1 numbers)
China - 1 bbl of oil services 150 people/day
UK - 1 bbl of oil services 44 people/day
U.S. - 1 bbl of oil services 15 people/day

My non-mathematical take...

Pre-peak prediction:
If demand ~ supply before peak oil... assuming supply does not drop of a cliff due to extraction or refining issues or peak oil realization...
1. Oil price will steadily rise as demand ~ supply. (here now)
2.There will be price spikes due to supply issues (refining or extraction) that will force short-term conservation. (yet to experience conservation)
3. After enough price spikes consumption rates will adjust as people/governments react with longer term conservation strategies; personel conservation, government rationing (in some nations).
4. Wealthier nations will still be able to maintain consumption rates (albeit less than Q1 2005 type numbers) iff global economy remains robust. i.e. will the stock market fall off a cliff? will the U.S. dollar dive?

Post Peak Realization
Peak oil realization is a recognition that pure production is shrinking. Pre-peak conservation may ease the coming oil price spike but there will be a spike here. This is the point of global economic woes.
- Massive potential drop in demand may be offset by massive panic to secure remaining oil OR drop in demand brings prices down temporarily thereby giving us a temporal pre-peak feeling for nations that can afford the new price levels.
- global economic fallout is eventual

I used the Mathematica packages to fit oil prices, and used the standard logistic fits for population growth and oil consumption.

Now, I will make the prediction that oil prices will trend ever upwards, with greater volatility than has yet been seen (this, unfortunately, gives little market signal in the volatile noise.) This seems to agree with my last model, the J-shaped curve.

Good luck world!

This may be something of a moot/minor point, but everytime I read that while Hubbert was proven right about the US peak, but he was 'wrong' about the global peak (as in today's Trumpet), I can't help but think it. It seems pretty clear to me that the only reason he was 'wrong' about the global peak is that he didn't forsee the demand destruction caused by the OPEC embargo and Iranian supply crunch, both of which were of course political 'peaks' of a sort. If you extrapolate the upslope of Hubbert's curve absent the substantial dip caused by these political disruptions, we'd likely already be past peak - and having to live in the world we all see coming. Again, it may be a minor point, but to me, it gives Hubbert and his theory even more credibility than it already has, and might help in convincing a few more of the optimists, and maybe even some of the sheeple.

Yup, people believe what they want. Even people on this forum who understand the ramifications of peak oil still differ on what the response will be. Then when people disagree with them they throw insults (like it matters).

But hey, we're only human.

Shorter clifman:

Hubbert's theory is perfect when we ignore politics, economics, technology, statistics, and price. If there is a discrepancy between theory and reality, reality is wrong. Facts which tend to disprove a theory actually prove the theory.

Not quite, see Jean Laherrere's ASPO Lisbon presentation. Hubbert's world peak prediction was well wide of the mark, his peak rate projection was about half of the current value.