Update [2006-1-21 2:25:16 by Stuart Staniford]: More graphs and a stability analysis added to the story below the fold.

Linearization of Kuwaiti oil production. Data source: American Petroleum Institute (via Jean Laherrere) and BP Statistical Review of World Energy . Click to enlarge.

For me, the reports that Kuwaiti reserves are much less than claimed are not news because they allege the Kuwaitis have been lying about their reserves. What is news is the new reported numbers for reserves. So would Hubbert linearization have given us the right answer?

According to Reuters , the Petroleum Intelligence Weekly story (itself behind a paywall) has these facts.

"PIW learns from sources that Kuwait's actual oil reserves, which are officially stated at around 99 billion barrels, or close to 10 percent of the global total, are a good deal lower, according to internal Kuwaiti records," the weekly PIW reported on Friday. It said that according to data circulated in Kuwait Oil Co (KOC), the upstream arm of state Kuwait Petroleum Corp, Kuwait's remaining proven and non-proven oil reserves are about 48 billion barrels. Officials from KOC were not immediately available for comment to Reuters. PIW said the official public Kuwaiti figures do not distinguish between proven, probable and possible reserves. But it said the data it had seen show that of the current remaining 48 billion barrels of proven and non-proven reserves, only about 24 billion barrels are so far fully proven -- 15 billion in its biggest oilfield Burgan.

I have personally never believed the publicly claimed numbers since the whole issue came to my attention. This graph just reeks:

History of OPEC claimed proved reserves. Source: BP Statistical Review of World Energy. Click to enlarge.

So, presumably the amount of oil left to pump, if PIW has the story straight, is somewhere north of 24gb, and perhaps south of 48gb. So what would our linearization have told us? I can't find that anyone did the exercise before, but I have production data from BP, and Jean Laherrere recently very kindly supplied me with a bunch of early data from an American Petroleum Institute study in 1958 (centennial year of US oil production). The production graphs looks like this:

History of Kuwaiti oil production. Data source: American Petroleum Institute (via Jean Laherrere) and BP Statistical Review of World Energy. Missing years have been linearly interpolated. Click to enlarge.

I have had to interpolate between 1958 and 1965, but it looks like that won't be too much in error. Note that the mathematical form of this data is a little more complex than either a logistic or a Gaussian :-). However, if we press boldly ahead on the theory that the linearization procedure is a robust if rough estimator even when the data sucks, we get:

Linearization of Kuwaiti oil production. Data source: American Petroleum Institute (via Jean Laherrere) and BP Statistical Review of World Energy. Line is fitted to data in purple only. Click to enlarge.

The straight line is fit to the purple data only, which is the nearest thing to a linear regime in this mess. Amazingly, the intercept is at 76gb. Given that current cumulative production is 36gb, this suggest there is 40gb to go. So this is in decent general agreement with the (24gb,48gb) range from the internally leaked information that Petroleum Intelligence Weekly has gotten hold of.

That suggests Kuwait is at 47% of their ultimate recovery - so close to the half-way point. Future declines are projected to be modest based on the K of just over 4%.

Finally, just to remind you of the implications for Saudi Arabia:

Hubbert Linearization of Saudi Oil Production. Credit Jean Laherrere. Click to enlarge.

If the same procedure works, they have produced 105gb out of 180gb or so, and are at around 55%-60% of their ultimate recovery. Note however that the K is higher at around 7%, suggesting significant declines ahead.

Update [2006-1-21 2:25:16 by Stuart Staniford]:

In comments, there was some discussion of the recent uptick in Kuwaiti production visible in the linearization. Here it is - this next graph is the monthly Kuwaiti production according to the EIA Table 1.1a

Monthly Kuwaiti oil production from January 2001 to October 2005. Data source: EIA Table 1.1a.

It doesn't look like that graph has finished increasing, despite the reports of near-term decline fears at Burgan. However, if we look at the percentage increase from the same month one year ago, we see the rate of increase is slowing down (roughly).

Year-on-year increase in Kuwaiti oil production for each month from January 2002 to October 2005. Data source: EIA Table 1.1a.

Update [2006-1-21 2:25:16 by Stuart Staniford]:

Don't read this next part unless you like highly technical discussions.

It should be obvious that in the linearization, taking a great big leaping extrapolation off that little linear area has got to be a rough approximation at best. Stability analysis confirms that. Probably the linearization estimate of URR is only good to a factor of 2 or so (with probably a larger error bar on the downside than the upside). K is maybe uncertain by 50%.

Recall that we developed an error estimation methodology for Hubbert linearization based on varying the start and end years of fitting the line and seeing how much the estimate changed. If it's very sensitive to the choice of years, then one has correspondingly less confidence in the extrapolation. This allowed us to place reasonable error bars on the US production (which is quite a mature area). Kuwait is much less certain, since it is less mature, and has had very large production variations for non-geological reasons.

Anyway, here's the stability surface, or perhaps instability surface would be a better term, for K:

Hubbert linearization estimate of Kuwait's K (y-axis intercept which controls speed of decline) as a function of start year and end year of fit. Click to enlarge.

The same thing as a density plot:

Hubbert linearization estimate of Kuwait's K (y-axis intercept which controls speed of decline) as a function of start year and end year of fit. This is a density plot from 0 to 10%, with 100 contours. Blue is zero, red is 10% or above, green is 5%. Click to enlarge.

Surface of the ultimate recovery estimate. Note that without the recent increase in production, we'd be estimating lower.

Hubbert linearization estimate of Kuwait's URR (eventual total recovery of oil in gb) as a function of start year and end year of fit. Click to enlarge.

The same thing as a density plot.