Convergence of the sum of many oil field productions

khebab · Moderator Joined: Sep 27, 2004 Posts: 935 Location: Canada

I explored a little bit the model by gradually increasing the level of randomness in the different variables.

Case 1: trivial case

All fields are identicals in shape (Isoscele triangles) and surface (slope= 5% and URR= 15), only the starting year is a gaussian N(11, 4.33). This ideal case stricly verifies the conditions of the Central Limit Theorem (see Illustration of the central limit theorem). ).

The resulting curve is fairly gaussian with maybe heavier tails. Also, the skewness value is decreasing with the number of points in the simulation (see figure in the lower left corner).

Case 2: shape fixed, URR gaussian

The URR is distributed according to a gaussian N(15, 2.89)

Parameters distributions: from left to right and top to bottom: field upslope distribution (in %), URR distribution (log-log representation), field starting year and peak year distribution.

Case 3: Isoscele triangles with a gaussian slope, URR gaussian

same as case 2 but we randomly choose the triangle slopes N(8.5, 2.31) (in %). The right tail is getting heavier and the skewness has increased.

Case 4: random triangles with gaussian slopes, URR gaussian

Not much difference with case 3 but the skewness value has decreased.

Case 5: random triangles with gaussian slopes, URR gaussian but big field produced first

Because big fields have a higher discovery cross-section and are economically more valuable, there is a good chance that they will be produced first and conversly the small fields will be produced last. Same as case 4 but we rank fields according to their size and the biggest are produced first. It has a good influence on the result where the production is much more gaussian especially in the tails.

Case 6: random triangles with gaussian slopes, URR lognormal but big field produced first

The distribution of the URR values is clearly not normal and is probably more like a lognormal distribution where big fields have a very low probably of occurence. The lognormal model is the same that have been used in a previous thread (A Statistical Model for the Simulation of Oil Production). Curiously, the impact of this modification is not very strong and the curve is just slightly more skewed.

Some conclusions

1- the production profile is well modeled by a gaussian when most of the underlying parameters are also gaussian distributed.
2- the logistic model do not seem to be a particularly better model especially for the tails
3- the distribution of the URR values do not seem to have a big impact on the resulting curve
4- when fields are produced by order of size, the production curve is getting more gaussian.
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pup55 · Expert Joined: May 26, 2004 Posts: 3692

All I can think of is that there is no compelling reason to believe that the shape of the distribution would be a lot different if n=15000 or n=20,000.

In other words, you have selected a sufficiently large number for N that within this order of magnitude, the shape of the sum of the curves will start to take on the shape of the individual curves (in this case, gaussian) pretty much no matter what.

I am thinking about the argument of new discoveries and /or reserves growth, and how the discovery of X number of new fields, including a number of super-giants, might influence the shape of the right hand side of the curve.

It looks as though even if X, the new fields, were large in number compared to the known existing fields (which for you is 10,000), the sumnation curve will be more or less the same shape unless the time distribution or the size distribution of the new discoveries is grossly different from the distribution of the currently known discoveries.

What I am saying is that it is possible to have new discoveries to avoid the problem of the right hand side of the curve. These discoveries would have to be sufficiently large and occur in a sufficiently different time sequence to substantially alter the curve shape. Per your post the other day, you might be able to estimate the probability of such an event happening. Example: The discovery of 10 more Ghawar-sized fields, at or about the present time, making the curve a lot broader and flatter than it is in the above examples. (example 6 might be the closest to this).

You would then be able to make a determination kind of like we were talking about the other day, such as that there is y probability that future discoveries would be sufficient to get us out of these problems.

Once you know what y is, no problem to have the conversation with Michael Lynch, who will tell you that we should go on living like we are because "we will probably discover sufficient oil to avoid any problems related to the peak", etc. etc.

JohnDenver · Light Sweet Crude Joined: Aug 29, 2004 Posts: 1866

khebab,
I know this is slightly off-topic from the issue you're considering, but I'll say it anyway. When I saw Stuart's recent Gaussian, which matches world production so beautifully over different orders of magnitude, the thing which intrigued me most was that it was made of linear segments whose slopes seem to be determined by economic/political factors, as Stuart pointed out.

This makes me think that the shape of the rising side of the Gaussian is determined by demand, not discovery/resources/geology. As a thought experiment, consider a parallel world where there is no constraint on the resource. In this world, there is a fortuitous discovery of a monstrous pool of oil which is (say) 500Gb in size, and is located on the surface like a lake. What would be the production curve in those circumstances? I think it's clear that production in this world will still be constrained -- not by the ability to mobilize supply, but rather by cartel activity which acts to prevent too much oil from flooding the market, thereby crashing prices and bankrupting all the players who invested in infrastructure prior to discovery of the lake.

Clearly, this effect has been a chronic, dominant feature of oil production on the rising side of the curve. The main goal of Rockefeller's strategy was to cartelize, and thereby constrain supply and stabilize prices. The same can be said for OPEC. So my theory is that the slope of the left side of the Gaussian is determined by cartel activity, which in turn is determined by demand/price. The lake will not be produced, even if it is discovered, because there is no way for the market to consume it. Producing it full-blast would be an act of suicide for the producer. It reminds me of something Mike Lynch said in his thread (I'm paraphrasing): predicting supply essentially boils down to predicting demand. I believe that is 100% true on the upside of the curve.

If I'm correct, it makes your question a lot more difficult to answer. Why should the rising and falling sides of the Gaussian be symmetric if the rising side is determined by economics while the falling side is determined by geology?

khebab · Moderator Joined: Sep 27, 2004 Posts: 935 Location: Canada

khebab · Moderator Joined: Sep 27, 2004 Posts: 935 Location: Canada

JohnDenver · Light Sweet Crude Joined: Aug 29, 2004 Posts: 1866

khebab · Moderator Joined: Sep 27, 2004 Posts: 935 Location: Canada

backstop

Khebab -

while parts of the math here go clear over my head, I'm interested to see the progress being made in the reliability of modelling the global supply curve.

I wonder if you'd consider providing, and updating, a "Current Best Estimate" of the decline rate you forsee, with of course such margin-of-uncertainty as you see fit ?

This would give some practical guidance on this critical issue. Of course if you were to say that there are simply too many unknowns (eg civil wars in major producers) I should quite accept that.

regards,

Backstop
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