Good match! Very interesting...

A few questions:

1. Is that a "backdated" discovery datebase from ASPO? Cause that's a potential source of error - it would systematically undercount more recent discoveries.

2. What kind of average is the 36 year off-set for production based on - is it weighted? I know there always appears to be a lag, but the size of the lag varies substantially, and the times to develop non-OPEC fields can vary a great dael - and may be decreasing on average. Also, OPEC producers aren't even trying to maximize production. But doesn't a production-lag model (however long it is) assume that they will do so? If nothing else, there reserve-production ratios a likely to be much lower than for non-OPEC. As the market share of OPEC rises, that effect will become stronger.

3. The projection for future discoveries looks a little low. The extrapolation line seems to come off the troughs in discovery, instead of a mean value between the troughs and peaks. It looks like the problem is that the extrapolation comes off a three-year moving average, the last value of which happens to be centered in a discovery trough (coincidentally missing the higher discovery rates of 2000-2001).

4. I'm skeptical because as soon as the historical data run out, the model takes the curve in a totally different direction. The fact that your model seems to be swamping the data - and is even in disagreement with the most pessismistic recent estimates from Campbell - is suspicious.

5. The older post mentions four pre-2000 shocks: 1973, 1979, 1984, and 1991. Which did you drop? And while 1973 and 1979 are obvious, the effects of the Gulf war were more transient, and the 1984 "end of recession" seems truly odd. The recession ended in 1982 - it lasted 3 quarters. What about the 1981 decision to end US domestic price controls (which had strangled domestic E&P), or the 1985 Saudi decision to abandon high prices and finally open their taps?

6. An unexplained fifth "reverse shock" has been added in 2001. Why? What does it represent?

The "reverse" shock is actually a sudden increase in extraction rate in the last few years.

And as Khebab has pointed out, the ASPO data only shows conventional oil strikes and the BP data shows all production sources. Which means this curve will extend a few more years beyond that shown, if I go back and make a deeper suppressive shock in the late 70's.


Eyeballing the area under the curves, it will extend the peak onset by a few more years. But then again, the ASPO data are estimates of discovery and could be high or low.

Given the fit to the curve was so good assuming that conventional sources matched all sources, this indicates that the extraction rate of conventional sources likely decreased linearly over the last 30 years with the linearly increasing non-conventional sources making up the gap in demand.
where t=time from when we started using nonconventional sources, and the rate is defined as proportion extracted of reservoir volume per year. I would consider this an economic argument governing substitutability of resources. The invisible hand of the oil industry at work trying to extend the plateau, so to speak.

If I stick in a suppressive extraction rate that decreased linearly by about 15% between 1974 and 1991, it gives a good eyeball match if you imagine the conventional source curve hovering below that of all sources.


As you can see, this extends the peak to 2008. Yes, about three more years due to the use of non-conventional sources. Whew! Now we can rest easy.

A groundwater class, eh?

I took a college class in limnology once. I learned that eventually all lakes will eventually fill up completely with muck.

My answer to everything is "I don't know anything but the mean". So for all the information you desire with respect to specific oil field characteristics, such as porocity, etc., I suggest we replace it with some empirically observed macro parameters. For example, humans are greedy creatures; they will extract an amount proportional to the amount of resources available. If you have a big oil field, they will extract at a high rate. If you have a small oil field, they extract correspondingly less. We don't know the exceptions to this rule (such as Ghawar probably didn't get extracted at that high a rate), therefore we can say absolutely nothing about the standard deviation. Like I said, lacking all available information, use the mean. Convolve enough of these means together, and we can approach a kind of central limit theorem for the production curves.

On another level, I think all I want to achieve with this exercise is to replace the logistic curve (i.e. the Hubbert curve) with something that reaches a canonical level of representation. My intuition tells me that knowing the details in oil extraction won't help in any of this. If you want to try it, go ahead, but for me, a simple model with some effective data regression techniques will hopefully take us beyond the logistic curve.

Keep it to the basics ... A well is draining a relative small area of the reservoir which is much larger. The rest of the reservoir exchanges matter with the area near the well. A two compartment approximation (i.e. 2 exponential terms) could provide a pretty good approximation for our purposes. Deffeyes is assuming a decline/ascent proportional to the amount of the oil still left in the ground (which gives you a uni-exponential curve). Problem with Deffeyes is that a uni-exponential curve has no maxima but at the beginning ... so he must be relying on a combo of logistic+exponential decay post peak.
However at least in his model , there are parameters with definite physical interpretation and not mambo-jambo stuff like the Ropper/logistic/Verhulst approximation.

I have to disagree WHT , if one had detailed mathematical models of matter fluxes inside an oil field one could derive macroscopic approximations via means of Neural Networks and use them in "macroscopic" applications for prediction. In fact there is a fair number of consulting companies which do this kind of work for the industry.
ElijahJones the model you are proposing (or something similar) is applied in convex hull/finite volume models of reservoirs ... problem is you need 3 detailed and different sets of data and a cluster to get results out of it. We neither have the data nor the computing power ... so realism suggests we stick to approximate models that can be fitted using production data only.

Point A: correct . I was thinking more of a Bayesian type of solution that bounds the estimate.
Point b: Good luck with your thesis . I finished mine before I found po.com!
Take care

Isn't this one of the lessons from information theory and maximum entropy principles? All the parameters that I incorporate into my model which happen to use the mean of some observable, have a standard deviation which equals the mean. That happens to give you the exponential function. In general, it is a safe bet that works for all kinds of analyses where you need to maximize the uncertainty because of a lack of complete information.

I suppose the confidence intervals in the solution space can be determined by systematically varying the means of the parameters. That sounds like a good idea and would both provide a good way to do data regression and get the sensitivity error bars at the same time.

So then I would suggest we have two classifications for the means. The first class comes about from estimates provided from industry experts and historical data. Such as:
How long does a discovery lay fallow on average before the decision to extract?
How long on average does it take to build a production rig?
How long on average before the rig is pumping to maturity?

The second class comes about from the NN "helper" applications that fuse the available information. These can solidify the assumptions that I have been making. Such as:
Is the rate of extraction proportional to that remaining in the reservoir?

And then we have the complete unknowns, such as how much is actually still underneath the ground?

Agreed that people do this kind of work in the industry. But "consulting companies" = "proprietary knowledge", and I thought that is why we are doing this here -- to let the amateurs finally get a chance to unlock the secrets. The cathedral versus the bazaar. That is partly what facinates me about this work.

As I said in a previous post we should try to decompose it in three or 4 different modelling exercises and then fuse them together.
Let's start with what I call macroscopic reservoir modelling:
The simple conceptual model of oil production in a space with a hole : the fluxes of material from the reservoir to the outside world is then (at first approximation) proportional to the amount that is still remaining:
Conservation of mass requires that the rate of decline in the material = rate of production, hence:
P(t) = dV/dt = -K*V(t)
Integration gives us: V(t)=Vo*exp(-k*t)
Notice two things about this :
a) the production attains a maximum at the beginning i.e. P(t) = k*Vo*exp(-k*t) and there is no "peak".
b) the constant k mixes both geologic factors AND economical factors with no clear way of separation among the two
Therefore a simple exponential curve does not reproduce the phenomenon .
The second approach conceptualises the oil field as two separate compartments:
One (small) compartment around the well and another one communicating with the rest of the reservoir (i.e. ? source rock)
The rate of transfer from the big compartment to the small one is driven by "geology" (porosity and all that), the second rate by the people operating the pumps. In this model there is a clear separation between geology, economy and the volumes of material that can be extracted appears as a parameter to be estimated from production data.
Material fluxes modelling in these complex systems (i.e. from BIG to small reservoir) need an accurate understanding of the specifics of the oil field, however a first approximation would be to treat those as constants.
The mathematical basis of this assumption is also sound in the following sense:
If the rate of transfer of material from BIG->small is an unknwon function, of time one can always expand it in Taylor series (contigent upon certain continuity assumptions) and keep only the first, second etc terms.
At first approximation only the first term is important and one ends up getting the formulas I analysed in a previous post in this thread.
If one has access to production data from period where the oil field was pumped at a stable manner (i.e. the rate constant describing the transfer from the small compartment to the real world was fixed) then one could use these data to obtain estimates (in the Bayesian sense) of the both geological parameters (Vo, rate of transfer BIG->small). Then at latter times he could use these probabilities to find out whether changes in the administration of field occured. Again this is only possible with the Bayesian perspective.
This is the way we use mathematics to arrive at dosage regimes of medications for example i.e. estimate the volumes that a drug is distributed or to time the administration of antidotes in case of poisoning by taking measurements (think of them as production data) and plugging them to equations. The principles are the same!
By the way, have you checked your PMs? I sent you a message about reservoir modelling and estimation via such linear transfer models

Here is a graph from IHS Energy about the distribution of oil discoveries



This comes from this presentation

Global Oil Supply Issues: Recent Trends and Future Possibilities

As to the timedate of these discoveries.. i have no data.

As for American info i suggest this website:

Michigan oil field data

I am willing to copy data into a spreadsheet to save you guys some time(whatever program you would like, ill download it )

My dad might also be willing to help. He is pensionated now and has a full life of mathematical (and statistical history) at three Dutch Universities. Ill try to summarize what's in this thread for him and ask him to take a look at it. Hopefully he can give some comments/directions.

As to data access, i only can look into public data. The exception to this are journals (through my university) like this one: Quarterly oil supply OECD

Another suggestions of mine is to involve the people from the oildrum in this project. They know a lot of things and are great analysts.

So do you have the data in the forrm of oil field volume, size (i.e. area in square meters etc) and counts?
That would be helpful. Excel would do fine ...

pfft no data publicly available that i know off.

At the DTI UK oil & gas database you can get the numbers of OIIP, recoverable reserves, Cumulative production, Water injection per well, oil production per well, wellhead pressure, days on production, field depth. Oil production and so on.

However i cannot find size (area in square meters) and i don't know what you mean with counts.

DTI data

Just specify what you would like to have in your spreadsheet, ill try to spend some time on it.

Another suggestion of mine is to meet on team/peak speak. Might be helpful to make some agreements on who does what in a easy manner.

Im now going to bed, ill try to find specific field by field data on size, production, wells tomorrow.

Yes we will do that tomorrow. It is getting late here and I am hunting on literature for a paper.
I ey balled DTI. Very interesting ... the production profile of those fields does not really much the Michigan fields you sent me.
There is greater heterogeneity in the upslope part of the production of North Sea oil fields, but once decline starts it seems to proceed at an exponential decline (fast initially, slower then) .
US fields peaked rapidly (within a couple of years from the day they were first drilled) and tapered of slowly. Peak date was at less than 50% of the URR .... typically at 30-40s. This is the only feature that is shared between the two areas.

I wonder whether the fields in North Sea were fragmented or somehow "different" than the US fields.
I will try some bi-exponential fittings at the Michigan oil fields .... and report back. But modelling North Sea is going to be a bitch .... it is as if people were simultaneously draining more than one compartments. Once the smaller ones went out ... production is sustained by a core compartment which now falls according to the US experience.
But at least for the North Sea ... I find it difficult to believe that a nice clean "Hubbert" curve can yield results. But of course I just started playing with the data