[khebab]

A lot of very interesting comments! thanks!

$this->bbcode_second_pass_quote('WebHubbleTelescope', 'I') checked on the Ricatti. It looks like you did an excellent job reproducing the math in some of your supporting posts. Weird how the URR seems really low (~1600) which causes the curve to do a nose-dive between 2010-2030. However, if you push up the URR to 2500, the curve flips upward crazily. You said something about adding another control function to suppress this, but this non-linear stuff sometimes has a mind of its own.

[WebHubbleTelescope]

Khebab's posting of the ASPO discovery curve got me motivated to try an experiment.

Looking at what EnergySpin wrote on Compartmental analysis explains the tact I took on the experiment. I added 3 latencies corresponding to (1) a "fallow" period (2) a "construction" period and (3) a "maturation" period to get the ASPO data shifted enough on the time scale to make sense. This essentially provided a good "active" discovery window that matched my previous triangular and Welch forcing function.

Everything lines up (oil shock perturbations included) if I choose 8-year average latencies for each phase, excepting for the initial ~15 year <i>1/e</i> extraction rate.


As usual, I included the explanation and source code here:
http://mobjectivist.blogspot.com/2005/1 ... -data.html

The fit scares me a bit, but the outcome scares me even more. Can we trust the ASPO data for estimated oil discoveries? Is it way underestimated? Or, are we cooked for sure?

[EnergySpin]

Lots of info here ....
I will try to provide input to a few issues but I feel we need to set up a timetable and a work - plan after we cool down
$this->bbcode_second_pass_quote('khebab', '
')We need to define what level of granularity (oil field or wells) is really necessary being careful to to go too low because reservoir modeling is a very very complex science! WHT used rather simple models which gave reasonnable results.

[EnergySpin]

$this->bbcode_second_pass_quote('WebHubbleTelescope', '
')
The fit scares me a bit, but the outcome scares me even more. Can we trust the ASPO data for estimated oil discoveries? Is it way underestimated? Or, are we cooked for sure?

[EnergySpin]

Let's play with the model a little bit to see if we can gain an understanding about North Sea or the Mexican fields.
As I said, contigent on the accuracy of the approximation ... sharp declines post peak do not show up when I explored the resulting curve with Mathematica (I admit that the exploration was limited though). So is there a mechanism that can account for such sharp drops?
One fairly obvious mechanism would be a change in the relative size of the V2 (which is the "mother" compartment feeding everything else) and V3 (a compartment that cannot be drained).
If somehow (?Earthquakes ) a volume of material was transferred from V2->V3, at the time the peak occured .... then the resulting drop post peak will be steeper than it would have been. Obviously this will lead to a reduction in the URR achieved. If such a mechanism were to operate in the ascent phase (i.e. pre-peak), then the most likely outcome would be an acute drop followed by a slow rise to a smaller peak.
Another mechanism would involve a reduction in the rate constant between V2 and V1 i.e. the "mother" compartment empties slowly in the smaller V1 compartment. If such a change were to happen at the peak, then the decline would be steep, and production would go to a lower value . If the change in this rate constant was such, that the inflow rate in V1 was much slower than the outflow rate i.e. k2 << k1 balancing the diffrence in size of the two compartments then extraction of the resource attains a plateau since dV1(t)/dt =0 =>V1(t) approx constant => P(t)=k1*V1(t) approx constant.
However both scenarios argue against a further sharp decline in the future .....A hypothetical discontinuity would have short-lived effects in the rate of decline.
Comments are welcome

[SilentE]

$this->bbcode_second_pass_quote('WebHubbleTelescope', '
')Everything lines up (oil shock perturbations included) if I choose 8-year average latencies for each phase, excepting for the initial ~15 year <i>1/e</i> extraction rate.


...

The fit scares me a bit, but the outcome scares me even more. Can we trust the ASPO data for estimated oil discoveries? Is it way underestimated? Or, are we cooked for sure?

[WebHubbleTelescope]

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.

[WebHubbleTelescope]

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.
$this->bbcode_second_pass_code('', 'ConstantRate(t) = ConventionalRate*(1-t/T) + NonconventionalRate*t/T') 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.

[WebHubbleTelescope]

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.

[EnergySpin]

$this->bbcode_second_pass_quote('WebHubbleTelescope', '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.

[EnergySpin]

$this->bbcode_second_pass_quote('ElijahJones', '
')The idea of estimating reserves from well data seems tricky. At best its an inverse problem that may not be well defined, so maybe you get a bounded parameter space instead of a crisp estimate. Use some simple interval arithmetic to get upper and lower bounds on reserves.

[WebHubbleTelescope]

$this->bbcode_second_pass_quote('ElijahJones', 'I')f you don't even know the standard deviation how can you judge your results, you need a standard error for confidence intervals?

[WebHubbleTelescope]

$this->bbcode_second_pass_quote('EnergySpin', '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.

[EnergySpin]

$this->bbcode_second_pass_quote('WebHubbleTelescope', '
')
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?

.

[Taskforce_Unity]

$this->bbcode_second_pass_quote('SilentE', '[')VERY GOOD QUESTION! I have no data on the distribution of the discovery for small fields (0-100 tbpd). Simmons is just saying that there are 4,000+ fields that have been discovered up to the year 2000 which are providing 53% of the world production!. That'it, that's all! In statistics, when we have no knowledge, you usually assume a uniform distribution which gives about 700 discoveries per decades. However, since discoveries have been declining since the 80s I assumed a uniform loss of 100 new fields per decades.

[EnergySpin]

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 ...

[Taskforce_Unity]

$this->bbcode_second_pass_quote('EnergySpin', 'S')o 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 ...

[EnergySpin]

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