[khebab]

$this->bbcode_second_pass_quote('EnviroEngr', 'L')et me know if tables, graphs, source-code spreads, etc. need formatted display here. There might be a couple options in phpBB that allow things we haven't tried before.

[khebab]

$this->bbcode_second_pass_quote('rockdoc123', '')$this->bbcode_second_pass_quote('', 'I')'ve seen a couple of mentions that field size has a Zipf distribution. FWIW...

[khebab]

Here the corresponding bar chart (without the small fields):


Figure 8

[WebHubbleTelescope]

$this->bbcode_second_pass_quote('EnergySpin', '')$this->bbcode_second_pass_quote('rockdoc123', 'E')nergySpin
I agree with your comment regarding the need to look at this with a stochastic view. I've actually played around with simpler models than Khebab used here...generally just for one or two pools. My assumptions are more general (assume peak production after 1 year ramp up...peak at 10% of URR...held for 2 - 5 years depending on field size and then declined at 10% /annum) but are what we normally use as first approximations. Usually I put in lognormal distributions for reserves and other assumptions regarding production/depletion. I've been using Crystal Ball in Excel but also have @Risk on my laptop. Pup55 sent me his Saudi depletion profile in excel format quite awhile ago and I have been meaning to fiddle around with that in Crystal Ball...unfortunately there are more things I would like to do than I have time for.
To my mind this whole discussion around Peak Oil could benefit greatly from discussing both reserves and production/depletion and demand from a stochastic viewpoint.

[SilentE]

$this->bbcode_second_pass_quote('EnergySpin', 'K')hebab opened a can of worms .... it will be interesting as hell
....
Maybe it is time to turn this into a real community project.

[SilentE]

$this->bbcode_second_pass_quote('khebab', '
')I finally found some info in Simmons's book in the appendix B (p. 374 and 375):
$this->bbcode_second_pass_code('', '
[i]volume and production in mb and mbpd[/i]
Field Size No of Tot.
(production vol.) fields Prod <1950 50s 60s 70s 80s 90s
1,000+ 4 8,000 2 1 0 1 0 0
500-1,000 10 5,900 2 3 3 1 1 0
300-500 12 4,100 3 1 6 1 1 0
200-300 29 6,450 8 4 6 9 1 1
100-200 61 7,900 5 8 13 13 11 11
0-100 4,000+ 36,200 ? ? ? ? ? ?
Total 61 32,350 20 17 28 25 14 12
')
the last line is taken from Figure B.1 p. 374 but there are no information on the time of discovery distribution. The production figures are for 2000.

[Taskforce_Unity]

Here's some thoughts from someone who doesn't understand half the words in this thread .

Are you guys intending to do a special statistical method for calculating the production increase and subsequent decline of fields with EOR techniques and waterflooding (based on fields that show this trend?)

If you need a data gatherer i am willing to spend some hours looking for production data.

[khebab]

$this->bbcode_second_pass_quote('SilentE', 'O')ne suggestion: if you present results, make sure you specify what type of numbers you're using: conventional only, "all liquids", future non-conventional, which types, etc...

[WebHubbleTelescope]

$this->bbcode_second_pass_quote('khebab', '
')That's the big challenge! how to include price fluctuations in a depletion model! the first to have proposed something is Guseo with the GBM model (Peak prediction based on the Riccati equation: 2007!).

[pup55]

the 4039 curve (red line) is a plausible scenario if you believe the US-EIA and others who predict demand will continue to grow at a current rate, and we have the reserves to pump.

But, do you really want to be around between 2030 and 2040? The backside of this curve will be really painful.

[pup55]

$this->bbcode_second_pass_quote('', 'u')sually assume a uniform distribution which gives about 700 discoveries per decades

[rockdoc123]

Pup55...this is a worthwhile endeavour. One of the challenges is that you need to treat exploration risk in any given basin as semi-dependant (your first discovery will lower the risk on subsequent discoveries) and between basins as independant. Rather than go into a huge discussion on probability and bore everyone with the formulas there is a really good reference book out there
Decision Analysis for Petroleum Exploration, 1975, Newendorp, Planning Press, Colorado, 668 pp.
This is a classic study in Bayesian logic applied to oil and gas problems, the chapter titled "Probabilities of Outcomes of Multiwell Drilling Programs" addresses some of the issues you probably need to think about when simulating..starts on page 327.
If memory serves me correctly IHS as information on statistical success rates in various basins which might also be useful as a model.

[SilentE]

$this->bbcode_second_pass_quote('khebab', '
')That's the big challenge! how to include price fluctuations in a depletion model! the first to have proposed something is Guseo with the GBM model (Peak prediction based on the Riccati equation: 2007!).

[SilentE]

WHT's work at Mobjectivist offers a constant-price Hubbert model, but derived from something other than the logistic model. It shows that although Hubbert got the mathematical basis for the curve wrong, he was right about the shape and its implications. And in the constant price environment of 1955-1970, Hubbert was near-dead on.

Although there were important external political factors that Hubbert could not predict (e.g., the Tex RR Comm), it seems to me that those factors were operating to Hubbert's benefit because they were operating to maintain a constant price. Hubbert's luck originates from the fact that the constant-price environment his theory required (an assumption of which he was unaware) persisted because of political interference until his peak prediction occured.

That means that a single WHT-Hubbert curve will only fit in a constant-price domain. It follows that the linearized derivative of the WH curve will also only give you a straight line to an accurate URR in a constant-price domain. When prices shift, URR shifts too! But that's sort of obvious: if you are estimating URR based on past production only in a constant-price domain, you are making the assumption that prices will not change. If prices change, more oil becomes "economical" to produce, so URR increases.

We can check this by examining a second period of roughly constant real prices: 1986-2000. Did production follow your curve? If so, then we can perhaps estimate part of the relationship - we know the factor by which prices rose, so perhaps we could link price increases to shifts in the curve?

It'll have to boil down to price elasticities of demand, both short and long term, and price elasticities of supply - new discoveries or "reserve growth". There's also going to be a technology factor, but from what I've seen it would be small. Y.H. Farzin (2000) provides some diretion here. http://papers.ssrn.com/sol3/papers.cfm? ... _id=246686

[EnergySpin]

Guys lots of info and suggestions in this thread ....
Lets try and settle the issues here , cause we can really make a much better job than other people who might have vested interests.
1) Regarding my suggestion to turn this into a community project. Which is the instrument that we should use? I liked the idea about sourceforge.net but at the same time, politeness mandates that we should not shoot down PO.COM by moving this intitiative elsewhere. After all , it is this site that got us together. So if our moderators can help us with formated displays and graphs we should continue posting here. Source code will have to be distributed somehow ; if this is not feasible through this web site, then by all means lets open a sourceforge project but we should be crossposting here as well. In addition maybe WHT could use his blog to cross post and TF_U use peakoil.nl to post PDF's as they are produced. This would ensure that the project attains the highest possible visibility.
2) Presentation of results : This is contigent upon a) the ability of our hosts to display graphical information and images and XML code. I have no way of posting in my department's web or ftp site and have IMG links pointing to those images. If someone else has this ability or maintains a blog, we could post there and cross link here, but it might also be easy to directly upload images. However this is a site administration issue so if Aaron or one of the other admins could let us know that would be great!!!!
If formulas have to be given we could use MathML (http://www.w3.org/Math/) ; Firefox directly presents equations written in MathML but IE needs a plugin like MathPlayer (available for free from Design Science : http://www.dessci.com/en/products/mathplayer/) . I could do all the rendering in MathML via Mathematica , but I have to know whether code posted in XML is rendered properly.
By the way there are many open source/free MathML WYSIWYG editors like MathCast (http://mathcast.sourceforge.net/home.html) so we are not limited to the big bad wolf from WRI.
Maybe one of the site administrators can answer the following question: can one post XML application code and have this displayed properly, or is this feature not implemented/disabled for security reasons?
4) Agenda for the community project. If we decide to go on with this, we should agree on what we try to accomplish. It is fairly obvious that the people who might be contributing are of different backgrounds, cultures-countries, have different political beliefs etc. It is important to realise that and try and mininize the potential of conflict by establishing and sticking to an agenda which deals with facts and predictions and nothing else. So I could be very happily co-exist with an Earth Firster and a Carbon Industry person in trying to estimate hydrocarbon production till they start to use the project to push a particular agenda. Using the project results is a different story though ... one is free to use them anyway he wants to, as long as he or she keeps the biases away while working on the project. Forgive the lenthy intro, but it is important to realise the truth in SilentE's statement found here:
$this->bbcode_second_pass_quote('', '
')Note to the unwary: under NO circumstances should you confuse friend-of-the-White-House Matt Simmons with LATOC-paranoid Matt Savinar.

[rockdoc123]

$this->bbcode_second_pass_quote('', 'M')odelling oil reservoir discovery = EXPLORATION. I found particularly enlightening the comments that rockdock made about log-normal distributions. Are these the terms "creaming curves" are understood? If we had access to discovery data we could estimate such distributions from start by using non-parametric kernel based methods and not rely on fixed parametric assumptions

[EnergySpin]

$this->bbcode_second_pass_quote('WebHubbleTelescope', '
')
I appreciate your take and expertise on data regression. But like Rockdoc, I have heartburn with the logistic model for more fundamental reasons. Why should it work at all for this class of behaviors? When did the strong non-linear component of the basic "predator/prey" get applied to oil depletion?

[EnergySpin]

$this->bbcode_second_pass_quote('rockdoc123', '')$this->bbcode_second_pass_quote('', 'M')odelling oil reservoir discovery = EXPLORATION. I found particularly enlightening the comments that rockdock made about log-normal distributions. Are these the terms "creaming curves" are understood? If we had access to discovery data we could estimate such distributions from start by using non-parametric kernel based methods and not rely on fixed parametric assumptions

[rockdoc123]

$this->bbcode_second_pass_quote('', 'A')) Creaming curve data =>Exploration to date and the potential for future exploration
B) Individual field (or preferably well!!) production data and history of extraction methods applied to them
C) Information about projects coming on-line
D) Reservoir modelling data on different fields. Since I'm certainly using the wrong terms here, what I mean by this: reconstructions of the geologic structures that you guys operate on so we can test ideas on simplified models of the way the reservoir is drained.

Realistically what are the chances of getting public data on A-D?

[khebab]

Statistical model for the distribution of field size:

In order to have a distribution of the oil field sizes, I checked the validity of lognormal model:


Figure 9

The blue points are Simmons data for the 6 oil field categories he defined (see Figure 8 ). The estimated sigma value is 4.2 when oil production is expressed in thousands of barrels per day. The fit is rather good.

Statistical model for the genration of random discovery data:

As discussed before, I'm missing a pdf for the small field discoveries. So I took the pdf of next category (Cat. 5) and rescaled it by the expected total numbers of discovery for small fields (4,000 up to the year 2000).

The algorithm to generate random discovery data is the following (this process is repeated N times):

$this->bbcode_second_pass_code('', '
N= total number of oil fields
D= random variable associated to the decade of the discovery (we cosnider 8 decades from the 40s to 2010s).
Category= random variable associated with the field size (from supergiants (Cat. 1) to small fields (Cat. 6)).
P= random variable associated with the mean daily production output of an oil field (in thousands of barrels per day).

1) Randomly choose a decade d according to the following distribution:

prob(D) = [0.0623 0.0970 0.1577 0.1572 0.1317 0.1314 0.1314 0.1314]

2) According to the value of D=d, randomly choose a field category:

prob(Category | D= d) =[
0.0057 0.0018 0 0.0011 0 0 0 0
0.0057 0.0055 0.0034 0.0011 0.0014 0 0 0
0.0086 0.0018 0.0068 0.0011 0.0014 0 0 0
0.0230 0.0074 0.0068 0.0103 0.0014 0.0014 0.0014 0.0014
0.0144 0.0148 0.0148 0.0148 0.0150 0.0150 0.0150 0.0150
0.9425 0.9686 0.9682 0.9715 0.9810 0.9836 0.9836 0.9836]

2) According to the value of D=d and Category= c, randomly choose a field production output:

prob(P= p | D= d, Category= c)= ModifiedLognormal(p|sigma)

3) Derive an URR from the value of p:

beta ~ Unform([50, 110[)
URR= beta x p / (365x1e6)
')

Remarks:
- The first decade (40s) is in fact covering the period 1900-1940.
- The last step (3) has to be more justified because I don't know how to relates a field average production output and its URR.

The function called ModifiedLognormal() is a resampling of the original learn lognormal distribution on Figure 1 (a technique called importance sampling I believe). This technique produces a modified lognormal distribution based on the different pattern of discoveries observed for each decades.
$this->bbcode_second_pass_code('', '
According to the value c of the realization of the random variable Category | D (ranging from 1 to 6) we do the following:

ModifiedLognormal:
1) beta ~ Uniform([minp(c) maxp(c)[)
2) We find the production p such as:
LogNormalCDF(p) >= beta

[minp(c) maxp(c)[ is the production interval defined for the category c. For instance, if c= 2 we have [minp(c) maxp(c)[= [500 1,000[ tbpd.
')
Results:

Here are the results from a small simulation from 40 runs with N= 5,500 fields.


Figure 10

Figure 11

Figure 12

We can see that small fields have a large contribution The average peak position is:

2013.95 +/- 2 years at 30.55 +/ 1.0 Gb

URR= 2.664 +/- 0.11 Tb


Figure 13

Conclusions:

1. This an optimistic scenario because I repeated the discovery pattern from the 90s to the following decades (2000s and 2010s). Clearly, it's not obvious that we will have the same pattern.
2. A quick simulation seems to replicate expected proportions between the different field categories (supergiants and small fields produced 20% and 53% respectively of the world total production in 2000). There is a peak for small fields production only in 2030 as well as for Cat. 5 fields. Maybe this kind of fields are being overlooked.
3. the statistical relationship between a field mean production and its URR is not trivial.
4. The choice of the number N of oil fields influence greatly the result.
5. The statistical model to simulate worldwide discoveries (Figure 10) seems to replicate well the data from Simmons (Figure 8 ).