[mididoctors]

There's no reason to believe that probability distributions (Gaussian, Gamma etc.) have any relationship at all with the oil depletion curve (other than a superficial resemblance). I find Smiley's derivation plausible, and it makes no reference to probability at all. It's a question of drilling an ever increasing hole in a pressurized reservoir. It's not a random process.

thats really not a great point.. the mirroring of process across different fields leads to a commonality that should in any mechanism produce some distribution commonality. to be truly random the pressure/production variables etc would have to be INFINITE... any mechanism sampled over and over that is a process MUST produce some distribution

clarification: this does not invalidate probability only the range of possible outcomes. . Probability itself does not insinuate a total randomness.

Boris
London

[mididoctors]

It's probably best for society to act on Campbell's prediction, whether it is right or wrong. In fact, I wish that Campbell would adopt that as his explicit position. I would respect him a lot more if he said: "We don't know the exact numbers. We can't and won't predict an exact date. However, we know that conserving petroleum is a win-win strategy which will be beneficial whether the peak comes soon or late." That would put a little rhetorical ju-jitsu on Lynch, deprive him of his primary debate tactic, and put the focus where it really should be.

rather a socialist central planning argument! which is paradoxical

there is some element here that lies in some "new" world view.

the long term view.

basically leave as much oil as possible in the ground

Boris
london

[khebab]

From another thread (]http://www.peakoil.com/fortopic7566-60.html), the opinion of shakespear1 that seems to work in the oil industry:

Khebab

Mr. Lynch appears to (From the ECONOMIST : Michael Lynch of DRI-WEFA, an economic consultancy) be a man that has not spent a lot of time scratching his head over seismic and logs. Not good credentials for me to understand what is going on, unless you want a voice to join the debate.

He apparently is "envisioning" something that might happen but that to this moment I have not seen. I have not seen any technology that was being introduced into the field on a large scale that can attack old fields and try to get beyond 20-30 % recovery. Old field for one have poor data, old rusty wells, majority of the wells probable in poor condition and with junk in them and if the field was water flooded with potential by-passed oil that will be tough to figure out where it is without good data. Data that an oil company will be hard pressed to spend as they are spending money on newer stuff.

Read this paper to try to understand this problem
http://www.dieoff.org/page197.htm

Look at Fig. 3 in this paper http://www.streamsim.com/papers/spe38889.pdf

Even though we are looking at a distribution of CO2, this is a helpful visualization of what HETEROGENEITY does to you. I NEVER have this "true" picture of the oil/gas saturation distribution down below. I never have the "true" permeability/porosity distribution in the reservoir. Thus when I sink a well and start to produce I really have no clue from where the oil came from and whether I left some behind.

We have much better software/hardware that could allow me to build finer models but I do not have the data to put in there.

We are doing more geostatistics now but the method of operation is still the same.

Head Geologist (Russia): When will I have your well placements?
I: In 4 weeks.
HG: Why so long? I need them in 2 weeks!!!!
I: Uhhh,
HG: In 2 wks or ....

End of discussion.

2 wks later

I: Here but rates will be around 300 m3/d
HG: WHATTTTTTT. We expect 500 m3/d.
I: Well that is what I am getting with this model. The area to the right is poor and the area given for drilling does not look good. Our geologist see high risk of poor reservoir here.
HG: I AM GOING TO FIRE YOU. Bring me a new forecast.

on and on ....

What happened?

We gave a new forecast and sweetened it ( too the risk ). Geology did not justify this. But the advice I got was to do it. We put our heads on the line.

The well was drilled and ... gave them close to 600 m3/d.

What happened? WE HAVE NO CLUE. Did they take our advice and get more data and try to get a picture of this reservoir? NOOOOO Just went on and drilled in another place where things looked good. And ... And they hit Crap. More data? Even after this NOOOO.

So will some of these companies spend money up front on old field to look for lost or upside potential. Maybe if the prices are in the 100 - 200 /bbl. Because in places where I have been they will not.

It is risky and you need to put up the money up front. Casino where people are risk avers when it comes to their careers. I would be if I could not get a guarantee that this magic bullet will deliver and increase of significant magnitude.

Water floods, CO2 and miscible floods are the best understood methods today. Some other methods have been tried but the reservoir heterogeneity works against it, thus short of mining down there I do not see anything at the moment to be this "ace" in the hole for the industry.

If people talk technology and mean computers and software then look out.

For your information you can et beyond 20-30 recovery if there is a strong water drive (lots of energy to move the oil along) In this case it could be around 60%. Sort of like a free water flood.

Are we at the PEAK? I go with Campbell and Laherrere. I read their work and it makes sense to me. Surprisingly in my circle of friends we do not discuss this much. Too busy working

Again, the US gov. MUST know this. You get the production data for the oil fields in Saudi etc, Decline It and voila you have a good idea of the total rates in the near future.

I am sure they get this data in real time ( remember many field are wired and transmit data ELECTRONICALLY ) by asking their workers in the NSA.
_________________
Regards

Henryk

[mididoctors]

I think it is important that skeptics like Lynch are addressed in a rational manner as his criticism of predictions of production rates may well be true in the short term...we do not know.

it is possable we have peaked and entered some treadmill like phase similar to NA gas where production can spike upwards despite the lifetime of wells running shorter and shorter..

to this end an over emphasis on the most pessimistic numbers or scenarios based around a crash in production with-in a few years that does not turn out to be correct may seriously undermine the issue of depletion politically and in the market where a return to business as normal would be a real ticking time bomb compared to one many think they have now.

another cry wolf would be a disaster after the level at which the issue has risen especially if the nature of the problem does not present itself like so many here think it will... I call this perception the "hollywood" version.

If this hollywood version does not manifest it self in a couple of years?

its quite possible we have peaked and we will not know for 5-10 years

YES we are all part of a ground swell opinion that has helped raise the issue... we have it in the mainstream great! well done everybody. now inject some serious healthy debate about how it can play out and how we can or must react. this includes a large voice that constantly reinforces the notion or possibilities of effects unfolding over years rather than months. something Democracies and civil society has up-till now not been very good at.

trying to keep a focus on events which unfold SLOOOOOOWLY..

everybody likes the price hikes and the market panic days because its exciting but the boring days and years are when we need to maintain pressure.

Boris
london

[WebHubbleTelescope]

WebHubbleTelescope, There isn't any scientific foundation to the Hubbert curve as far as I know. Why should the gamma distribution be better than the gaussian curve? Simply to avoid nit-pickers? I think that would be playing into their hands. There is no hope in making a model that can accurately predict the production profile and we should say up front that the hubbert curve is just a rough estimate, nothing more. It isn't based on geology or physics. Heck, it isn't even scientific at all and we shouldn't try to dress it up to be something it's not. That's just asking for the nit-pickers to come and tear you apart.

People don't understand modeling and prediction. We usually have to deal with limited information and make the best out of it. In the absence of crystal balls, we have to use techniques such as Markov theory and Bayesian analysis. Gamma distributions fall out of this.

I wouldn't want to dismiss how probability & statistics can help our understanding.

[WebHubbleTelescope]

There's no reason to believe that probability distributions (Gaussian, Gamma etc.) have any relationship at all with the oil depletion curve (other than a superficial resemblance). I find Smiley's derivation plausible, and it makes no reference to probability at all. It's a question of drilling an ever increasing hole in a pressurized reservoir. It's not a random process.

Maybe if pup55 reads this, he would know more, but I don't think anybody is actually modeling resource peaks with the Gaussian curve.

First of all, if someone refers to a bell curve, it means Gaussian. If anything, we should probably get away from using this term as it leads to confusion.

Second, probability plays a huge part of predictive models. Given the lack of a crystal ball, we use rates and averages of past behaviors to predict future behaviors. This all fits into a Markovian view. You don't have to bring up the "random process" to trash this line of thought. The phrase "stochastic process" more or less describes the situation.

[mididoctors]

WebHubbleTelescope, There isn't any scientific foundation to the Hubbert curve as far as I know. Why should the gamma distribution be better than the gaussian curve? Simply to avoid nit-pickers? I think that would be playing into their hands. There is no hope in making a model that can accurately predict the production profile and we should say up front that the hubbert curve is just a rough estimate, nothing more. It isn't based on geology or physics. Heck, it isn't even scientific at all and we shouldn't try to dress it up to be something it's not. That's just asking for the nit-pickers to come and tear you apart.

People don't understand modeling and prediction. We usually have to deal with limited information and make the best out of it. In the absence of crystal balls, we have to use techniques such as Markov theory and Bayesian analysis. Gamma distributions fall out of this.

I wouldn't want to dismiss how probability & statistics can help our understanding.

I agree or at least think i understand the difference.

A scientific theory of oil production is not a possibility compared with the laws of motion as the variables are ridiculously complicated never mind the input of human choice.

this basically leaves statistical modeling a flawed art but what else do you do?

the science is in the issue but the issue is far from some pure science. if it is some new psychohistory mass behaviour science its in its very early fetal stages

Boris
London

[WebHubbleTelescope]

Probability itself does not insinuate a total randomness.

Boris
London

Exactly. Unless we truly understand this, you can't make any headway in making predictions. For example, you can get a lot of mileage out of predictions where we assume a historical average, independent on the randomness of the underlying mechanism.

Of course none of this works if we suddenly discover a trillion barrel deposit of oil in somebody's backyard, but no mathematics can account for this. The best we can do mathematically is assume stationary processes.

[khebab]

WebHubbleTelescope, There isn't any scientific foundation to the Hubbert curve as far as I know. Why should the gamma distribution be better than the gaussian curve? Simply to avoid nit-pickers? I think that would be playing into their hands. There is no hope in making a model that can accurately predict the production profile and we should say up front that the hubbert curve is just a rough estimate, nothing more. It isn't based on geology or physics. Heck, it isn't even scientific at all and we shouldn't try to dress it up to be something it's not. That's just asking for the nit-pickers to come and tear you apart.

Ths gaussian model is certainly the easiest model to handle. On the contrary, non gaussian behaviors are a lot more harder and requires more data and prior knowledge. In some cases the choice of a particular distribution to describe the likelihood of a random variable is based on certain assumptions on the underlying physical process. For instance, the gamma distribution is related to the Poisson distribution and Possion process which is used to model migration and birth and death phenomenon. The gaussian distribution is related to thermal noise or Brownian motion and is also a consequence of the powerful Central Limit Therorem. In case of well, several peaks can be observed because of the use of different recovery techniques. In that case, a mixture of gaussian could be used.

[WebHubbleTelescope]

I agree or at least think i understand the difference.

Boris, I can tell that you "get it".

this basically leaves statistical modeling a flawed art but what else do you do?

the science is in the issue but the issue is far from some pure science. if it is some new psychohistory mass behaviour science its in its very early fetal stages

Most people look at things from a deterministic point of view, and the mass perception problem needs addressing. A large segment of the population also thinks in terms of black & white decision making.

It is definitely not the same thing as having 20 gallons in your tank and watching it drain away. Much more to it than that.

[JohnDenver]

Web, Boris, anyone, do you have a reference to any modeling which uses the Gaussian distribution to forecast the peak in oil production? I'm asking because the Hubbert curve and Gaussian curve are two entirely different things (which just happen to look similar).

The Hubbert curve:


The Gaussian curve:


I realize that the Gaussian distribution is a wonderful thing, and has many uses in predicting various phenomena. What I'm wondering is whether it has been actually used to predict the year of peak oil, by anyone, ever.

[JohnDenver]

In case of well, several peaks can be observed because of the use of different recovery techniques. In that case, a mixture of gaussian could be used.

That would be more of the same pointless curve fitting that Lynch is ridiculing.

Suppose you have a two humped curve, like the curve for Russian oil production. How do you know you will need a two humped curve, when you are still on the upslope of the first hump? Clairvoyance?

The only thing mixtures would be useful for is fitting the curve after the fact; in other words, they would be totally useless.

[khebab]

In case of well, several peaks can be observed because of the use of different recovery techniques. In that case, a mixture of gaussian could be used.

That would be more of the same pointless curve fitting that Lynch is ridiculing.

Suppose you have a two humped curve, like the curve for Russian oil production. How do you know you will need a two humped curve, when you are still on the upslope of the first hump? Clairvoyance?

The only thing mixtures would be useful for is fitting the curve after the fact; in other words, they would be totally useless.

I agree with you on that, the number of terms in the mixture is an unknown random variable that has to be assumed or estimated. Ultimately the knowledge of the URR dictates if the second peak will be significant or not.

[khebab]

Web, Boris, anyone, do you have a reference to any modeling which uses the Gaussian distribution to forecast the peak in oil production? I'm asking because the Hubbert curve and Gaussian curve are two entirely different things (which just happen to look similar).

The Hubbert curve:


The Gaussian curve:


I realize that the Gaussian distribution is a wonderful thing, and has many uses in predicting various phenomena. What I'm wondering is whether it has been actually used to predict the year of peak oil, by anyone, ever.

You're first equation is the first derivative of the logistic functio (). The logistic function) which is widely used in economics and biology:

The classic logistic curve was discovered by Verhulst in 1845 in connection with population studies. It was used to propose that population growth increases to a midpoint (tm) and then decreases to zero, giving what is known as an S-curve. In this application, where there is no negative growth, total population stays constant at the asymptote (U). In the 1920s Pearl and Reed used the logistic curve to model the US population.

It can also be used in modelling oil cumulative production under the formula

Q = U/1+EXP(b(t-tm))

where t is the reference date (year)

Q is Cumulative Production at the reference date (t)

U is Ultimate Recovery

tm is the date at midpoint

b is a factor describing the slope

But in practice it is more convenient to use the derivative of the logistic curve to model how annual production starts and ends at zero with a peak in between. It is in effect the Hubbert curve, although there are variants such as the Gauss curve, the Cauchy curve, the sine wave and even the parabola.
....
The Gauss formula is

P= U/s*(2pi)1/2*EXP(-(tm-t)2/2s2) using the three parameters: U, tm and s (standard deviation)

it can be written:

P=Pm Exp(-(tm-t)2/2s2)

with Pm= U/s*(2pi)1/2 = 0.4 U/s, (strictly 1/(2pi)1/2=0.3989)

In figure 1, the Hubbert curve is plotted together with a Gauss curve of the same ultimate (3200), peak and peak-time. The curves are very close to each other, Gauss being a little fatter at the top and leaner at the base. The maximum of the derivative is the inflection point.

src: dieoff.org

[mididoctors]

Web, Boris, anyone, do you have a reference to any modeling which uses the Gaussian distribution to forecast the peak in oil production? I'm asking because the Hubbert curve and Gaussian curve are two entirely different things (which just happen to look similar).

The Hubbert curve:


The Gaussian curve:


I realize that the Gaussian distribution is a wonderful thing, and has many uses in predicting various phenomena. What I'm wondering is whether it has been actually used to predict the year of peak oil, by anyone, ever.

I have absolutely no idea what distribution modeling went into Hubberts curve

Boris
london

[mididoctors]

In case of well, several peaks can be observed because of the use of different recovery techniques. In that case, a mixture of gaussian could be used.

That would be more of the same pointless curve fitting that Lynch is ridiculing.

Suppose you have a two humped curve, like the curve for Russian oil production. How do you know you will need a two humped curve, when you are still on the upslope of the first hump? Clairvoyance?

The only thing mixtures would be useful for is fitting the curve after the fact; in other words, they would be totally useless.

no not really as if there is a correlation in change in practice or circumstance to a change in the curve you are operating in a useful model.

this is my point about lynch using the model to start with as both he and other analysis have to account for the discrepancy..

if it wobbled about massively for absolutely no detectable reason at all then you have a fundamental problem with your modeling.

Boris
london

[nero]

{I think this thread has gone way off the original topic, and it might be worthwhile if a moderator came along and separated out the discussion of the hubbert curve et al into a separate thread with an apropriate name.}

Ok the logistics curve sounds like a starting point for a theoretical basis for the hubbert bell curve. That makes alot more physical sense than the gaussian curve. First because physically there is no justification for the gaussian curve (IMO). We are not modelling the frequency of something occuring that has some inherent uncertainty around a constant value. maybe we could make a gamma distribution for rate of discovery of oil under ideal conditions, I haven't thought about that carefully but anyways what the hubbert curve is modelling is the production not the discovery.

The logistics curve has the advantage of having some physical reason for its use. Physically it is most easily understood by the differential equation

P' = rP(K-P)

This describes the classic S curve where something starts growing exponentially until it nears a constraint at which point the constraint starts to limit the rate of growth and the growth slows down to nothing. The problem of using the logistics curve is that you can't make a physical justification for it's use in this case. For oil production P' = rate of production, P is the cumulative production, K is the ultimatly recoverable reserves and r is a constant determining the growth rate.

But the rate of increase of oil production has not been limited physically by cumulative production. More realistically it is limited by the current rate of production. (ie the percentage increase of production is limited due to physical constraints on the ability of the industry and the economy to grow). I would suggest the differential equation such as

P'' = rP'(K-2P)

makes more sense. It has been a while (and differential calculus was never my strong suit) but that also will physically look like an S curve and the first derivative also is a bell curve like shape. It also is symetrical looking although it has boundary conditions at t=0.

So why isn't this model used instead ofthe logistics curve? Can anyone explain why the logistics curve is a good model for historical oil production?

[khebab]

So why isn't this model used instead ofthe logistics curve? Can anyone explain why the logistics curve is a good model for historical oil production?

That's a good question, the main reason seem to be historical. The main property of the curve is its "gaussianity" in order to satisfy the central limit theorem. A few arguments from Laherrere:

Hubbert predicted the cumulative production of oil over time in the United States, correctly forecasting a peak of annual production in the early 1970s. He was criticised at the time on the grounds that an individual oilfield’s production profile is assymmetrical whereas his profile was (almost) symmetrical. But in fact it occurs that the present oil production profile for the US 48 States is strongly symmetrical. This symmetry occurs since the sum of skewed asymmetrical curves from a large number of individual oilfields tends to be symmetrical, because the sum of a skewed probability distribution of a large number (>30) of events trends towards a symmetrical normal distribution.

This relates to the Central Limit Theorem, a well-known tenet of statistics, that explains how the distribution of the mean from a skewed distribution tends to become normal as the sampling size increases. This symmetry reflects also the correlation with the discovery curve [Ivanhoe, King Hubbert Center letter 97/1], which is almost symmetrical because of the cyclic status of exploration and the law of diminishing returns.

src: Jean Laherrere
Laherrere proposed other models also.

[nero]

This symmetry occurs since the sum of skewed asymmetrical curves from a large number of individual oilfields tends to be symmetrical, because the sum of a skewed probability distribution of a large number (>30) of events trends towards a symmetrical normal distribution.

I think this is utter hogwash. What exactly is the "skewed probability distribution". The production curves from the individual fields are NOT probability distributions. What exactly is he referring to by "skewed probability distribution". What "events" is he talking about? The only reason why the sum of the production curves will form a bell curve is if you ASSUME they will form a bell curve, by say assuming the date the individual fields enter into production are normally distributed.

The central limit theorem is talking about how the distribution of the mean estimate will look as the sample size increases. So applying this, if we took a random sample of fields from the historic data and averaged their start dates and then repeated this many times the distribution of these estimated mean start dates (by say producing a histogram of the estimates) will be normally distributed no matter what the actual probability distribution of the actual start dates.

If you go one step further and instead of averaging the start dates of several large samples instead sum the production profiles of the individual fields in each of the samples and then use the peaks of these summed production profiles as estimates of the actual peak production date, those estimates of peak production will also be normally distributed around the actual peak production date. But the individual summed production profiles of the samples taken do not have to look like a normal probability distribution. They aren't probability distributions at all they are estimated production profiles.

[khebab]

What exactly is the "skewed probability distribution".

The skewness measures the degree of asymmetry of a distribution. By skewed, I think he means actually non gaussian.

The production curves from the individual fields are NOT probability distributions.

Why not? the observed production value can be modeled as a realization of a random process.

The only reason why the sum of the production curves will form a bell curve is if you ASSUME they will form a bell curve, by say assuming the date the individual fields enter into production are normally distributed.

The central limit states that the sum of N independent random variable (whatever is their p.d.f) will follow a gaussian probability density function (Central Limit Theorem -- from MathWorld).

The central limit theorem is talking about how the distribution of the mean estimate will look as the sample size increases. So applying this, if we took a random sample of fields from the historic data and averaged their start dates and then repeated this many times the distribution of these estimated mean start dates (by say producing a histogram of the estimates) will be normally distributed no matter what the actual probability distribution of the actual start dates.

correct.