[dmtu]

Pup,
If you are willing, I'm betting Aaron or Admin would put your .xls in the downloads section. I'd like to see it just to try and understand the data set and math. I've done some simple stuff in relation to mine production benchmarking so I might even learn something I can use!

[pup55]

EE:

http://www.roperld.com/minerals/depletth.exe

See if this is not a zip file with the equations on it

The formula for the symmetrical model is:

Q(sub-t)=1/2 Q(inf) *(1-tanh(t-t (sub 1/2)/2*tau))

where Q (sub-t) is the remaining quantity for a given year
Q-inf is the ultimate recoverable quantity
t is the year
t (sub 1/2) is the guesstimate of the peak year
and tau=1/k where k is the "fudge factor" for the curve fatness.

The asymmetrical model is slightly different. Both rely on hyperbolic tangent to give it the distinctive shape.


I calculate Q(sub-t) for a given year and subtract the previous year to arrive at the "production value" for each year.

dmtu:
Put an email address in my personal message box and I will send it to you.

[ohanian]

$this->bbcode_second_pass_quote('pup55', 'E')E:

http://www.roperld.com/minerals/depletth.exe

See if this is not a zip file with the equations on it

The formula for the symmetrical model is:

Q(sub-t)=1/2 Q(inf) *(1-tanh(t-t (sub 1/2)/2*tau))

where Q (sub-t) is the remaining quantity for a given year
Q-inf is the ultimate recoverable quantity
t is the year
t (sub 1/2) is the guesstimate of the peak year
and tau=1/k where k is the "fudge factor" for the curve fatness.

The asymmetrical model is slightly different. Both rely on hyperbolic tangent to give it the distinctive shape.


I calculate Q(sub-t) for a given year and subtract the previous year to arrive at the "production value" for each year.

dmtu:
Put an email address in my personal message box and I will send it to you.

[ohanian]

$this->bbcode_second_pass_quote('pup55', 'E')E:

http://www.roperld.com/minerals/depletth.exe

See if this is not a zip file with the equations on it

The formula for the symmetrical model is:

Q(sub-t)=1/2 Q(inf) *(1-tanh(t-t (sub 1/2)/2*tau))

where Q (sub-t) is the remaining quantity for a given year
Q-inf is the ultimate recoverable quantity
t is the year
t (sub 1/2) is the guesstimate of the peak year
and tau=1/k where k is the "fudge factor" for the curve fatness.

The asymmetrical model is slightly different. Both rely on hyperbolic tangent to give it the distinctive shape.


I calculate Q(sub-t) for a given year and subtract the previous year to arrive at the "production value" for each year.

dmtu:
Put an email address in my personal message box and I will send it to you.

[ohanian]

gnuplot> plot 'walmart2.txt'
gnuplot> F=3000
gnuplot> H=1995
gnuplot> k=1
gnuplot> Z=1970
gnuplot> q(x)=0.5*F*(1.0 - tanh((x-Z) - (H-Z)/(2.0*k)))
gnuplot> FIT_LIMIT=1e-3
gnuplot> show variables


Variables:
pi = 3.14159265358979
F = 3000
H = 1995
k = 1
Z = 1970
FIT_LIMIT = 0.001

gnuplot> fit q(x) 'walmart2.txt' via F,Z,H,k

<<Lots of numbers and Iterations scroll past on the screen>>
Iteration 6
WSSR : 301389 delta(WSSR)/WSSR : -0.000530409
delta(WSSR) : -159.859 limit for stopping : 0.001
lambda : 0.0018104

resultant parameter values

F = 0.121088
Z = 1968.28
H = 2015.93
k = 2.47001

After 6 iterations the fit converged.
final sum of squares of residuals : 301389
rel. change during last iteration : -0.000530409

degrees of freedom (ndf) : 31
rms of residuals (stdfit) = sqrt(WSSR/ndf) : 98.6014
variance of residuals (reduced chisquare) = WSSR/ndf : 9722.23

Final set of parameters Asymptotic Standard Error
======================= ==========================

F = 0.121088 +/- 38.28 (3.161e+004%)
Z = 1968.28 +/- 7493 (380.7%)
H = 2015.93 +/- 9.87e+004 (4896%)
k = 2.47001 +/- 4057 (1.642e+005%)


correlation matrix of the fit parameters:

F Z H k
F 1.000
Z -0.177 1.000
H 0.252 -0.901 1.000
k 0.290 -0.835 0.988 1.000

<<trying again with F=>>
gnuplot> F=4000000

gnuplot> fit q(x) 'walmart2.txt' via F,Z,H,k

Iteration 6
WSSR : 5.33927e+013 delta(WSSR)/WSSR : -1.536e-006
delta(WSSR) : -8.20115e+007 limit for stopping : 0.001
lambda : 0.783324

resultant parameter values

F = 3.8465e+006
Z = 1967.65
H = 122850
k = 10153.1

After 6 iterations the fit converged.
final sum of squares of residuals : 5.33927e+013
rel. change during last iteration : -1.536e-006

degrees of freedom (ndf) : 31
rms of residuals (stdfit) = sqrt(WSSR/ndf) : 1.31238e+006
variance of residuals (reduced chisquare) = WSSR/ndf : 1.72235e+012

Final set of parameters Asymptotic Standard Error
======================= ==========================

F = 3.8465e+006 +/- 8.457e+005 (21.99%)
Z = 1967.65 +/- 1.318 (0.06698%)
H = 122850 +/- 2.941e+006 (2394%)
k = 10153.1 +/- 2.466e+005 (2429%)


correlation matrix of the fit parameters:

F Z H k
F 1.000
Z -0.095 1.000
H 0.355 -0.641 1.000
k 0.358 -0.637 1.000 1.000

[ohanian]

$this->bbcode_second_pass_quote('pup55', 'E')E:

http://www.roperld.com/minerals/depletth.exe

See if this is not a zip file with the equations on it

The formula for the symmetrical model is:

Q(sub-t)=1/2 Q(inf) *(1-tanh(t-t (sub 1/2)/2*tau))

where Q (sub-t) is the remaining quantity for a given year
Q-inf is the ultimate recoverable quantity
t is the year
t (sub 1/2) is the guesstimate of the peak year
and tau=1/k where k is the "fudge factor" for the curve fatness.

The asymmetrical model is slightly different. Both rely on hyperbolic tangent to give it the distinctive shape.


I calculate Q(sub-t) for a given year and subtract the previous year to arrive at the "production value" for each year.

dmtu:
Put an email address in my personal message box and I will send it to you.

[pup55]

go to:

http://www.roperld.com

in the bottom frame, click on "david l roper"
Scroll downward in the bottom frame, to "interdisciplinary studies" and click on "crude oil depletion"
when the next page loads, click on "depletion theory"

Equation 2 is what I have been using for the model. You and EE will be able to see a picture of this thing. We are back to this problem of not being able to see equations in "equation form". My guess is that one of the brackets/parenthesis is misplaced.

You are quite right, post-peak, the model has to be the mirror image of
the pre-peak. But, I think it works using t-sub-1/2 (the estimate of the peak" as the midpoint and calculating forward and backward from there.

Send me your email (in the private message box) and I will send you this spreadsheet, maybe you can dedude from that what is happening.

[ohanian]

$this->bbcode_second_pass_quote('pup55', 'g')o to:

http://www.roperld.com

in the bottom frame, click on "david l roper"
Scroll downward in the bottom frame, to "interdisciplinary studies" and click on "crude oil depletion"
when the next page loads, click on "depletion theory"

Equation 2 is what I have been using for the model. You and EE will be able to see a picture of this thing. We are back to this problem of not being able to see equations in "equation form". My guess is that one of the brackets/parenthesis is misplaced.

You are quite right, post-peak, the model has to be the mirror image of
the pre-peak. But, I think it works using t-sub-1/2 (the estimate of the peak" as the midpoint and calculating forward and backward from there.

Send me your email (in the private message box) and I will send you this spreadsheet, maybe you can dedude from that what is happening.

[Soft_Landing]

$this->bbcode_second_pass_quote('', 'T')he three "knobs" if you will, are Q-inf, which is the total area under the curve (how big the curve is), k, which is the "fatness" of the curve, and some guesstimate of T-50 or the "peak".

[EnviroEngr]

Quick Shortcut:

L. David Roper -- Crude Oil Depletion

[pup55]

Thanks, EE for your help with the links to Roper's paper.

SL: I think the main function of the T-50 estimate is just to orient the curve along the X-axis. If you knew the function, and had enough data points to fit the first part of the curve accurately, this would probably be unnecessary or calculate-able. The area under both the predicted and actual curves (in essence, cumulative production) probably ought to be equal. This should be calculateable by integrating the "predictive function" from t=0 to t=your last data point, and setting it equal to "cumulative actual production" for the same interval. Then, you should be able to back-work it to get T-50.

Still gotta have a pretty good estimate of Q-inf, plus have to re-calculate for every new data set.

Also the Lahererre paper cited the other day:

http://dieoff.org/page191.htm

compares the logistic curve to the gaussian, and notes that the gaussian gave a higher, delayed peak, at least in the example he showed. Still, it would probably be interesting to build another spreadsheet using this function and compare the peak calculations to the other two models just out of curiosity.

Alternately, if there is a better model, I will run it. I am an equal opportunity modeler.

[Soft_Landing]

i don't know if this'll work, but here's a link to a spreadsheet.

see if you can download it.

Verhulst.xls

Good Luck

[pup55]

ah.... our models are synchronized!

Only problem is I am using an archaeic version of excel which does not have tools:solution. I have to settle for goal seek, which does not allow me to select multiple cells to run.

Good work!

[Soft_Landing]

First of all, thanks pup55 for getting me off my proverbial and figuring out how Roper's model actually works. The formulas were first posted quite a while ago, but I figured I could avoid them if I just looked the other way.

$this->bbcode_second_pass_quote('', 'S')L: I think the main function of the T-50 estimate is just to orient the curve along the X-axis. If you knew the function, and had enough data points to fit the first part of the curve accurately, this would probably be unnecessary or calculate-able. The area under both the predicted and actual curves (in essence, cumulative production) probably ought to be equal. This should be calculateable by integrating the "predictive function" from t=0 to t=your last data point, and setting it equal to "cumulative actual production" for the same interval. Then, you should be able to back-work it to get T-50.

[pup55]

Actually I built both models at the same time, but only posted the "highlights" in:

http://peakoil.com/fortopic2082.html

because I did not observe too much difference in peak date, plus can't do graphics because too cheap to pay for my own website.

Be that as it may, it looked to me like the trick on the Verhulst model is the estimate of the time gap between "peak" and T-50, which greatly affects the downslope of the curve.

I think he observed this phenomenon in certain examples of mineral depletion wherein people either got smart and were more efficient at mining the remainder, or looked for substitutes, or there was "demand destruction" on the downside of the depletion curve.

I suppose if you made observations of enough individual countries' depletion curves (after they had peaked), and took some kind of aggregate "k" and "n" for typical oil depletion examples, you could apply it with some objectivity to the global data and estimate the global peak. This would not necessarily give you better reliability, but at least you would have some defense from the skeptics.

[seahorse]

So, what's the final verdict? Can a model accurately predict a peak for an entity like wal-mart? If not, then how could it ever be possible to predict a peak for something like oil with all its unknowns?

Understand my questions come from a layperson that barely got through 6th grade math. However, the fact that models are so difficult to plug numbers into, and the fact that there is some much interpretation in the values inserted, seems only to buttress what Michael Lynch says, which is, all these predictions of peak oil are meaningless.

Interested to know what you all think.

[Soft_Landing]

$this->bbcode_second_pass_quote('', 'U')nderstand my questions come from a layperson that barely got through 6th grade math. However, the fact that models are so difficult to plug numbers into, and the fact that there is some much interpretation in the values inserted, seems only to buttress what Michael Lynch says, which is, all these predictions of peak oil are meaningless.

[seahorse]

We may all be approaching a "peak" model from the wrong angle. Everyone is trying to make a model for a "peak" of all oil (light, heavy, tar sands). However, the world is literally driven by light sweet crude, so what happens if when the world peaks in light sweet crude? As we all know, light sweet crude is the oil of choice, as it drives most of our transportation. It is in fact the price of light sweet crude that has gas prices running high and has everyone revisiting the peak oil issue. The Saudis, for example, have lots of heavy sour crude that they recently couldn't sale even at a discount, b/c everyone wants light sweet.

So, what are the repercussions of a peak in light sweet crude? There are millions of cars in the world that need it, most refineries are set up to refine it and not heavy crude. What is the cost of trying to convert everything (cars/refineries) to run on diesel, and still yet, how do you get Americans to buy and drive diesals? I read somewhere that to build a refinery to process heavy crude its about $8 billion (Oil and Gas Journal I believe). We have what, about 20+ refineries now in the U.S. most of which are processing light sweet crude? How much does it cost to convert them, assuming that's possible, I don't know.

So, all other depletion models aside, what is the depletion model for light sweet crude? Isn't a more restricted model of light sweet crude only warranted (even from pure economic cost to society)? Would a peak in light sweet crude have the same effect on society overall as a peak in all oils?

I would like to see a world depletion model for light sweet crude if it can be done. Everyone projects the world demand for total oil in BPD, but what is the world BPD demand from here to 2020 for light sweet crude only, and can that demand be met? If not, what is the peak date for light sweet crude?

I know the Saudis are trying now to produce more light sweet crude (since their heavy didn't sale), but how much can they add, will it be enough, and can anyone else add any? It seems the main sources of today's light sweet crude have been U.S. (decline), North Sea (decline), Nigeria (many problems not much left in expansion capacity), Gulf, and a few others.

Interested in your thoughts.

[pup55]

http://www.woodmac.com/pdf/crudequality.pdf

You are on to something, Seahorse. In fact, the above source was charging 25000 brit pounds in 2002 for a report of this exact thing.

It's obviously of critical importance to somebody running an oil refinery who needs to know how to modify his production process to accept nastier crude going forward.

Unfortunately, the normal sources (BP review, anyway) do not have data broken out into what is "light and sweet" vs. other. The methodology is that these guys have gone through and identified each field and which field produces which grade, and from that has come up with a composite. Evidently, there are varying degrees of "lightness and sweetness" and they will all deplete at different rates as the individual fields die.

On the bright side, evidently there is a career in this sort of research, for somebody with the means and opportunity and motivation to do it. In fact, I would go so far as to say that someone could turn the info on this website into a pretty nice, high dollar consultancy report. We should probably start copyrighting our posts.

On the not-so-bright side, these characters were thinking $15 crude going forward, and $30 worst-case as of 2002, so you know their prognosticating ability was not necessarily up to the level of their other research.


(c) 2004 by pup55. All rights reserved.

[Cool Hand Linc]

If we know that American is in decline. Post peak. We have seen the curve and can derive an estimated Q-inf that should be close.

Looking am many countries that have already peaked and getting an average Q-inf.

Knowing the exact amount of oil left isn't required. Being close is. Oil will never run out anyway. It will just get to costly to continue to produce. Energy IN must be less than the energy OUT or the pumping will stop. At least for energy. (Oil could still be used for a lubricant.)

So is it possible to look at countries that are well past peak and derive an estimated Q-inf to use for other countries?

Hubbert predicted to the year when peak in America would occur.