Most of us are familiar with the curve fitting techniques used by Laherrère, Hubbert, etc. in order to predict the position of the peak of oil production. This approach has been widely criticized in particular by Michael Lynch because of the apparent arabitrary curve model employed and the large uncertainty about the URR (Ultimate Recoverable Ressource):
Quote:
Obviously, pure Hubbert models have no room for economics since the basic differential equation is the classical logistic. The under estimation of Hubbert model is a known aspect but no analysis is given in order to introduce more flexible tools capable, for instance, to track an intervention or a systematic perturbation. Lynch supposes that the origin of the problem relies on the strong assumption of a static URR (Ultimate Recoverable Resource). The impact of technology in expanding resources is sometimes reasonable but a lot of systematic interventions may affect normal evolution. For instance, the forced production of PrudhoeBay in Alaska was a positive shock, or, on the contrary, the negative effect ofaccidents in pipelines (Piper Alpha disaster) in the North Sea depressed regular production. These accidents led to examine restructuring of UK offshore safety legislation followed by major changes to the Petroleum Reven Tax. These radical interventions are not recognized by a simple Hubbert model
Quote:
Evidence is given to a common effect of that shocks, i.e., a transition to low-energy tools (computers, electronics, robotics, bio-engineering, etc.) as compared with traditional industrial products, steel-car, chemicals, etc.. The role of the "well-informed spectators" of the oil game, i.e., journals, specialized consultants, institutes, is important as they "massage the message" and, clearly, influence oil price-settings. This result contributes to enhance our work which highlights the surprising weak relationship between observed prices, oil demand and supply. The decade post 1986 is relatively stable with some exceptions that confirm paradoxical behaviours of the quantity-price relationship.
In this paper oil production is considered as a diffusion model based on a complex differential equation called generalized Bass models (GBM). Solving this equation leads to the famous Riccati formula. This approach do not require the knowledge of the URR and is able to model price shocks like for instance the 70's oil shock!
Quote:
In the sequel we may consider oil as a production directly controlled by correlated diffusion processes, i.e., individual mobility, heating, electricity production, chemical applications, etc., so that crude oil production may be thought as a parallel diffusion process. Such production is influenced by regulatory or strategic interventions of political and economical nature which are usually
persistent and conceptually deterministic.
What's amazing with this new model is that shocks are explicitely modeled:
Quote:
The subtle and shifty deviation originated in the post{war period beyond 1951 has generated an incremental consumption of oil not fully balanced by the feedbacks of 1970's. This deviation from the Hubbert model (exactly centered on the world oil data until 1950) is recovered by the GBM model with three shocks with an abrupt contraction of the diffusion process depletion component. The contraction is quite severe. The present model forecasts an URR of 1524 Gbo, a peak positioned in 2007 with a production of 76.34 mb/d, a depletion of 90% URR in 2019 with a production of 55.33 mb/d and a 95% saturation during 2023 with a production of 36.13 mb/d.
The prediction results are quite pessimistic:
Quote:
The subtle and shifty deviation originated in the post{war period beyond 1951 has generated an incremental consumption of oil not fully balanced by the feedbacks of 1970's. This deviation from the Hubbert model (exactly centered on the world oil data until 1950) is recovered by the GBM model with three shocks with an abrupt contraction of the diffusion process depletion component. The contraction is quite severe. The present model forecasts an URR of 1524 Gbo, a peak positioned in 2007 with a production of 76.34 mb/d, a depletion of 90% URR in 2019 with a production of 55.33 mb/d and a 95% saturation during 2023 with a production of 36.13 mb/d.
It's a very exciting work that use a mathematical economic model that should please Michael Lynch . Note that this paper has been reviewed by Campbell. _________________ ______________________________________
http://GraphOilogy.blogspot.com
Interesting that he considers the demand spike in the 50's to be a "shock". I wish they had explained the variables in equations (1) and (3) a little better, so I guess we will have to look up the references for more detail.
Also, his fit of the verhulst curve to the historical data is a little different from ours. It looked like he minimized his error prior to 1950, with the result that the "shock" of the 60's of really high production and the subsequent "corrections" are all well above the verhulst curve.
Interesting that he considers the demand spike in the 50's to be a "shock". I wish they had explained the variables in equations (1) and (3) a little better, so I guess we will have to look up the references for more detail.
I agree, the variable a not very well defined and quite esoteric!
Code:
m: potential market or carrying capacity
z'(t): instantaneous adoptions (daily world production?)
D(t): oil price
x(t): intervention fonction or common intervention tool (function of oil price?)
Their "2007 peak" is about 8 millon bpd below current production. What is up with that? _________________ "The world is changed... I feel it in the water... I feel it in the earth... I smell it in the air... Much that once was, is lost..." - Galadriel
Evidence is given to a common effect of that shocks, i.e., a transition to low-energy tools (computers, electronics, robotics, bio{engineering, etc.) as compared with traditional industrial products, steel{car, chemicals, etc.. The role of the "well-informed spectators" of the oil game, i.e., journals, specialized consultants, institutes, is important as they "massage the message" and, clearly, influence oil price-settings
don't deserve the mf-ing time of day. _________________ "By the time individuals discover that remaining resources will not be adequate for the next generation, the next generation has already been born. " David Price
Their "2007 peak" is about 8 millon bpd below current production. What is up with that?
That's a good question, probably because they used the 2003 BP energy review their prediction may be a little bit too pessimistic. _________________ ______________________________________
http://GraphOilogy.blogspot.com
Why do they have a URR of ~1500 gbo? Someone explain why this is not too low?
From what I understand the URR is estimated from the non linear fit between the Riccati model and the actual data, it's not a prior assumption. _________________ ______________________________________
http://GraphOilogy.blogspot.com
Ok, I managed to reproduce the article results. Apparently, the parameter estimation is performed by a nonlinear least square algorithm (ex: Marquardt). The parameter values proposed by the author are the following (see Table 3 p. 27):
The data used here are from the 2005 BP review provided by pup55 (see thread Updated Verhulst model). We can observe that there is a significant discrepancy between the fit and the data between 1900 and 1965 which is not present on the figure in the article. Obviously, there is a problem in the data, maybe pup55 has the answer.
The oil production noted z'(t) is given by the following GBM differential equation:
Code:
z'(t)= (p + qz(t)/m)(m - z(t))x(t)
where z(t) is the cumulative oil production given by the Riccati equation. m is the equivalent of the URR so (m - z(t)) is the quantity of oil left at the time t (proven reserve). x(t) is called the control model and has a great influence on the resulting curve. In particular, x(t) is used to model discontinuities in the curve like the 70s oil shock. If x(t)= 1, the GBM becomes the simpler Bass Model. In the GBM, x(t) is used to model the effect of pricing and investment (see the link provided by Ohanian above for more details).
I used the following control model (3 exponential shocks) noted gbm3e in the article:
Code:
x(t)= 1 + E1 + E2 + E3
with Ei=ci x exp(bi x (t - ai))
the signs of ci and bi are important and influence greatly the shape of the curve.
I performed a new least square estimation using the Marquardt algorithm. I excluded the data from 1900 to 1965 because of the unexplained poor fit for these points:
Code:
F(x): 2.209514e-006
Nb of Iterations: 500
Parameters:
URR= 0.84 p= 0.000021 q= 0.096700
Control model
Shock 1: c1= -0.163277 b1= -0.015254 q1= 80.484536
Shock 2: c2= 0.001622 b2= 0.125247 q2= 51.070223
Shock 3: c3= -0.125364 b3= 0.061326 q3= 75.000000
The new URR went down to 0.84 * 1524= 1280 Gb, and the peak production date is now in 2005:
Figure 3
Other control model functions are possible in particular prices fluctuations can be injected into the model. _________________ ______________________________________
http://GraphOilogy.blogspot.com
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