100 comments on The Shock Model: A Review (Part I)
Comments can no longer be added to this story.
| Show without comments | PDF version
100 comments on The Shock Model: A Review (Part I)
Comments can no longer be added to this story.
| Show without comments | PDF version
Search The Oil Drum with Google
Support The Oil Drum
Recently on TOD:World
TOD:Campfire
- What "Lower Consumption" Means
- Tricking and Treating the Future
- Meeting Energy Decline Part-Way - Potatoes?
TOD:Europe
- EROWI - energy return of water invested
- An interview with Stoneleigh - the case for deflation
- The Future of European Transport: iTREN-2030
TOD:Canada
- In this house, we obey the laws of thermodynamics!
- The Round-Up: October 24, 2008
- Compressed Air Energy Storage - How viable is it?
TOD:Australia/NZ
- The Bullroarer - Saturday 7th November 2009
- The Bullroarer - Friday 30th October 2009
- Details of Solar Flagships Released
TOD:Net Energy
Blogroll
Energy Sites
- The Coming Global Oil Crisis
- Die Off
- Dry Dipstick
- Energy Bulletin
- From the Wilderness
- Life After the Oil Crash
- Peak Oil Crisis
- Peak Oil News and Message Boards
- Powerswitch
- Rigzone
- Matthew Simmons
- Wolf at the Door
Environment & Sustainability Sites
- The Daily Green
- EcoGeek
- Eco Street
- Green Car Congress
- Green Options
- green.alltop.com
- Gristmill
- RealClimate
- Sustainablog
- Treehugger
- WorldChanging
Blogs
- The Big Picture
- Casaubon's Book
- Cleantech Blog
- Clusterf
k Nation (Jim Kunstler) - The Cost of Energy
- David Strahan
- The Energy Blog
- Entropy Production
- European Tribune
- GraphOilology
- Health After Oil
- jeffvail.net
- Mobjectivist
- Peak Energy (Australia)
- Peak Energy (USA)
- R-Squared
- Resource Insights
Finance & Economics Blogs
- Calculated Risk
- The Crash Course
- Ecological Economics
- Econbrowser
- Environmental Economics
- Infectious Greed
- The Mess That Greenspan Made
- Mish's Global Economic Trend Analysis
Organizations
Peak Oil Primers
Beware email scams!
Beware email scams claiming to be from this site. We do not have any job openings. If anyone contacts you about a job at The Oil Drum, do not reply to them, and definitely do not give them any personal information or send them money. Read more here.
“The infrastructure of suburbia can be described as the greatest misallocation of resources in the history of the world.”
—JH Kunstler
User login
Contact
- Content: editors at theoildrum dot com
- Tech support: support at theoildrum dot com
Personnel
- Editors: Nate Hagens, Gail the Actuary, Prof. Goose
- DrumBeat Editor: Leanan
- Contributors: ace, Engineer-Poet, Heading Out, jeffvail, JoulesBurn, Sam Foucher, Robert Rapier
- TOD:Campfire: Glenn, Jason Bradford
- TOD:Europe: Chris Vernon, Euan Mearns, Francois Cellier, Jerome a Paris, Luís de Sousa, Rembrandt, Rune Likvern, Ugo Bardi
- TOD:Canada: benk, Libelle
- TOD:ANZ: Big Gav, Phil Hart, aeldric
- Emeritus: Stuart Staniford
- Technician: Super G
License
This work is licensed under a Creative Commons Attribution-Share Alike 3.0 United States License.
GAIA Host Collective
My big problem with the shock model is its tough to prove you have constrained the model enough to be a good predictive. It has to many parameters. Its however a good model for current production and if you feel you have it constrained correctly it probably a good model for the real decline rate post peak.
So I'd like to see how it behaves under further constraints.
A obvious way to introduce further constraints is to use HL as one of the constraints on the model.
Lets assume HL gives two pieces of information that are reasonably accurate.
1.) Maximum total URR.
2.) Minimum or earliest peak date and highest peak production rate.
If HL is wrong and the shock model is at least reasonably predictive you will have obvious disagreements between the two models.
Underlying this assumption is that the URR is a constant and the areas under the two curves are equal with HL representing the theoretical best production model.
By using both approaches and assuming that the shock model is a better fit both for current production and future if constrained I think that we get a better total model.
I'd feel a lot better about the shock model if the constraints where tightened so we know that the parameters are not just better curve fitting.
I don't think HL is required and suspect the additional constraints can be developed using other methods but without them its hard to prove the shock model.
In general the problem is that you need to prove all the inflection points are real and not artifacts of the model.
The more you have in your model the higher the burden of proof needed. So far I don't think this has been done.
I disagree with assumption #1. I have repeatedly read Hubbert's 1956 paper and it is apparent to me that Hubbert did not derive URR. Instead he had pre-existing estimates of URR that he considered as upper and lower bounds - 150GB and 200GB. I have come to the personal conclusion that Deffeyes simplification of Hubbert's technique is erroneous on at least that one count. This does not mean that Hubbert was wrong as he used a different process.
"Hubbert Linearization" was invented by Deffeyes as an attempt to simplify the mathematics of what Hubbert did but Deffeyes apparently leaped to a conclusion that it can predict URR. Instead, I believe that an HL plot can only be valid if it lies within the upper and lower bound of estimated URR for a given producing region.
Ghawar Is Dying
The greatest shortcoming of the human race is our inability to understand the exponential function. - Dr. Albert Bartlett
I agree with GreyZone. In 1956 Hubbert had a range of URR estimates based on his geologic analysis. It was his upper bound that actually turned out to be right for US production. If you haven't read the 1956 paper, do so. It is very interesting.
Hubbert presented the logistic equation later WHT and Deffeyes have documentation on it. I don't disagree with anything you just said. My understanding is the logistic curve was introduced by Hubbert. And yes like any curve fitting method you need at least some reason to thing the data and the model are in rough agreement.
The main point is that the focus should be on the dampening term and in cases where bot HL and shock apply its instructive to understand how the the real term and the empirical term happen to give the same answer.
Its easy enough to throw out HL just takes a small amount of work to correlate the two models. The reason this is important is we have used the empirical HL model a lot we need to show how we moved to a new model. And a bit on why the old one worked.
Its just curve fitting in one case we have a non-physical logistic curve that fits and a better model that fits the data. All you need to do is show the terms in the better model that correlate with the terms in the empirical model.
This can be done with simple parameter variations to show where and when the two models are close.
Another reason to do this is it gives us a better understanding of the physical dampening terms vs the term used in the logistic. Its hard to grok why the logistic one works. And its not obvious what the real term should be.
One problem with the Logistic model is that it's not related to the physical reality of the oil extraction process (which is one of WHT's main argument). It's basically an empirical curve fitting approach that happens to have one of the most easiest fit possible (i.e. a straight line) hence its popularity.
The shock model needs a discovery model to enable it to be used in the same way as the Logistic is used, namely as a self-contained model that uses only discrete parameters but that can fit a URR along with a production curve. The fact that the Logistics model can subsume both a physical discovery model and a physical extraction model at the same time blows my mind. It's almost as if it is too good to be true, and what we will eventually find is that it is indeed too simplistic to be true.
Thus, the effort we put into this analysis.
:)
Funny you say that its fascinating that it seems to work well when used correctly.
To be honest I'm interested in a better model like the shock model simple to see if it sheds some light on why a logistic function seems to work so well for oil production.
Nothing short or brilliant insight would have cause you to choose it for a simple empirical model.
I really wish Hubbert hand explained why.
Short of this we know that at least in some cases a physical model must match the logistic so maybe it will give us some insight.
I have a new theory on the why of the Logistic model. It is called the Theory of Convenience.
http://mobjectivist.blogspot.com/2007/04/how-to-generate-convenience.html
I always thought the Logistic model makes absolutely perfect sense in the context of reproducing biological entities with a constrained food supply. But I can't for the life of me treat oil molecules as reproducing entities unless we replace oil with people as the random variable. And that to me is a scary thought. To paraphrase Soylent Green, "Oil is people!".
Hubbert was very concerned with human population. Hubbert was alive as the Green Revolution kicked off and he surely new that it was powered primarily by fossil fuels.
That's a scary thought, WHT, but what if it is right?
Ghawar Is Dying
The greatest shortcoming of the human race is our inability to understand the exponential function. - Dr. Albert Bartlett
I agree with your analysis in the link what's fascinating is you can get a good fit using HL.
In any case we have examples where the logistic is providing a very good fit. I'd like to see the more realistic shock model applied to the same examples so we can see why the real shock model converges on the hl. You basically have the right answer its hidden in a trick dampening term. But why that form and is it really just a proxy which it should be for the correct dampening term.
Using the shock model you should be able to derive the correct equation that hl just happens to approximate and more important we can find the "real" terms that are the key to this approximation.
I'm happy too throw out HL but you need to show in a few cases where it does work why it worked on the other side this will also show how it fails.
Then we can just dump it.
Hopefully we can shoot it in the head correctly.
But it is pointing to a damping effect that should also arise in the shock model. What I've not seen you do is explain the correlation. So what is the relationship between the correct shock model and the empirical logistic equation.
What in the real model leads to this fudge factor working ?
Thats the one piece I'd like to see once you have that we can dismiss HL and use a better model.
I think this boils down to the non-linear damping term and what does this correlate with in the shock model ?
I don't think the form of the growth term is all that important.
And if you think about it the important piece of all of these model is the dampening effect the growth term can be any form even linear. The shock model seems to give the correct growth side but what exactly is the dampening term and why does the logistic one fit ?
Next you seem to imply a non-linear dampening effect is bad but why ?
To wrap up the growth in production can be modeled fairly well the shock model seems to have the most important parameters whats not well understood is how to model the complex process related to the field geology that result in peak and decline.
The logistic works because of a fudge factor that causes the curve to fit but contains no intrinsic physical interpretation.
At least thats my problem. Its not the growth but the decline
I don't understand. And of course I don't understand the shock model well enough to pull this out. Finally the model presented so far in this thread does not seem to be the right one on the decline side in the first place which is the juicy part :)
Don't agree re:Verhulst, and I'll be schizo about it.
1. I agree that the damping term makes no physical sense, but the source term makes no more sense than the damping term. Oil wells (I'm no expert here, so feel free to correct me) don't breed, so a source term that is proportional to the current number of wells makes no physical sense.
2. OTOH, the Verhulst equation converges to a value which in population dynamics is the maximum sustainable population. Perhaps one really can associate global URR with this limit (which is really what we do when we do HL). One can further stretch the analogy to argue that initial growth is logistic because the more we have, the more uses we find for this magic black goop and the more effort we expend finding the stuff. But eventually diminishing returns hits: fields deplete, new sources become scarce, and we asymptote (big wavy hands here -- in this case the functional form of the damping can be argued) to a limit.
3. OT3H, there is an underlying assumption that changes in production are continuous. Is that reasonable? At fine enough resolution that does not appear to be the case. If the behavior is essentially logistic, whether it is continuous or discretized can make a huge difference. Three possibilities here: a) the system is logistic and continuous; b) the system is logistic and discontinuous but the growth rate is small enough to avoid the chaotic regime; c) the system is not logistic. b) is interesting because that would imply that URR depends on the growth rate (how hard we suck).
I'm not arguing in favor of HL and actually never have.
As a empirical model it works. Any real model will give a similar result which means it probably will have a interesting dampening term. Where both models work my interest in in the nature of the dampening term. Because as you know stated an attempt to match HL to physics is pretty wacked.
On the source side I think thats less important since changing the source function is really just a matter of better curve fitting in the case of the shock model it can be matched to the physical process. I'm not saying its not important in that sense but it the dampening term that leads to peak and decline and at least for HL is a very strange non physical term but since the curve can match real production what is the form of a physical dampening factor that gives the same answer ?
As of now I can only see the matching if the real model has a similar set of conditions as hl but that does not make sense why would something like a logistic function drop out ?
Empirical curve fitting does not require the function to have any physical meaning but when you have such a strange function gives a good fit it makes you wonder what the real model will give.
A post postmortem on the abandoned HL model and why it happens to work is interesting. And I think needed before we abandon the method. The answer may be trivial but its needed to justify abandoning HL.
The flip side is also true if HL is still giving a better fit than a physical model you have to question the physical model. Or on the same hand if you have to add too many parameters to the physical model to make fit you have to question the model.
I don't like the damping term in the Logistic model either but I also don't necessarily like the exponential growth term.
Importantly, the shock model by itself has no growth term, apart from the "growth" from discovery to maturation of individual wells. The actual significant growth occurs in the discovery model, and this has little to do with extraction and more to do with technical prospecting. Note that the shock model assumes a discovery model, albeit in this case based on real data. This is where I marvel/wonder about the Logistic model, in that you cannot factor out a discovery profile along with an extraction profile from such a simple function. Whereas, you can come arbitrarily close to generating a Gaussian by convolving many small ditributions together (i.e. the Central Limit Theorem).
My current conjecture is that discovery follows a power law, most likely a cubic, which comes about by technology increasing the width of a prospecting zone linearly with time over the years. However, this is definitely not an exponentially increasing function.
http://mobjectivist.blogspot.com/2007/03/cubic-growth-discovery-model.html
That curve you see above is the shock model "deconvolved" to show a conjectured original discovery profile dated back to when oil was first discovered.
That makes sense to me. But the logistic is both exponential growth and nonlinear dampening is it exponential I can't tell because you did not integrate it. And I'm too lazy to try.
But to overcome exponential growth you need a exponential decay so I think I'm right just guessing.
My best guess is the model of two competing exponentials happens to result in something similar to what your saying.
The insight is to recognize that oil production results in two competing exponential functions. I don't think this is obvious from a physical model. So the contribution of HL to a physical model is to accept that the model may need to include the concepts of exponential growth and decay.
My guess right now is that growth is not exponential but that decay is but its delayed by a time constant before it sets in. The exponential growth part of HL is not important and its swamped by the decay term later and when it is in force the difference between a exponential and cubic etc is small. It just acts to fudge the lack of time delay in the decay function.
So the real model is a none exponential growth curve that gets obliterated when exponential decay sets in the decay is offset in time.
The reason decay is exponential goes back to Fractional Flows
With fractional flow diagrams you get catastrophic failure this step function averages out to a exponential decay function.
Please consider using a time delayed exponential decay that can be models as a generic version of fractional flow issues.
I've I'm right I believe this comment is important.
If I'm right and decay is a time delayed exponential thats I think very important.
Yes, two competing exponentials is exactly the right way to put it. The first is order 1, proportional to P, and the second is order higher than 1, proportional to a power of P. So the growth is strong initially and the high order damping is sitting in the background, waiting to take over as soon as the power law starts asserting itself.
He needed two exponentials since he did not know when to start the decay process. The reason for the strange equation is he is starting exponential decay at t0 which is not correct so he needed a function that allowed oil to be created to offset the exponential decay. The easiest way to do this is to allow the oil to "breed". He knew the decay function was eventually exponential but its difficult to determine when you should turn it on.
So HL is a good simple compromise equation that works.
But the shock model should model decay as a exponential thats delayed by time t from when the field starts production.
We actually know about when it kicks in from HL is between the first inflection point and the peak for sure by the time
the field is 60% depleted but this is I suspect late.
The underlying physical process that governs the decay depends on each field but its either fractional flow in a water drive field or expanding gas cap or loss of pressure.
If you think about it all of these processes lead to individual wells effectively ceasing production instantly compared with the productive lifetime of the well.
But this process does not really turn on until the field has
been in production for some time for quite a while you can
model the field as a big pool of oil in rock and ignore depletion effects or at the least its a linear function.
To fine tune the model you may allow a little for a linear depletion function that starts at t0 not sure its worth the effort.
Yes their is a little bit of play but from a big model wells are either in production or they cease production.
Lets finish the shock model and I think I can now explain why HL works and why the shock model is a better model and
we no longer need HL :)
Although turns out its not really a bad model if you understand how it works which explains why it fits the data.
In any case I'm happy now. The only real issue I see is when should exponential decay start for a field ?
One more thing if you change recovery methods sequentially you effectively turn off the exponential decay and restart the model. So if its just simple pressure drive then you go into exponential decay then turn on water drive the decay term goes back to zero or linear and everybody is happy for a bit longer. This is because your back to a big pool of oil moving and the new decay process is turned off for a time.
So at the field level depending on how its developed you could have multiple exponential decays that are turned on and off by changes in the way the field is produced.
Again in general the exponential decay function become a factor when the field can no longer be treated as a big pool of oil in rock.
A possibility. Because of the stationarity of the model's premise the "restarting" has to be spread uniformly over time; only real oil shocks (i.e. economic decisions, etc) can be applied at an instant in time.
I think the recovery transition you refer to has a lot to do with when "reserve growth" kicks in. So that before you select the new recovery method, your proven reserves are a specific amount and then after you kick in the new recovery, the reserve growth re-estimates get applied.
I believe that is the new functionality that the oil shock model needs for it to work better as a predictor than as a historical analysis tool.
But the shock model should model decay as a exponential thats delayed by time t from when the field starts production.
That's in there if you look at Figure 1. Choose the delay corresponding to the Maturation latency.
What I'm thinking is fractional flow introduces another declining exponential with a lot larger decline rate then what your modeling right now. It kicks in as the system switches from mainly oil moving to mainly water moving then decays to
a non-zero constant. This could be seen as the remaining reserves suddenly shrinking also ? So I'm saying its two exponential decay terms.
In any case I'll wait to see how you put it into the shock model. The interesting part is how you roll off the plateau.
Its this second term from fractional flow that is dominate and steep coming of the plateau.
This is the best I can do as it stands now for modeling the maturation+extraction profile for an "average" well. Starting from first extraction it lloks like this, for a given Maturation time constant and extraction time constant:
I contend that you can never create a flat plateau on an extraction model that requires a statistically averaged set of profiles to work. By the same token, we can't change the tail behavior either. This is a basic central limit theorem kind of argument.
The only possibility I can offer is that you create another shock model that operates in parallel to this one and works on the "after plateau" regions. But then you would have to estimate a new Maturation time constant for this model, which defeats the purpose, and only adds extra complexity.