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Marchetti's Curves - Why the Hubbert Peak is a problem

by Luis de Sousa Mon Jul 9th, 2007 at 05:58:08 AM EST







This is a digest of an article posted at The Oil Dum : Europe on the Energy Susbstitution Model developed by Cesare Marchetti in the 1970s at IIASA. Using data from the latest BP Statistical Review the evolution of the energy market is compared with the model to understand why the Hubbert Peak of fossils fuels represents a problem today.




Cesare Marchetti is a renowned Italian researcher that started working in the field of Nucelar Energy in the 1950s. We would be at Euroatom in the 1960s and moved on to the IIASA in the 1970s, where we would stay for life. We would broaden his studies to Energy Systems, Transport Systems, Population Dynamics and much more.

Among his many research projects, those that would have more impact would be the concept of hydrogen as an energy vector (later name Hydrogen Economy), the concept of atomic isle and the self sinking of nuclear residue. While at IIASA he developed the Energy Substitution Model, that explained the energy market dynamics.

Using data for Wood, Coal, Oil and Natural Gas, Marchetti found that the long term market penetration of these energy sources was ruled by logistic growth and decline. In his first paper on the Energy Susbstitution Model [pdf]  from 1977 the results published were these:










The Energy Substitution Model identified by Marchetti in 1977. Click for full image.

This chart showed a very important thing: all of the Industrial Age energy sources follow a similar trend when entering the market. It takes 40 to 50 years for an energy source to go from 1% to 10% of market share and an energy source that eventually comes to occupy half of the market will take almost a century to do so, from the epoch it reaches 1%.

Using the data from the latest BP Statistical Review of World Energy, it is interesting to compare the 1970s model with what happened henceforth:










The Energy Substitution Model from 1977 and data from the BP Statistical Review of 2007. Wood fuel data from FAOSTAT. Click for full image.

Although overall the market didn't follow the model,  it is essential to observe that the growth trends were only broke during the Oil crisis, Nuclear energy's spectacular growth occurred between 1975 and 1985. Besides this brief event never the growth trend was surpassed.

The last time an energy source crossed over 1% share of the energy market was 35 years ago. The last time an energy source crossed over 10% share of the market was more than 50 years  ago. This is why the Hubbert Peak is a problem today.

Read the full text at The Oil Drum Europe.



The early Energy Substitution Model is described and analyzed in detail in the following papers:

Marchetti, C., 1977
Primary Energy Substitution Models: On the Interaction Between Energy and Society,
Technological Forecasting and Social Change, 10:345--356

Marchetti, C., 1979
Energy Systems -- The Broader Context,  
Technological Forecasting and Social Change, 14:191--203

Marchetti, C., and Nakicenovic, N., 1979
The Dynamics of Energy Systems and the Logistic Substitution Model part I part II,
RR-79-13, International Institute for Applied Systems Analysis, Laxenburg, Austria

Display:
This (from the longer article) is one key point to debate:
The last time an energy source crossed over 1% share of the energy market was 35 years ago. The last time an energy source crossed over 10% share of the market was more than 50 years ago. This is why the Hubbert Peak is a problem today.

To have a new energy source with 10% of the market by 2010, it had to have crossed the 1% threshold by 1970 the latest. Using the same metaphor, It seems that Alice feel in love with some flowers and forgot about picking more.

Does this mean that abandoning Nuclear energy was an error? Possibly. But more relevant than abandoning Nuclear energy was doing it without opting for an alternative. Abandoning Nuclear could have been an option back in the 1970s if a clear alternative had been pursued with proper research and development.



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by Migeru (migeru at eurotrib dot com) on Mon Jul 9th, 2007 at 06:18:03 AM EST
I just read the first paper. Wow. Thanks for bringing it up.

Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Mon Jul 9th, 2007 at 11:25:56 AM EST
In the first paper, Marchetti writes:
I started from the somewhat iconoclastic hypothesis that the different primary energy sources are commodities competing fora market, like different brands of soap or different processes to make steel, so that the rules of the game may after all be the same. These rules are best described by Fischer and Pry, and can be [summarised] in saying that the fractional rate at which a new commodity penetrates a marketis proportional to the  fraction of the market not yet covered.
One can write this as

F'/F = a(1-F)

He then shows some examples from actual data, and says

All of them refer to competition between two products. In the case of energy we have three or four energy sources competing most of the time and it is mathematically impossible that [the sum of all the F's equal 1], so I had to extend the treatment slightly with the extra stipulation that one of the fractions is defined as the difference to one of the sum of the others. This fraction follows approximately an equation of [the above type] most of the time, but not always. It finally shows saturation and change in coefficients. The fraction dealt with in this way corresponds to the oldest of the growing ones. The rule can be expressed in the form: First In, First Out.
After thinking about this for a while, I think Marchetti made a mistake there, though maybe not a very serious one.

With two products, with market shares F and G adding up to 1, one can write

F'/F = a G

which implies

F' = a F G

and, given that F' + G' = 0,

G'/G = -a F

So, in the case of two commodities the Fischer-Pry model is compatible with F + G = 1. Now, suppose we have F1, F2, F3, ... Then, Marchetti is right that

F1'/F1 = a1 (1 - F1)
F1'/F2 = a2 (1 - F2)
...
Fn'/Fn = an (1 - Fn)

is incompatible with F1 + ... + Fn = 1. However, realising that 1 - F1 = F2 + F3 + F4 + ... + Fn, one can see that the "proper" generalisation of the Fischer-Pry model to n > 2 commodities is

F1'/F1 = a12 F2 + a13 F3 + ... + a1n Fn
F2'/F2 = a21 F1 + a23 F3 + ... + a2n Fn
...
Fn'/Fn = an1 F1 + an2 F2 + ... + an{n-1} F{n-1}

which is compatible with F1 + ... + Fn = 1 as long as a{ij} = - a{ji}.

The coefficients a{ij} are a measure of the rate at which the ith commodity takes market share away from the jth one (or loses market share if the coefficient is negative).

So, question: do we have the necessary data to fit this extended model and compare it with Marchetti's simpler one?

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Mon Jul 9th, 2007 at 06:29:27 PM EST
[ Parent ]
Sorry for leaving this unanswered yesterday, but I had to leave.

It would be interesting to use the data prior to, say 1975, to see the result. I don't have data prior to 1965, but for Oil, Coal and Natural Gas they likely exist.

Do you want to dig deeper into this? We could try to find that data.

You might find me At The Edge Of Time.

by Luis de Sousa (luis[dot]a[dot]de[dot]sousa[at]gmail[dot]com) on Wed Jul 11th, 2007 at 03:20:32 AM EST
[ Parent ]
Yes, I would actually love to see the data.

Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Wed Jul 11th, 2007 at 03:34:33 AM EST
[ Parent ]
Got it, thanks!


Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Wed Jul 11th, 2007 at 06:34:49 PM EST
[ Parent ]
This is the logistic plot of the "market shares"

It seems that, in terms of market share both nuclear and gas have recently peaked, and the slack is being picked up by coal. As for oil, it peaked during the 1970's oil shocks.

Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Fri Jul 13th, 2007 at 05:55:42 PM EST
[ Parent ]
And this is the year-on-year fractional variation:

15 years of "business as usual", and the only salient feature in the last couple of years seems to be the rise of coal.

Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Sat Jul 14th, 2007 at 07:54:59 AM EST
[ Parent ]
Regarding the secular increase in the aggregate amounts of energy used, I am reminded that although the differential equation

dX1 = a X2 dt
dX2 = -a X1 dt

describes a circle of constant radius, the stochastic (Ito) differential equation

dX1 = a X2 dt
dX2 = -a X1 dt

implies

d(X1^2 + X2^2) = 2X1 dX1 + 2 X2 dX2 + dX1 dX1 + dX2 dX2 = a^2 (X1^2 + X2^2) dt

or

d(R^2) = a^2 R^2 dt

that is, R^2 grows exponentially with time in the stochastic case, even though it is constant in the ordinary case.

So, the secular 2% increase in total energy use might be "explained" by interpreting the extended Fisher - Pry - Marchetti model as a stochastic (Ito) differential equation.

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Wed Jul 11th, 2007 at 07:20:12 AM EST
[ Parent ]
Pfft! Brainfart alert!
the stochastic (Ito) differential equation

dX1 = a X2 dt
dX2 = -a X1 dt

implies

d(X1^2 + X2^2) = a^2 (X1^2 + X2^2) dt

should be
dX1 = X2 (a dt + s dz1)
dX2 = X1(- a dt + s dz2)

implies

d(X1^2 + X2^2) = a^2 s^2 (X1^2 + X2^2) dt + X1 X2(s1 dz1 + s2 dz2)

Same conclusion, more complicated formulas.


Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Wed Jul 11th, 2007 at 07:33:10 AM EST
[ Parent ]
More brainfarts. I give up.

Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Wed Jul 11th, 2007 at 07:39:33 AM EST
[ Parent ]
I now have a formula for a best estimate of a{ij} at each step:

a{ij} = [(dFi/Fi) Fj - Fi(dFj/Fj)] / [sum{k} Fk^2]

I will apply it to the BP+FAO data to see what the coefficients look like over the past 40 years.

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Fri Jul 13th, 2007 at 05:49:30 AM EST
[ Parent ]
of ProgressiveHistorians, a community site dedicated to the intersection of history and politics, I would be honored if you would cross-post this excellent diary there.

The Crolian Progressive: as great an adventure as ever I heard of...
by Nonpartisan on Tue Jul 10th, 2007 at 11:43:02 PM EST
Ok. What do I need to do?

You might find me At The Edge Of Time.
by Luis de Sousa (luis[dot]a[dot]de[dot]sousa[at]gmail[dot]com) on Wed Jul 11th, 2007 at 03:10:59 AM EST
[ Parent ]
points to a deeper problem:  

Our civilization, throughout its history, has treated ALL energy sources as non-renewable, and exploited them to exhaustion, even when they were not intrinsicly so.  

You could say that we got our warning when Europe deforested, and everything else since then has just been conning and delusion.  

Why?  Because trees are renewable, AND YET we harvested them into (practical) extinction.  

Without an underlying change of mind, we will do this to every resource that exists--as we ARE doing--until we simply turn up unlucky and find no new resource to loot out.  

That is bound to happen sometime.  

Tant pis.  It looks like somtime is now.  

Not only do we not have a future, we NEVER had a future:  This was our fate from the outset.  It is all there in the Greek myth of Erischthon.  

How does that one end?  Starving, and then devouring ones own flesh--to starve FOREVER.  

The Greeks knew:  They had already done that.  The Greek civilization that DID do that is pretty well lost from history, even from archaeology.  The dark age that followed it consumed all the evidence and traces, except for a few broken-down piles of stone, a few graves the robbers missed, and a few stories of warning.  

You can't toy with the Fates.  

It is SERIOUSLY unwise to try.  

We will soon learn in full.  

Thank you for your interesting, depressing, diary.  

The Fates are kind.

by Gaianne on Wed Jul 11th, 2007 at 02:11:39 AM EST
Our civilization, throughout its history, has treated ALL energy sources as non-renewable, and exploited them to exhaustion, even when they were not intrinsicly so.

Jared Diamond gave examples of Japan in the Edo period (reversed deforestation) and then some Pacific island where they decided to limit the population to 1000 or so, and get rid of all pigs. Societies can be aware and manage the resourses.

But aghr... those examples are not exactly of "our" civilisation, or are they?

by das monde on Wed Jul 11th, 2007 at 11:11:02 AM EST
[ Parent ]
But aghr... those examples are not exactly of "our" civilisation, or are they?  

Too true.  A different current, that has only touched ours recently.  What is the hope of learning from it?  

The Fates are kind.

by Gaianne on Thu Jul 12th, 2007 at 10:50:38 AM EST
[ Parent ]
Your evidence that all these curves are logistic points to a deeper problem: Our civilization, throughout its history, has treated ALL energy sources as non-renewable, and exploited them to exhaustion, even when they were not intrinsicly so.
Considering "all these curves" refer to non-renewable resources (coal, oil gas, nuclear) it's not surprising that our civilisation has treated them as non-renewable. The only renewable source in the data is wood, and 1) its share of primary energy production is in decline; 2) by construction in the Marchetti model it is not a logistic decline; 3) even though its market share is declining, wood is not exchausted: its rate of consumption is still growing.

Given the information in this diary and in Marchetti's first paper it is not obvious that the absolute consumption (as opposed to "market" share) of each energy source is logistic.

But you are right, from other sources we know that we are perfectly able to exploit renewable resources to extinction (fisheries and European forests are good examples).

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Wed Jul 11th, 2007 at 06:51:16 PM EST
[ Parent ]
Considering "all these curves" refer to non-renewable resources (coal, oil gas, nuclear) it's not surprising that our civilisation has treated them as non-renewable.  

I might have said it better.  Look at it this way:  How SHOULD a civilization treat a non-renewable resource?  Sparingly, perhaps?  That the curves are logistic shows that our attitude is NOT sparing.  

The Fates are kind.

by Gaianne on Thu Jul 12th, 2007 at 10:58:55 AM EST
[ Parent ]
Actually, logistic consumption seems like a reasonable way to go about it. Given that you will use the resource, using it at a rate proportional to how much is left ensures that you never run out of it.

It is using a renewable resource like it's non-renewable (depleting the stock instead of just harvesting the new production) that is insane.

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Thu Jul 12th, 2007 at 11:15:55 AM EST
[ Parent ]
Which has merit.  

But if resources were utilized this way, you would see a short steep upslope representing the development of the technology and utilization of the resource, and then a long slow downslope representing its sparing (but logaritmic) utilization.  

What we see in stead is maximization:  The resource is simply utilized as fast as possible, and the upslopes and downslopes are nearly the same.

The Fates are kind.

by Gaianne on Thu Jul 12th, 2007 at 02:43:24 PM EST
[ Parent ]
When substantially less than the total amount available has been consumed, effectively the amount available appears infinite and there's no reason not to grow exponentially. When a majority of the amount available has been consumed, the end is in sight and one can consume a constant fraction of what's available. The logistic curve, where the up and down slopes are mirror images, is the simplest way to bridge the gap.

Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Thu Jul 12th, 2007 at 06:30:16 PM EST
[ Parent ]
amount available appears infinite  

What can I say?  From the OUTSET the end was foreseen.  "Appears infinite" maybe, but it is a WILLFUL delusion.  

The Fates are kind.

by Gaianne on Thu Jul 12th, 2007 at 09:18:21 PM EST
[ Parent ]
Hmm, look at it this way.

Assume that the growth of estimated reserves is logistic, and assume that consumption is a constant fraction of estimated reserves. Since the growth phase of a logistic is very approximately exponential, you get exponential growth.

The "Zeno approach" is unrealistic, also in that it assumes superexponential growth at the beginning, as the technology develops (quickly going from zero consumption to its all-time maximum value). To assume that this is possible is to ignore all the frictions in training people, investing, building infrastructure, and then when the target rate of consumption has been achieved, laying everyonw off and disusing the plants used to build the infrastructure.

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Fri Jul 13th, 2007 at 03:33:44 AM EST
[ Parent ]
(Is that what you are doing?)  

So, if I understand you right, humans are NOT smarter than yeast.  

Maybe we need a better theory.  

The Fates are kind.

by Gaianne on Fri Jul 13th, 2007 at 05:13:07 AM EST
[ Parent ]
So, if I understand you right, humans are NOT smarter than yeast.  

In groups, when we're not paying attention? No, we're not.
by Colman (colman at eurotrib.com) on Fri Jul 13th, 2007 at 05:24:29 AM EST
[ Parent ]
In groups, when we're not paying attention? No, we're not.  

So then, we need to learn to pay attention?  

Come to think of it DeAnander has been saying that for months . . .

Straight Zen.  

The Fates are kind.

by Gaianne on Fri Jul 13th, 2007 at 06:07:40 AM EST
[ Parent ]
Almost everyone here has been saying that for a long time.
by Colman (colman at eurotrib.com) on Fri Jul 13th, 2007 at 06:08:48 AM EST
[ Parent ]
What I'm doing is telling you that your model assumes perfect information. For instance, that from the outset you know reliably what the total amount of reserves is.

I also don't understand what's wrong with logistic growth. Unless you have perfect information you can't do much better than that.

What is wrong is overshoot and collapse. If yeast achieves logistic growth, it's pretty smart. Probably smarter than humans. Though I don't think yeast achieves logistic growth either.

You've also (or was it DeAnander?) in the past claimed that even the Lotka-Volterra model (prey = renewable resource, predator = us) is "a wrong model". I don't see how it fails to represent human collective behaviour, as far as the hypotheses go. It also predicts overshoot and collapse.

I don't believe in master planning, be it theological, capitalist or socialist. Do you?

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Fri Jul 13th, 2007 at 05:30:46 AM EST
[ Parent ]
You don't believe master planning happens, or you don't believe its (ever) a good thing?
by Colman (colman at eurotrib.com) on Fri Jul 13th, 2007 at 05:33:28 AM EST
[ Parent ]
it's a good thing.

I'm having a bad run on that this week.

by Colman (colman at eurotrib.com) on Fri Jul 13th, 2007 at 05:34:02 AM EST
[ Parent ]
Everyone runs around trying to imagine what they would do if they had perfect information, and then they go and apply their conclusions to the real world and wonder why it didn't work.

So, I believe it happens all the time, and I believe it can never work.

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Fri Jul 13th, 2007 at 05:37:06 AM EST
[ Parent ]
Just what any mathematician knows, before pulling out a calculator ;)  

Too much to ask, right?  

In our case, all resources are finite.  So you know you will run into trouble in ten years, or ten million years.  Which is it?  You watch and see.  Well before it happens you should be making your plans to recognize it and switch out when you need to.  

But really, everything we are arguing about was predicted decades ago, sometimes centuries.  That's why I used the word "willful."  

To be specific, the troubles we are in right now were perfectly plain by the 1970s.  We did not seek to switch out, even then:  We raced at the cliff.  

If yeast do that, that is their problem.  But when WE do that, it is OUR problem.  

Now I am not arguing you are wrong--or at least, not always wrong, but since there certainly are peoples who did not follow our path it would be good to know how they did it--what their mind was.  

You can certainly do better than logistic growth--if it leads to destruction--by anticipating that.  You do not have to limit yourself to responding to first derivatives, and then discovering afterward that you have walked into a dead-end box.  

I don't see how it fails to represent human collective behaviour  

Well, it predicts some human behavior, particularly OUR human behavior, but since we are destroying ourselves perhaps the model is fine as a description of us but very bad as advice.  That is, it describes well precisely what we should not do.  We should do something else.  

It would be better to follow a model that does not lead to self-destruction, even if self-destruction can be modeled very well.  

I don't believe in master planning,  

Anyone who does not do their own master planning is courting trouble--this is true for individuals and groups.  Plans have to be flexible to work.  But if they do not exist, they certainly don't work.  

The Fates are kind.

by Gaianne on Fri Jul 13th, 2007 at 05:57:45 AM EST
[ Parent ]
I claim logistic growth does not describe destruction. You get overshoot and collapse when you couple the logistic equation with delayed feedback.
To be specific, the troubles we are in right now were perfectly plain by the 1970s.  We did not seek to switch out, even then:  We raced at the cliff.
Well, yes, I wonder if Dennis Meadows will live long enough to get the Nobel Prize in Economics for The Limits to Growth.

Anyway, can we agree that these logistic or predator-prey models approximately describe the way our civilisation currectly functions?

The questions are: how else could it function? [I still haven't seen a simple model of that, can you provide one? Use however many derivatives you like, and delayed feedback]; how do we get there from here?; how many people can be sustained?

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Fri Jul 13th, 2007 at 06:11:42 AM EST
[ Parent ]
You forgot the last question, though it might be implicit: how does the new system protect itself from change? One of the strengths of the existing system, from its point of view, is that it's very resistant to change because the short-term interests of many people depend on its not changing.
by Colman (colman at eurotrib.com) on Fri Jul 13th, 2007 at 06:14:54 AM EST
[ Parent ]
I think I have a partial idea of how to get there from here, though: guarantee everyone a living income (say, above relative poverty level: 60% of median). Rewards those who do work but let people not work if they don't feel like they need more income than the guaranteed minimum. Share work by limiting the working week. If the absolute living standard starts to sag, more people will be motivated to work to make up the difference. If anyone rants about the protestant work ethic, lock them in an insane asylum.

Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Fri Jul 13th, 2007 at 06:22:41 AM EST
[ Parent ]
Oh, and tax wealth (property).

Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Fri Jul 13th, 2007 at 06:23:15 AM EST
[ Parent ]
Wind in 2006 was around 0.3% of total global consumption (and near 1% of global electricity). It should pass the 1% in five years or so.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Wed Jul 11th, 2007 at 07:59:51 AM EST
In terms of F/(1-F), for the purposes of adding it to the charts,

  1. F = 0.3% <> F/(1-F) = 1/332 = 10^{-2.5}

  2. F = 1% <> F/(1-F) = 1/99 = 10^{-2.0}

Assuming the logit is linear in time and goes from -2.5 to -0.53 in 6 years, one could estimate

  1. F/(1-F) = 10^{-1.5} = 1/32 <> F = 3%

  2. F/(1-F) = 10^{-.5} = 1/3.2 <> F = 24%

  3. F/(1-F) = 10^{.5} = 3.2 <=> F = 76%

Of course, this assumes there isn't another energy source that starts growing after wind (biomass, solar, geothermal, a nuclear fission renaissance, nuclear fussion...). But it shows that tripling its market share in 6 years is an extremely rapid increase.

Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Wed Jul 11th, 2007 at 08:14:52 AM EST
[ Parent ]
Gah, more brainfarts
2030: F/(1-F) = 10^{-.5} = 1/3.2 <> F = 24%

2042: F/(1-F) = 10^{.5} = 3.2 <=> F = 76%



Can the last politician to go out the revolving door please turn the lights off?
by Migeru (migeru at eurotrib dot com) on Wed Jul 11th, 2007 at 08:16:42 AM EST
[ Parent ]
It also assumes a switch to electric heating and transportation.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Wed Jul 11th, 2007 at 08:50:14 AM EST
[ Parent ]
I think that follows from the calculation.

In other words, the inputs to the model are the flavours of primary enrgy and their historical market shares. The outputs are forecasts of market share.

Given a forecast market share of 76% for wind in 2042, it follows that transportation and heating must be electric.

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Wed Jul 11th, 2007 at 08:52:56 AM EST
[ Parent ]
mmm, we may have a case in model run amok (you know, when the model says that 253% of families own a car, etc...)

Pierre
by Pierre on Wed Jul 11th, 2007 at 09:19:08 AM EST
[ Parent ]
If you look at Marchetti's original chart, many energy sources seem to peak around 70%.

In this case the model just assumes wind is the last energy type to enter the mix and is not replaced by anything else down the line. Also, nothing is said about total energy consumption, only market share. Even optimists admit that Oil and gas will be rather scarce by 2040 and too precious to burn for energy.

The problem with nuclear fission is that (as Luis' chart shows) it seems to have peaked at 10% (possibly for political reasons), and oil at 50%.

Extrapolation is always unreliable but in this case. due to the logistic assumption, you can't have 150% of energy from wind.

Can the last politician to go out the revolving door please turn the lights off?

by Migeru (migeru at eurotrib dot com) on Wed Jul 11th, 2007 at 09:29:49 AM EST
[ Parent ]


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