The Rupture Index *

* An informal model of the global fossil fuels supply chain as a scale-free network

[editor's note, by Dave] Throughout, I will refer to the the global fossil fuels supply chain construed as a network by the acronym GFFSC. There is only a little math in this post. I will be referring to some pages where they do the math. This is meant to be a "naive", intuitive treatment. The mathematicians among us can take the ball and run with it.

I spend a lot of time worrying about ruptures in the GFFSC and what their effects will be. Standardly, these are called oil shocks at TOD. I just picked up the July 1-7 issue of New Scientist and there were two related articles of interest to me, "The Net Reloaded" and "Life is Unpredictable". Sorry, they are both behind a paywall. But I will refer to them in the text below. Ever since Stuart had mentioned Didier Sornette in his excellent post Is Oil In A Price Bubble?, I had also been thinking about so-called endogenous versus exogenous origins of crises, as Sornette puts it. The latter are forcings from outside the network. In other words, oil shocks. The former are due to the inherent self-organizing nature of the network itself.

Finally, it occurred to me to model the GFFSC as a scale-free network somewhat analogous to the internet and see where that went. I have never seen this kind of analysis done before and thought it would be interesting as a new take on peak oil and our current dilemma.

If you are worried about oil shocks, it is natural to ask the questions "what are the hot spots we need to worry about" and "what is the overall tolerance of the GFFSC" to ruptures in production or consumption of fossil fuels in those places. A related question involves the degree of disruption in a given place (if we can define that).

The standard theory of scale-free networks is that they follow a power law distribution. But before we get into that, let's make the basic analogy between the GFFSC and the internet. Our naive model runs as follows.

  1. A node in the network is a country.
  2. A link (or connection) in the network is the exchange of some fossil fuel between two nodes.
  3. Nodes have links to themselves. This is simply the case where fossil fuel production is used to meet domestic consumption. On the internet, this is a analogous to internal links within a website.
  4. Links come in two flavors, outgoing (exports) and incoming (imports) with respect to some fossil fuel. Links are always reflexive ie. bidirectional (my exports are your imports). On the internet, site X may link-in site Y but not vice-versa. In other words, X exports traffic to Y and Y recieves imported traffic from X. In this sense, the analogy holds and the lack of across the board cross-linking makes no difference to this analysis.
  5. Links are not all created equal. They must be weighted (as is done in neural networks). The weight for a given fuel (eg. natural gas) could be simply the amount moved along the link in one direction or another, in this case as measured in billion cubic feet per day. Generalizing, one could use British Thermal Units (btu) to measure the weight, thus covering all fossil fuels. Importantly, weights apply to intrasite (domestic consumption) connections.
And that's it. Pretty simple, hey? Just like the internet except for the weight (#5 -- although we could make an analogy there, too). Looked at this way, a number of the stories we write or the comments that are posted are about changes in the network including
  • new (or recent) connections (Angola/China for oil )
  • stronger/weaker connections (US/Qatar for natural gas)
  • lost, or dropped connections (Indonesian exports for oil)

Finally, I must mention two aspects of the GFFSC not covered here. First, inventories are discounted. I consider those to be fossil fuels that have already been delivered (if imported) and as hedges against lost connections. Second, spot cargoes are "free floating" links looking for an attachment. They are not directly considered here but do highlight the dynamic nature of the GFFSC.

Now, from Wikipedia (see the scale-free link above):

A scale-free network is a specific kind of complex network that has attracted attention since many real-world networks fall into this category. In scale-free networks, some nodes act as "highly connected hubs" (high degree [of connectivity]), although most nodes are of low degree....

In physics, such right-skewed or heavy-tailed distributions often have the form of a power law, i.e., the probability P(k) that a node in the network connects with k other nodes was roughly proportional to k−γ, and this function gave a roughly good fit to their observed data.

Pursuing our analogy, Russia or the US are both hubs -- they are highly connected. Outer Mongolia and even Chad are not -- they have a low degree of connectivity.

But here we need a conjecture and an assumption. The conjecture is that if we assessed and counted all the import/export links in every country of the world, we would get a power law distribution. The assumption is that the conjecture is true. In any case that is my intuition about the GFFSC ie. that it is like the internet, it is scale-free to some large extent. But to strengthen our conjecture and assumption, we must add in the weight W of the connections to the degree of connectivity. So, I am really assuming that the measure of a country's importance in the network comes from some function f(D,W) where D is the degree of connectivity. A hub has a high value for f, a singly connected node (eg. the Falkland Islands) has a low value. Once we've made this move, I believe that the conjecture becomes much more plausible. One large difference between the internet and the GFFSC, however, is the overall size.

There are only so many countries in the world but the internet is made of literally billions of nodes. We could consider individual oil fields or producing basins as nodes in our GFFSC graph. This would make the network bigger but still considerably smaller than the internet. However, the power law distribution can apply to a smaller network. The standard use of the power law in the analysis of the peak oil situation applies to oil field reserves as Khebab did recently in What can we learn from the oil field size distribution? originally from his Graphoilogy weblog. Highly recommended. His analysis considers the top 2092 world oil fields (excluding the US and Canada) with sizes greater than 50 Mb (million barrels). Specifically, I am making the claim that S(g) is close to 1 as shown below.

Although the scientific community is still debating the usefulness of the scale-free term in reference to networks, Li et al (2005) recently offered a potentially more precise "scale-free metric". Briefly, let g be a graph with edge-set ε, and let the degree (number of edges) at a vertex i be di. Define

This is maximised when high-degree nodes are connected to other high-degree nodes. Now define

where smax is the maximum value of s(h) for h in the set of all graphs with an identical degree distribution to g. This gives a metric between 0 and 1, such that graphs with low S(g) are "scale-rich", and graphs with S(g) close to 1 are "scale-free". This definition captures the notion of self-similarity implied in the name "scale-free".

Visually, a power law distribution often looks like this.

Highly connected nodes and a power
law (non-gradual) relaxation

Looked at another way, here's Wikipedia's illustration of a scale-free network.

The dark nodes are hubs -- Click to Enlarge

My strong intuition is that the GFFSC is not a random network. And if you think about it, that is just obvious. There are two standard results as regards scale-free networks. The first is that strongly connected nodes (using our function f above) garner more connections over time. This is known as the rich get richer or winners take all. The second result is that a disruption (oil shock) in a highly connected hub can have a cascading effect in the network, thus bringing it down. Let's take our analogy further for both results.

Regarding the rich getting richer, as oil declines continue in various countries (eg. the UK, Indonesia, Mexico), export connections in the network are dropped though they may be replaced by incoming links -- imports. On the other hand, for the rich, like Saudi Arabia or Russia, the number of connections increases. For example, China has recently renewed efforts to establish connections with Saudi Arabia and other Middle East suppliers. This results in a higher degree of weighted connectivity for both countries. The rich get richer. In particular, as Wikipedia notes, "these scale-free networks do not arise from chance alone". What is required to model a network this way is to define a growth process. In the usual case, this is referred to as preferential attachment (see the scale-free networks link cited above). In the case of the GFFSC network, this can be described by this fairly simple formulation which quotes Billie Holliday:

Them that's got shall get
Them that's not shall lose

Those who have the fossil fuels and export capacity and can easily support their own needs or can pay for their required imports will thrive -- the value of f(D,W) increases. Those who can not do either will suffer -- the value of f(D,W) decreases.

For our original topic, oil shocks, the analogy is even stronger. If a strongly connected fossil fuel consuming or producing nation (hub) is "taken out" to a some (undefined for now) extent, the results for the network as a whole could be disastrous. We need to look more closely at this question. Would the effects cascade thoughout the entire network causing damage everywhere? Or is the network resilient enough to absorb the loss of a hub and keep the damage in the immediate network neighborhood?

As described in the first New Scientist article "The Net Reloaded", John Doyle of MIT casts some doubt on the internet as a scale-free network following a power law distribution. Speaking of the internet, we read

After finding that this power law described the statistics of internet routers, Barabisi and colleagues [who discovered the scale-free network/power law result for the internet] used a theoretical network with the same proportion of highly connected routers to model the net, and from this idea came the idea that eliminating highly connected routers [hubs] could shut the net down. Doyle argues that this approach, which superficially attractive, ignores a simple fact: the highly connected routers are ISPs [internet service providers] on the edges of the network, close to end users.... Take down highly connected routers around the US and you'll knock out ISP's that serve users in certain neighborhoods.... [But] the bulk of internet data ... will flow unimpeded....

The router example reveals the weakness of scale-free models as a predictor of how a system will behave .... A useful model would specify what the nodes do, where they are in the network and how their connections work.

Toward making a more accurate model of how the internet behaves, Doyle and others have developed the highly optimised tolerance (HOT) model as briefly described in the link above. "With HOT", Doyle explains, "we're trying to explain [in simple models] that are more faithful to the specifics of the domain, what is general about complex networks". Look here to find out more about HOT modelling of complex networks.

Following Doyle, we must pay attention to the specifics of the network domain which I've defined as the Global Fossil Fuels Supply Chain [GFFSC]. I do not know how HOT would model this domain but in terms of fault tolerance concerning the vulnerability of hubs to disruptions in that domain, we can observe the following:

  1. There is no little or no spare capacity in the network. This is a bit like saying that there is an internet routing system without extra bandwidth. If a major hub like Saudi Arabia (eg. Ras Tanura or Abaqaiq) goes down, the withdrawal of oil supplies on the world market guarantees a cascading ripple effect over the entire network due to the supply & demand pricing mechanism. In this sense, the GFFSC network is more of a scale-free network than the internet is. Unlike Doyle's formulation, the ISP router hubs do not lie on the periphery of the network. Think of it this way. If the Saudi hub is crippled, does that affect Angolan imports to China? Can China lose its Saudi Arabian exports network connection but strengthen it's Angola import link to compensate? If there were spare capacity (bandwidth) in the system, fungible oil can be re-routed to compensate for disruptions in the system. But that is not the case now and I speculate that it will never be the case.
  2. On the other hand, if a general war between Chad and Sudan occurs and the export link from Sudan to China is dropped, describing a case where the degree and strength of connectivity is so much lower, can China establish new import links with other suppliers or strengthen it's import links with it's important current suppliers (Saudi Arabia, Angola and Iran)? Probably. Chad and Sudan lie on the periphery of the network.
So we see that viewing the GFFSC as a scale-free network described by a power law distribution reveals the extent of the security problem. The GFFSC as I have called it is taut as a bowstring. This is why I worry about oil shocks.

A Note on Intrinsic and Extrinsic Affects on the GFFSC

Here we return to the work of Sornette linked in at the top. In his paper Endogenous versus Exogenous Origins of Crises summarized at the cited link we find
Analysis of precursory and aftershock properties of shocks and ruptures in finance, material rupture, earthquakes, sales, etc: we find ubiquitous power laws similar to the Omori law in seismology that allow us to distinguish between external shocks and endogenous self-organization.

This question, whether distinguishing properties characterize endogenous versus exogenous shocks, permeates many systems, for instance, biological extinctions such as the Cretaceous/Tertiary KT boundary (meteorite versus extreme volcanic activity versus self-organized critical extinction cascades), commercial successes....

We study the precursory and recovery signatures accompanying shocks in complex networks, that we have tested on a unique database of the Amazon sales ranking of books and on time series of financial volatility. We find clear distinguishing signatures classifying two types of sales peaks. Exogenous peaks occur abruptly and are followed by a power law relaxation, while endogenous sales peaks occur after a progressively accelerating power law growth followed by an approximately symmetrical power law relaxation which is slower than for exogenous peaks....

Please read the whole text. Sornette is talking about being able to distinguish endogenous versus exogenous influences on network behaviour after the fact. For peak oil, we are right in the middle of things. But I think it is possible to make a few observations. Among endogenous (intrinsic) causes, we note the following.

  1. As more weight is added to intra-node links (domestic consumption), other import/export connections in the network are weakened or lost. This is not analogous to the internet but rather is a specific property of the network domain we are describing.
  2. As oil field production in a country declines (eg. Mexico, Cantarell), we observe the same effect as in #1 above.
  3. Extrapolation of the discoveries curve trend is correct. The big fields are found first and are mostly all accounted for. Any large field discovered now would be a statistical outlier. This in turn suppresses the creation of new, strong connections in the GFFSC. New EOR techniques for increasing URR in oil fields will have a negligible or even damaging effect going forward regarding #2 above.

The basic observation is that Sornette's Amazon sales ranking of books is analogous to fossil fuels sales ranking of exports.

As for exogenous (extrinsic) causation (aka oil shocks) we note the following types that could affect hub nodes in our scale-free GFFSC network.

  • Wars
  • Labor Disputes
  • Terrorism
  • Natural Disasters
  • Economic Recessions
  • Political Upheavals (Coups)

This brings us to the work of Nassim Nicolas Taleb, an applied statistian who wrote the 2nd article in New Scientist Life Is Unpredictable. In particular, he is referring to Black Swans in which he distinguishes between what he terms "type one" randomness (eg. throwing a dice) and "type two" randomness (eg. a 10 kilometer bolide hitting the Earth). This latter is a Black Swan. His analysis claims that events of the latter type are effectively unpredictable and simply a matter of luck. Why do Harry Potter or The DaVinci Code win while many other worthy efforts lose? While I agree that life is unpredictable, particularly for type two randomness, I dispute any claim that the exogenous factors that could cause oil shocks (excepting perhaps Natural Disasters) fall into this category. For example, here is a list of recent conflicts in the Middle East. Not only are there current conflicts, but it would seem that new conflicts, arising from Iran and Israel for example, are fairly predictable in the future.

Still, we must admit that luck regarding exogenous events is unavoidable as it affects the GFFSC in the future. However, in line with our modeling of the supply chains as a scale-free network, I do conjecture that the rich will get richer and the poor will remain that way or become even more impoverished. For example, South American countries like Argentina are already feeling the pinch. I hope this post will stimulate some discussion of the ideas contained herein. Obviously, there is lot of stuff I didn't get to discuss. Personally, I'm not feeling particularly lucky about the future of the GFFSC. In my view it appears to be a real-world scale-free network subject to a power law distribution and the endogenous and exogenous factors affecting it as described above. To finish up on a lighter note and acknowledging the role of luck in our future, we end with a famous quote from the movies.

I know what you're thinking. Did he fire six
shots or only five? Well, to tell you the truth,
in all this excitement, I've kinda lost track
myself. But being as this is a .44 Magnum
[peak oil], the most powerful handgun in the
world, and would blow your head clean off,
you've got to ask yourself one question:
Do I feel lucky? Well, do ya punk?

Dirty Harry fired five shots, not six.

I'm not sure of the practical utility of modeling the GFFSC as a scale-free network. In an abstract sense a model like this for descriptive purposes makes sense, but in practical terms how does it help?
Hello Prodigal Son,

In practical terms, at least to me, it clearly indicates that JIT and minimizing pipelines and storage hubs to maximize profitability increases worldwide vulnerability to both endogamous and exogenous events.  The increasing power concentration inevitably leads to polarization and systemic breakdowns, but ASPO's Depletion Protocols could be a force to help normalize resource flows across the network and reduce the tendency for reduction to the minimal hub concentration.

In short, a spider seeks to maintain it's whole web to maximize it's catch versus a few strands w/intermittent blobs of silk.  We should be doing the same.

Bob Shaw in Phx,Az  Are Humans Smarter than Yeast?

Since your talking about dynamic forcings I doub't you would get any real numbers out of such a network. Basically your looking for ruptures or tears. But the tensile strenght or response of the network is abstract and basically impossible to caclulate. I'm not saying its not the right model.

Now if you can prove a positive feedback loop its easy since your on a exponetial growth pattern so you don't need to know in detail the nature of the force just the overall time scale for doubling thus it will blow up real soon now.

For peak oil I'm assuming the price of Oil doubles every two years lets say that gives us four years before rupture.

Take the Arctic and Ice loss the doubling period is lets say ten years ( there is the winter damping effect )
So if were even close the Arctic will be ice free within 30 years +/- 10 years.

My point is if you prove that you have a feedback loop and can have even a order of magnitude guess as to the doubling period ( half life ) you don't need any more sophisticated analysis for a complex problem.

So for peak oil we have much less time to respond then most people realize.

Explosions are easy.

About 30% increase per year for oil price, cuts $200 / bbl line by about 2011.

What do you mean by 'rupture' in "For peak oil I'm assuming the price of Oil doubles every two years lets say that gives us four years before rupture." ? and what might be the implication / effect of 'rupture'?

I think the Arctic is projected to be summer ice free by about 2010. Year round ice free Arctic won't be far behind.

However, situations are more complex: multiple positive and negative feedback loops are in effect, the resultant is perhaps a delicate balance of competing loops, a tiny difference here and there could become profound in a decade or two.

If business as (near) usual is the objective we have already well passed the time of response to peak oil. We are well into the catastrophic effect avoidance time and eating it fast. Yum.

By ruputure its the point at which the oil base economy starts breaking down. It would be a combination of war and major depression this is probably somewhere around the 200+ dollars a barrel.

The current predictions for a ice free artic are within 100 years.

My assertion is that once a strong feedback loop sets in it will be much sooner, 2030 with the simple metric that the amount of ice lost doubles in ten years.

Positive feedback loops have a nasty effect of soon swamping other mechanisms.

I propose that in both cases peak oil and the Arctic we have already entered positive feedback scenarios.

In the case of peak oil its triggered by the peak of light sweet oil and the "refinery" depletion factor of 25% for replacing with heavy sour grades that greatly magnified the effects of depletion beyond most estimates.

In the case of the arctic the magnifier is simple mechanical break up of ice that's not modeled. Indeed in the collapse of the one antarctic ice sheet mechanical failure prevailed.

In both cases the biggest factor for acceleration into a non-linear or positive feedback condition has been and unmodeled but significant non-linear factor.

The two kill links on the web for global warming.

I watch the artic melt everyday.

I think you could be correct that we are in the very early stages of dominant positive feedback loops for both CC and PO. In the case of PO it could be the incentive to constrain production.
With China's CO2 emissions increasing at 15% per year, don't look for a change in that trend.
WRONG! Dirty Harry fired all six shots and then clicked the revolver on the empty cartridge to scare the s**t out of the bad guy.

Love that movie!

BTW, I carry a 44-40, both in handgun and carbine.

You're right, of course! But's let pretend he only fired five.
You both are, actually.  He had the empty chamber in the first scene, and scared the bad guy into giving up.  In the last scene, he still had one left and killed the Scorpio killer with it, giving the same speech (just a little grimmer).
For example, Central American countries like Argentina are already feeling the pinch.

Dave, trivial (unless you're Argentinian) but I think you'll find Argentina is in South America not Central America.

I'll make that edit.  

When you write a post over 3000 words and make last minute changes, sometimes mistakes happen.

have a good one, Dave

Hmmm.  The Babarisi stuff is a stretch since the model abstracts away too much detail that's important about how the Internet really works (and all the practical stuff that smart network administrators do to make sure it doesn't go down).  However, this seems even more of a stretch since the import-export graph can be dynamically reconfigured as soon as there's a shock - even while ships are in transit potentially.  And economics tells us that arbitrage opportunities will force that reconfiguration fairly promptly.  (This is in contrast to the Internet case where the physical location of fibers at least somewhat constrains the potential topologies of the graph).   So it's not clear to me that the structure of the import-export graph tells us anything beyond "the larger the fraction of oil supply that is taken off the market by a shock, the worse the consequences".

There might be a little more luck in applying it to the pipeline network within a country, which at least is not subject to hasty reconfiguration.  But again, whether analyzing this graph will provide much insight beyond "Interchanges with a lot of capacity are very important; don't let terrorists blow them up", I'm not sure.

Re: "this seems even more of a stretch since the import-export graph can be dynamically reconfigured as soon as there's a shock - even while ships are in transit potentially. And economics tells us that arbitrage opportunities will force that reconfiguration fairly promptly".

I believe my point, given the lack of spare capacity and a major failure at a Hub node, was just the opposite of your observation. I was also merely re-framing our view of the global supply chain and exogenous shocks to the system. Here, I strongly disagree that "arbitrage will force that reconfiguration fairly promptly".

Re: "the larger the fraction of oil supply that is taken off the market by a shock, the worse the consequences".

Depends. Nigeria is off by at least a third (about 0.650/mbd) but is not well connected in the graph in the sense I describe. This has not had devastating effects on the global market despite MSM reports. My view of things would predict that. Compare that to an oil shock should somebody (America, Israel) bomb Iran's nuclear facilities.

I tried to qualify my comparison of the GFFSC and the internet in the text but started with that premise.

best, Dave

Suppose country A exports 5mbpd to 10 countries (by tanker), each of whom gets 0.5mbpd.  Country B exports 5mpbd by tanker to a single other country (all 5mbpd going to one large consumer).  Clearly, country A is far more highly connected in the graph.

What do you believe is going to happen in the alternate scenarios where A or B's production goes off line?

Considering A or B, their overall weights are not equal with respect to C where the exports go. So, this represents a more sophisticated model than I described. In the first case, country A, 0.5/mbd go to C. In the second, country B, 5.0/mbd go to C. Considering the amount of fossil fuels moving across the network connections, they are the same.

So we have to consider how to define f(D,W) for both A, B and C, which I left undefined, to see what's going on. With respect to C, if A goes offline in the first case, who cares? They can live with it or the market will solve it (if the spare capacity exists), so they have lost little. In the second case, where C is apparently highly dependent on B and vice versa, then the SHTF, weakening C after some catastrophe in B and weakening B by default (lost revenue and some sort of chaos). Here, I don't believe the market can solve the problem given the real world fact that there is no spare capacity in the system. They're both screwed and, in my view, so is everyone else.

An imperfect, still to be debated model, as I have admitted. But there are some things to think about.

I believe the two scenarios are almost identical. In either case, the consuming countries will all bid for the tanker cargoes, and the highest bidders will get them. Who can bid the highest is independent of whether it is A or B that goes off line. Thus the initial structure of the graph is irrelevant to the impact of the shock - only the total lost supply really counts.
So, the "spot market" rules all? It's a "free for all"? What would that do to prices? And then how would that affect the network as I've defined it?

Of course only the total lost supply really counts. How does that ripple through the supply chain? Rich get richer? Looks like a power law distribution?

I only have questions at this point.

OK, here's an analogy that I just thought of. As you personally know about me, I wrote a website called Searchtuna that performs some automated browsing on the web to do research. My main connection (5.0/mbd) was with Google. They ranked my research reports (that I provided a link to so they could be culled - indexed - by Google) highly.

Then, they dropped my website from their index altogether (thought it was spam? competition?). In any case, the rankings for Searchtuna dropped off the planet.

Suppose Searchtuna is country C receiving large imports from country B (Google). The country B drops goes "offline", whether if it's oil exports or internet traffic? What happens to C if there is little spare capacity (Yahoo, MSN, other search engines) in the system? B holds a virtual monopoly on exports to C.

Again, more food for thought.

You can find out why a page was dropped from the index here:

I agree with Stuart in proposing some sanity checks. At this point it appears that the connectedness of the nodes and the ability to siphon off amounts of material between the nodes makes the situation look more like trying to solve a 2-D diffusion problem.

The first rule of diffusion is that material flows from regions of high concentration to low concentration at a rate inversely proportional to the distance between them.  
(This is where the analogy to the internet breaks down, as that has a largely instantaneous transit time independent of the distance)

Still, I do find it interesting to look at things from a fresh perspective and this is one of those cases.

Off topic, but what you say of the Internet is not quite true. Long haul latencies on the Internet are dominated by the speed of light in fiber and the topology of the fiber. I've had occasion to think about this quite a lot in the context of worm spread - there are some interesting theoretical problems involved in detection and prevention of worms where the relevant latencies start to matter a lot. See The Top Speed of Flash Worms.

Diffusion theory does not apply if particles can migrate at the speed of light.
Hello Stuart,

Your phrase: "But again, whether analyzing this graph will provide much insight beyond "Interchanges with a lot of capacity are very important; don't let terrorists blow them up", I'm not sure."  But I think practical applications are possible, see my earlier post.

Now I am no Arachnid Scientist, but I would imagine an aging spider encountering it's declining peak energy would gradually shrink it's spiderweb area vs going to the few strands of silk blobs.

IF the unwashed masses understood Peak Everything, the best societal conservation response should be similar to the gradual process of the shrinking spiderweb.  Our current wasteful ways have created a global spiderweb more like a solid silk plate versus the sparse elegance postPeak required.  The nightime satellite pictures of global electrical glow springs to mind.

The key goal is to keep the spiderweb trap area maximized as long as possible, to provide the greatest good and prevent violence, before it must entropically shrink.  Hopefully by this time pop. controls have kicked in to reduce headcounts.

ASPO's protocols of proactive energy mitigation could help towards this end.  Imagine future satellite photos largely dark, but the optimal, minimal energy strands are still there; the reduced shared carrying capacity still is maximizing the spidertrap area to provide the greatest good.

An example of this might be where everyone globally has a small refrigerator, but no other electric devices including no lightbulbs in the house, nor even a lightbulb inside this small refrigerator [the sun sets causing darkness--we need to accept that reality again].  No combustive transport, but electrified RR & trolley transit.  Lots of manual permaculture labor, but people will be pleased to go home to a cold beer or ice cream. Everyone's electric meter would provide this minimal current flow [.3 amps?], but any attempt to draw more power to run some other device would be futile.

Any excess grid energy would be to provide hospital & dental care power, or anything else deemed absolutely essential to that habitat's survival.  This leveling of the detritus-driven humanimal ecosystem worldwide is fair-- no more wolves to gnats-- we would all be equal as humans again.  A global Foundation, if there is still time, could easily drive society towards this end if the topdogs would get their collective act together.

The current economic trend of energy hub concentration to benefit a lucky few will lead to disaster.  Phx, at the ends of the TX & CA pipelines; the outer ring of the spiderweb, should volunteer to Powerdown to reduce the future chance of total cutoff.  A pipeline shipment, once a month, might be sufficient to keep this highly efficient outer ring webstrand up for decades.  Lather, Rinse, and Repeat around the globe.

Until something like this starts happening, my beliefs remain a fast-crash doomer, but working and hoping for an alternative.

Bob Shaw in Phx,Az  Are Humans Smarter than Yeast?

Yep sorry my PhD was in Theoretical chemistry and dude you lost your units a looong time ago with this model.

Trust me calculating acceleration and or fracturing ( same thing ) is a bitch.

Your model has crude velocities and accelerations are basically empirical plus you have now knowledge of when the model failed since your using scaling laws i.e. its a fractal geometry.

Agian the abstract model is correct but I think you need to add maybe the concept of folding. Thus if you weight the distances and assume constant velocity for the net you allow new links on folding instead of ruptures.

In a dynamic since you can think of this abstract net as a real net cast into the wind. Wind resistance will leas to it folding my suggestion is that you allow it to relink to a simpler geometry when folds pass a tolerance.
Its like if you tossed a sheet off a tall building when the geometry convoluted you recalculate and relink.

This is basically what we do when a chemical bond forms in chemistry. We recognize that the problem has changed then re org.

Anyway I hate theories that don' simply predict there own failure with infinities and this is one of those.

And since I'm a computer guy now I assure you being able to model a problem as a network or simpler and true a tree is not a surprise read about grammars. Using a tree or graph is rediscovered on a regular basis outside of computer science.

Its unsurprising it works since 99.99% of stuff can be modeled that way except that  we can't model tears or fractures  in a system without experimental params.

Another example take a sheet of the thinnest silk inside a chamber with strong a blast injectors and fold it into a simple origami. Thats a chemical reaction.

Good one Dave, this may be a model worth exploring and might possibly have predictive abilities in response to disruptive events.

The basic premise of the model seems to fit the production / refining / distribution of oil products. Perhaps the critical questions are: how well the model will accept the important oil production, refining and distribution data and how accurately the model will respond to changes in data.

I'd not seriously considered global modelling of the production and distribution process and its response to shocks, do you think this could be a promising method?

Interesting Comments:
Angry Putin says he will not sell fuel for 'peanuts'

BTW, the Saudis are raising their oil prices, despite the fact that they complained about a "lack of buyers."

Do yout think the net exporters are beginning to realize what power they have?

is there a link for this?
I've heard of theatre tickets being in more demand when the price is raised.
Never thought it would happen with oil :-)
Actually that happens all the time, thusly:
  1. Scalpers start raising prices on a limited number of tickets to a popular event.
  2. News of extensive scalping gets people excited; now it is a "must see" event.
  3. Prices skyrocket to insane levels as the "buzz" increases.

What is happening here is that the whole demand curve is shifting.

Only when "all other things stay the same" does quantity demanded always go down when price rises.

Alas, I know much about this topic but will draw upon vast reserves of unused willpower to quit now;-)

How long has it taken? (for the Saudis to become less stupid).

They have been well behind the pricing curve for, let me see, close to 30 years now. If they are finding it hard to keep up production levels it makes absolute sense to increase prices to, say, $100 / bbl and wait for the market to catch up (it will only take a week, lol).

Or would that be a dead giveaway that Saudi production has peaked?

They have not even begun to glimpse their potential power, $1000 / bbl oil is not much more than the twinkle of an eye away. But perhaps they fear being annexed by US force in the interests of 'democracy'.

The problem is the western economies are actually not that strong at the moment. Thus increasing fuel costs are becoming the straw that broke the camels back.

So to extend the Saudi saying.

My grandfather rode a camel I drove a car my son flies a airplane and my grandson rides a camel and its back was broken by a western straw.

I think Putin has a point. If one's country has a depletable resource the most responsible way to produce it is at one's country's consumption level (or even below it if cheap external supplies are available).

Effectively the developed nations, especially US, have raped the oil producing countries of their resource. Now those countries want to develop some have largely squandered the resource that would help them.

Sadly the greed of rulers, corruption, power and influence of oilcos, and US interests, mean that...

I tried to grow peanuts in UK last year, got an average of 2 pods and 4 peanuts per plant, so not viable, but the intense cadmium yellow flowers were lovely.

Hello Westexas,

Yep, the upcoming G8 conference should be 'can't miss' TV for us TODers.  Any speculation on betting lines?

  1. Temporary negotiation walkout by the US & European participants--my hunch: 40% chance.

  2. Putin jumpstarts negotiations for more deals with fellow Asians--my hunch: 60% chance.

  3. Western MSM going nuts--my hunch: 100%

Bob Shaw in Phx,Az Are Humans Smarter than Yeast?
My take: hot air and photo ops, no substantive negotiation - 90% :-)
Hello Smekhovo,

Thxs for responding.  Let's see how the CFR editorially weighs in on the Conference [notice the link description includes the word "BREADCRUMBS"--Yikes!]:

The decision to hold the July 15-17 Group of Eight (G8) summit in St. Petersburg was meant to symbolize Russia's full integration into the club of the world's richest industrialized democracies. Instead, with U.S.-Russian relations at their lowest ebb since the collapse of the Soviet Union, mostly due to the Kremlin's rollback of democracy and its use of energy as a tool for foreign policy, a number of experts and politicians have said that Russia is not a suitable host for such a privileged club.

Energy security:
Amid escalating energy prices, G8 members are hoping to hammer out an agreement that calls for transparent and predictable national energy policies, encourages competition, improves the investment environment for developing energy-related projects, and increases access to energy markets in the post-Soviet region. Although Russia holds the world's largest reserves of natural gas and remains the second-largest exporter of oil, it holds different views from the West on what energy security means, writes Stuart McMillan of the University of Canterbury in the National Business Review. "Russia wants to achieve security of demand," he says. "The others in the group want security of supply."

The two countervailing forces, Legvold says, are risk aversion by the Europeans, who are ever distrustful of Russia as a reliable energy partner, and the Kremlin's monopolistic tendencies, as highlighted by its heavy-handed approach to erecting pipelines and cutting gas subsidies to its former subjects. Energy also needs to be used more efficiently. CFR Senior Fellow Stephen Sestanovich recently told the Senate Foreign Relations Committee that if Russia used its vast reserves of natural gas as efficiently as Canada, it would save three times the amount it exports to Europe. "Russia is not just the world's greatest energy producer," he said. "It's the world's greatest energy waster."
This Asia Times article basically says the IMF publically castrated Putin:
With less than 10 days before the Group of Eight (G8) summit meeting at St Petersburg, the United States has quietly yanked the carpet out from under the prestigious forum.

The International Monetary Fund (IMF) announced last week a list of countries that will initiate consultations to "produce a common vision for action, with balanced contributions and collective benefits, to address vulnerabilities that affect ... the international financial system". The list of countries is headed by the US, of course, and includes China, Saudi Arabia and Japan.

Washington has implied that the G8 [1] is not necessarily the lead forum for exercising "multilateral surveillance" when it comes to dealing with the issues and imbalances of the world economy. The list of invitees to the IMF high-level talks on global financial imbalances is a virtual "who's who" of countries that Washington considers relevant to addressing pressing issues of financial imbalances in the world economy.

 And the list excludes Russia, the host of the G8 summit on July 15.

Of course the Bilderbergers [check out the guest list!] have recently concluded their Ottawa Conference with no Russian representation as far as I can tell.  Purportedly deciding what to do about high oil prices and that pesky fundamentalist president of Iran, Mahmoud Ahmadinejad:
Bilderberg says the privacy of its meetings helps encourage freewheeling discussion.

An unsigned press release, sent by fax, confirmed this meeting would deal with energy issues, Iran, the Middle East, terrorism, immigration, Russia, European-American relations and Asia.

"The meeting is private to encourage frank and open discussion," said the release. "There will be no press conference."
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Sounds to me that the West really wants to rub Putin's nose in the mess that occurred in UK-Russia and elsewhere, but as evidenced in his last interview--This is one agitated Russian Bear. We will see how the G8 goes.

Bob Shaw in Phx,Az  Are Humans Smarter than Yeast?

The west doesn't have any leverage or credible threats against Russia.
Hello Smekhovo,

Agreed, but I think they will stupidly continue to attempt to torment the agitated bear anyhow.

Bob Shaw in Phx,Az  Are Humans Smarter than Yeast?

'...rollback of democracy...'

Yes, I think the rollback of democracy has major PO implications.  Unfortunately for us USA'ians, it's the rollback of democracy  HERE IN THE U.S. that I'm concerned with.  If the populace had the facts, and a choice, I think powerdown and localize and produce (etc.) would be preferable to endless (resource) war.

FACTS are hard to come by these days, especially in the MSM, and CHOICE has been seriously compromised (who's counting the votes?...)

I'm a bit out of touch with G8 dynamics but it certainly seems the resource-rich folks are waking up.  

Interesting times...

The Kuwait news the other day made me consider whether this was the begining of the end of cheap energy...

"Facts are hard to come by these days . .  ."

Compared to when?

Why not? Peanuts are high in protein...
Maybe he has a hypersensitivity to aflatoxin.

Your analysis appears to be a fresh way to look at the global interactions between "nodes" within the supply chain and I think it has great potential for predictive value if the data inserted into the model is fairly accurate for at least most of the nodes.  It may actually greatly assist in filling in some "sketchy" data from certain nodes by observing the behavior of the links to more trusted nodes.

I believe your theory may be useful in unifying much of the data put forth by Westexas (imports/exports) and others here at TOD.  It would be a HUGE effort to insert real data into your model, but could be done.

Now if you just apply some Game Theory ( between the nodes you could perhaps predict which nodes may go to war, bluff about going to war, or assist other nodes to maximize their returns in the game.

Wow...this is starting to sound like Risk.

I applaud your creative efforts.

I suggest everyone interested in system dynamics, and in Dave's theory, read the following 20 page article by Donella Meadows:

The opening paragraph indicates why it may be of interest.

Folks who do systems analysis have a great belief in "leverage points." These are places within a complex system (a corporation, an economy, a living body, a city, an ecosystem) where a small shift in one thing can produce big changes in everything.

It is fascinating and is completely applicable to the analysis of the oil distribution/economic/usage system.

I highly recommend it not only because I think it may be useful in describing the system but because it may also be useful in developing solutions.

Just read the concluding words - my poor brain already throughly befuddled after an hour or two with the big brains on TOD.

It concludes with the exhortation to work at throwing yourself into the humility of Not Knowing.

Phew. No problems there.

This also sounds like the Butterfly Effect.

It seems we are all trying to find an approximate model which could conceivably assist us, given sufficient data points and mathematical methods, with a method of predicting peak oil and the process of disintegration of thecurent society. As the society is conscious and active , consisting of live human beings who continuously adjust themselves and react using such models to anticipate and change theeir reactions, this whole process is difficutl to impossible. It is probably much easier to predict the stock markets or event he  weather than what will happen in this case except in a very broad way. So we are back to our starting point with hunches and intuition according to who is a doomer or not depnding  on our personalities.
Dave, congratulations for this good post and your innovative thinking!

There are a lot of good ideas in that post to chew on. I was wondering also if cellular automata could be used to model indiviual agent behavior (i.e. exporting and importing countries). They have been used to model complex systems with good success.

Well, thanks. Stuart wasn't too happy with it. That's a disappointment to me since I was trying to take a new approach. The way I see it, try to innovate and perhaps fail. But lay the groundwork for future work.

Perhaps someone else could produce a "deeper" model of the GFFSC network than my first attempt.

That is exactly how the innovation process works (IME).
Actually, what I think would help a lot is if you drew and labelled the network.

I have a feeling that those who doubt the worth of the approach are concerned as to whether the model can successfully offer quantitative insights. My guess is also that those that like it do so because it helps enhance their efforts at reasoning with the problem.

To the extent that's true, having an actual version of the network would be a helpful next step.

I don't know how many remember or know of "Infomagic's" Charlotte's Web Y2K series.  Although Y2K was a dud in many people's opinion, I think it has a bearing on this discussion.

To quote one part:

"For a business with multiple systems (which they all have) the chance of a system failure can be computed as: 1-(1-f)**n, where "f" is the failure rate and "n" is the number of systems."

It seems to me that this is directly applicable to Dave's great post.

Read the essays here starting about page 5: