Thursday, January 27, 2011

An Export Land Model Analysis for the USA-Part 1

As Matt Simmons pointed out several years ago, the critical problem with post-peak exporting regions is that we would have two exponential functions (declining production and generally increasing consumption) working against net exports. From the point of view of importers, it is quite likely that we are facing a crash in oil supplies. In my opinion, what I have described as the “Iron Triangle” is doing everything possible to keep this message from reaching consumers.

In an essay posted on The Oil Drum blog in January 2006, I warned of an impending net oil export crisis, and I used what I called the Export Land Model (ELM) to illustrate the detrimental effect on net oil exports of declining production and increasing consumption.

It has taken me four months to get here, but I am finally in a position to use my analysis of trends in petroleum production and consumption for the USA, and its top ten import sources, to do an “export land model” analysis for the USA.  Actually, I have been doing a running analysis as I finished each country, but now its time to step back and look at the data from a broader perspective. 

But first, some background.

Overview of the Export Land Model
As you can see from the quote at the top of this article, the concept of the “Export Land Model” as coined by Jeffery Brown, was inspired by the late Matt Simmons and is based on a simple but important idea.  The net amount of oil available for export from an oil producing country (i.e., an “Export Land”) should equal that country’s total production, minus its domestic consumption.  It follows therefore, that if you can accurately predict the future trends in an export land’s oil production and consumption then you can also predict what that country’s future net oil exports will look like. 

This is particularly important in the period after peak oil, when oil production begins to decline from the exporting countries, but the domestic consumption rate may still be increasing.  The Export Land Model shows that the rate of decline in oil exports will be even faster than the decline in production if there is also increasing domestic consumption.  For example, if the production rate was exponentially decreasing, and, the domestic consumption rate was exponentially increasing, then the export rate, represented by the difference of production minus consumption, would decline at a double exponential rate.  In this kind of scenario, net exports hit zero long before production does.   This has very serious implications for oil importing countries, like the USA.  If the USA cannot produce or import the amount of oil it has in the past, then its consumption must go down. 

Export Land Model analysis done by Brown and Foucher
In the original article from 2006, Hubbert Linearization Analysis of the Top Three Net Oil Exporters, Brown noted that two of the top three oil producers, Norway and Russia were producing below their peak production levels and suggested that the third, Saudi Arabia, was on the verge of declining production:

As predicted by Hubbert Linearization, two of the three top net oil exporters are producing below their peak production level.   The third country, Saudi Arabia, is probably on the verge of a permanent and irreversible decline.   Both Russia and Saudi Arabia are probably going to show significant increases in consumption going forward.  It would seem from this case that these factors could interact this year produce to an unprecedented--and probably permanent--net oil export crisis.

The prediction of production data was referring to an earlier 2005 posting by Stuart Staniford, titled When Does Hubbert Linearization Work?, which presented production data for Saudi Arabia, Romania, USA, Iran, and Norway.

In a subsequent article (also described in a 2007 article by Sam Foucher, Declining net oil exports--a temporary decline or a long term trend?, published at The Oil Drum), A Quantitative Assessment of Future Net Oil Exports by the Top Five Net Oil Exporters Brown, and his colleague "Khebab," did a more detailed analysis of the top five oil exporting countries (Saudi Arabia, Russia, Norway, Iran, UAE), again based on the using the linearized version of the Hubbert equation to estimate future production, and, “a Monte Carlo analysis based on the observed growth rates over the last 10 years” to estimate future consumption.   The main conclusion from the study was that future net exports from these top five exporters were all likely to decline in the future.  Their average rate of the decline in exports was estimated to be -6.2%/yr, with net exports hitting zero in about 2031.

My reasons for doing a Export Land Model Analysis of the USA
There is not single a person that I have explained the idea of the Export Land Model to that does not understand its implications for the USA.  But usually, the follow-up questions are something like: “well just how important is this for the USA, and, how does this apply to USA’s actual import sources?”  For instance, of the above-mentioned top five exporters, only one, Saudi Arabia is a top five exporter to the USA (see e.g., Where in the world does the USA import its oil from?).  

I could only offer a vague response, concerning the fungibility of oil.  That is, if there are export declines in the top five producers, then this will probably track through the entire global market, including the specific exporters that are important to the USA. 

There have also been criticisms in the use of the linearized version of  Hubbert’s logistic equation to model oil production, some of which I have discussed in a previous series (see e.g., Refining the Peak Oil Rosy Scenario Part 4: Testing Hubbert’s linear and nonlinear logistic models) and which the interested reader can easily find discussed in detail at other websites, such as The Oil Drum

So, I embarked on what turns out to have been a long project to assess for myself how the Export Land Model applies to the USA.  Long project, because I had to analyze the production and consumption data for 11 countries—the USA and its top ten import sources, and, assess the relative amounts of petroleum that get exported to the USA.

Features of my approach
There are several things about my approach that differ from what Brown and colleagues did:
1) After having high hopes for using the linear logistic model, I abandoned it in favor of a non-linear least squares (NLLS) analysis of the logistic model.  NLLS can be readily implemented within an Excel spread sheet, and, I found it to give more reasonable results, when tested on simulated data (see e.g., part 4, part 5 and part 6 of my earlier series).

2) I developed and tested a modified version of the nonlinear logistic equation (referred to here and in past articles as the modified Hubbert Equation), to handle situations where the production data seriously deviates from a simple logistic curve. (see e.g., Refining the Peak Oil Rosy Scenario Part 7: An improved logistic model)

3) I analyzed both production and consumption data using the Hubbert equation (or the modified Hubbert Equation), for the reasons discussed in Refining the Peak Oil Rosy Scenario Part 4: Testing Hubbert’s linear and nonlinear logistic models).

4) Like Brown et al., I primarily relied on petroleum production as reported in a massive spread sheet, the BP statistical review.  Petroleum production in the BP statistical review “includes crude oil, shale oil, oil sands and natural gas liquids.”  However, in a few cases where a more detailed analysis was needed (e.g., some individual components USA production), or, the data was not present in the BP statistical review (e.g., Angolan or Iraqi consumption; Brazil ethanol production), I have turned to data provided by the Energy Information Agency (EIA). 

5) My analysis considers not only the net exports a country produces, but also the percentage of net exports that specifically gets exported to the USA.  In some cases, like Mexico, this is not a big deal, because virtually all exports go to the USA.  In the case of Canada, even more than its net exports goes to the USA, forcing Canada to be both a major petroleum exporter and importer (due to an agreement under NAFTA, see Canada—Petroleum Superpower or Super-slave?).  Along similar lines, up until recently, Brazil also exported to the USA, but was a net importer.  In most cases, however, only a fraction of a country's net exports goes to the USA, and estimating the size of this fraction is about as important as the petroleum production and consumption analysis itself.

Why the top ten?
I have analyzed the petroleum production and consumption trends for the USA and its top ten import sources for 2009: Canada;  Mexico; Venezula (direct and indirect via the USVI); Saudi Arabia; Nigeria; Russia; Algeria; Angola; Iraq; and Brazil (and no, those north sea oil producers, the UK and Norway are not among the top ten exporters to the USA). 

Previously, in Where in the world does the USA import its oil from?, I pointed out that the top ten export sources, when added to the USA’s domestic production, consistently accounted for 86 (85.8±2.5) percent of the USA’s consumption over the last 36 years:

This suggested to me a simple prediction formula for estimating USA consumption:

            Predicted consumption = (production USA + Imports top ten) / 0.86

That is, if one takes the sum of USA production plus imports from the USA's top ten export sources and divide this sum by 0.86, the result should give a good estimate of USA consumption. 

In Figure 2 shows exactly that: the black open circles equals the USA's reported production plus the top ten's reported USA exports, all divided by 0.86. 

Also shown in Figure 2 is the USA's reported production and consumption rates for 1949-2009 (from the BP statistical review) and the reported imports to the USA from these top ten export sources for 1973-2009 (from the EIA publication, U.S. Total Crude Oil and Products Imports). All rates are in units of billions of barrels per year (bbs/yr)

The agreement between the reported consumption and predicted consumption looked remarkably good to me.  For instance, linear regression analysis of reported USA consumption (the red circles) versus predicted consumption, shown in Figure 2 (the black open circles), gives an r2 equal to 0.90 (see inset Figure 1).  That is, 90% of the variation in USA consumption over the period 1973-2009 is explained by this simple prediction formula. 

These findings lead me to believe that, given an accurate estimate of the USA's future production plus future imports from the top ten export sources, I could make a pretty good prediction of what the USA's consumption will be going forward.

Export Land Model analysis for the USA—My best estimate
Well, without further adieu, Figure 3 shows all the data in Figure 2, plus my best estimated predictions for USA production and the import trends for the top ten import sources going forward for 2010 to 2030.  The solid red line shows my prediction for USA consumption for 2010-2030 based on the above formula.

There is a steep decline in consumption predicted for the period from 2010-2022.  An inflection point, at 2023, reflects the prediction that net export from some major suppliers, Mexico, Venezuela, Saudi Arabia, have dropped to zero by 2023 and the USA is now importing its oil mainly from Canada, Iraq and Brazil.  Over the next twenty years, net exports from several of the top ten import sources are predicted to go to zero for: Mexico (2014), Venezuela (2022), Saudi Arabia and Russia (both 2023), Angola (2024), and Algeria (2030).  A small amount of exports still comes from Nigeria until 2039, when its exports are also predicted to go to zero.

The predicted decline in USA consumption is part of a trend that started in 2005, when the US reached its peak in petroleum consumption at 7.6 bbs/yr.  By 2009, consumption had dropped from the peak by about 10%.  According to the prediction curve, by 2013, consumption will be about 80% of the 2005 peak, and by 2021, about 60% of the 2005 peak. 

The predicted petroleum consumption rate declines at a rate of -3 to -4 %/yr from 2011 until 2023, and then tapers off to less than -1%/yr from 2025 on.  That is a decline rate that the USA has experienced before, and therefore is not necessarily the "end of the world," but probably the end of the world as Americans have known it recently.  For instance, from 1978 to 1982, the consumption rate declined from a peak of 6.88 to 5.58 bbs/yr.  That was a -19% decrease over five years, or about -3.75%/yr.  Of course, by 1984, consumption was on its way back up—but I'm not expecting that to happen this time.   Rather, this time, after experiencing a -20% decline from 2005 to 2013, there would be another -20% decline from 2013 to 2021, and then no prospects for an upswing through the 2020s and beyond.   

The predicted 40% decline in consumption from 2005 to 2021 is not unprecedented for a global superpower to experience either.  From 1990 to 1996, Russia's consumption went from 1.87 bbs/yr to 0.98 bbs/yr and consumption has stayed flat thereafter (see e.g., Figure 2 here).  That's a -48% decline in only 7 years—a whooping decline rate of -6.8 %/yr!  But once again it was not the end of the world for Russia, but it did end of Russia's (or the Soviet Union's) place as a global superpower.  The USA's petroleum consumption from 2010 to 2030 might well follow a similar trend as Russia's did from 1990 to 2010, but be a little bit more spread out. 

No way—your wrong man!

And that's the way it is
–Walter Cronkite. CBS news

Well no...that's not necessarily the way it is, and even Walter knew that. 

There are a lot of explicit (and some implicit) assumptions wrapped up into Figure 3.  In my previous series of articles on Trends in Petroleum Production and Consumption, I have given my analysis rational for each of the eleven countries shown in Figure 3 and the interested reader is directed to these articles for more details. 

Although Figure 3 represents my best estimates, I would be amazed if the Land Export Model that I have presented here turned out to be exactly correct.  For example, here are some of the major assumptions I have made in arriving at the predicted consumption curve shown in Figure 3:

1) USA production continues its downward trend, as represented by the modified Hubbert equation fit to the total production data from 1980-2009.

2) Canada continues to export more than its net exports to the USA, as per its obligation under NAFTA, and Canada's production continues to increase, as represented by the modified Hubbert equation fit to the 1980-2009 production data.

3) Mexico's production continues to follow its short-term trend, as represented by the Hubbert equation fit to the 1999-2009 production data (i.e., no net exports by 2015).  

4) Venezuela's production continues to follow its production trend from 1985-2009, as represented by the Hubbert equation fit, and, Venezuela continues to send 75% of its net exports to the USA (i.e., no net exports by 2023). 

5) Saudi Arabia's production continues to follows the trend represented by the Hubbert equation fit to 1985-2009 production data; domestic consumption continues its exponential increase, and Saudi Arabia continues to send 18% of its net exports to the USA (i.e., no net exports by 2024). 

6) Nigeria's production continues to follows the trend represented by the Hubbert equation fit to 1983-2009 production data, and, Nigeria continues to send 53% of its net exports to the USA.

7) Russia's production continues to follows the trend represented by the Hubbert equation fit to 1999-2009 production data, Russia continues the linear trend of sending an 0.6%/yr increasing proportion of its net exports to the USA, and, Russian domestic consumption stays flat (i.e., no net exports by 2023). 

8) Algeria's production continues to follows the trend represented by the Hubbert equation fit to 1995-2009 production data, and, Algeria continues to send 30% of its net exports to the USA (i.e., no net exports by 2030). 

9) Angola's production increases at 30%/yr, its ultimately recoverable petroleum equals 13.5 bbs, and, Angola continues to send at least 24% of its net exports to the USA (i.e., no net exports by 2025). 

10) Iraq's production remains at 1 bbs/yr (this was scenario 3 in my original trend analysis for Iraq), Iraq's domestic consumption follows the upward trend represented by the Hubbert equation fit to 2003-2009 consumption data, and, Iraq continues to send at least 26% of its net exports to the USA.

11) Brazil's production continues to follows the trend represented by the Hubbert equation fit to 1980-2009 production data for the sum of crude oil, LPG and RG, plus, the modified Hubbert equation fit to the ethanol production data for 1995-2010, and, Brazil continues to send 12% of its net production to the USA.

Here's one more prediction: some readers will find some of these assumptions to be overly pessimistic, and other readers will find some of these assumption overly optimistic (maybe even the same assumptions!).  And, you maybe right! 

In part two, I will explore some of these pessimistic and optimistic scenarios in further detail—I hope that you will join me, and, feed back is always welcomed.


  1. Great article.
    I just found the site. I see a lot of reading in my near future.

  2. I certainly enjoyed reading your summary of the development of Jeff Brown's, et al "Export Land Model" and how that concept expands into a impact on the US. I have followed the development of this concept for several years and have felt its effects on our future lives has been greatly underestimated.

    The key factor I see is that the impact of falling resources levels will happen much, much more quickly than anyone expects.

    As one who studies and writes of disaster scenarios, I look forward to seeing what you expect the results to be from your analysis.

    Sam Penny
    the Prudent RVer

  3. Have you considered what the supply issues will be for the USA because of the increase in demand from China and India? China is selling almost 1 million cars to their people per month and building 1000Km of roads per year. Will the USA Suppliers start sending more of their oil to them? At some point the world demand will overtake the supply. Some say by 2012.

  4. Thanks for doing the work of evaluating the ELM.

    Jeffrey Brown's is one of the few rational voices in the whole peak oil fiasco, which has been dominated by failed novelists, Luddites, astrologers, conspiracy theorists, neo-pagans, and other buffoons.

    It pains me to think of what we've lost because of the bungled message that has been projected in the last ten years. One can only imagine how much better prepared we might be if only the likes of Brown, Deffeyes, Campbell, et al. had been allowed to dominate the field.

    When there's no peer review, there's no credibility.

  5. Hi Sam

    “The key factor I see is that the impact of falling resources levels will happen much, much more quickly than anyone expects. “

    I agree, but its not just falling resources—its the accelerating use of the remaining resources—its hard enough for the human mind to understand exponential change, let alone double exponential change!

    That appears to be the case for the “export lands” when they are entering the peak and decline side of the oil production curve. I will talk a bit more about this in part 3.

    “As one who studies and writes of disaster scenarios, I look forward to seeing what you expect the results to be from your analysis.”

    Many of my articles are all about exploring different future scenarios from a quantitative viewpoint—I think that you will like part 2 which explores some of these future scenarios in some detail.

  6. “Have you considered what the supply issues will be for the USA because of the increase in demand from China and India?”

    This is an excellent point, but no, I haven’t considered this directly. I do consider this issue indirectly when I discuss the issue of oil’s fungibility in part 3.

    It may be interesting to do a follow-up ELM analysis for China and India, but, I don’t know where I can find the analogous historic data showing the import sources into these countries and the percentages of exports, etc....

    Instead, in a future article, I plan to do a global ELM analysis to see if I can quantify what the global flows of oil may look like in the future.

  7. Thanks Mike

    Yes, I think Brown and Foucher’s work to bring attention to the ELM concept as it applies to oil was very important, but unfortunately it seems to remain on the fringes, in that most of the focus remains on oil production. But as this analysis shows, it is the drop in exports that will probably bite the USA first.

    And, of course, the ELM applies to other types of resources (rare earth elements spring to mind) but I am not aware of any type of an ELM analysis being done in other areas. Maybe this is due to the absence of readily available data.

    For instance, I was only able to do the present analysis because the data was freely available and published at BP and the EIA.

  8. “Great Article” are welcome to freely peruse through my past articles, most of which are along the same lines as this one. And don’t be afraid to ask questions—there is a good chance that I will respond.

    If you think that anything that I have written has been of value to you, then you can do me a favor in return.

    The next time you want to buy something from amazon, come back to this blog and enter the item into the amazon search engine over to the right hand side of the page. It will take you to the amazon’s page to order the item. There is no additional cost to you, you stay anonymous, and, I get a small reward. The same goes for my pages at squidoo.

  9. Following are a couple of recent articles that you might be interested in. Note that if we extrapolate the 2005 to 2009 rate of decline in the ratio of US oil consumption to production, the US would approach zero net oil exports around 2024.

    Jeffrey J. Brown

    Peak oil versus peak exports

    Egypt, a classic case of rapid net-export decline and a look at global net exports:

  10. Thanks westtexas,

    The USA's net petroleum exports hit zero around 1950 (Fig 2 consumption, red circles, exceeds production, blue circles), so I'm not sure what you mean when you say, "the US would approach zero net oil exports around 2024."

    Egypt is an interesting case, and, there are several others just in the MENA countries, as I presented in my two posts in February and March: See Survey of Oil Exports from North Africa and Survey of Oil Exports from the Middle East.

  11. Nice post....

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