Be sure to click the "HD" button to watch the video in full high definition!
Results of Linearization: U.S. Oil Production
The Hubbert linearization for the U.S. produce a fascinating set of results.The US reached a logistic peak of 3.27 billion barrels of oil produced annually in 1976.The model predicts steady declines for each year thereafter.
The area under the curve represents the total oil that will be produced in the United States.The regression equation revealed this quantity to be about 230 billion barrels before depletion.The logistic peak in 1976 also represents the point at which the model estimates that half of the total oil in place will have been extracted.
Remember that the model was constructed from production data.No prior knowledge of the oil in place was required.The establishment of the linear relationship between P/Q and Qfenabled the construction and date fitting for the entire curve.
The logistic curve is even more impressive when actual data are superimposed on the same axes.Actual production closely follows the logistic predictions on both sides of the curve.Just as Hubbert predicted, domestic oil production has declined since 1970.
Since actual production has closely followed the logistic predictions, we can use the curve to make a critical inference.In addition to declining production rates, U.S. oil fields are quickly being depleted.Since the area under the curve represents the total oil in place, we can estimate that over 86% of the oil the United States will ever produce has been extracted.The remaining 14% will be produced at decreasing annual rates in the coming years.
Why is the decine in United States’ oil production important?
Most consumers know that the U.S. imports massive quantities of oil for its energy needs.The decline of domestic oil production may seem to be inconsequential.Even if people are aware that U.S. oil is being depleting fast, they assume that we can simply import more petroleum from major producers in the Persian Gulf and other oil-rich lands.Even in tight oil markets, swing producers like Saudi Arabia have managed to escalate production to meet demand.
The example of the United States is instructive for two reasons.First, it demonstartes that a country’s oil production will eventually peak and decline even with advanced exploration and drilling technologies.However, the curve also presents an idea that is both more subtle and more profound.As Hubbert demonstrated, it is possible to estimate production peaks while annual production is still growing.
As the next entry will demonstrate, it is possible that the world is at or near its production peak.This has profound implications for growth forecasts that call for a doubling of crude oil output as part of overall economic expansion.Most importantly, the event is obfuscated by annual production growth.Consumers and officials will be caught unprepared for its implications to the delicate supply and demand balance, not to mention future growth.
If production is close to peaking (or has already peaked) we must take immediate action to help lessen the impact to our economy, society and standard of living.Next time, we will examine these prospects along with the limitations of the analysis.
Be sure to click the "HD" button to watch the video in full high definition!
Hubbert Linearization:U.S. Oil Production
As I described in my previous entry, Hubbert linearization is important because it simplifies the process for building oil depletion models.I will explain the mathematics behind linearization and then apply the technique to U.S. oil production.After exploring what happened in the United States, it will be possible to estimate global production peaks and declines.These figures will demonstrate the urgency of exploring energy alternatives.
If the mathematics behind the calculations are not of interest to you, feel free to skip to the next section which details the implications of the model.
Hubbert’s curve is the first derivative of a logistic function.The area under the curve represents all of the oil that will be produced from the country or field in question.The peak of the curve represents the time period at which half of the available oil has been produced.The Hubbert curve makes it possible to estimate what percentage of oil has been recovered at any point in time.It also predicts annual production volumes.
Since the curve is the first derivative of a logistic function, the most important piece of information is the total amount of oil in place.If this bit of information is known, it is possible to construct the curve based on annual production and the area under the curve (the total oil in place.)
Because of the complexity in Hubbert’s analysis, it is easier to use linearization to estimate the total oil in place.Only one variable is needed: production data.The first step in the process is to plot the production data (P) as a fraction of cumulative production (Q) on the vertical (y) axis.Cumulative production (Q) is placed on the horizontal (x) axis.
As the chart to the left shows, the relationship between P/Q and Q becomes linear as production matures.This linear relationship follows the simple y = mx + bformat for graphing a line in a plane.Hubbert’s logistic differential equation has a linear property – we can exploit this relationship with the linear representation of P/Q versus Q.
After the denominator Q becomes sufficiently large, P/Q begins to decline linearly.In the chart of U.S. production, this begins in 1958 and continues to 2007.A simple linear regression for these points yields the important y = mx + b equation we need to build our logistic representation of production.In this case, the regression yeilds the following equation:Y = -0.000247x + 0.0569
[One interesting side note on the regression:In this example the analysis is conducted from 1958-2007 with an adjusted R2 of 98.5%.A logical question to ask is whether or not this kind of model is possible earlier in the life of a country’s oil production.The answer (as Hubbert demonstrated) is yes.For example, I ran a linear regression of variables from 1958-1978.The results are almost identical.In the first example, the intercept equals 0.0569 and the slope equals -0.000247.In the second case, the intercept equals 0.0566 and the slope equals -0.000244.This results in an almost identical amount of oil in place:230.3 billion barrles and 232.0 billion barrels respectively.The main difference is a reduction in R2.It falls to 85.7%.There is a logical reduction in certainty when fewer data points are used.However, the end results are almost identical.]
Plotting the line represented by the regression equation gives x and y intercepts.The x intercept is crucial.The x axis represents the total quantity of oil produced (Q).The intercept is an estimate of the total oil that will be produced (Qf).Remember, this is the most important piece of information needed to build Hubbert’s logistic curve!The U.S. model predicts that total production will equal around 230 billion barrels when supply is exhausted.
The slope in the regression equation is also important.It represents the annual production as a fraction of cumulative production.This completes the set of variables needed to form a production function.The chart to the left shows the translation of the y = mx + b equation to the oil production variables.
Algebraic manipulation (demonstrated in the video) yields an equation for annual oil production:P = Qa(1 – Q / Qf )
The inverse of this equation gives a measure of time: years per billion barrels.To complete the linearization process and build a Hubbert curve, plot the projected production and this inverse value in 1 billion barrel increments of cumulative oil production.To add actual years to the plot, look at the actual cumulative production (Q) and match it to the corresponding value in the model.Then, subtract or add 1/P for values above and below the target year respectively.An example of this process is shown to the right.
In my next entry I will apply this methodology directly to the United States' historical oil production levels. This will demonstrate how the model works and help illustrate the decline in domestic oil production. It will also provide the foundation from which we will explore global production and its potential to unbalance global supply and demand.
Be sure to click the "HD" button to watch the video in full high definition!
In my last series of entries, I explored the relationship between the demand for gasoline and population growth in urban settings.Using the city of Atlanta as an example, I concluded that stringent fuel economy requirements are insufficient to curtail long-term energy demand.
I argued that these measures are a first step to reducing our dependece on fossil fuels. True conservation requires change.Americans must rethink their views on mass transit, commuting, and the way cities are designed.Unfortuanately, most people are unaware of the urgency of our energy situation.Our country prospered in an era in which energy was cheap, abundant, and easy to obtain.Today, the landscape is different.
Why are consumers unaware?
The average American consumer’s interaction with energy is limited to paying utility bills or buying gasoline.Most people’s experience with energy begins and ends when he or she pays the market price for a natural gas, power, or gasoline bill.
Comsumers’ insulation from the workings of energy production have left them conditioned to believe that there are near-limitless supplies of oil, natural gas and electricity.Some may understand that fossil fuels are a finite resource. However, energy producers are so adept at meeting demand that the concept of depletion is largely ignored or forgotten.
There is no scarcity of energy in America; prices rise and fall but lines at the gas station or brownouts in the evenings are limited to extreme circumstances.Ocassionally, huricanes disrupt refinery activity and cities experience brief gasoline shortages.Consumers write-off price increases to “speculation”, Big Oil profiteering, or price gouging.After a while, even the most severe price run-ups return to normal.
Given these consumer interactions, it is not surprising that there is little urgency to reform energy policy.However, forces are in play which threaten to disrupt the delicate balance between theglobal supply of and demand for energy.
The time for contemplation and planning is quickly running out.President Obama has taken the first step with his fuel economy measures.In ths study, I will explain why it is imperative that the United States continue a rapid and comprehensive reevaluation of its energy policy immediately.
What has changed?
While American consumers have enjoyed cheap, abundant energy for years, demand outside of Western Europe and the former Soviet Union was almost nonexistent.Today, the advance of globalization has brought unprecedented growth to China, India, South America, and other new populations.
Consumers in these countries have observed the standard of living in the West and rightfully want to enjoy the same comforts.Economic prosperity has wheted consumers’ demand for new housing, automobiles and electronics.
The impact of globalization has also been felt in the West.Our spending habits spawned massive industrial manufacturing abroad and focused our economy on services.Americans embraced the suburban model and began to commute to work.
These developments would not have been possible without cheap, abundant energy.So far the world has been able to meet this demand.Much of this demand (particularly in transportation) comes from crude oil.Because of the amazing abilities of a few key producers like Saudi Arabia, American consumers have been able to enjoy the benefits of cheap energy even as global demand began to accelerate.
Unfortunately, like any fossil fuel, oil is a finite resource.It will be depleted.Just because consumers have been conditioned to believe that producers can meet unlimited demand doesn’t mean the notion is true.Global oil production will peak, decline, and eventually lose economic viability.It is not a question of if, but of when.
Most alarming is the lack of awareness among consumers.This study, while far from comprehensive, will attempt to demonstrate how the production of oil could be peaking right now.The implications are clear:America has developed a lifestyle predicated on cheap oil and global economic development assumes a stable supply of cheap energy.The end of cheap oil (and cheap energy) threatens our standard of living and the global economy unless we take immediate action.
Now is the time to reevaluate our commuting habits, mass transportation, and the way we live.We must begin the transition from fossil fuels.The longer we delay, the more economic and social disruption we will incur.
Introductory Case Study: US Oil Production
Before examining the global oil situation, it is instructive to review the history of oil production in the United States.The discovery of oil on January 10, 1901 at Spindletop in Beaumont, Texas marked the beginning of the oil industry in the United States.For the next 50 years, exploration and drilling made the United States the world’s dominant oil producer.Oilmen proclaimed that the bounty was endless; Shell researcher M. King Hubbert’s 1956 prediction of future declines were casually dismissed.[The text of Hubbert’s presentation to the American Petroleum Institute is available here.]
In 1970 the United States produced 3.52 billion barrels of oil.From this point forward, production declined just as Hubbert postulated.Remember, Hubbert made his prediction back in 1956 when production was at 2.5 billion barrels annually and climbing.The accuracy of his prediction astonished oil executives.As time elapsed and production continued to decline into the 1980’s and 1990’s, the concept of peak production turned into a reality.
Oil production in the United States has followed a rough bell curve.Hubbert, a trained geologist and physicist, used complex differential equations to model the production of oil based on the quantity of oil already produced (extracted from the ground) and reserves available.Hubbert’s mathematics are dense, but there is a useful shortcut which demonstrates the core philosophy behind Hubbert’s depletion model.
I first encountered this method while reading Beyond Oil: The View from Hubbert’s Peak.Kenneth Deffeyes, Professor Emeritus at Princeton, applies a technique common in population biology to oil production and depletion.The concept, now called Hubbert linearization, uses a simplified mathematical process to uncover the key features of the Hubbert curve.All credit for this method belongs to Professor Deffeyes.I will demonstrate and explain the method and update it with new information for US and global production.Any errors or omissions in the explanation are mine.
In my next entry, I will explain the mathematics behind Hubbert and begin to apply it to the United States' historical oil production numbers. Future entries will deal with global ramifications and potential shortcomings in the model.
I have completed filming the first three entries in my series on energy depletion. I am proud of the analysis and I hope it is as informative to read as it was for me to research.
I filmed these first three videos in full high definition. Since YouTube has some issues with file formats, I'm only going to upload the first video tonight to make sure it looks good. After I confirm that YouTube is working properly I will upload the following two entries tomorrow morning. Given YouTube's slow upload times, I hope to have them available to view tomorrow evening.
As always, thank you for your patience and continued support. The site and I have been in a period of transition in the past month. Most importantly, I relocated to North Carolina and formed a new LLC to house my strategic and financial consulting services. Economic Outlook is now produced by Kramer Strategic Services, LLC. Don't worry - this won't change the site's content or the opinions I express. I remain committed to presenting my unbiased analysis of our most important economic topics. I am simply making Economic Outlook a part of my business entity.
As always, be sure the follow Economic Outlook on Twitter and YouTube.
I apologize for the delay in the new oil depletion entries. The reason for the delay is a good one - I have incorporated my own company, Kramer Strategic Services, LLC. I'm in the process of making some slight revisions to the site to move it under the purview of the company. I'm also updating the video introductions and making some cosmetic changes. Don't worry - the promised new entries are complete and ready to go but I want to complete the transition before posting anything new.
Come back on Monday for the first part of the oil depletion discussion!
I have some good news to announce: two major new entries are on their way. These two entries explain my assertion that the era of cheap energy is drawing to a close. I am proud of the analytic work in these articles and hope it will be an informative introduction to the major issues in play.
The entries are not posted yet because I am in the process of moving and upgrading my video equipment. I have relocated from Atlanta to the Research Triangle area in North Carolina. After finishing my degree at Emory, I decided that the RTP had the best mix of opportunities for my skills and ambitions. I am unpacking in the new house right now, so I will post the new entries early next week.
The first is complete and just lacks filming, which brings me to my second piece of news. I have upgraded all of my video equipment to broadcast in full 1080i high definition. Since the entries typically feature just me speaking, this probably isn't that important. Still, it will be nice to have the best technology available for the broadcasts since they will be archived on YouTube for as long as people want to view them.
I am excited about these two new entries (which may expand if I keep adding new information) and appreciate your patience as I get everything set up.
EDIT: Please note the entry on July 2, 2009 regarding a postponement until the completion of a transition to Kramer Strategic Services, LLC.
Now that we have seen how gross consumption will increase despite efficiency gains, it is important to examine ways to target peoples' habits. By improving efficiency and changing the way we think about their commutes, it is possible to maintain or even reduce overall consumption. This is critically important as global energy demand rises during economic recovery. It will also reduce our dependence on fossil fuels and lessen carbon dioxide emissions over time.
What are Some Strategies for Reducing Consumption?
This iteration of the model gives an example of how to reduce overall consumption more effectively.All of the variables remain the same except for the percentage of single-car commuters.The figure is reduced from 78% to 68% - one in eight drivers shifts to carpools or public transit.The results are dramatic.
If these drivers made the switch today, total daily demand for gasoline would decrease to 3.8 million gallons per day, down from 4.4 million in the base case.These gains are carried through the life cycle of the President’s efficiency measures.All four curves are shifted downward.The constant growth scenario saves 10.2 billion gallons of fuel over the lifetime of the plan.Population growth still increases demand but the effects are dampened over the next twenty years.
A delay of demand growth is the critical lesson this model demonstrates.By increasing the time it takes for gross demand to expand, governments are able to develop further conservation measures, expand mass transit infrastructure and change people’s habits.A smooth transition away from fossil fuels will reduce the overall impact to our economy.Rapid increases in demand enhance the likelihood of oil price shocks and propagate more economic disruption than if municipalities have adequate time to prepare for change.
This chart summarizes the key argument the model presents.The most optimistic adoption scenario saves Atlanta over 6.4 billion gallons of gasoline through 2033.However, the daily demand for gasoline increases to 4.21 million gallons in 2025 and 5.18 million gallons in 2033.Fuel economy conserves the resource but aggregate demand still grows.Once all vehicles are replaced by more efficient counterparts, the consumption of gasoline will still increase alongside the growth in Atlanta’s population.
A more likely scenario shows even more sobering results.The overall savings through 2033 are similar to the optimistic view (6.23 billion gallons) but consumption soars to 5.01 and 5.78 million gallons per day in 2025 and 2033 respectively.Today’s consumption is around 4.2 million gallons per day.Even aggressive economy standards fail to suppress demand growth.
The best way to decrease demand is to reduce the source of consumption – driving itself.Assuming the same levels of growth, shifting just one in every eight commuters to a carpool or public transportation increases overall fuel savings and decreases gross demand.Demand in 2033 (5.04 million gallons per day) equals the demand in 2025 in the probable growth scenario.As discussed above, delaying demand growth gives administrators more time to prepare alternatives.
An even more substantial shift in commuter behavior would reap even greater results.If one-third of all workers switched to carpools or used public transportation, the Atlanta area would save over 16.4 billion gallons of gas through 2033.Daily consumption would decrease to below 4.0 million gallons per day for at least the next 20 years.If drivers made the shift today, gross demand would decrease so far below today’s consumption that gross demand wouldn’t return to today’s levels until sometime after 2033.
What This Information Tells Us
This information gives decision makers a powerful tool to use in coordination with fuel economy measures.President Obama has taken the first step in what should be a multi-part process to change the way Americans view their commutes.As our population increases, we need to use better fuel economy as a bridge to a time when public transportation is more accessible and driving habits are changed.Reducing our reliance on single-passenger automobiles is the only way to suppress long-term demand fundamentals in a growing country.
Atlanta demonstrates the difficulty in making this transition.Public transportation is under-funded and residents are unwilling to make capital investments in what they view as a mismanaged organization.These are valid complaints and government officials need to make MARTA service more timely and dependable.Rather than invest in expanding rail systems, Atlanta continues to widen its interstates.This is both a misallocation of resources and a strategic failure.The same lessons in public policy can be applied to many metropolitan transportation systems.Until viable alternatives are available, people will rely on their cars.Overcoming the inertia to develop effective systems is a monumental social and political challenge.
Citizens must rethink their bias against public transportation and be willing to sacrifice some of the benefits of driving.Some of this change will come as energy prices continue to increase and the opportunity cost of not using public transit becomes too substantial to ignore.However, if gasoline prices remain low, Atlantans will continue to drive through long commutes which increase both the rate of gasoline consumption and greenhouse gas emissions.Fortunately, carpooling requires much less effort than the construction of new transit systems.It is possible to set up carpool networks and begin this process today at almost no cost.If people are willing to make the effort, carpooling is one option that would have an instant impact on daily consumption.Educating the public and encouraging its adoption is something the administration can begin immediately.
Energy prices, fuel economy, and viable alternative transportation are inextricably related in any strategy to reduce our dependence on fossil fuels.The Obama administration understands this imperative and has taken the first step in the process.Hopefully they will have the political fortitude to continue the project and call for more fundamental sacrifices from the American public to lessen our dependence on fossil fuels.
I am also happy to share the Excel model with anyone who would like to see it. Just send me an email from the link on my profile.
I am an MBA graduate from the Goizueta Business School at Emory University. This site offers my unique perspective on today's economic issues.
Feel free to contact me through the email address on my profile.
All work copyright Kramer Strategic Services, LLC.
The Hubbert linearization for the 
The logistic curve is even more impressive when actual data are superimposed on the same axes. Actual production closely follows the logistic predictions on both sides of the curve. Just as Hubbert predicted, domestic oil production has declined since 1970. 
