A recent story [Xin] reports that the world's estimated usage of oil for 2006 is as follows:

"The Organization of Petroleum Exporting Countries [expects] that worldwide demand for crude oil will rise by 1.9% [from 2005 to] 2006, to [an average of] 84.8 million barrels per day.

On average, how many barrels of oil per day were used in 2005, according to this estimate for 2006? Assuming 2006 usage averages 84.8 mbd (millions of barrels per day), and given the 1.9% increase this would represent, average daily usage for 2005 in barrels (not millions of barrels) per day was: ______________ barrels/day.

How many gallons per year do you use?

Petroleum, which literally means "rock oil," is used in many settings in addition to being distilled into gasoline for "standard" (internal combustion engine based) cars. Petroleum is also used to make heating oil, for example. In addition, we as citizens use up oil indirectly even when not driving due to the "embedded energy" in the products we buy, since it takes energy to obtain raw materials, to process them into "products" and to to transport everything -- and much of that energy today comes from oil.

How much does this come to in barrels (or in gallons, to use a more common measure) in terms of oil burned annually per American?

In the diagram below, use the fact that there are 42 U.S. (liquid) gallons in a barrel of petroleum to quantify this. Start with 84.8 mbd (millions of barrels per day) that is, with 84,800,000 bbl/day.

Amount of oil used up by the entire World       84.8 mbd (84,800,000 bbl/day)           ___________ bbl/yr (barrels per year)       ___________ gal/day (gallons per day)         _______________ gallons/yr

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II. Oil consumption in the U.S. -- A burning question.

An often-cited fact is that "the United States consumes about one-quarter of all of the world's [annually used] oil, while being only 1/20th of the world's population." To be more precise, note first that in 2006, World population is roughly 6.5 billion and the population of the U.S. is about 300 million.

1. Thus, the United States represents about ____% of world population

2. If U.S. consumption represents fully one-quarter (or 25%) of the world's oil consumption for 2006, this would come out to the U.S. consuming about ___________ barrels per day.

3. This comes out to about _________ millions of barrels, that is, ___________________barrels each year, used by the U.S. (Use commas to show thousands, millions, positions!)

4. Thus each U.S. citizen (on average) uses about ___________ barrels -- or __________ gallons -- of oil each year (this does not count the so-called "oil barrel equivalents" we use in coal, natural gas, etc). How much oil is burned on a "per person, per day" basis?
   
   
   

5. Carry out a similar computation to find out how much oil is burned (on average) on a "per person, per day" this time using averages for the whole World.

6. Looking at the final numbers in the previous two parts, exactly which two "groups of people" are actually being compared? Does this make our previous answer an overestimate or an underestimate of "how much more oil we use in our country"?

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Below you will be led to discover and quantify two dramatic (or at the very least, quite vivid) ways of visualizing answers to the "how much oil?" question.

1. First Visualization: Volume

   The world uses roughly 85 million barrels of oil each day (true fact). Given that a barrel is about 40 gallons,

   1. How many gallons of oil (petroleum) per year does the world use? ____________________.

   2. (Hence, as an aside, the world burns __________________gallons every hour).

   3. Approximately How many liters of oil per year are used? ____________________
      (use that there are about 3.785 liters in every gallon)

      How many cubic feet are there in a cubic yard? Answer: 27 since a cubic yard is (1 yd × 1 yd × 1 yd) which is the same as (3 feet × 3 feet × 3 feet).

      Since a liter is a cube "0.1 meters (or one-tenth of a meter) by 0.1 meters by a 0.1 meters" (while a cubic meter is "1 meter × 1 meter × 1 meter") and using the same method-of-reasoning as above, we can conclude that there are ______ liters in a cubic meter.

      Use the same type of reasoning (along with the fact that a kilometer is 1,000 times longer than a meter) to answer: there are ______________ cubic meters in a cubic kilometer (the answer is a large number).

      Combining the previous two results, how many liters are there in a cubic kilometer? _____________________?

      How many liters are there in a cubic mile? ____________________. (STOP! First, note that 1 mile is about 1.61 kilometers, hence, the same "how many cubic feet are there in a cubic yard" reasoning tells us, using our calculator, that one cubic mile has __________ cubic kilometers in it. Now use the previous item to answer the first question in this item)
      

      A few open-ended questions...

      If you were writing a newspaper story what geometric or visual representation might you use to represent the amount of oil used in the world each year?

      So far humanity has burned up almost exactly 1 trillion barrels of oil (1,000 billion, or 1,000,000,000,000 barrels) as of spring 2006. How could you visualize this volume?
   
   
   

2. Second Visualization: Surface Area

   • As we saw earlier, the world currently consumes about 30.95 billion barrels of oil per year. This means the world uses up almost exactly ______ trillion gallons of oil per year.

     The surface of the earth is 509,600,000 square kilometers, or (509,600,000)*(1,000,000) square meters. By dividing the previous number into the surface area of the Earth, we can find out that "one gallon of oil is used up for every [certain number of] square meters" the entire planet over. Specifically,

     (509,600,000,000,000 sq m) ÷ (1,300,000,000,000 gal)

     = (509,600)/(1,300) = 392 square meters. The area of a circle or radius "r" is π·r², so "392 square meters" is roughly the same as the area of a circle of radius r where π·r² = 392, so r² = 392÷π.

     Taking the square root of both sides in the last equation, we see that "each year, we burn a gallon of oil for each 392 square meter region" is equivalent to saying, "each year, we burn a gallon of oil each parcel on Earth, where that parcel has the same area as a circle of radius 11.17 meters (radius of about 36 ½ feet).

     However, about 70% of the Earth is covered by water and so to find out how much oil is used up each year per "what size portion of Earth's land", it would be one gallon burned (each year) for only (about) 30% as much land as that earlier "392 sq m" region. This would amount to annually using up one gallon of oil for each parcel of land on Earth, where each parcel would be 117.6 square meters in size, or about the area of a circle of radius _____meters, that is, a circle whose radius is about _____ feet

     This "one gallon of oil" is burned up, each year, for every segment of that land area on the entire surface of the earth -- not just the inhabited parts, but for every such parcel, every such bit of land in the Sahara desert, every such bit of land in the Amazon, every such bit of land in every city, town, field, hillside, etc, on planet Earth.

     

     Now let us examine the entire history of the use of oil; we've used up, as of spring/summer 2006, almost exactly 1,000 billion (that is 1 trillion) barrels of oil, or about 42,000 billion gallons (42 trillion gallons).

     Let's again compare this new, larger amount of oil (total consumed so far, rather than how much we use every year), and what size parcels we'd have to divide the Earth's land area into, in order for there to be one gallon for each parcel. Carry out the calculation below, given a figure of land surface area of about 148,326,000,000,000 meters squared on Earth:

   • There would be one gallon for every parcel of area __________ square meters (this would be a square __________ meters on a side (a square __________ feet on a side).

     However, an often better way to visualize such a small area as this, is to imagine yourself at the center of a circle, so you are sweeping out an area around you with your arms or a rod; how large a radius would it take to sweep out a circle whose area is __________square meters (same answer as above)? It would have a radius of __________ meters or equivalently, it would have a radius (sweeping arm) of about __________ feet.

     Notes:________________________________________________________________________________

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IV. When will we "Run out" of Oil?

Getting Divisive. According to several estimates, the 1,000 billion barrels of oil (1 trillion barrels) we have used up so far represents about half of the total oil that is recoverable [PO]. In other words, there are about 1,000 billion barrels of petroleum which could be used up if humanity so chose.

Dividing this 1,000 billion barrels by the expected oil usage level for 2006, what number does the quotient equal and what are the units? __________ (you will need to use the bbl/yr figure derived earlier).

But (a) what does this number, with those units, actually represent in real world terms? And (b) What assumptions are being made?

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"Right Answer, Wrong Question"

The figure of "32 years and change" might be called "how many years before we run out of oil" and one assumption it makes is that there aren't more than about 1,000 billion more barrels of recoverable oil. A second implicit assumption is that, despite environmental concerns, humanity will nevertheless choose to burn up the entirety of all that oil. Are there other implicit assumptions? What do you think? [Pause before continuing].

There are deeper underlying assumptions, that turn out to be either unlikely, or simply incorrect. For example, a third implicit assumption is that the figure of about 85 million barrels per day (or just under 31 billion barrels per year) will remain constant during those 32 or so years. Would an economic slowdown change that fact? It's certainly a short-term possibility. However the long-term trend has been of ever-higher levels of annual global oil consumption, which suggests that there would be somewhat less than 32 years left as oil usage increased from year to year.

A more fundamental difficulty is that the very question that was posed above, forces us into a questionable model in which we count the number of years left -- as if after 32 years and 4 months or so of the world using 85 million barrels of oil per day, the world will use 0 barrels per day the next day when it's all run out. Such a drastic change is certainly not economically or socially desirable! In fact, it turns out that this "plateau then a cliff" model for the level of oil usage, is not only undesirable, but is also not geologically correct. One cannot "produce" oil at a constant level until it all runs out since oil does not work like a gas tank (the commonly used term "produce" it put in quotes since human beings today are not actually producing any new oil; we are merely pumping already-existing oil out of the ground, oil that was produced by geological forces over millions of years).



Peak oil ≠  "Running Out"

Each oil well in fact goes through a bell shaped curve of production: the number of barrels "produced" per day goes up for a while, reaches a maximum, and then declines. The same is true for an oil field containing many oil wells. The same is true for entire countries. For example, U.S. oil production (extraction) reached its peak in 1970 (!) because of these geological facts, despite the fact that no place on earth has been more heavily explored for oil and drilled, and that no other country surpasses the technical and technological oil expertise in the U.S., the U.S. has never suprpassed its 1970 barrels/day rate.

This is because of the geological nature and limits of maturing, aging oil wells and fields. Dozens of other countries have peaked in oil as well, and when enough of them do, the entire world's oil "production" level will peak as well. Clearly this will happen long before we pull the last barrel of oil out of the ground, so this will happen much sooner than 32 years from now.

If the oil "optimists" are correct and there are not 1 but 2 or so trillion more barrels of oil left, then even putting environmental concerns about oil burning aside, the growing level of world demand for oil means it would be far sooner than 64 years from now when the "last barrel" is extracted, if ever higher extraction rates were possible. But in fact the "bell curve" nature of oil extraction means peak would happen long before even that (earlier) "last barrel" date. We would not have run out of oil, but once oil peak is reached, what is arguably the world's most important commodity -- used for transportation, heating, plastics, pharmaceuticals and more -- would start to diminish: the amount we could 'produce' would be less and less each year, instead of more and more as we have been used to.

Peak Oil is a big issue and links are provided below. The key mathematical or quantitative analysis lesson here is that it's possible to have the right answer to the wrong question: numbers by themselves, without context, can not only miss moral issues (e.g. a liveable environment), but can even miss the point numerically if we "ask the wrong question" of the mathematics, like "how many years before the oil runs out?"

A U.S. Geological Survey public education poster begins with this very point: "Q: When will the oil run out? A: Wrong question! The right question is when [peak oil] will take place." Meanwhile, Matthew Simmons, CEO of the world's largest Energy Investment Bank and others have pointed to evidence oil peak is very near and is unlikely to come any later than 2010 [MS]. Further, North American natural gas production seems to have peaked in 2001 or 2002 (see also Julian Darley [JD]) and world-wide natural gas production is expected to peak not much later than 10 years after oil production peaks. Even coal production peak appears to be an issue that will come up long before coal "runs out" supposedly several centuries from now, were the human race to make the fateful decision to use it all [GV].

Will peak oil save us from global warming? This is unlikely for several reasons. One reason is that scientific studies show cuts over ten times Kyoto (50-70% cuts) are needed in fossil fuel emissions to avert dangerous climate change, while peak oil means 'merely' a lower rate of increase, followed by an initially slow decrease. Even this initially slow decrease however, is likely to cause economic crises in a world whose main economies are based on perpetual growth rather than steady-state economic models. Another reason Peak is unlikely to save us from global warming is more ominous: it may push policy towards more use of coal (this has already started; Julian Darley refers to a big push for coal as a 'cyanide solution' to the problem of peak oil; former oilman Jeremy Leggett warns similarly) -- or even towards experiments attempting to disturb and exploits gas hydrates, which a geologist, writing in the Baltimore Sun, describes as a "ticking time bomb" if we keep burning fossil fuels, even if we don't attempt to disturb them [AJ].



As noted, then, the environmental issues are big and inter-related, and a good starting point is the References section below. For the purpose of this quantitative analysis exploration, there are other lessons those concerned about the environment will want to take to heart: First, that math can provide the "right answer to the wrong question" as we have just seen. Moreover, that in a world where we are flooded with dozens of messages per week from politicians, and easily dozens or more messages per day from advertisers, we need to skeptically ask what exactly the numbers mean, and in particular, to demand the wider context. Often only independent research by an individual or group can unearth that, for example, "when will the oil run out" is a question that does not really make sense and that another question needs to be asked; likewise about environmental and economic contexts and assumptions.

We need quantitative literacy, in short, not just to be able to "answer some questions" (which is an important skill to be sure, especially if they are questions we're able to formulate ourselves) but in addition, quantitative literacy, if we are to achieve a satisfying and fulfilling future, is also needed for us to "question some answers" as citizens living in our neighborhoods (and living on this Earth) together.

References

[AJ] "Ticking Time Bomb" by John Atcheson, http://www.commondreams.org/views04/1215-24.htm See also, "New scientific theory, hydrate hypothesis, suggests global warming catastrophe" by Brad Arnold, http://planetsave.com/ps_mambo/index.php?option=com_content&task=view&id=6724&Itemid=69 and the more technical report that "Humans are performing a high-stakes climate experiment" on Earth at, http://www.innovations-report.de/html/berichte/umwelt_naturschutz/bericht-55436.html

[GV]The Peak in U.S. Coal Production by Gregson Vaux, http://www.fromthewilderness.com/free/ww3/052504_coal_peak.html

[JD] Julian Darley reports on and analyzes the June 2003 US Dept of Energy (DOE) Natural Gas (crisis) Summit

http://www.fromthewilderness.com/free/ww3/071203_no_parachute.html

See also MP3 streams, interviews, etc at

http://www.globalpublicmedia.com/topics/natural_gas and the book at http://www.globalpublicmedia.com/products/165

[PO] See e.g. "Peak oil in the U.S. Congress" by Rep. Roscoe Bartlett [R-MD] at http://www.energybulletin.net/12751.html "The Twilight Zone" by Jeremy Leggett, http://www.energybulletin.net/5627.html and ASPO, the Association for the Study of Peak oil & Gas at http://www.peakoil.net/ In addition, a wealth of articles, news, and interviews on peak oil and related topics can be found at http://www.globalpublicmedia.com and http://www.peakoil.com and attempts towards citizen responses at http://www.postcarbon.org

For a more mathematical overview of peak oil, but one accessible at the undergraduate level, see Sylvia Forman's "Mathematics and Oil: Do They Mix?" in Math Horizons, Sept 2005.

[MS] Interview with Matthew Simmons, http://www.globalpublicmedia.com/interviews/609

[USGS] US Geological Survey, "Are We Running Out of Oil? [Wrong Question!]"

http://geopubs.wr.usgs.gov/open-file/of00-320/of00-320.pdf

[Xin] "Crude price roars to four-month high" at http://news.xinhuanet.com/english/2006-01/21/content_4080231.htm

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Created 2000-2006 by Dr. Harel Barzilai. Some rights reserved. Reproduction and use with attribution for noncommercial educational purposes is permitted and encouraged. Details at http://creativecommons.org/licenses/by-nc-sa/2.0/   Acknowledgement: Part of this work was made possible with kind support (Fall 2005-Spring 2006) from the Professional Development Mentors Program (PDMP) at Salisbury University, a collaboration of the Faculty Development and the Learning Technology committees.