Gasoline and M&Ms

by Shane L. Larson

Have you ever noticed in the movies that the best villains are not brutish monsters, but rather they are cold, calculating, brilliant minds with a powerful command of math and science?  They embody in a subtle and startling way the deeply ingrained mathphobia of modern American society — if you have the brains to master math and science, you have the power to threaten the core values of our society.  Your devious plans can often be defeated by the solidarity of the common folk, and maybe a good dose of apple pie and deep seated hutzpah of the Chuck Norris/Bruce Willis type.  According to the movies, brawn is always a plausible way to defeat a Death Ray Laser of Doom built by numbers and math and science.

Math and science, like most knowledge, can be used for evil.  But science is a funny thing; in many ways it is beyond the idea of “good” and “bad”.  It is built on quantitative data, numbers that can be measured.  Numbers simply are, and it is human values that place judgements of “good” and “bad” on them.  Numbers embody ideas in a way that is, in many instances, beyond reproach.  “Data” — large collections of numbers — represent well defined aspects of the world that are easily verifiable: the height of a tree, the mass of an automobile, the number of tax-exempt businesses in Enid, Oklahoma.  Numbers can be combined together in powerful ways using well-defined mathematical operations.  One could argue about the numbers one begins with (”Did you remember all those businesses on the south side of Enid?”), but the computation of numbers once the beginning is agreed on, is irrevocably beyond argument.  There are not multiple, arguable ways to “add” or “multiply” numbers together — these are unassailable mathematical concepts.  That is, if you believe in math (that was a joke — here is another joke [just to be clear — this is a parody!]: ).

One of the great beauties of numbers is their application to the world — what you and I call science and engineering.  You can build bridges with them, create iPads and Kindles, design a blender that can crush ice and bananas into the perfect smoothie, build a better pacemaker for your mother-in-law, or throw a forty ton Boeing 767 into the air and see it flies instead of crashing to the ground in a smoldering heap (like so many earlier experiments in aviation: ).

Numbers can also can embody — “quantify” in the language of the science nerds — things that most of us have a gut feelings about, but maybe not a true empirical sense about.  For instance, which is better for you: a thick slice of cucumber or a thick slice of summer sausage?  Unless you are some kind of crazy person, you probably know that the cucumber is better for you.  We quantify that concept in a variety of ways.  One is through a number that embodies the energy content of the food: the calories.  Another number is the mass of fats in the food. Our dietary scientists have discovered that many fats have long term health effects by using a powerful assessment of numbers known as statistics.

The mathematical foundations of statistics are robust and detailed, but you are familiar with statistics and use them every day.

  • ME: How long does it take to get to the airport?
  • YOU: Usually 25 minutes.
  • ME: How much do you weigh?
  • YOU: About 75 kilograms.
  • ME: What kind of gas mileage do you get?
  • YOU: Around 25 miles per gallon.

“Usually.”  “About.”  “Around.” These are words masquerading as a statistical concept known as the “average.”  You’ve on multiple occasions taken some data (stood on the bathroom scale each morning).  The number is not the same everyday; it fluctuates down (when you’ve been controlling your portions and walking your pet iguana) and up (when you indulge in too many bratwursts at your summer barbecue). You know the number hovers at “about” 75 kilograms, in the approximate middle of the entire set of numbers you’ve seen spin by on your scale.  You have unconsciously (and successfully!) estimated a mathematical average in your head.  On any given morning, you probably couldn’t guess the reading on your scale exactly, but your average will be close.  This is the nature of statistics; you don’t get a definitive prediction, but you get “in the ballpark.”

Perhaps one of the most important numbers to modern society is one you have never heard of, but experience every day: EROI, Energy Return On Investment.  The basic premise is one that balances the benefit of a task against the effort of completing a task.  You make judgement calls like this every day, based on internal statistics you have built up over years of experience. Close your eyes and let the everyday scenes of your life slide by.  You have company coming over for an evening dinner — do you get out the Comet and scouring brush and clean the bathtub or do you draw the shower curtain?  You’re a bit late getting going in the morning — do you pack a lunch, or plan to buy lunch at work today?  It’s tax time — do you file your own returns, or do you have your CPA prepare them for you?  You want to bring boxes from the basement storage upstairs — do you do it yourself, or is it worth making your kids help out?  Everyday we make judgement calls about personal investments of time and effort.

The idea of EROI is easily applied to the questions that swirl around the use of energy in modern society.  Why do we use oil and fossil fuels?  Because we get a lot of energy out of coal and oil, and they are (currently) easy to get out of the ground.  High energy output for minimal investment — the EROI of fossil fuels has traditionally been high.  Let’s do a little math about EROI.  We quantify energy using a specific number; with food that number is usually called a “calorie” which is related to a fundamental unit of energy used by physicists and engineers called a “Joule.”  A joule is a quantifiable amount of energy.  It is approximately the amount of energy needed to lift a Harry Potter novel up over your head.  In some ways it might seem to be a lot of energy; your arms would get very tired if you lifted that same novel up and down over your head 100 times.  By a similar token, it is a very small amount of energy; a single M&M has about 14,400 J of energy (about 3.44 Calories, in our usually dietary energy vocabulary); for a single M&M, you can lift that same Harry Potter novel up and down more than 14,000 times!

Suppose I buy a bag of M&Ms at the checkout line for $1.29.  What is the EROI?  All told, there are 240 Calories in the bag, or 1 million Joules of energy.  The energy returned on my investment then is

EROI = 1 million J/$1.29 = 779,000 J/$

Now let’s think about energy in the way that we normally think about energy in society.  A gallon of gasoline has a useable energy content of about 130 million Joules.  If you (currently) spend $3.50 on a gallon of gas, the EROI of that gas would be

EROI = 130 million J/$3.50 = 37 million J/$

You get almost 50x more energy on your investment from gasoline than M&Ms.  What about household electric?  Current standard electric rates in the western United States average about $0.12/kWhr.  One kWhr is 3.6 million Joules of energy.  So the EROI on residential electric is

EROI = 3.6 million J/$0.12 = 30 million J/$

Is 30 million J/$ a good return on our investment?  It depends on how far that 30 million Joules of energy goes.  The total daily energy capacity of a typical nuclear power plant (like the Watts Bar Nuclear Power Plant in Rhea County, Tennessee) or of a hydroelectric dam (like the Bonneville Dam on the Columbia River) is 100 trillion Joules.  The average American household uses about 113 million Joules of energy every day (  For a city the size of Salt Lake City, Utah (2.3 million people in the greater urban area), that’s about the entire energy output of the Bonneville Dam or Watts Bar every day.  There are many such energy generation stations, and many such population centers like Salt Lake City, and so the system is well balanced in terms of current demand and production capability.  This is the basis of our modern society — cheap energy.  Prices fluctuate up and down, but by and large, we sit in the ballpark of tens of millions of Joules of energy per dollar.

The cost of energy, particularly energy like electric and refined petroleum, is fixed by the effort required to get the energy into useable form — the cost of building and maintaining the electrical grid, and the cost of building refineries and shipping the products around the world.  The cost of new sources of energy, fossil fuel or otherwise, will have different EROIs because the effort required to get them is different.

Consider oil.  There has been enormous debate about the reserves of energy that Earth harbors, but the simple fact remains that all the easy oil has been found.  There may be vast reserves of oil in the Arctic, or in the tar sands of Canada, or in the deep ocean of the Gulf of Mexico.  But getting at those petroleum reserves is hard — it costs money because the technology required to extract the petroleum is expensive, and the associated risk is enormous (as the recent Deepwater Horizon accident in the Gulf demonstrated).  Consider the cost of extracting oil from the Canadian oil sands.  Current estimates of the cost (the investment) range from $20 to $40 per barrel of oil.  The average production cost per barrel of oil from the Middle East is about $1 per barrel, while the average production cost per barrel of oil from North America is about $6 per barrel.  If that cost is passed directly on to the products refined from the oil, like gasoline, the current price could increase by 500% or more!

For the moment, throw all environmental arguments aside; ignore all the machinations about climate change and carbon loading the Earth’s atmosphere.  Restrict your attention to the oil reserves of Earth, and let’s talk about the future.  The amount of oil is not the issue; the cost of getting the oil is.  All the easy oil is gone.  Now it gets hard.  There is a cost in capital and energy to get at the remaining oil reserves, whether they are in tar sands, or below the deep ocean, or in the Arctic.

The end result is that the investment is higher for the same amount of energy, the amount of energy contained in a single barrel of crude oil.  The increase in investment will skyrocket, and the EROI will plummet from the current value of 30 million J/$ that we enjoy, to perhaps only 1 million J/$ or less.  At 1 million J/$, you’ll be paying $37 per gallon of gasoline.  The easy oil will be gone, though there will be plenty of oil left on the planet.  The question for the future is this: can new energy technology beat the EROI on the hard oil?  Can we beat the price of 1 million J/$ with photovoltaics? With nuclear? With geothermal or wind?  This is the deep question, and it is driven by the same common denominator: the economics we are willing to tolerate. In this case, an appropriate economic factor to think about is the energy return on investment — EROI.

The truth of numbers is they precisely define how hard life is.  We would do well to remember that.  John Wayne said it best himself — “Life is hard.  It’s harder if you’re stupid.”


NOTE: This piece was inspired by Joseph Tainter, a colleague of mine at Utah State University, who introduced me to the concept of EROI.


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