Curve Fitting

[Update - I read a more detailed description of Hubbert's work. One thing I missed in this article was that Hubbert added the constraint of the total size of oil reserves; in other words, the area under the production curve. That makes the point of this post a lot less relevant. See my post at http://northern-flicker.blogspot.com/2006/10/hubberts-method.html for my updated take.]

I haven’t read Hubbert’s work in-depth. I do have some experience with curve-fitting though, and can already offer a cautionary note. Generally speaking, even if you know that some data are going to end up being in the shape of a bell-curve, you can’t successfully fit the curve until the shape of the curve is already well-defined. For example, take this dataset:



Are you thinking what I’m thinking? OMG, this curve is so going to flatten. So you assume some sort of bell shape, run the data through your curve-fitting algorithm, and get something like this:



If that was a curve-fitting homework assignment, you would totally get an A. But now let’s see how the rest of the data actually turned out:




D’oh!! It's still a bell-curve, with similar shape parameters, just bigger. You can also get an excellent curve fit to these points; an outstanding one by any numerical standard.

Conclusion: even if you know the shape of a bell curve, you can’t predict the peak purely by mathematical means until it has already happened.

Peak Oil and Hubbert’s Peak

Much of the peak-oil arguments center around the work of M. King Hubbert, who was a big-shot geologist for Shell Oil. Hubbert developed a set of formulas predicting a bell-shaped curve for oil production over time: slow in the beginning, speeding up, levelling off and peaking, and then falling at the same rate that it rose. Hubbert used these formulas in the 1950’s to estimate when American oil would peak, and successfully predicted a peak in the early 1970’s.

The concept of “peak oil” means different things to different people. Some people use it as a general term to describe the eventual slowdown and then dwindling of oil production. I get the feeling that most people use it in Hubbert’s sense: that production over time rises, reaches some high point, maybe plateaus there for a while, and then inexorably declines. A lot of people take that behavior as a given, where the only unknowns are when the peak occurs, how high it is, and how fast or slow the rate of decline is.

I think it’s important to realize that there are a number of implicit assumptions being made in that case. These assumptions include: the amount of demand, rate of discovery, and efficiency of extraction. For example, take the graph of US production. There are two peaks here; the second one occurring when the Alaskan oilfields hit their stride. You could argue that the curve has an overall bell-shape, but note that the “plateau” was relatively long-lasting – about fifteen years between the first peak (1970) and the second (1985).


Source: http://www.eia.doe.gov/emeu/aer/txt/ptb0502.html.

One thing you can assert with confidence: if you assume that the amount of oil in the ground is fixed, then eventually production will near zero. But when will that happen?

No Energy Crisis, continued

Here is a paper that confidently argues against the notion of a near-term oil shortage: http://web.mit.edu/ceepr/www/R2004-171.pdf. By M.A. Adelman, an economics professor at MIT, 2004.

“It is commonly asked, when will the world’s supply of oil be
exhausted? The best one-word answer: Never. Since the human
race began to use minerals, there has been eternal struggle —
stingy nature versus inquisitive mankind. The payoff is the
price of the mineral, and mankind has won big, so far.”

One of the main arguments presented here is that you can’t ignore the effect of prices on oil production and discovery. As prices go up, it becomes more and more economical to recover oil that had previously been disregarded as being unsalvageable.

On, 24-7

So that friend of mine, who got me hooked on the energy subject, went through his house to cut down on items that draw an electrical current, even when turned off. For example, any consumer-electronics device that supports a remote has to be “on” at some level for the remote to work. Interesting idea; I decided to take an inventory at my house. It wasn’t pretty …

· Stove (runs a clock)
· Microwave oven (ditto)
· Cordless phone in the kitchen
· Cell phone battery charger
· Answering machine
· Carbon monoxide detector
· TV (living room)
· VCR (living room)
· DVD player
· DVD recorder
· Stereo receiver
· CD player
· Vibrator/massager for a recliner
· Cordless phone (bedroom)
· Clock/radio
· TV (guest bedroom)
· VCR (guest bedroom)
· Clock/radio
· Clock in a bedroom
· Fan (remote controlled; go figure)
· Stereo (basement)
· Battery charger (basement)
· Baby monitor base
· Baby monitor speaker (kitchen)
· Baby monitor speaker (bedroom)
· Garage door opener
· Garage door opener nightlight
· Thermostat
· Automatic sprinkler controller
· Three motion detectors for outdoor lights

There are some others that I’m not sure of (like the refrigerator). There is also the porch light, which we keep on all night (required by the neighborhood covenant). Also, when the computer is on, which is during most of the day, there is the computer, monitor, power strip (has some led’s always lit), cable modem, two scanners, and a printer. Not sure whether those draw current all the time or not.

One obvious conclusion here is that we have way too much s--- in our house. I’m not sure what the cumulative current from all that is (I can probably estimate it from power bills), but it’s certainly more than it needs to be given how often we actually use those devices listed above. I’ll be discussing conservation later . . . .

No Energy Crisis

Here are the main arguments that there is no imminent energy crisis. By the way, right now I’m just trying to establish what the current lines of thought are. I’m trying to avoid expressing an opinion right now.

A lot of experts don’t believe it. In particular, the American government doesn’t. See http://www.eia.doe.gov/oiaf/ieo/oil.html for its 2006 report, which estimates that oil production will not peak before 2030. In fact, that report estimates that production will increase by 50% before peaking.

We’ve been here before. Remember the energy crisis of the 1970’s? People were really worried then, and the problem went away before we knew it.

The size of known oil reserves increases year after year. For a number of reasons: more exploration, better technology to recover oil, and, as prices rise, previously unrecoverable (i.e., too expensive to recover) oil becomes recoverable.

Referencing my previous post, here is an item-by-item rebuttal to the arguments indicating an energy crisis:

· It all starts with oil
Yes, oil is a critical resource for the world-wide economy. If/when our supply of oil recedes, then coal, natural gas, uranium, wind, solar, biomass, and other energy sources will replace it.

· Oil is a fossil fuel, and is not readily replenished.
I was surprised to find that there is some debate on this. Well no, actually I wasn’t surprised, because no matter how firm you think a fact is, you can always find someone who thinks its false. Hooray. Welcome to the internet.

In fact, commentary on this whole peak oil subject is riddled through with wackos and conspiracy theories of all stripes. You could probably start a fun blog just detailing all of them. But for now I’m more interested in looking at the wheat, not the chaff, even if it some psycho mind-blowing chaff.

Anyways, the abiotic theory of oil generation holds that oil is not a fossil fuel. Oil is generated by physical forces and/or bacteria deep within the earth’s crust. As far as I can tell, this theory is not accepted by any petroleum geologists or oil companies, who you think would be interested. There have been no successful significant experiments confirming this or denying the fossil fuel theory (again, as far as I know). I’m going to rule this one out right now, and accept that oil is a fossil fuel.

· Oil production is peaking.
Not according to OPEC or the U.S. government.

· After oil production peaks, it drops, often symmetrically, as fast as it rose in the beginning.
The only evidence that production drops fast is due to some curve-fitting models that have insufficient empirical support. As noted above, production is sensitive to price.

· Why are gas prices skyrocketing?
Several different arguments here:
1. Demand is catching up to production, making pricing volatile, especially with regards to market disturbances (Katrina, Iraq war).
2. The oil market is not free; it is partially controlled by OPEC and also interfered with by governments.
3. The U.S. has a refinery shortage.

· For the past few years, the annual rate of oil discovery is lower than the annual consumption rate.
Again, not according to government estimates.

The next step is to take a pass at rebutting the rebuttals.

Energy Crisis?

Is the world facing an imminent energy crisis? That’s the subject that’s been on my mind the past few weeks.

Conventional wisdom says we’re not. But there are enough dissenting voices to raise doubts in my mind, so I want to dig into it some more.

Obviously, it’s a hard question to answer. I don’t have any background, personal connection or other insight into the energy business. I’m dependent on finding out what other people think. And chances are, nobody really knows. A lot of people act like they do, but their predictions are all over the map. Everyone has their own set of biases to color their thinking; something that must be taken into account. I have my own biases. But I can read, I have access to good libraries and the Internet, and (hopefully) I can think critically, so I’ll see what I can figure out.

Here is the argument supporting a near-term energy shortage in the world, as I understand it.

It all starts with oil, because of its centrality to our modern industrial infrastructure, its being the resource most in danger of having imminent shortages. There are many other energy sources, but none with the ability to support our current transportation infrastructure (names, cars, trucks, and airplanes).

Oil is a fossil fuel, and is created naturally, but slowly. The world’s current reserves took millions of years to build up. We are depleting them faster than they grow, so logically it is just a matter of time until we exhaust the supply.

Oil production is peaking. U.S. output peaked around 1970. The North Sea oilfields are peaking currently (see http://www.eia.doe.gov/emeu/cabs/North_Sea/Oil.html). For another example, the data for Venezuela (one of the top four exporters of oil to the U.S.) is unclear, but it appears to have peaked by 2000 (see http://www.eia.doe.gov/emeu/cabs/Venezuela/Oil.html). The big wildcard here is Saudi Arabia, where production numbers aren’t publicly released, but there is evidence that they are peaking as well. (Note: isn’t the Internet awesome? In the old days, you’d have one person saying ‘X’, another saying ‘Y’, and you just have to pick whom you trust more. It’s great having real, relatively unbiased data out there, so we can all draw our own conclusions.)

After oil production peaks, it drops, often symmetrically, as fast as it rose in the beginning. Production graphs are generally in the shape of a bell curve. For example, here is a chart of U.S. production over time. It's quite striking.



From Beyond Oil, Kenneth Deffeyes, 2005.

I couldn’t find all of the numerical data online, but a table of the numbers from 1954 on is available at http://www.eia.doe.gov/emeu/aer/txt/ptb0502.html.

If this is true, we have declining production meeting a rising oil demand. That can’t be good.


The annual oil discovery rate is dropping. In fact, oil discoveries peaked in the 1960’s and have been declining since, and are currently well lower than consumption rates. For example, in 2002, six billion barrels of new oil were discovered. But the world consumed 27 billion barrels of oil that year. (Source: The End of Oil, Paul Roberts) While this doesn’t directly imply a near-term crisis, it does lend weight to the idea that oil’s time is limited.

Gasoline prices are at an all-time high, even in inflation-corrected dollars. Why is this the case if the world has plenty of oil?


Each of those assertions can be debated. When we continue: why all of that is wrong.

Thinking About Oil

For the past few years, I’ve been thinking that I should invest a little money into alternative energy companies. Partly because I want them to succeed, and wouldn’t mind helping fund them, a little, and partly because I figured at some point oil prices are going to take off, and alternative energy will become big.

Well, I didn’t take that idea anywhere. A few months ago, a friend of mine was telling me about his latest research hobby, which was to try to analyze “peak oil”, whatever that was, and try to draw conclusions about what investments to make. Hmmm, interesting project. One day I was over at his house, and started flipping through some of the books he checked out from the library on peak oil. I checked out a few for myself, and got hooked.

I was just a kid when the energy crisis of the 70's hit, and it worried me quite a bit. The crisis went away, but I've always wondered how things have progressed. A number of books on the market now are quite alarmist, stating that we are hitting the point of peak oil production, and the future may be dire.

So here are some of the questions I want to ask.

· What is the future of oil production? Is it keeping up with demand? Is it peaking, or has it peaked? What happens after it peaks?
· What happens to our society when there is not enough oil?
· What sort of energy policies should our society be pursuing?
· What should we be doing as individuals?


The books I read, of course, gave their answers to those questions. I always like to draw my own conclusions, and want to use this blog as a forum for that. I won’t limit myself to the energy field, but that’s where I’ll start.

Can I blog?

Now would be a good time to mention that I’m not sure how this blog will play out. For example, it would take dozens of hours to finish articles the way I’d like. With a job and children, it will take quite a while to scrounge up that time. If I wait till I have everything the way I like it, I’ll never get anything out. So my plan now is to post incrementally, and then maybe combine things into a polished document at the end. That will be a challenge for me, since (i) I tend to want to perfect my thoughts before releasing them into the world, and (ii) I’m always learning new things and reshaping those thoughts. So we’ll see. But here goes.

Northern Flicker

Hi, and welcome to my blog. I hope you find it interesting, entertaining, enlightening, or otherwise of value.