Saturday, January 14, 2012

U.S. Energy Supply - Let's Do Some Math

There's a notion out there that the United States isn't facing a near-term energy crisis. The idea, seen here, http://www.kiplinger.com/businessresource/forecast/archive/The_U.S._s_Untapped_Bounty_080630.html, is that if we more fully extracted from known and estimated domestic energy resources, we would be just fine for at least 300 years. Like most too-good-to-be-true propositions, this one has its own issues:

Assumptions:

1. The US has a 300-year supply of energy, at current rates of consumption. This includes petroleum in its various forms, as well as known and projected finds in natural gas, coal, etc. Alternative energies are estimated; see #2 for their proposed effect on supply and consumption.

2. Increased efficiency in using current sources in combination with the development of new and/or alternate ones will cause our consumption in absolute terms to remain constant in spite of population growth.

Interesting.

OK. Assumption #1 could make sense, with some caveats. It is easy enough to use publicly available information to come up with a reasonable estimate of current monthly usage of petroleum products, solar, wind, coal, hydro, etc. Given the nature of all the data, it would further be reasonable to overstate our usage somewhat, in order to be generous in our later averaging. We'll leave out smaller issues like whether power companies along the Canadian border ever sell electricity to Canada, and the opposite. We're just talking about macro numbers here.

I believe it would be appropriate to measure such usage not just in terms of barrels or cubic meters or metric tons, but also in our total BTU consumption. For example, having the metrics for both estimates of energy source volume as well as energy source output can help us compare the utility of different grades of coal or crude oil. Not all crude is create equal, and in the BTU output department this rapidly becomes a question of profitability for the entire supply chain. Do we use it to make plastic, which doesn't add to our energy supply, or might it be worthwhile to refine it into some sort of fuel? This is a macro problem, because in every instance in which part of our 300-year supply doesn't go toward the production of energy, we are removing it from that supply. If we are blending the energy and non-energy usage of our energy sources, then we deserve to be ridiculed for not using good sense in designing our estimate models.

The next bit is even more challenging: we must come up with a way to identify and quantify known reserves of various energy sources, whether they be coal seams, oil deposits (shale, coastal, wildlife refuge, and so forth), gas deposits, and of course proposed wind farm sites, solar sites, and all the other energy assets we can think of. This is, after all, an extremely important question; no statistician will ever feel comfortable making estimates based on estimates based on estimates, and then projecting out centuries into the future, without having substantial caveats.

Firstly, I think it important to understand that consumption varies. As time moves forward, will we continue to encourage people to drive greener cars by way of tax subsidies? Will we have the political will to keep after the auto manufacturers by way of increasing CAFE standards? The Republicans have routinely poo-pooed the idea of subsidizing green jobs or renewable energies. Is there a way to take this into account? These and other questions are important to keep in mind as you read the following math walkthrough. Remember that I'm taking their supply estimates at their word; they could in reality turn out to be much greater or much lesser. Obviously this would affect our numbers, so we would always need to be in a constant state of refinement as we track real numbers as they happen, revising the models as needed.

The following are just a few rough calculations. Let's walk through this:

300 years is 3600 months.

Think of this as though it were a loan with no interest rate, so that our 300-year supply becomes easy to amortize. Thus, much like a monthly mortgage payment, we can easily see how long it will take to deplete our 300-year supply, if one or more of our assumptions are wrong. For easy numbers, let's say that our total "loan" is $3,600,000 (for a total repayment rate of $12,000 per year). Thus, at current rates of consumption, we are "paying down" our "loan" (I.e., depleting our supply) by $1000/month. If absolutely nothing changes on either side, then we will completely deplete our energy supply in 300 years.

Yes, I know this is drastically oversimplified. However, as I discuss below, so is this whole 300-year setup. The longer I think about this rationally, the more websites and sources I see that seem to be shouting this figure (or similar) from the rooftops, the more convinced I am that its expositors are relying on their viewers' disinclination toward math and physics.

So, we've got this $3.6million loan, and we are paying it down $1000 per month. In our simplified scenario here, we are thinking of this as a zero percent loan. The principal (supply) is fixed in our scenario. Currently, the US gets around half its oil from abroad. With only 50% domestic production, a substantial amount of the chaos in the assumptions about oil is largely out of our hands. Although this article claims this 300-year supply would be achievable "without importing a single barrel of oil," I don't bother giving that credence. No country anywhere will deplete their own reserves any faster than they need to.

That having been said, what I'd like to do is calculate the effect of a very small but steady increase in our usage. Now, like the people that came up with the 300-year concept, I'm going to use somewhat unrealistic numbers, like a perfectly steady rate of consumption increase.

So, what happens if Assumption 2 is just a smoodge off? Say, efficiency of new technologies isn't quite overcoming population growth, the net effect of which is that our annual consumption is climbing 1% per year. A perfect 1% rate of increase would mean that each year we increase our payment by 1% over the previous one. Doesn't sound like much, does it? Well, at a 1% rate of increase, how early do we run out, in our perfect 300-year scenario? What about a 2% annual increase? 3%? Given historical increases of 4-8%, and given the ever-increasing appetite of emerging market nations, I think this question is perfectly reasonable, if not mandatory.

Using a simple Rule of 70 approach, we can be highly accurate:

At 1% annual growth, our annual consumption rate doubles every 70 years. Keep it simple and forget that along the way we will be taking a bit more out of our 300-year supply each year. Let's just double it at years 70 and 140:

Years 1-70: we use 70 years' worth of our supply.
Years 71-140: we use 140 years' worth. We have 90 years' worth left at the start of Year 141.
Years 141-210: we would use 280 years' worth, but we don't have that much left.

1% per year increase, on average, really simplified, drops that 300-year supply to ~165 years, because we would run out in Year 165 or so.

2% per year, using the same formula, we run out in Year 120 or so.

3% per year, using the same formula, we run out in Year 100 or so.

If we are able to uncover another year's worth of supply, in whatever form, then we simply have another 12 months before the reckoning. If, however, we have a BP-like event, which effectively shuts down production--even for a short period--of a healthy reserve, concurrently wasting resources in the form of spillage, then somewhere, somehow, we will have to lean a bit more heavily on different sources. Supposing three oil derricks are disabled one fall due to a severe storm? If they aren't producing, then some other site needs to crank out more for us.

All such minor interruptions must be factored in, even if roughly. Major ones should as well, for that matter. When they aren't, our projections lose at least some of their integrity. When you couple those oversights with the many other ones already discussed, these projections have no integrity. We would be just as "accurate" if we said that we'll wind up somewhere between just fine and totally screwed.

In any case, the 300-year claims just don't hold up to scrutiny. Their disregard for basic realities is appalling, and they shouldn't be used as an argument against the promotion and reasonable subsidization of renewable alternatives--indeed, these numbers should reinforce the sense of urgency we should have in developing and improving non-fossil fuel and renewable energy technologies.

The shoddiness of these blatantly unrealistic and contrived "facts" reflects badly on their creators, and the fact that they are routinely used in order to misinform the public is irresponsible and unethical.

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