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These are random occasional observations by Al Bartlett on items reported in the Peak Oil Review.

Peak Oil Review, Vol. 5, No. 9, March 1, 2010

1) In the Ed Stein cartoon, one has an interesting contrast between the giant hyperbolic cooling tower and the small orange cylindrical building to the right of the tower. The small orange building houses the nuclear reactor. There is nothing nuclear about the giant tower, although in the minds of many, the tower is the visual symbol of a nuclear plant. Coal-fired electric plants sometimes have these same large hyperbolic cooling towers.

Why the cooling tower? The Second Law of Thermodynamics says that all heat engines doing work must discharge waste heat. For either coal or nuclear plants, this discharged heat is approximately two-thirds of the chemical energy released by the burning coal or of the nuclear energy released by the nuclear reaction. This is a lot of waste heat. You can make small changes in this fraction of heat that is wasted by changing operating temperatures, but this results in changes in efficiency of only a few percent.

So what do you do with this waste heat? The hyperbolic cooling tower is a structure in which the exhaust steam from the turbines is condensed and the heat released in the condensation is used to evaporate water which comes out of the top of the cooling tower as whisps of steam.

There are other ways of getting rid of the waste heat. I believe that the big wartime reactors at Hanford, Washington heated the Columbia River by a degree or two.

In cogeneration, the exhaust heat from the turbines is used for heating buildings if they are not too far away from the generating plant. Heating buildings via cogeneration is commonplace in Europe.

2) In the Briefs we read that Mexico’s oil production fell from 2.685 million barrels per day to 2.615 million in the space of one year. This gives an average rate of decline of 2.6 percent per year. Let’s see how this is calculated.

Rate of decline = (100 / 1) ln (2.615 / 2.685) = – 2.642 percent per year. The 1 in the denominator is the 1 year and the minus sign with the answer indicates a decline.

Here are the keystrokes:

2.615 ÷ 2.685 = ln x 100 =

When one has a steady decline there is a “halving time” that is analogous to the “doubling time” that one has with steady growth.

Halving time in years = 100 x (ln 2) / Annual percent growth

The keystrokes here are:

100 x 2 ln ÷ 2.642 = 26.24 years

Thus, if the decline in the Mexican production continued steadily at this rate it would reach half of its current value in 26.24 years.

The halving time is called the “half-life” when one is speaking of the steady decay of a radioactive substance.

Vol. 5, No. 7, February 15, 2010

1) Page 5. From the Commentary by Roger Baker: “Why not subsidize research that could lead to the restructuring of US food production based on energy efficient agriculture?”

Before we start restructuring agriculture we need to think about preserving agricultural land. On Thursday February 11 my daughter and I rode the California Zephyr from Chicago to Denver. Leaving Chicago the train runs through many western suburbs of Chicago. But to my surprise, at several places along the track west of the established suburbs there were thousands of new homes as far as the eye could see from the train. A few years ago this land was all agricultural land, probably some of the best agricultural land in the U.S., and now it has produced its last crop, namely new homes. Reforming agriculture is important, but first we must save the agricultural land.

2) Pages 2-3. “The cost of discovering each new barrel of oil has risen three-fold over the last decade as technology has pushed the frontiers of exploration into ever more remote areas…”

What’s the average annual percent increase in the “cost of discovering each new barrel of oil during the last decade?”

Answer: Just under 11 percent per year.

Here are the keystrokes to do this calculation with an inexpensive Texas Instruments TI-30XA hand-held scientific calculator. Here’s the formula:

Percent = 100 x (1/10) x ln(3)

The 10 in the denominator is the “decade,” the 3 is the “three-fold” and the 100 converts the fraction to a percent. Here are the keystrokes:

3 ln ÷ 10 x 100 = 10.986… This is just under 11% per year.

Dr. Albert A. Bartlett, professor emeritus of physics at the University of Colorado in Boulder, has delivered versions of his famous talk—“Forgotten Fundamentals of the Energy Crisis”—to 1783 audiences world-wide during the last 40 years. Albert.Bartlett@Colorado.EDU

(Note: Commentaries do not necessarily represent the Peak Oil Review’s position; they are personal statements and observations by informed commentators.)