Insulators on high-voltage electricity transmission line.

For more than three decades, Vaclav Smil has been developing the concepts presented in his 2015 book Power Density: A Key to Understanding Energy Sources and Uses.

The concept is (perhaps deceptively) simple: power density, in Smil’s formulation, is “the quotient of power and land area”. To facilitate comparisons between widely disparate energy technologies, Smil states power density using common units: watts per square meter.

Wonkometer-225

Smil makes clear his belief that it’s important that citizens be numerate as well as literate, and Power Density is heavily salted with numbers. But what is being counted?

 

Perhaps the greatest advantage of power density is its universal applicability: the rate can be used to evaluate and compare all energy fluxes in nature and in any society. – Vaclav Smil, Power Density, pg 21

A major theme in Smil’s writing is that current renewable energy resources and technologies cannot quickly replace the energy systems that fuel industrial society. He presents convincing evidence that for current world energy demand to be supplied by renewable energies alone, the land area of the energy system would need to increase drastically.

Study of Smil’s figures will be time well spent for students of many energy sources. Whether it’s concentrated solar reflectors, cellulosic ethanol, wood-fueled generators, fracked light oil, natural gas or wind farms, Smil takes a careful look at power densities, and then estimates how much land would be taken up if each of these respective energy sources were to supply a significant fraction of current energy demand.

This consideration of land use goes some way to addressing a vacuum in mainstream contemporary economics. In the opening pages of Power Density, Smil notes that economists used to talk about land, labour and capital as three key factors in production, but in the last century, land dropped out of the theory.

The measurement of power per unit of land is one way to account for use of land in an economic system. As we will discuss later, those units of land may prove difficult to adequately quantify. But first we’ll look at another simple but troublesome issue.

Does the clock tick in seconds or in centuries?

It may not be immediately obvious to English majors or philosophers (I plead guilty), but Smil’s statement of power density – watts per square meter – includes a unit of time. That’s because a watt is itself a rate, defined as a joule per second. So power density equals joules per second per square meter.

There’s nothing sacrosanct about the second as the unit of choice. Power densities could also be calculated if power were stated in joules per millisecond or per megasecond, and with only slightly more difficult mathematical gymnastics, per century or per millenium. That is of course stretching a point, but Smil’s discussion of power density would take on a different flavor if we thought in longer time frames.

Consider the example with which Smil opens the book. In the early stages of the industrial age, English iron smelting was accomplished with the heat from charcoal, which in turn was made from coppiced beech and oak trees. As pig iron production grew, large areas of land were required solely for charcoal production. This changed in the blink of an eye, in historical terms, with the development of coal mining and the process of coking, which converted coal to nearly 100% pure carbon with energy equivalent to good charcoal.

As a result, the charcoal from thousands of hectares of hardwood forest could be replaced by coal from a mine site of only a few hectares. Or in Smil’s favored terms,

The overall power density of mid-eighteenth-century English coke production was thus roughly 500 W/m2, approximately 7,000 times higher than the power density of charcoal production. (Power Density, pg 4)

Smil notes rightly that this shift had enormous consequences for the English countryside, English economy and English society. Yet my immediate reaction to this passage was to cry foul – there is a sleight of hand going on.

While the charcoal production figures are based on the amount of wood that a hectare might produce on average each year, in perpetuity, the coal from the mine will dwindle and then run out in a century or two. If we averaged the power densities of the woodlot and mine over several centuries or millennia, the comparison look much different.

And that’s a problem throughout Power Density. Smil often grapples with the best way to average power densities over time, but never establishes a rule that works well for all energy sources.

Generating station near Niagara Falls

The Toronto Power Generating Station was built in 1906, just upstream from Horseshoe Falls in Niagara Falls, Ontario. It was mothballed in 1974. Photographed in February, 2014.

In discussing photovoltaic generation, he notes that solar radiation varies greatly by hour and month. It would make no sense to calculate the power output of a solar panel solely by the results at noon in mid-summer, just as it would make no sense to run the calculation solely at twilight in mid-winter. It is reasonable to average the power density over a whole year’s time, and that’s what Smil does.

When considering the power density of ethanol from sugar cane, it would be crazy to run the calculation based solely on the month of harvest, so again, the figures Smil uses are annual average outputs. Likewise, wood grown for biomass fuel can be harvested approximately every 20 years, so Smil divides the energy output during a harvest year by 20 to arrive at the power density of this energy source.

Using the year as the averaging unit makes obvious sense for many renewable energy sources, but this method breaks down just as obviously when considering non-renewable sources.

How do you calculate the average annual power density for a coal mine which produces high amounts of power for a hundred years or so, and then produces no power for the rest of time? Or the power density of a fracked gas well whose output will continue only a few decades at most?

The obvious rejoinder to this line of questioning is that when the energy output of a coal mine, for example, ceases, the land use also ceases, and at that point the power density of the coal mine is neither high nor low nor zero; it simply cannot be part of a calculation. As we’ll discuss later in this series, however, there are many cases where reclamations are far from certain, and so a “claim” on the land goes on.

Smil is aware of the transitory nature of fossil fuel sources, of course, and he cites helpful and eye-opening figures for the declining power densities of major oil fields, gas fields and coal mines over the past century. Yet in Power Density, most of the figures presented for non-renewable energy facilities apply for that (relatively brief) period when these facilities are in full production, but they are routinely compared with power densities of renewable energy facilities which could continue indefinitely.

So is it really true that power density is a measure “which can be used to evaluate and compare all energy fluxes in nature and in any society”? Only with some critical qualifications.

In summary, we return to Smil’s oft-emphasized theme, that current renewable resource technologies are no match for the energy demands of our present civilization. He argues convincingly that the power density of consumption on a busy expressway will not be matched to the power density of production of ethanol from corn: it would take a ridiculous and unsustainable area of corn fields to fuel all that high-energy transport. Widening the discussion, he establishes no less convincingly, to my mind, that solar power, wind power, and biofuels are not going to fuel our current high-energy way of life.

Yet if we extend our averaging units to just a century or two, we could calculate just as convincingly that the power densities of non-renewable fuel sources will also fail to support our high-energy society. And since we’re already a century into this game, we might be running out of time.

Top photo: insulators on high-voltage transmission line near Darlington Nuclear Generating Station, Bowmanville, Ontario.