Wind turbine on site of Pickering Nuclear Generating Station.

How big is that hectare? It depends.

Also published at Resilience.org.

link to Accounting For Energy seriesThe Pickering Nuclear Generating Station, on the east edge of Canada’s largest city, Toronto, is a good take-off point for a discussion of the strengths and limitations of Vaclav Smil’s power density framework.

The Pickering complex is one of the older nuclear power plants operating in North America. Brought on line in 1971, the plant includes eight CANDU reactors (two of which are now permanently shut down). The complex also includes a single wind turbine, brought online in 2001.

Wonkometer-225The CANDU reactors are rated, at full power, at about 3100 Megawatts (MW). The wind turbine, which at 117 meters high was one of North America’s largest when it was installed, is rated at 1.8 MW at full power. (Because the nuclear reactor runs at full power for many more hours in a year, the disparity in actual output is even greater than the above figures suggest.)

How do these figures translate to power density, or power per unit of land?

The Pickering nuclear station stands cheek-by-jowl with other industrial sites and with well-used Lake Ontario waterfront parks. With a small land footprint, its power density is likely towards the high end – 7,600 W/m2 – of the range of nuclear generating stations Smil considers in Power Density. Had it been built with a substantial buffer zone, as is the case with many newer nuclear power plants, the power density might only be half as high.

A nuclear power plant, of course, requires a complex fuel supply chain that starts at a uranium mine. To arrive at more realistic power density estimates, Smil considers a range of mining and processing scenarios. When a nuclear station’s output is prorated over all the land used – land for the plant site itself, plus land for mining, processing and spent fuel storage – Smil estimates a power density of about 500 W/m2 in what he considers the most representative, mid-range of several examples.

Cameco uranium processing plant in Port Hope, Ontario

The Cameco facility in Port Hope, Ontario processes uranium for nuclear reactors. With no significant buffer around the plant, its land area is small and its power density high. Smil calculates its conversion power density at approximately 100,000 W / square meter, with the plant running at 50% capacity.

And wind turbines? Smil looks at average outputs from a variety of wind farm sites, and arrives at an estimated power density of about 1 W/m2.

So nuclear power has about 500 times the power density of wind turbines? If only it were that simple.

Inside and outside the boundary

In Power Density, Smil takes care to explain the “boundary problem”: defining what is being included or excluded in an analysis. With wind farms, for example, which land area is used in the calculation? Is it just the area of the turbine’s concrete base, or should it be all the land around and between turbines (in the common scenario of a large cluster of turbines spaced throughout a wind farm)?  There is no obviously correct answer to this question.

On the one hand, land between turbines can be and often is used as pasture or as crop land. On the other hand, access roads may break up the landscape and make some human uses impractical, as well as reducing the viability of the land for species that require larger uninterrupted spaces. Finally, there is considerable controversy about how close to wind turbines people can safely live, leading to buffer zones of varying sizes around turbine sites. Thus in this case the power output side of the quotient is relatively easy to determine, but the land area is not.

Wind turbines in southwestern Minnesota

Wind turbines line the horizon in Murray County, Minnesota, 2012.

Smil emphasizes the importance of clearly stating the boundary assumptions used in a particular analysis. For the average wind turbine power density of 1 W/m2, he is including the whole land area of a wind farm.

That approach is useful in giving us a sense of how much area would need to be occupied by wind farms to produce the equivalent power of a single nuclear power plant. The mid-range power station cited above (with overall power density of 500 W/m2) takes up about 1360 hectares in the uranium mining-processing-generating station chain. A wind farm of equivalent total power output would sprawl across 680,000 hectares of land, or 6,800 square kilometers, or a square with 82 km per side.

A wind power evangelist, on the other hand, could argue that the wind farms remain mostly devoted to agriculture, and with the concrete bases of the towers only taking 1% of the wind farm area, the power density should be calculated at 100 instead of 1W/m2.

Similar questions apply in many power density calculations. A hydro transmission corridor takes a broad stripe of countryside, but the area fenced off for the pylons is small. Most land in the corridor may continue to be used for grazing, though many other land uses will be off-limits. So you could use the area of the whole corridor in calculating power density – plus, perhaps, another buffer on each side if you believe that electromagnetic fields near power lines make those areas unsafe for living creatures. Or you could use just the area fenced off directly around the pylons. The respective power densities will vary by orders of magnitude.

If the land area is not simple to quantify when things go right, it is even more difficult when things go wrong. A drilling pad for a fracked shale gas may only be a hectare or two, so during the brief decade or two of the well’s productive life, the power density is quite high. But if fracking water leaks into an aquifer, the gas well may have drastic impacts on a far greater area of land – and that impact may continue even when the fracking boom is history.

The boundary problem is most tangled when resource extraction and consumption effects have uncertain extents in both space and time. As mentioned in the previous installment in this series, sometimes non-renewable energy facilities can be reclaimed for a full range of other uses. But the best-case scenario doesn’t always apply.

In mountain-top removal coal mining, there is a wide area of ecological devastation during the mining. But once the energy extraction drops to 0 and the mining corporation files bankruptcy, how much time will pass before the flattened mountains and filled-in valleys become healthy ecosystems again?

Or take the Pickering Nuclear Generation Station. The plant is scheduled to shut down about 2020, but its operators, Ontario Power Generation, say they will need to allow the interior radioactivity to cool for 15 years before they can begin to dismantle the reactor. By their own estimates the power plant buildings won’t be available for other uses until around 2060. Those placing bets on whether this will all go according to schedule can check back in 45 years.

In the meantime the plant will occupy land but produce no power; should the years of non-production be included in calculating an average power density? If decommissioning fails to make the site safe for a century or more, the overall power density will be paltry indeed.

In summary, Smil’s power density framework helps explain why it has taken high-power-density technologies to fuel our high-energy-consumption society, even for a single century. It helps explain why low power density technologies, such as solar and wind power, will not replace our current energy infrastructure or current demand for decades, if ever.

But the boundary problem is a window on the inherent limitations of the approach. For the past century our energy has appeared cheap and power densities have appeared high. Perhaps the low cost and the high power density are both due, in significant part, to important externalities that were not included in calculations.

Top photo: Pickering Nuclear Generating Station site, including wind turbine, on the shoreline of Lake Ontario near Toronto.

Insulators on high-voltage electricity transmission line.

Timetables of power

Also published at Resilience.org.

accounting_for_energy_2For 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-225Smil 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.