More than one way to fall off a cliff

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Wonkometer Warning MH-225The “energy cliff” is a central concept in ecological economics, and it’s based on a very simple ratio. But for me this principle was a slippery thing to grasp, and I eventually realized some of the most common graphs used to illustrate the Energy Cliff were leaving me with a misleading mental image.

This column takes a closer look at Energy Return on Energy Invested (ERoEI, EROEI or simply EROI) and the Energy Cliff, concluding with the question of how and whether the Energy Cliff might be experienced as a historical phenomenon.

The Energy Cliff as a mathematical function

Below are two frequently used versions of the Energy Cliff graph, based on the pioneering work of Charles Hall. They illustrate the relationship between Energy Return on Energy Invested and the percentage of energy production that is “surplus”, i.e., not needed by the energy sector for its own work and therefore available for use by the rest of society.

Chart accessed via

Chart accessed via

Chart from Tim Morgan, Life After Growth, Kindle edition, locus 980

Chart from Tim Morgan, Life After Growth, Kindle edition, locus 980

In each case the EROEI is shown on the horizontal axis with lowest values at the right. The apparent suddenness of the drop-off in surplus energy depends on the relative scales of the axes and maximum value shown for EROEI, but in each case the drop-off becomes nearly perpendicular as EROEI falls below 10 – thus the name “Energy Cliff”.

Simple enough, eh? But after seeing this graph presented in several books and essays, I still found the concept hard to master. I kept asking myself, “How does that work again?” or “Why does energy supply drop off so suddenly?”

The problem, I realized, is that the impression these graphics leave in my mind is at odds with the intent. As these examples show, the “Energy for society” or “Profit energy” dominates the graphic visually, and the “Energy used to procure energy” or “Cost energy” seems like such a small sliver that it couldn’t possibly be that important. Mathematically naïve as that impression may have been, it nevertheless made it difficult for me to retain a clear understanding of the Energy Cliff.

The solution for me was to play with the graph until I felt I understood it clearly, using imagery that reinforced the understanding.

It was most helpful, I found, to present the graph not as an unbroken continuum between the two variables, but as a bar chart showing discrete values of Energy Return on Energy Invested: 1, 2, 3, 4, etc up to 50.

The Energy Cliff as a Bart Chart

Visualizing the numbers this way minimizes the tendency to see the surplus energy, or Net energy output, as one massive block. Just as importantly, it allowed me to easily focus on the relationship between specific values of Energy input and Net energy output.

For example, at the far right end of the graph is the ERoEI value 1. This corresponds to a bare break-even scenario. An oil well with this ERoEI would not be worth drilling: we would use up one barrel of oil to drill and operate the well, and it would spit out exactly one barrel in return, leaving us with no surplus energy for our efforts.

An ERoEI of 2 corresponds to a Net energy output of 50%. To return to our Proverbial Oil Corp., we burn one barrel of oil to drill and operate a well, and the well spits out two barrels, leaving us with a net gain of 1 barrel or 50% of the Total energy output.

Our oil wells with ERoEI of 3 give us 3 barrels total for every one we invest, for a net energy gain of 2 barrels or 66.6%, wells with ERoEI of 4 give us a net energy output equal to 75% of their total energy output, wells with ERoEI of 5 give us a net energy output equal to 80% of their total energy output, and so on.

We can also see clearly that the Energy input and Net energy output percentages change very slowly for ERoEI values above 20 – at which point Energy input is 5% and Net energy output is 95% of Total energy output).

There is another simple tweak to this chart that can vividly illustrate the sudden drop-off: animation. (And since most of us use supercomputers capable of guiding a moon mission for our morning reading, why not throw in some animation?)

The animated Energy Cliff – click chart to set in motion

The animated Energy Cliff – click chart to set in motion

By focusing attention on just a narrow range of ERoEI values at a time, this moving bar graph illustrates the fact that Net energy output changes slowly throughout most of the range, and then drops off suddenly and swiftly.

The animated graph relies on the element of time as a key facet of the presentation. That begs the question: can the Energy Cliff chart be read as a function of time?

The Energy Cliff as a historical phenomenon

It is easy to look at the Energy Cliff graphic as a chronological progression, given the convention of viewing timelines with past on the left and future on the right. That would be a mistake – there is no element of time in the chart – but it might be a useful mistake if made consciously.

It’s true that ERoEI rates have been declining slowly for the past 50 years, and many new energy technologies today have ERoEI rates of 10 or lower. And in fact, the Energy Cliff chart is sometimes presented as evidence that an impending energy crisis is mathematically inevitable. While that would be an unwarranted extrapolation from a graph of a simple exponential curve, it isn’t hard to cherry-pick data that graphs to a shape similar to the Energy Cliff.

Consider the following table of ERoEI rates over time.

Selected ERoEI rates over time

This table starts with EROEI rates before the industrial age, and finishes with rates that could plausibly represent the collapse of industrial society. When graphed these numbers show a drop-off much like the Energy Cliff, with the addition of a steep slope going up at the outset of industrial civilization. The values are roughly scaled chronologically, to represent the length of time during which very high EROEI prevailed – basically, the 20th century.

Net Energy over time - chart 1 copy


The numbers cherry-picked for this chart include, crucially, an EROEI for photovoltaic panels in Spain as calculated by Charles Hall and Pedro Prieto, which was the subject of spirited discussion recently on Resilience. At 2.45, this EROEI is far below the level needed to support a highly complex economy. If this number is correct and turns out to be representative of photovoltaics more generally, then the scenario suggested in the above chart is plausible. As high EROEI petroleum sources are depleted, we turn to bottom-of-the-barrel resources like tar sands, and then to solar panels which are even less energy-efficient. Complex industrial society soon collapses, and the vast majority of us must return to the fields.

For a very different picture, we could use the EROEI for solar panel installations presented by Ugo Bardi in Resilience, from a study by Bhandari et al. In this view, photovoltaics in Spain have an EROEI of 11–12, safely out of the drop-off zone of the Energy Cliff. In this scenario we’d have no need for last-ditch fossil fuels from tar sands, solar panels would produce enough surplus energy to create more solar panels and keep industrial society rolling cleanly along, and the Energy Cliff would be a mathematical function but not a historical reality.

Net Energy over time - chart 1 copy


These two charts are equally over-simplified, ignoring other renewable resource energy technologies with widely varying EROEI rates such as hydro-electric generation. It’s unknown how long we might stretch out the dwindling supply of high-EROEI fossil fuels, or whether there will be a collective decision to clamp down on carbon emissions and leave fossil fuels in the ground. And I’m unqualified to make any judgment on whether the Hall/Prieto or the Bhandari assessment of photovoltaics is most realistic.

In presenting these two different charts I merely want to illustrate that while the Energy Cliff graph of a mathematical function is simple and direct, extrapolating from this simple function to forecast historical trends is fraught with uncertainty.

Top graphic: “The Fool” in the Rider-Waite Tarot deck dances gayly at the edge of a precipice.


Naomi Klein, photograph by Joe Mabel, distributed via Wikimedia Commons

A renewable energy economy will create more jobs. Is that a good thing?

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In a tidal wave of good news stories, infographics and Facebook memes about renewable energy job creation, the implicit, unquestioned assumption is that More Jobs = A Healthier Economy.

A popular Facebook meme, based on the Stanford University Solutions Project, celebrates the claim that in a renewable energy-powered Canada, 40% more people will work in the energy sector.

From the Environment Hamilton Facebook page.

From the Environment Hamilton Facebook page.


In elaborate info-graphics, the Solutions Project provides comparable claims for all 50 US states and countries around the world – although “assertion-graphic” might be a better term, since the graphics are presented with no footnotes and no clear links to any data that might allow a skeptical mind to evaluate the conclusions.

From The Solutions Project website.

From The Solutions Project website.

And Naomi Klein, author of This Changes Everything and one of the proponents of The Leap Manifesto, cites the Energy Transition in Germany and notes that 400,000 new jobs have already been created. In her hour-long talk on the CBC Radio Ideas program and podcast, Klein gets at some of the key issues that will determine whether More Energy Jobs = A Good Thing, and we’ll return to this podcast later.

To start, though, let’s look at the issue through the following proposition:

The 20th century fossil-fueled economic growth spurt happened not because the energy industry created many jobs, but because it created very few jobs.

For most of human history, providing energy in the form of food calories was the major human occupation. Even in societies that consumed relatively high amounts of energy via firewood, harvesting and transporting that wood kept a lot of people busy.

But during the 19th and 20th centuries, as the available per capita energy supply in industrialized countries exploded, the proportion of the population employed supplying that energy dropped dramatically.

The result: instead of farming to provide the carbohydrates that feed humans and oxen, or cutting firewood to heat buildings, nearly the whole population has been free to do other activities. Whether we have made good use of this opportunity is debatable, but we’ve had plenty of energy, and nearly our entire labour force, available to run an elaborate manufacturing, consumption and service economy.

Seen from this perspective, the claim that renewable energy will create more jobs might set off alarms.

What’s in a job?

Part of the difficulty is that when we speak of a job, we refer to two (or more) very different things.

A job might mean simply something that has to be done. In this sense of the word, we don’t usually celebrate jobs. If we need to carry all our water in buckets from a well five kilometers from home, there are a lot of jobs in water-carrying – but we would probably welcome having taps right in our kitchens instead. Agriculture employs a lot of people if the only tools are sticks, but with better tools the same amount of food can be raised with fewer people working the fields.

So when we think of a job as the need to do something, we typically think that the fewer jobs the better.

When we celebrate job-creation, on the other hand, we typically mean something quite different –  a “job” is an activity that is accompanied by a pay-cheque. Since in our society most of us need to get pay-cheques for most of our lives, job-creation strikes us as a good thing to the extant that pay-cheques are involved.

Here’s the wrinkle with renewable energy job creation: the renewable energy transition will likely create jobs in the sense of adding to the quantity of work that must be done (which we normally try to minimize) and jobs in the sense of providing pay-cheques (which we typically want to maximize). The two types of job-creation are at cross-purposes, and the outcome is uncertain.

Allocation of energy surplus

Widespread prosperity depends not only on what work is done and what surplus is produced, but on how that surplus is allocated and distributed.

In the middle of the 20th century in North America and Europe, only a few people worked in energy supply but they produced a huge surplus. At the same time, the products of surplus energy were distributed in relatively equal fashion, compared to the rising levels of inequality today. The mass consumption economy – a brief anomaly in human history which is ironically referred to as Business As Usual – depended on both conditions being met. There had to be a large surplus of energy produced (or, more accurately, extracted) by a few people, and this surplus energy had to be widely distributed so that most people could participate in a consumer economy.

Naomi Klein gives prominent emphasis to the second of these two conditions. In her CBC Radio Ideas talk, she says

There’s a group in the US called Movement Generation which has a slogan that I quote a lot, which is that “transition is invevitable, but justice is not.” You can respond to climate change in a way that people putting up solar panels are paid terrible wages. In the US prison inmates are making some of the solar panels that they’re putting up. … There has to be a road map for responding to climate change in an intersectional way, which solves multiple problems at once.”

She cites the German Energy Transition as an encouraging example:

There are 900 new energy co-operatives that have sprung up in Germany. Two hundred towns and cities in Germany have taken their energy grids back from the private companies that took them over in the 1990s, and they call it “energy democracy”. They’re taking back control over their energy, so that the resources stay in the communities and they can use the profits generated from renewable energy to pay for services. They’ve also created 400,000 jobs as part of this transition. So they’re showing how you solve multiple problems at once. Lower emissions create good unionized jobs and generate the revenue we need to fight the logic of austerity at the local level.”

In Klein’s formulation, democratic control of the energy economy is a key to prosperity. Because of this energy democracy, the new jobs are “good unionized jobs” which “fight the logic of austerity”. But is that sustainable in the long run?

As Klein says, in Germany’s “energy democracy” they use “the profits generated from renewable energy to pay for services”. But that presupposes that the renewable energy technologies being used do indeed generate “profits”.

It remains an open question how much profit – how much surplus energy – will be generated from renewable energy development. If renewable energy developments consume nearly as much energy as they produce, then in the long run the energy sector may produce many pay-cheques but they won’t be generous pay-cheques, however egalitarian society might be.

Book cover, Life After Growth by Tim MorganEnergy sprawl

Tim Morgan uses the apt phrase “energy sprawl” to describe what happens as we switch to energy technologies with a lower Energy Return on Energy Invested (EROEI).

‘energy sprawl’ … has both physical and economic meanings. In physical terms, the infrastructure required to access energy and deliver it to where it is needed is going to expand exponentially. At the same time, the proportion of GDP absorbed by the energy infrastructure is going to increase as well, which means that the rest of the economy will shrink.” (Life After Growth, Harriman House, 2013, locus 2224)

As Morgan makes clear, energy sprawl is not at all unique to renewable energy transition – it applies equally to non-conventional, bottom-of-the-barrel fossil fuels such as fracked oil and gas, and bitumen extracted from Alberta’s tar sands. There will indeed be more jobs in a renewable resource economy, compared to the glory days of the fossil fuel economy, but there will also be more energy jobs if we cling to fossil fuels.

As energy sprawl proceeds, more of us will work in energy production and distribution, and fewer of us will be free to work at other pursuits. As Klein and the other authors of the Leap Manifesto argue, the higher number of energy jobs might be a net plus for society, if we use energy more wisely AND we allocate surplus more equitably.

But unless our energy technologies provide a good Energy Return On Energy Invested, there will be little surplus to distribute. In other words, there will be lots of new jobs, but few good pay-cheques.

Top photo: Canadian author and activist Naomi Klein, photographed by Joe Mabel in October 2015, accessed via Wikimedia Commons

Oil well in southeast Saskatchewan, with flared gas.

Energy at any cost?

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If all else is uncertain, how can growing demand for energy be guaranteed? A review of Vaclav Smil’s Natural Gas.

Near the end of his 2015 book Natural Gas: Fuel for the 21st Century, Vaclav Smil makes two statements which are curious in juxtaposition.

On page 211, he writes:

I will adhere to my steadfast refusal to engage in any long-term forecasting, but I will restate some basic contours of coming development before I review a long array of uncertainties ….”

Link to Vaclav Smil series list.And in the next paragraph:

Given the scale of existing energy demand and the inevitability of its further growth, it is quite impossible that during the twenty-first century, natural gas could come to occupy such a dominant position in the global primary energy supply as wood did in the preindustrial era or as coal did until the middle of the twentieth century.”

If you think that second statement sounds like a long-term forecast, that makes two of us. But apparently to Smil it is not a forecast to say that the growth of energy demand is inevitable, and it’s not a forecast to state with certainty that natural gas cannot become the dominant energy source during the twenty-first century – these are simply “basic contours of coming development.” Let’s investigate.

An oddly indiscriminate name

Natural Gas is a general survey of the sources and uses of what Smil calls the fuel with “an oddly indiscriminate name”. It begins much as it ends: with a strongly-stated forecast (or “basic contour”, if you prefer) about the scale of natural gas and other fossil fuel usage relative to other energy sources.

why dwell on the resources of a fossil fuel and why extol its advantages at a time when renewable fuels and decentralized electricity generation converting solar radiation and wind are poised to take over the global energy supply. That may be a fashionable narrative – but it is wrong, and there will be no rapid takeover by the new renewables. We are a fossil-fueled civilization, and we will continue to be one for decades to come as the pace of grand energy transition to new forms of energy is inherently slow.” – Vaclav Smil, preface to Natural Gas

And in the next paragraph:

Share of new renewables in the global commercial primary energy supply will keep on increasing, but a more consequential energy transition of the coming decades will be from coal and crude oil to natural gas.”

In support of his view that a transition away from fossil fuel reliance will take at least several decades, Smil looks at major energy source transitions over the past two hundred years. These transitions have indeed been multi-decadal or multi-generational processes.

Obvious absence of any acceleration in successive transitions is significant: moving from coal to oil has been no faster than moving from traditional biofuels to coal – and substituting coal and oil by natural gas has been measurably slower than the two preceding shifts.” – Natural Gas, page 154

It would seem obvious that global trade and communications were far less developed 150 years ago, and that would be one major reason why the transition from traditional biofuels to coal proceeded slowly on a global scale. Smil cites another reason why successive transitions have been so slow:

Scale of the requisite transitions is the main reason why natural gas shares of the TPES [Total Primary Energy System] have been slower to rise: replicating a relative rise needs much more energy in a growing system. … going from 5 to 25% of natural gas required nearly eight times more energy than accomplishing the identical coal-to-oil shift.” – Natural Gas, page 155

Open-pit coal mine in south-east Saskatchewan.

Open-pit coal mine in south-east Saskatchewan. June 2014.

Today only – you’ll love our low, low prices!

There is another obvious reason why transitions from coal to oil, and from oil to natural gas, could have been expected to move slowly throughout the last 100 years: there have been abundant supplies of easily accessible, and therefore cheap, coal and oil. When a new energy source was brought online, the result was a further increase in total energy consumption, instead of any rapid shift in the relative share of different sources.

The role of price in influencing demand is easy to ignore when the price is low. But that’s not a condition we can count on for the coming decades.

Returning to Smil’s “basic contour” that total energy demand will inevitably rise, that would imply that energy prices will inevitably remain relatively low – because there is effective demand for a product only to the extent that people can afford to buy it.

Remarkably, however, even as he states confidently that demand must grow, Smil notes the major uncertainty about the investment needed simply to maintain existing levels of supply:

if the first decade of the twenty-first century was a trendsetter, then all fossil energy sources will cost substantially more, both to develop new capacities and to maintain production of established projects at least at today’s levels. … The IEA estimates that between 2014 and 2035, the total investment in energy supply will have to reach just over $40 trillion if the world is to meet the expected demand, with some 60% destined to maintain existing output and 40% to supply the rising requirements. The likelihood of meeting this need will be determined by many other interrelated factors.” – Natural Gas, page 212

What is happening here? Both Smil and the IEA are cognizant of the uncertain effects of rising prices on supply, while graphing demand steadily upward as if price has no effect. This is not how economies function in the real world, of course.

Likewise, we cannot assume that because total energy demand kept rising throughout the twentieth century, it must continue to rise through the twenty-first century. On the contrary, if energy supplies are difficult to access and therefore much more costly, then we should also expect demand to grow much more slowly, to stop growing, or to fall.

Falling demand, in turn, would have a major impact on the possibility of a rapid change in the relative share of demand met by different sources. In very simple terms, if we increased total supply of renewable energy rapidly (as we are doing now), but the total energy demand were dropping rapidly, then the relative share of renewables in the energy market could increase even more rapidly.

Smil’s failure to consider such a scenario (indeed, his peremptory dismissal of the possibility of such a scenario) is one of the major weaknesses of his approach. Acceptance of business-as-usual as a reliable baseline may strike some people as conservative. But there is nothing cautious about ignoring one of the fundamental factors of economics, and nothing safe in assuming that the historically rare condition of abundant cheap energy must somehow continue indefinitely.

In closing, just a few words about the implications of Smil’s work as it relates to the threat of climate change. In Natural Gas, he provides much valuable background on the relative amounts of carbon emissions produced by all of our major energy sources. He explains why natural gas is the best of the fossil fuels in terms of energy output relative to carbon emissions (while noting that leaks of natural gas – methane – could in fact outweigh the savings in carbon emissions). He explains that the carbon intensity of our economies has dropped as we have gradually moved from coal to oil to natural gas.

But he also makes it clear that this relative decarbonisation has been far too slow to stave off the threat of climate change.

If he turns out to be right that total energy demand will keep rising, that there will only be a slow transition from other fossil fuels to natural gas, and that the transition away from all fossil fuels will be slower still, then the chances of avoiding catastrophic climate change will be slim indeed.

Top photo: Oil well in southeast Saskatchewan, with flared gas. June 2014.

Wind turbine on site of Pickering Nuclear Generating Station.

How big is that hectare? It depends.

Also published at

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

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.