Category — Energy Density/Power Density

“Power density (W/m²) is perhaps the most revealing variable in energetics…”[1]- Vaclav Smil

It may be a bit of an exaggeration to say that understanding power density may be all the average person requires to put our energy sources and needs into perspective, but there is some merit in this argument. Unfortunately, this view of energy matters remains little discussed, probably because it appears rather academic.

This post attempts to overcome this by further illustrating the concepts. It will also demonstrate how industrial-scale wind and solar PV electricity generation plants fail to meet this important, high-level standard of performance for electricity sources required by mankind, particularly in developed societies, but increasingly in developing and even undeveloped societies.

This is even without taking into account:

(1) The persistent erratic (short term – minutes) and unreliable (medium to long term – hours to days) nature of electricity production that wind and solar PV provide; (2) their high costs; and (3) many other considerations described here.

This is not to diminish the importance of these other matters, but the contemplation of them all together is fairly elaborate and perspective is easily lost.

In summary, power density is the “gold standard” as a high-level pass/fail measure of an energy source’s value to humanity. [Read more →]

It is the second most famous term in the history of economics after Adam Smith’s metaphor invisible hand. It describes the competitive market process in the real world. It was coined in 1942 by the famous, iconoclastic Austrian-American economist Joseph Schumpeter, who would reminisce:

I set out to become the greatest lover in Vienna, the greatest horseman in Austria, and the greatest economist in the world. Alas, for the illusions of youth…. As a horseman, I was never really first rate.

“Creative Destruction” …

The best businesses rise to the top in consumer-driven markets. Less competitive firms contract and even disappear. Creative destruction is the process whereby the bad is eliminated, the better replaces the good, and past performance gives way to new strategies and victors. No firm is forever, and financial loss is a characteristic of capitalism, as is the more used term profit.

Protesting against the textbook “perfect competition” model, under which a multitude of price-taking firms were optimally efficient at equilibrium rest, Schumpeter focused on the real world of change. “[C]apitalist reality, he said, is “the new commodity, the new technology, the new source of supply, the new type of organization … which strikes not at the margins of the profits and the outputs of the existing firms but at their foundations and their very lives.”

He famously continued: [Read more →]

“While incremental improvements can be expected with biomass, wind and solar, what is needed for them to become viable is an order of magnitude increase in productivity…. As significant future energy sources these technologies are dead ends, which is why the government, and not the private sector, is funding them.”

When it comes to power, density is the key. Energy density. The reason that solar power, wind power, and ethanol are so expensive is that they are derived from very diffuse energy sources. It takes a lot of energy collectors such as solar cells, wind turbines, or corn stalks covering many square miles of land to produce the same amount of power that traditional coal, natural gas, or nuclear plants can on just a few acres.

Each of these alternative energy sources is based on mature technology. Agriculture and fermentation have their roots in prehistory, windmills date back at least to 65 B.C., the photovoltaic effect was discovered in 1839. Yet nowhere in the world are these technologies serving as primary energy sources without significant government subsidies.

Solar and Wind

While incremental improvements can be expected with biomass, wind and solar, what is needed for them to become viable is an order of magnitude increase in productivity. As old and as well-researched as solar power, wind power, and other renewable energies are, such improvements are possible but unlikely. As significant future energy sources these technologies are dead ends, which is why the government, and not the private sector, is funding them.

Industry is more than willing to risk research dollars on technologies that show real promise, but it is not willing to flush shareholder money down a rat hole. Politicians, however, operate from different incentives. When a crisis, real or imagined, makes headlines, they want voters to see them doing “something” about it, and they must move quickly because election cycles and constituent attention spans are short. [Read more →]

“The release of energy from splitting a uranium atom turns out to be 2 million times greater than breaking the carbon-hydrogen bond in coal, oil or wood. Compared to all the forms of energy ever employed by humanity, nuclear power is off the scale. Wind has less than 1/10th the energy density of wood, wood half the density of coal, and coal half the density of octane. Altogether they differ by a factor of about 50. Nuclear has 2 million times the energy density of gasoline. It is hard to fathom this in light of our previous experience. Yet our energy future largely depends on grasping the significance of this differential. “

- William Tucker, excerpted from his lecture, Understanding E=MC₂

William Tucker has powerfully explained how the future of technologically advanced civilizations depends upon a sophisticated ability to convert the highest energy densities into increasingly denser power performance, and in the process compacting the time and space necessary to do productive work.

In fact, Tucker wrote an excellent book about this, Terrestrial Energy: How Nuclear Energy Will Lead the Green Revolution and End America’s Energy Odyssey. In light of the excerpt from that book recently posted at Master Resource, I thought readers of this forum might find my review from two years ago (see below) of interest, particularly if they have not yet read Tucker’s book.

The Primacy of Energy Density

Rockefeller University’s Jesse Ausubel has demonstrated that the trend in energy usage continues along a decarbonizing trajectory. Improvements in technology combined with a communal desire to live longer and more healthfully have spurred this phenomenon. Given a choice, who wants to live in a town where thousands of chimneys cast off carbon by-products like sulfuric smoke and soot? Civilization will continue decarbonizing apace, whether this aligns with climate change alarmism, or not. [Read more →]

Editor note: Del Torkelson of The American Oil & Gas Reporter covered Robert Bryce’s address talk to the Permian Basin Petroleum Association at its annual meeting in Midland last October. Torkelson’s  summary is reprinted with permission.]

“One of the reasons I wrote Power Hungry: The Myths of “Green” Energy and the Real Fuels of the Future (Public Affairs: 2010) is that our discussions are fundamentally wrong-headed,” author and journalist Robert Bryce told the Permian Basin Petroleum Association.

“Politicians generally do not understand the issues of energy and power, and in particular, the issues of scale.”

Bryce expounded on a number of key themes, including density, the distinction between energy and power, and the future of natural gas and nuclear generation. He also pointed to signals that suggested ordinary citizens were losing patience with green energy sources.

Green Backlash

Bryce’s comments touched on topics covered in both Power Hungry and an earlier book, Gusher of Lies. The writer riffed on a number of subjects pertinent to oil and gas producers:

• On his insistence that the density of traditional fuels made them more environmentally friendly than so-called green energy sources, Bryce calculated, “A well producing 60 Mcf a day–by definition a stripper well–has a power density of about 28 watts a square meter, 23 times the power density of a wind turbine. If you start with a source that has low power density, you have to counteract the lower power density with other inputs such as steel, transmission lines, concrete, land and manpower.”
• Regarding the suggestion that natural gas is a bridge fuel, Bryce countered that it was more. “A bridge to what?” he asked. “It is clean, it is domestic, it is relatively cheap. This is the fuel we have been looking for.” [Read more →]

[Note: This article has been updated to Twenty Bad Things about Windpower — go here.]

Trying to pin down the arguments of wind promoters is a bit like trying to grab a greased balloon. Just when you think you’ve got a handle on it, it squirts away. Let’s take a quick highlight review of how things have evolved.

1 – Wind energy was abandoned well over a hundred years ago, as it was totally inconsistent with our burgeoning more modern needs of power, even in the late 1800s. When we throw the switch, we expect that the lights will go on — 100% of the time. It’s not possible for wind energy, by itself, to ever do this, which is one of the main reasons it was relegated to the dust bin of antiquated technologies (along with such other inadequate sources like horse power).

2 – Fast forward to several years ago. With politicians being convinced by lobbyists that Anthropological Global Warming (AGW) was an imminent threat, a campaign was begun to favor all things that would purportedly reduce CO₂. Wind energy was thus resurrected, as its marketers pushed the fact that wind turbines did not produce CO₂ in their generation of electricity.

3 – Of course, just that by itself is not significant, so the original wind development lobbyists then made the case for a quantum leap: that by adding wind turbines to the grid we could significantly reduce CO₂ from fossil fuel electrical sources (especially coal). This argument became the basis for many states’ implementing a Renewable Energy Standard (RES) — which mandated that their utilities use an increased amount of wind energy.

4 – Why was a mandate necessary? Simply because the real world reality of integrating wind energy made it a very expensive option. As such, no utility company would likely do this on their own. They had to be forced to. [Read more →]

Editor’s note: This is the conclusion of the series that provides an essential basis for the understanding of energy transitions and use. The previous posts in this series can be seen at:

Part I – Definitions

Part II – Coal- and Wood-Fired Electricity Generation

Part III – Natural Gas-Fired Electricity Generation

Part IV – New Renewables Electricity Generation

America’s dominant mode of electricity generation is via combustion of bituminous and sub-bituminous coal in large thermal stations. All such plants have boilers and steam turbogenerators and electrostatic precipitators to capture fly ash, but they burn different qualities of coal that may come from surface as well as underground mines, have different arrangements for cooling (once-through using river water or various cooling towers) and many have flue gas desulfurization to reduce SO₂ emissions. Consequently, these conversions of chemical energy in coal to electricity feature widely differing power densities: for the power plants alone they are commonly in excess of 2 kW/m² and can be as high as 5 kW/m². When all other requirements (coal mining, storage, environmental controls, settling ponds) are included, the densities inevitably decline and range over an order of magnitude: from as low as 100 W/m² to as much as 1,000 W (1 kW)/m².

In contrast, compact gas turbines plants (the smallest ones on trailers and larger facilities that can be rapidly assembled from prefabricated units), which can be connected to existing gas supply, can generate electricity with power density as high as 15 kW/m². Larger stations (>100 MW) using the most efficient combined-cycle arrangements (with a gas turbine’s exhaust used to generate steam for an attached steam turbine) will operate with lower power densities, and if new natural gas extraction capacities have to be developed for their operation then the overall power density of gas and electricity production would decline to a range similar to that of coal-fired thermal generation or slightly higher, that is in most cases to a range of 200-2000 W/m². [Read more →]

Photovoltaic Electricity Generation

Satellite measurements put the solar constant – radiation that reaches area perpendicular to the incoming rays at the top of the atmosphere (and that is actually not constant but varies with season and has negligible daily fluctuations) – at 1,366 W/m². If there were no atmosphere and if the Earth absorbed all incoming radiation then the average flux at the planet’s surface would be 341.5 W/m² (a quarter of the solar constant’s value, a sphere having four times the area of a circle with the same radius: 4?r²/?r²). But the atmosphere absorbs about 20% of the incoming radiation and the Earth’s albedo (fraction of radiation reflected to space by clouds and surfaces) is 30% and hence only 50% of the total flux reaches the surface prorating to about 170 W/m² received at the Earth’s surface, and ranging from less than 100 W/m² in cloudy northern latitudes to more than 230 W/m² in sunny desert locations.

For an approximate calculation of electricity that could be generated on large scale by photovoltaic conversion it would suffice to multiply that rate by the average efficiency of modular cells. While the best research cells have efficiencies surpassing 30% (for multijunction concentrators) and about 15% for crystalline silicon and thin films, actual field efficiencies of PV cells that have been recently deployed in the largest commercial parks are around 10%, with the ranges of 6-7% for amorphous silicon and less than 4% for thin films. A realistic assumption of 10% efficiency yields 17 W/m² as the first estimate of average global PV generation power density, with densities reaching barely 10 W/m² in cloudy Atlantic Europe and 20-25 W/m² in subtropical deserts. [Read more →]

Editor’s note: This is Part III of a five part series that provides an essential basis for the understanding of energy transitions and use. The previous posts in this series can be seen at:

Part I – Definitions

Part II – Coal- and Wood-Fired Electricity Generation

Boilers of electricity-generating stations burning coal can be converted to burn liquid or gaseous hydrocarbons (fuel oil, even crude oil, and natural gas) and such conversions were fairly common during the 1960s and the early 1970s. Burning natural gas rather than coal has clear environmental advantages (it generates less, or no, sulfur dioxide and no fly ash) but the overall conversion efficiency of the boiler-steam turbogenerator unit changes little. In contrast, gas turbines, particularly when coupled with steam turbines, offer the most efficient way of electricity generation. This results in much higher power densities than is the case with coal-fired plants. Overall densities of the fuel extraction and electricity generation process are also kept high because of the relatively high power densities of natural gas production (depending on the field they vary by more than an order of magnitude, with minima around 50 W/m², maxima well over1 kW/m²) and even more by the fact that new gas-powered generation often does not need any major new infrastructure as it can tap the supply from existing fields and pipelines.

Gas turbines were first commercialized for electricity generation by Brown Boveri in Switzerland during the late 1930s but in the US their installations became common only during the late 1960s, spurred by the November 1965 US Northeast blackout that left 30 million people without electricity for up to13 hours. Nationwide capacity of gas turbines rose from just 240 MW in 1960 to nearly 45 GW by 1975, a nearly 200-fold rise in 15 years. This ascent was interrupted by high hydrocarbon prices (as well as by stagnating electricity demand) but it resumed during the late 1980s. By 1990 nearly half of the 15 GW of all new capacity ordered by the US utilities was in gas turbines and by 2008 almost exactly 40% of the US summer generating capacity (397.4 GW) was installed in gas-fired units, either single- or combined-cycle gas turbines (CCGT). Unlike a single gas turbine that discharges its hot gas, CCGT uses the turbine’s hot exhaust gases to generate steam for a steam turbine, boosting overall efficiency. While the best single gas turbines can convert about 42% of their fuel to electricity, CCGT convert as much as 60% and are now the most efficient electricity generators. [Read more →]

Editor’s note: This is Part II of a five part series that provides an essential basis for the understanding of energy transitions and use. The opening post on definitions was yesterday.

Baseline calculations for modern electricity generation reflect the most important mode of the U.S. electricity generation, coal combustion in modern large coal-fired stations, which produced nearly 45% of the total in 2009. As there is no such thing as a standard coal-fired station I will calculate two very realistic but substantially different densities resulting from disparities in coal quality, fuel delivery and power plant operation. The highest power density would be associated with a large (in this example I will assume installed generating capacity of 1 GW_e) mine-mouth power plant (supplied by high-capacity conveyors or short-haul trucking directly from the mine and not requiring any coal-storage yard), burning sub-bituminous coal (energy density of 20 GJ/t, ash content less than 5%, sulfur content below 0.5%), sited in a proximity of a major river (able to use once-through cooling and hence without any large cooling towers) that would operate with a high capacity factor (80%) and with a high conversion efficiency (38%).

This station would generate annually about 7 TWh (or about 25 PJ) of electricity. With 38% conversion efficiency this generation will require about 66 PJ of coal.

Assuming that the plant’s sub-bituminous coal (energy density of 20 GJ/t, specific density of 1.4 t /m³) is produced by a large surface mine from a seam whose average thickness is 15 m and whose recovery rate is 95%, then under every square meter of the mine’s surface there are 20 t of recoverable coal containing 400 GJ of energy. In order to supply all the energy needed by a plant with 1 GW_e of installed capacity, annual coal extraction would have to remove the fuel from an area of just over 16.6 ha (166,165 m²), and this would mean that coal extraction required for the plant’s electricity generation proceeds with power density of about 4.8 kW/m²:

800 MW/766,000 m² = 1,044.4 W/m²

An even larger area would be needed by a plant located far away from a mine (supplied by a unit train or by barge), [Read more →]