Power Density

by Vaclav Smil

  I address these questions in the book's closing chapter, but anybody even slightly familiar with the advances in modern ferrous metallurgy and with the growth of global pig iron production can anticipate the answer. The combined effect of technical innovations has not brought an order of magnitude reduction in specific charcoal demand (a tonne of fuel needed to produce a tonne of hot metal), while the worldwide iron smelting industry grew by an order of magnitude during the twentieth century and has yet to reach its global peak. This means that the impact of today's charcoalbased iron smelting would be even greater than it would have been more than 100 years ago, when the extent of its practice forced the switch to coke-fueled blast furnaces. Obviously, power densities matter.

  In this chapter I extoll the explanatory utility of rates, sort out the various meanings of power densities used by scientists and engineers, provide a clear definition of the key measure used in this book, offer its brief typology, and explain some of its inherent complications and uncertainties.

  By 2014, energy-its resources, consumption, and future supplies, its economic importance and trade and strategic implications, and the environmental impacts of its use-had been a matter of intense public interest, policy-making attention, and expanded scientific inquiries for two generations. The proximate causes of the sudden elevation of energy matters to worldwide prominence during the early 1970s were the quintupling of the price of crude oil sold by the member states of the Organization of the Petroleum Exporting Countries (OPEC) and a temporary embargo of all oil shipments to the United States and the Netherlands (Smil 1987).

  As these events were taking place, most people, even in affluent countries, were largely ignorant of basic energy matters. Few could explain the background and the importance of the unfolding changes, and supplying the essential framework would have required assessing realistic options by referring to numbers other than the constantly repeated new record levels of crude oil prices. By 1978 those prices had steadied, but soon they doubled as the Iranian monarchy fell and the ayatollahs took over Iran, at that time the world's fifth largest oil producer. But that price spike was also relatively short-lived, and by 1985 OPEC's oil price had fallen by two-thirds from its 1981 peak. Saddam Hussain's invasion of Kuwait in August 1990 resulted in only a brief price rise, followed by a decade of stable and low oil prices: during the closing years of the twentieth century they were (in constant monies) almost as low as in 1975 (BP 2014).

  As concern over high oil prices and the security of energy supply receded, a new concern became prominent with the growing realization of the role played by CO2 emissions from the combustion of fossil fuels in the process of anthropogenic global warming (IPCC 1995). Understanding planetary energy balance, the physics of greenhouse gases, and the complex atmosphere-hydrosphere-biosphere interactions governing the global biogeochemical carbon cycle is a challenge far more difficult than appreciating the intricacies of global energy supply and use. During the first decade of the twenty-first century-with higher oil prices, fears of resource shortages, and concerns about global warming-anxieties about energy futures were on the rise again, but the quality of the discourse did not improve. People paying attention to post-2000 news heard claims of an imminent peak in global oil production but had no knowledge of crude oil's energy density or of the actual dynamics of the global hydrocarbon reserves.

  Similarly, most people who heard that the unfolding global warming would be unprecedented in its rapidity knew nothing about actual CO2 emission factors or about the relative decarbonization of the global energy supply. Understanding complex energy matters, formulating informed arguments, and making sensible choices can be done only on the basis of a quantitative understanding that must be both relatively broad and sufficiently deep. There is a natural progression in this understanding, from simple quantities to rates that relate those variables to basic physical attributes, to time and space.

  Power of Rates

  Most phenomena are best understood when expressed as rates, specific ratios relating two variables. In the scientific sense, all rates are derived quantities. They are defined in terms of the seven base units of the Systeme international d'unites (SI): length (the SI base unit is a meter, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), temperature (kelvin, K), amount of substance (mole, mol), and luminous intensity (candela, cd). Speed (velocity, m/s) is perhaps the most commonly used rate in everyday affairs, while the rates frequently encountered in scientific and technical inquiries include mass density (kg/m3), amount of substance (mol/m3), and luminance (cd/m2)-as well as energy and power.

  Those energy-related derivations start with force (newton, N, is m x kg/s2). The energy unit, joule (J); is a newton-meter (m2 x kg/s2), and the unit of power (watt, W) is simply the rate of energy flow Q/s or m2 x kg/s3). In turn, these units can be used in specific rates as they are related to the base variables of length, mass, time, substance, and current, or to individuals or groups of people, to give fundamental insight into the nature and dynamics of energy systems: only when the absolute values are seen in relative terms can we truly appreciate their import and make revealing historical and international comparisons. Tables in the appendix list all principal units and their multiples and submultiples.

  Certainly the most common class of these higher-order derivatives comprises quantities prorated for an individual in a given data set, and average national per capita rates are perhaps the most frequent use of this measure. When they are used to quantify natural endowment (water resources, cropland, standing forest phytomass, fossil fuel reserves) they refer to a particular year, but when they are used to express average supply or consumption they become double rates, prorated not only per capita but also over a specific time period. In the case of food supply (measured in kcal/capita or in MJ/capita) the rate is per day, and-as illustrated by contrasting the United States with Japan-those rates alone tell us a great deal about a nation's food supply, dietary habits, overeating, and excessive food waste.

  US food per capita availability (the total at the retail level) now averages about 3,700 kcal/capita/day, and as that mean places babies and octogenarians in equivalency with adults (whereas the normal daily food intake of babies and octogenarians should be either below or barely above 1,100 kcal), it implies a supply of more than 4,000 kcal/day for adults (FAO 2014; USDA 2013b). Obviously, if that were an actual average consumption, the American population would be even more obese than it already is. US food consumption surveys show an actual daily intake averaging only about 2,000 kcal/capita. These surveys are based on individuals' recall of food intake in a day and hence are not highly accurate, but even after adding 10% to their mean there is still a gap of 1,500 kcal/day, which means that the United States wastes 40% of its food supply.

  An excellent confirmation of this loss comes from the modeling of metabolic and activity requirements of the US population by Hall and co-workers (2009). They found that between 1974 and 2003, that rate was between 2,100 and 2,300 kcal/day, while the average food supply rose from about 3,000 to 3,700 kcal/day, resulting in food waste rising from 28% of the retail supply in 1974 to about 40% by 2004. In contrast, no other affluent economy has been wasting so little food as Japan: the country's recent average per capita food supply has been only between 2,500 and 2,600 kcal/day, while annual studies of dietary intake show consumption of just over 1,800 kcal/capita, resulting in food waste of less than 30% (Smil and Kobayashi 2012).

  In the case of raw materials and finished products, and for such key financial indicators as GDP or disposable income, per capita rates are usually given for a calendar year, while the availability of such essential quality-of-life indicators as number of doctors or hospital beds is expressed, obviously, per 1,000 people rather than per capita. But all of these indicators also illustrate a common problem with average per capita rates: their simplistic international comparisons-ignoring differences in the quality of statistics and, even more important, in the qualitative differences and the w
ider socioeconomic setting of specific variables-may mislead and confuse rather than reveal and explain. Similar caveats apply, to a greater or lesser extent, even to seemingly straightforward energy-related variables.

  Population Density

  There are three kinds of densities in common use. The first and the most commonly used rate relates the number of individual items (be they organisms, people, or artifacts) to a specific area. This spatial density is not among the SI derived units, but the measure is common in ecological and population studies. In the first case, the densities of small organisms (plants, insects, invertebrates, small mammals) are measured as the number of individuals or their collective mass per square meter (m). A more common rate for larger animals is individuals or total mass per hectare (ha) or square kilometer (km2), a rate that is also used for numbers and mass of trees, and for other phytomass (woodlands, grasslands, wetlands).

  When population densities are expressed in relation to agricultural land, the rate is almost always given as an inverted value, ha/person, ranging from about 1.25 ha/capita in Canada and 0.5 ha/capita in the United States to less than 0.1 ha/capita in China and Bangladesh and to negligible areas (even to nothing) in many small island and desert nations (FAO 2014). In agronomic studies the density of planting or transplanting is also expressed per hectare. For example, corn densities in Iowa are now as high as 100,000 plants/ha, but while yields initially increase with higher densities, they level off, and optimum yields with no soil quality constraints range between 70,000 and 80,000 plants/ha (Farnham 2001). For comparison, the highestyielding hybrid rice varieties are grown with up to 200,000 plants/ha (Lin et al. 2009).

  Regional and national population densities are measured in individuals/ km2. This measure is particularly misleading as it prorates populations over entire national territories regardless the land's habitability: even in countries with a relatively homogeneous population density it will hide large regional differences. For example, even in the generally densely populated Netherlands it subsumes differences ranging over two orders of magnitude, from cities with more than 5,000 people/km2 to rural regions with fewer than 50 people/km2. Much larger differences in intranational population densities are common in all countries with very large territories, as well as in nations located in and and semiarid climates, particularly in North Africa. Canada is an excellent example of these huge disparities among affluent countries; Egypt, with less than 4% of its territory under annual and permanent crops, offers the extreme example in the and world. Moreover, continuing urbanization means that nationwide population densities are becoming universally less representative.

  The density of human populations can be also expressed in mass terms, and in this case care must be taken to specify the mass: either as live weight or in absolutely dry terms. The most densely populated parts of Asia's still expanding megacities have residential densities on the order of 50,000 people/km2, which (using a conservative age - and sex-weighted mean of 45 kg/capita) translates to a live weight anthropomass of more than 2 kg/m2, a rate unmatched by any other mammal and three orders of magnitude higher than the peak seasonal zoomass of large herbivorous ungulates grazing on Africa's richest grasslands (Smil 2013a).

  The average densities of services (be they health, commercial, or recreational: doctors' offices, hospitals, food stores, children's playgrounds, sports playing fields) offer simple but revealing ways to focus on spatial inequities and their consequences. For example, a study by Bonanno and Goetz (2012) revealed that even after controlling for missing variables, biases, and lags, the density of stores selling fruits and vegetables (as opposed to many small establishments where only packaged and fast foods are available) was associated with higher shares of adults who consumed fruits and vegetables regularly and had lower obesity rates.

  Mass and Energy Density

  The second density category includes those derived SI units that relate variables to volume: mass density and energy density. SI mass density is measured in kg/m3, but in practice it is often expressed also in g/cm3, kg/dm3, or t/m3 (the number will be identical for these three rates). The densities of common materials (all expressed in g/cm3, with water as the yardstick at 1) range from 0.65 to 0.75 for most wood species to just short of 1 for plastics (polyethylene goes from 0.915 to 0.970 for its low - and high-density varieties). Concrete has densities between 2.2 and 2.4, aluminum and its alloys are just above that, at 2.6-2.7, and steel alloys cluster mostly between 7.7 and 7.8 (Smil 2013b).

  In SI terms, energy density is a derived unit measured in J/m3, but in energy publications this density is often expressed (with the exception of gases) in mass terms as MJ/kg or GJ/t. This may be a cause for confusion because in SI nomenclature, J/kg is a derived unit called specific energy. In SI units this specific energy is also often measured in J/g, MJ/kg, or GJ/t. Accurate conversions between these two rates (from volume to mass or, in SI terms, from energy density to specific energy) require analyses of individual fuels. Energy density is one of the key determinants of the structure and dynamics of an energy system: there are many reasons to prefer sources of high energy density, particularly in modern societies demanding large and incessant flows of fuels and electricity.

  Obviously, the higher the density of an energy resource, the lower are its transportation (as well as storage) costs, and this means that its production can take place farther away from the centers of demand. Crude oil has, at ambient pressure and temperature, the highest energy density of all fossil fuels (42 GJ/t), and hence it is a truly global resource, with production ranging from the Arctic coasts to equatorial forests and hot deserts, and with enormous investment in an unmatched worldwide shipping infrastructure (long-distance pipelines, oil loading and offloading terminals, giant tankers) and high-throughput processing in large refineries.

  In contrast, wood and crop residues (mostly cereal straws), the two most common traditional phytomass fuels, have low energy densities, with crop residues at just 14-15 MJ/kg, while wood (depending on the species and the degree of dryness) ranges from less than 15 MJ/kg for fresh-cut branches to about 17 MJ/kg for air-dried wood and to almost 20 MJ/kg for absolutely dry woody matter. Charcoal is the great exception as the pyrolysis of wood produces nearly pure carbon with a specific energy of nearly 30 MJ/kg. This means that twice as much straw or air-dried fuelwood has to be burned to yield the same amount of energy, and charcoal's smokeless combustion-as opposed to the often very smoky burning of wood in open fires or in poorly designed stoves, which causes millions of premature deaths every year (Subramanian 2014)-is another welcome advantage of charcoal for indoor use. Traditional societies paid a high energy and environmental price for these advantages because making a unit of charcoal in simple clay kilns required up to 10 units of wood.

  Some coal varieties are as energy dense as charcoal: early coal extraction often produced the highest-quality anthracites (much like charcoal, they are nearly pure carbon, with a specific energy of up to 30 MJ/kg) and excellent bituminous coal (25-27 MJ/kg). As coal mining progressed, the average energy content of the product declined, particularly with the shift to the less expensive and much safer surface extraction methods. The specific energies of most steam coals are now 22-26 MJ/kg, but those of the poorest lignites are less than 10 MJ/kg. The transition to liquid hydrocarbon introduced fuels of unrivaled energy density: crude oils range from gasoline-like light liquids to heavy varieties that might need heating for transportation, but their specific energies span a narrow range around 42 MJ/kg; with densities ranging between 0.75 and 0.85 kg/m3, this translates to 32-39 MJ/m3. Because of these high densities, refined liquid fuels dominate all transportation (and other portable) uses.

  Natural gas (mostly methane, CH4 with small shares of higher alkanes, collectively known as natural gas liquids) has a higher hydrogen share (75%) than liquid hydrocarbons and hence it contains 53.6 MJ/kg-but its liquefaction requires considerable energy input for refrigeration, and it is used only for (still expensive) intercontinental shipments of l
iquefied natural gas (LNG). In its gaseous form methane's energy density is 35 MJ/m3, amounting to less than 1/1,000 the energy density of gasoline. A higher hydrogen content explains this progression of higher energy density. The very low energy density of natural gas is no problem when the fuel is delivered by pipelines for stationary combustion in electricity-generating gas turbines or in industrial, commercial, and household furnaces.

  Finally, in the third category of density are those derived SI rates that relate a basic quantity (current, luminous intensity) or a derived unit to space: they include current density (A/m2), luminance density (cd/m2), illuminance density (lm/m2), electric flux density (C/m2), and magnetic flux density (Wb/m2). Power density is not an official name given to any derived quantity on the list of SI units. The rate, measured in W/m2, is listed among the derived quantities but is given a rather restricted scope: it is called heat flux density or irradiance (flux of solar or other radiation per unit area). In this book, power density always refers to the quotient of power and land area, and I demonstrate that this rate is a key variable in energy analysis because it can be used to assess the suitability and potential of specific energy resources, the performance and operating modes of energy converters, and the requirements and structures of complex energy systems.

  In all of these respects, energy density is an insufficiently revealing measure. For example, crude oils, regardless of their appearance and physical differences, have a uniformly high energy density, but if they were present in minuscule reservoirs strewn over a large area, the power density of their extraction would be too low to warrant their commercial exploitation; in contrast, the Middle Eastern oil fields supply the whole world precisely because they produce high-energy-density fuel with unmatched power densities. Similarly, US bituminous coal, mined with high power densities, is shipped to Europe, where energy-dense hard coal deposits remain unexploited because their thin seams deep underground cannot be extracted at acceptable cost (or with power densities comparable to American mining).