Power density

Thermal electricity generation

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Thermal electricity generation Steam-driven generation of electricity remains the dominant way of producing the most flexible kind of energy. The two most important options to raise steam for large turbogenerators are either by burning pulverized coal in boilers or by fissioning uranium in nuclear reactors. Burning gas in boilers is much less common (because gas turbines are much more efficient) and using crude oil or refined liquid fuels for electricity generations is rare still (because liquids are too expensive). Gas turbines have made major inroads during the past two generations because they offer one of the best means to cover, almost instantly, peak electricity needs.

Core structures of thermal stations (boilers, reactors, turbogenerator halls) are quite compact and plant sites are mostly occupied by essential infrastructures (cooling ponds, lakes or towers, air pollution control equipment and disposal of captured waste, switchyards, fuel off-loading and storage). Many plants also claim additional land held in reserve for possible expansion or serving as a buffer zone, and nuclear plants require a safety belt that excludes permanent habitation. This means that some thermal electricity generation (particularly nuclear stations, and plants burning natural gas) can proceed with very high power densities –- while plants with large adjacent lakes used for cooling, plants with large areas reserved for on-site storages of captured fly ash and sulfates from flue-gas desulfurization, and plants with extensive (often forested) buffer zones will have much lower density ratings.

Thermal electricity generation is clearly in a high power density category but its surprisingly large range of values means that its outcomes can be orders of magnitude above any renewable alternatives (mine-mouth coal-fired station burning high-quality fuel, gas-fired plants burning LNG) –- or that it can have almost as low power density as the best instances of large-scale PV generation (coal-fired stations burning low-quality fuel from surface mines with high overburden:seam ratio). Here is the sequences of diminishing power densities for coal-fired electricity generation, from its burning core to complete plant-and-fuel claim

Large boilers have power densities in low 106 Wt/m2 of their footprint; boilers and turbogenerator halls, are in mid-high 105 We/m2; stations including all of their essential on-site infrastructures, in mid 103 We/m2; stations including coal extraction and delivery, in low 103 We/m2 or high 102 We/m2 (largely determined by coal quality and shipping distance). Power densities will be lower for stations burning inferior coal and requiring large areas for on-site waste disposal: suggested design parameters for Indian plants show the rates in low 102 We/m2. Actual generation power densities for coal-fired stations in the US, Europe and Asia confirm the model calculations, as they range from high 102 to mostly low 103 We/m2 for the plant sites only; depending on the mining methods, coal quality and coal shipping, inclusion of the entire coal-to-electricity chain may leave the densities well above 1,000 We/m2 or lower them not just to mid-102 We/m2 but in some instances to just above 100 We/m2.

Stations burning heavy oil and crude oil are located either in or near oil-producing regions or have their fuel delivered by tankers to coastal locations and power densities of their generation are typically well into 103 We/m2 and either remain of the same order of magnitude after including fuel extraction or fall to ratings in high 102 We/m2. Natural gas-fired central electricity generating plants do not need any land for extensive on-site waste deposits and continuing gas supply by pipelines or LNG tankers reduces their fuel storage requirements. As a result both the plants using abundant gas supplies in major producing regions or those importing LNG (very important in Japan, often on reclaimed coastal land) generate electricity with densities of mostly between 2,000-6,000 We/m2. Even after including the claims of natural gas production power densities for the entire extraction-generation sequence remain typically on the order of 103 We/m2.

More natural gas is now burned in gas turbines rather than in boilers of large central stations. Gas turbines have limited ratings (100 to mid-102 MW) but that makes them highly suitable to deliver peak power on demand; they also can be deployed rapidly (many models are mobile) and operate with very high power densities, commonly 104 We/m2. This makes it possible to site new gas turbines on the land belonging to the existing central coal- or gas-fired stations. The same is obviously possible for combined-cycle plants (gas turbines with attached steam turbogenerators); their generating power densities will be also on the order of 103 We/m2.

Power densities of nuclear reactors (expressed per unit of their footprint and not, as is the custom in the industry, per unit of reactor volume) are 106 Wt/m2 but subsequent energy flow (expansion of pressurized steam rotating a large turbogenerator, creation of vacuum by cooling, steeping up the current for HV transmission) are the same as in fossil-fueled central stations and hence the layout of nuclear plants and their overall land requirements are also very similar. Because these plants do not require any extensive fuel storage and do not generate any waste from controlling air pollutants they can be quite compact, rating between 2,000-6,000 We/m2. As in the case of other thermal power plants we now have to proceed beyond the plant sites: as must be expected, land claims for the entire uranium cycle will significantly lower the densities of the entire fuel-generation-disposal sequence.

The most productive underground uranium mines (tapping the richest ores) have exceptionally high extraction densities (104 We/m2) while typical surface operation produce the ore with power densities ranging from high 102

We/m2 to low 103 We/m2, and those in situ leaching projects for which we have reliable data work with power densities of roughly 400-600 We/m2. Milling of ores to produce U3O8 concentrate proceeds with high power densities and production of fuel rods filled with slightly enriched UO2 is even less space-intensive, but the enrichment process has fairly low power densities once the claims for its electricity requirements are included.

Different assumption regarding uranium mining, processing, fuel enrichment and eventual radioactive waste disposal produce the range of overall power densities very similar to that of coal-fired plants, with rates as high as high as 103 We/m2 and as low as low- to mid-102 We/m2 –- or (as I showed in a detail calculation) even lower if all electricity required for uranium enrichment were to be derived from such a low power density source as hydrogenation. For comparison, several recent studies offer all-inclusive rates of 230 to 960 We/m2 for the US nuclear generation, a good agreement with my detailed, step-wise quantification.

Early generating plants served their immediate neighborhoods but modern stations 9be they hydro or nuclear, coal-fired or wind-powered) are connected to load centers (cities, industries) by HVAC transmission lines. Their rights-of-way, rising with voltage, add up to mostly between 4-6 ha/km, while HVDC links (mostly from distant hydro stations) need at least 40% less land for handling the same capacity. Naturally, short high-capacity links will have higher power densities –- a 200 km, 1 GW, 765 kV line would rate about 80 W/m2 of its ROW –- but the means for large utilities or for nationwide grids will be typically no more than 30-40 W/m2 of ROW.

Energy uses As huge as it is in absolute terms (roughly 17 TW in 2013), global energy use remains a tiny fraction of the Earth’s natural radiation balance: it prorates to 0.03 W/m2 of the Earth's surface and to 0.125 W/m2 W/m2 of ice-free land, the latter rate being less than 0.07% of the mean global insolation, and a small flux compared to 2.3 W/m2 of aggregate radiative forcing due to greenhouse gases. Average power densities of energy use within national territories ranges over four orders of magnitude: countries with sparse rural population (such as those in Africa’s Sahel region) rate only 10-4 W/m2, Netherlands and Belgium reach about 3 W/m2. Densely populated and industrialized urban areas use about 75% of the world’s energy and the global average of their power density reaches roughly 20 W/m2.

That, too, is roughly the US urban mean including all treed and grassed area within cities; after their exclusion the power density per unit of impervious US urban surfaces is about 35 W/m2. Worldwide, annual urban means range between 10-100 W/m2; downtowns average in excess of 100 W/m2 and their hourly extremes often approach and can substantially surpass 1,000 W/m2, and that much can be the annual mean for the densest city blocks in Manhattan, a flux equalling or exceeding insolation noon-time insolation. Variability of rates among individual buildings in the same climate is highly influenced by their function and construction.

Power densities of detached houses and apartments now differ less than just a generation or two ago because the ownership of many household energy converters is now so common and, for many of items (lights, refrigerators, electric or gas stoves, washing machines, TVs, computers, cellphones) it has approached or reached saturation. Moreover, high efficiencies cut the household rate in North America and Europe by half or more since the 1960s. The most efficient commercial buildings now need less than 10 W/m2 of floor area, a tenth of the 1970s level. But in temperate climates, with winter heating and now also with common summer cooling, typical power densities are around 20-30 W/m2 of floor area in single- and multi-family housing.

Schools have similar rates and among other commercial and public buildings parking garages and warehouses have the lowest power densities, hospitals the highest (about 70 W/m2 of floor area). All of these are on-site usage rates and in terms of primary energy (needed to generate electricity) they would be at roughly twice a high. And adjustments from floor area to power density of building footprints yield some very high power densities: from 100 W/m2 for a two-story family house in cold Canadian climate to roughly 1,000 W/m2 for nearly 40-story housing estate towers in Hong Kong, 2,000 W/m2 for a 50-story luxury hotel in hot climate, and more than 6,000 W/m2 for Burj Khalīfa, the world’s tallest building.

Energy converted by road vehicles is the second largest component of urban fuel use. There are large differences between rush-hour peaks and low-density traffic and between congested downtowns and major arteries and residential roads: free-flowing traffic of cars and trucks will have short-term power density of about 500 W/m2 of a paved lane and this may nearly double when vehicles have to idle. When the vehicular energy use is prorated over the entire right-of-way (lanes, shoulders, medians) the densities are roughly halved (and cut even more in rural settings), and further major reduction comes from counting parking lot space. When using the entire urban areas and averaging the traffic on annual basis the rates are usually less than 5 W/m2.


Comparisons of power densities inform us in two important ways: they reveal the hierarchies of supply and use, that is power densities of all major processes to produce primary energies and electricity, and of all common categories (household, industrial, commercial, transportation) of final energy uses; and contrasts of supply and usage rates allow us to quantify relative claims of particular energy requirements and to assess the future demands for land devoted to energy industries. Of course, we should constantly keep in mind that very few power densities have very narrow ranges, and that there will be many specific cases whose ratings will be far from the quoted typical performances or well outside the usual ranges.

Perhaps the most consequential reality is that the extraction and conversion of fossil fuels and uranium produce useful heat and electricity with power densities that are usually at least two and up to five orders of magnitude higher than the exploitation of renewable flows. Only in exceptional cases some forms of renewable energy conversion (most notably Alpine hydrostations with high heads and small reservoirs) have higher production power densities than do extractions of fossil fuels and generation of thermal electricity. Production of phytomass in general, and of liquid biofuels in particular, has the lowest power densities of all commercially exploited resources. This is a fundamentally unalterable outcome of inherently low efficiency of photosynthesis and environmental constraints on phytomass yield. Annual or perennial energy crops can be produced with higher power density than woody biomass: the latter has higher energy density, but the former has a higher rate of growth.

Although yields have been impressively increased during the latter half of the 20th century for both field crops and plantation trees, and although further increases are coming, there is no realistic expectation that the most desirable liquid fuels can be produced with power density significantly surpassing 0.5 W/m2 in temperate and 1 W/m2 in tropical environments where the current rates are less than half of these thresholds. Moreover, if all inputs needed to produce biofuels (machinery, fuel, fertilizer) were to be energized solely by renewable energies rather than (as has been, and will continue to be, the case) by fossil fuels and nuclear-derived electricity, then the power densities of such completely renewable operations would drop to less than 0.1 W/m2.

Hydro projects with large dams and low capacity factors can be as land-intensive as phytomass production, while of some of the world’s largest plants and smaller Alpine-type stations can generate electricity with power densities up to two orders of magnitude higher. High land requirements of hydrogenation are best illustrated by the fact that it supplies less than 3% of the world’s primary energy but accounts for more than half of all land occupied by the world’s energy infrastructure. Wind turbine spacing result in power densities hardly better than the best phytomass production, but when counting only actual (physical) land claims the rate goes up by an order of magnitude and (depending on locations) it rivals, or surpasses power densities of PV solar generation. Central solar power is not significantly less land-intensive but it has much higher capacity factors. No other mode among today’s commercial conversions of renewable energy can do better than flat plate solar collectors that can supply hot water with power densities between 50-100 W/m2.

Extreme values for power densities of coal extraction span three orders of magnitude (from < 100 W/m2 to > 1,000 W/m2) but typical rates in large modern surface mines are very similar to those in large oil fields, being at least close to 1,000 W/m2 and commonly two to four times as high. Coal and natural gas extraction make up the largest land claims of fossil fuel-based thermal electricity generation, and while the plants themselves are fairly compact a great deal of space may be claimed by cooling and captured waste disposal. This may reduce power densities of some coal-fired stations to the same order of magnitude as large solar PV generation, while the fastest growing choice, gas-powered turbines, is highly compact, with power densities of 103 We/m2. Power densities of nuclear generation (including production and processing of fissionable fuel) are broadly comparable to those of coal-fired power plants (102-103 We/m2).

Power densities of energy production range over five orders of magnitude, from low 10-1 W/m2 for liquid biofuels to low-mid 104 W/m2 for the world’s richest hydrocarbon deposits, but final energy uses of modern high-energy societies fall mostly between 101 and 102W/m2 for homes, commercial buildings, industrial enterprises and densely populated urban areas. This means that modern civilization extracts fuels and generates thermal electricity with power densities that are commonly at least one, usually two, and sometimes three orders of magnitude higher than are the power densities of final energy uses in urban areas (where most people now live) and in individual buildings, commercial and industrial establishments.

For example, fuels to supply urban areas are extracted and delivered with power densities that are higher than power densities of large cities (10-30 W/m2, including roads and urban vegetation). Thermal electricity is typically generated with power densities that are one, and often two orders of magnitude higher (300-3,000 We/m2) than power densities of electricity use in one or two-storey houses (10-50 We/m2). And liquid fuels for transportation (gasoline, kerosene) and produced (including extraction and refining) with power densities that are one to two orders of magnitude higher than power densities of urban traffic. And even the common uses with very high power densities (300-1,000 W/m2 for supermarkets, high-rises, energy-intensive factories, downtowns of megacities) either overlap or are slightly surpassed by power densities with which the requisite electricity and fuels are delivered by modern, predominantly fossil-fueled energy system.

This system has evolved to extract fuels with high power densities that surpass (or at least match) power densities of fuel and electricity use of highly urbanized modern societies. These concentrated energy flows are diffused through pipelines, railways and high-voltage transmission lines to final users. As a result, space claimed by extraction and conversion of fossil fuels is a small fraction of rights-of-way needed to distribute fuels and electricity: American extraction, processing and conversion of coals and hydrocarbons takes up less than 20% of land that is required for pipeline, railway and transmission rights-of-way and it occupies less than 0.1% the country’s territory.

In contrast, future societies powered solely or largely by renewable energies would rely on an opposite approach by concentrating diffuse energy flows, producing useful heat or electricity with low power densities ranging mostly between 0.2 W/m2 for liquid biofuels to 20 W/m2(for solar PV and wind (occupied space only). In order to energize large cities, where most of people will live, any society dependent entirely on renewable energies would have to concentrate their diffuse flows captured with low power densities in order to bridge the gaps between production and use that will amount to several orders of magnitude. As a result, future societies that will inherit today’s housing, commercial, industrial and transportation infrastructures would need at least two, or three, orders of magnitude more space to secure the same flux of useful energy if they were to rely on a mixture of biofuels and water, wind and solar electricity.

Obviously, when stated that way the comparison is incomplete because it must also take into account the fundamental differences between the two energy categories. Conversions of renewable energies harness continuous, or recurrent (periodically interrupted) natural energy flows, while production of fossil fuels depletes finite resources whose genesis goes back 106-108 years. Even so, this fundamental difference and the eventual need to move beyond fossil fuels cannot alter the power density gap between fossil and renewable energies, leaving the nuclear electricity generation as the only commercially proven high power density alternative. There are several bold proposals for with current PV conversions –- ranging from harnessing solar energy with much higher power densities than it is possible giant buoyant PV panels in the stratosphere (StratoSolar 2014) to the Moon-based PV beamed to the Earth by microwaves (Girish and Aranya 2012) –- but there are no earl prospects for their commercialization.

Aggregate land claims

Systematic quantifications of many specific kinds of land use (in addition to such standard data as arable or forested land) are fairly recent; as I have already shown, even such obviously important categories as the area of urban land or impervious surface area of the US have been reliably assessed only during the past 10-15 years. At this point it may be superfluous to stress that the aggregates hide many qualitative differences and that all the numbers I will offer in this section have no claims to high accuracy, and that their aim is to do just a bit better than getting the right order of magnitude. I am confident that even for the global totals, and definitely for the US aggregates, even the most /uncertain numbers have error margins no greater than ±75%, most fall within ± 50% range and some are off by less than ± 25%.

Global energy system Global data for extraction of fossil fuels, their processing and transportation, and for electricity generation and transmission are fairly reliable (BP 2013; IEA 2014; UN 2014) and I use them, converted to annual powers for the year 2010, together with fairly liberal averages of specific power densities, that is assuming relatively low rates, in order to err on a high side of aggregate land claims. Moreover, in order to avoid the appearance of unwarranted accuracy, all itemized results are rounded upwards to the nearest 100 km2 and all category totals are rounded to the nearest 1,000 km2. The only category that is deliberately excluded from this global aggregate are the rights-of-way of railroads that the coal-carrying trains share with other cargo.

Extraction of nearly 14 TW of fossil fuel (including on-site processing of coal and natural gas) claimed about 12,000 km2 (and most likely not less than 10,000 and not more than 15,000 km2), and crude oil refining added about 1,000 km2. Tanker terminals and natural gas liquefaction facilities occupied only about 300 km2. When assuming either average rights-of-way width of 15 m or average throughput power density of 300 W/m2 the world’s refined oil product and natural gas pipelines (whose total length reached about 2 Gm in 2010) pre-empted other land use on almost 30,000 km2. Aggregates for global electricity are more error-prone. Fossil-fuelled stations required about 1,500 km2, nuclear power plants added at least 600 km2.

Any errors in these values are negligible compared to the estimates for hydrogeneration; my best estimate of land claimed by water reservoirs used for hydrogeneration is on the order of 100,000-150,000 km2. ICOLD’s register of dams contains data on nearly 38,000 structures taller than 15m (ICOLD 2014). About 72% are single-purpose dams (50% built for irrigation, 18% for electricity generation); among the multipurpose dams irrigation (24%) and flood control (20%) are more important than power generation (16%). Consequently only about 20% of all dams are used solely or primarily to generate electricity and hence even if we use one of the higher estimates of global reservoir area (about 600,000 km2) hydrogenation would claim at least 120,000 km2. Rights-of-way for high voltage transmission can be estimated in two ways: assuming that the total line length of about 1 Gm claims 5 ha/km, or that the transmission of 2.3 TW in 2010 proceeded at an average rate of 40 W/m2. The two totals are, respectively, 50,000 and about 58,000 km2, a close agreement for this kind of global aggregates.

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