Power Density Primer: Understanding the Spatial Dimension of the Unfolding Transition to Renewable Electricity Generation (Part II – Coal- and Wood-Fired Electricity Generation)
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 GWe) 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.
800 MW x 8,766 hours = 7.0 TWh
7.0 TWh x 3,600 = 25.2 PJ
25.2 PJ/0.38 = 66.3 PJ
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 GWe 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:
19.95 t x 20 GJ/t = 399 GJ
66.3 PJ/399 GJ = 166,165 m2
800 MW/166,165 m2 = 4,814.5 W/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), and from a major river (hence requiring cooling towers), burning lower-quality sub-bituminous coal (18 GJ/t) extracted from a thinner (10 m) seam and containing relatively high shares of ash (over 10%) and sulfur (about 2%) and having a low capacity factor (70%) and conversion efficiency (33%). Coal extraction needed to supply this plant would proceed with power density of only about 2.5 kW/m2:
700 MW x 8,766 hours = 6.14 TWh
6.14 TWh x 3,600 = 22.09 PJ
22.09 PJ/0.33 = 66.94 PJ
10 m3 x 0.95 x 1.4 t = 13.3 t
13.3 t x 18 GJ/t = 239.4 GJ
66.94 PJ/239.4 GJ = 279,615 m2
700 MW/279,615 m2 = 2,503.4 W/m2
With this base range in mind, we can now proceed to examine power densities of natural gas-fired generation using large gas turbines and then four major modes of renewable electricity generation.
Wood-Fired Electricity Generation
Photosynthesis is an inherently inefficient way of converting electromagnetic energy carried by visible wavelengths of solar radiation into chemical energy of new plant mass: global average of this conversion is only about 0.3% and even the most productive natural ecosystems cannot manage efficiencies in excess of 2%. The best conversion rates for trees grown for energy can be achieved in intensively cultivated monocultural plantations. Depending on the latitude and climate, these can be composed of different species and varieties of willows, pines, poplars, eucalyptus or leucaenas. Burning sawmill residues or wood chips in fairly large boilers in order to generate steam and/or electricity is a well-established and a fairly efficient practice – after all, energy density of dry wood (18-21 GJ/t) is much like that of sub-bituminous coal.
But if we were to supply a significant share of a nation’s electricity by using tree phytomass we would have to establish extensive tree plantations that would require fertilization, control of weeds and pests and, if needed, supplementary irrigation –- and even then we could not expect harvests surpassing 20 t/ha, with rates in less favorable locations as low 5-6 t/ha and with the most common yields around 10 t/ha. Harvesting all above-ground phytomass and feeding it into chippers would allow for 95% recovery of the total field production but even if the fuel’s average energy density were 19 GJ/t the plantation would yield no more than 190 GJ/ha, resulting in harvest power density of 0.6 W/m2:
190 GJ/31.5 Ms = 6,032 W
6,032 W/10,000 m2 = 0.6 W/m2
700 MW/0.35 = 2 GW
2 GW/0.6 W/m2 = 3.33 Gm2 (333,333 ha)
?3.33 Gm2 = 57,735 m
Plantation of fast-growing hybrid poplars: whole-tree harvesting of this phytomass has power densities below 1 W/m2.