Unless otherwise specified, energy values are in joules and power values are in watts.
: : btu = 1054.5 // joule btu= 1054.5 : quad = 1e15 * btu // joule quad= 1.0545e+18 : hour = 3600 // seconds hour= 3600 : day = 24 * hour // seconds day= 86400 : // mean tropical year https://en.wikipedia.org/wiki/Year : year = 365.24219 * day // seconds year= 3.15569e+07 : : foot = 0.3048 // meter foot= 0.3048 : inch = foot / 12 inch= 0.0254 : mile = 5280 * foot // meter mile= 1609.34 : // https://physics.nist.gov/Pubs/SP811/appenB.html : : // oil heat value : oilval=6.2e6 * btu // 6.2 million Btu per barrel oilval= 6.5379e+09 : // coal heat value : coalval=21e6 * btu // 21 million Btu per ton coalval= 2.21445e+10 : // http://www.eia.doe.gov/neic/infosheets/apples.htm : : // natural gas heat value : gasval=1025 * btu // 1025 BTU per cubic foot gasval= 1.08086e+06 : // (average, somewhat variable) : // http://www.eia.doe.gov/cneaf/electricity/st_profiles/california/ca.html : : // For warm-up (not main point) estimate US coal usage and reserves: : // coal: current US use is about 1000 million short tons per year : uscoal_t_rate = 1e9 / year // tons per sec uscoal_t_rate= 31.6888 : uscoal_rate = last * coalval // watts uscoal_rate= 7.01732e+11 : uscoal_q_peryear = last / quad * year // quads per year uscoal_q_peryear= 21 : // http://www.eia.doe.gov/emeu/aer/txt/ptb0703.html : : // coal: current US proven reserves are about 500,000 million short tons : // of which 270,000 million is classified as "recoverable" : uscoalres_t = 2.7e11 // tons uscoalres_t= 2.7e+11 : uscoalres = last * coalval // joules uscoalres= 5.97902e+21 : // http://www.eia.doe.gov/cneaf/coal/page/acr/table16.html : : uscoalyears = uscoalres / uscoal_rate / year // years uscoalyears= 270 : : // Note 80% of the coal mined in the US is used to produce electricity. : // Conversely, more than half of the electric power produced in the US : // comes from coal. : // http://www.eia.doe.gov/kids/non-renewable/coal.html : : // Useful graphic, showing US energy inputs and outputs: : // http://en-env.llnl.gov/flow/pdf/USEnFlow00-quads.pdf : : // ============ : : // Repeat the calculation for the whole world, not just the US. : // Also include all energy, not just coal. : // Coal: world recoverable reserves: 1,083,000 million short tons : coalres_t = 1.083e12 // tons coalres_t= 1.083e+12 : coalres = last * coalval coalres= 2.39825e+22 : // http://www.eia.doe.gov/emeu/iea/table82.html : : // Crude oil: world reserves, estimated by US DOE : // http://www.eia.doe.gov/emeu/international/reserves.html : doe_oilres_b = 1.212e+12 // barrels doe_oilres_b= 1.212e+12 : // However, that appears to reflect only "proven" reserves, : // which is not the best estimate; better estimates are higher: : // http://www.radford.edu/~wkovarik/oil/2worldoil.mideast.html : // http://greatchange.org/ov-korpela,US_and_world_depletion.html : oilres_b = 2.272e+12 // barrels oilres_b= 2.272e+12 : oilres = last * oilval oilres= 1.48541e+22 : : // Natural gas: world estimated reserves: 5,501 trillion cubic feet : gasres_f = 5501e12 // feet gasres_f= 5.501e+15 : gasres = last * gasval gasres= 5.94582e+21 : // http://www.eia.doe.gov/emeu/international/reserves.html : : // ====================================================================== : : // Estimate world's supply of uranium, "proven" and : // "probable" reserves: : unatres_t = 3e6 // tons natural uranium unatres_t= 3e+06 : : // Fraction of natural uranium that is useful(*) U235: : // less than one percent : u235res_t = 0.01 * unatres_t // at most u235res_t= 30000 : : // Useful(*) energy equivalence factor, tons of coal per : // ton of natural uranium: 1e5 : unatval = 1e5 * coalval unatval= 2.21445e+15 : : // Calculate energy equivalent of uranium supply : ures = unatres_t * unatval ures= 6.64335e+21 : : carbonres = coalres + oilres + gasres carbonres= 4.47824e+22 : totres = carbonres + ures totres= 5.14258e+22 : carbonfrac = carbonres / totres carbonfrac= 0.870817 : coalfrac = coalres / totres coalfrac= 0.466352 : oilfrac = oilres / totres oilfrac= 0.288846 : gasfrac = gasres / totres gasfrac= 0.11562 : ufrac = ures / totres ufrac= 0.129183 : : // world annual energy usage (2001): 404 quads : // http://www.eia.doe.gov/oiaf/ieo/world.html : world_rate = 404 * quad / year // watts world_rate= 1.35e+13 : world_years = totres / last / year world_years= 120.713 : : // world annual energy usage (2025 estimate): 640 quads : // http://www.eia.doe.gov/oiaf/ieo/world.html : w_2025_rate = 640 * quad / year // watts w_2025_rate= 2.13861e+13 : w_2025_years = totres / w_2025_rate / year w_2025_years= 76.1999 : : // Uranium in perspective: : u_versus_coal = ures / coalres u_versus_coal= 0.277008 : // =less than 28% of actual coal supply : // =roughly 3e11 tons of coal-equivalence : u_versus_carbon = ures / carbonres u_versus_carbon= 0.148347 : // =less than 18% of actual carbon-fuels supply : : //(*) Note that the evaluation of useful energy-content : //would go up by a couple orders of magnitude if breeder : //reactors were widely used -- but they are not, apparently : //because they pose risks that the government and the nuclear- : //power industry can't tolerate. So for the next many years : //at least, the foregoing calculation will remain valid. : // : //This calculation seriously calls into question the claims : //that uranium is an "abundant" source of energy. : // : //============== : // : //Nuclear power is also not as cheap as it was predicted to : //be. Currently it is about 6 cents per kwh versus 4 cents : //for gas or coal at current prices. OTOH it wouldn't take : //too much of a perturbation in the fossil-fuel market to : //tip the scales. : // : //============== : // : //A related calculation: The cost of the Yucca Mountan facility : //is variously estimated, but it's got to be over 50 billion : //dollars. Of this, less than half will be recovered via fees : //charged to nuclear utilities, at present rates. Taxpayers : //will get stuck with the rest. If the cost of the facility : //were properly asessed to the industry, nuclear-power rates : //would go up by a fraction of a cent per kwh. So, the cost : //of long-term storage is a noticeable but not overwhelmingly : //huge piece of the pie, if you believe that Yucca Mountain : //does actually solve "the" long-term storage problem -- and : //at some point it depends on what we mean by "long" term. : // : //====================================================================== : // : // Tangentially amusing calculation : // Total US energy consumption (2001) : // http://www.eere.energy.gov/consumerinfo/refbriefs/da8.html : us_rate = 97.1 * quad / year // watts us_rate= 3.24467e+12 : : // Electrical output of a solar photovoltaic cell: : // 550Wh/m^2/day in Austin, averaged over the 24-hour cycle : // http://linas.org/theory/solar-electric.html : // assuming 11% efficiency and semi-desert insolation : // costing $10 per watt : spv_persqmeter = 550 * hour / day // watts, average spv_persqmeter= 22.9167 : spv_area_required = us_rate / spv_persqmeter spv_area_required= 1.41586e+11 : side = sqrt(last) side= 376279 : side_mi = last / mile side_mi= 233.809 : spv_install = 10.00 // dollars per watt, installed spv_install= 10 : spv_life = 10 * year spv_life= 3.15569e+08 : spv_unit_price = spv_install / spv_life spv_unit_price= 3.16888e-08 : //xx Summer 2001 wholesale avg $40.70 per megawatt-hour : //xx http://www.pjm.com/contributions/news-releases/2003/20030402_anniversary.pdf : //xx current_wholesale = 40.70 / 1e6 / hour // dollars per joule : // 1Q 2006 wholesale roughly $50.00 per megawatt-hour : // http://www.edison.com/files/2006_1Q_charts.pdf : current_wholesale = 50.00 / 1e6 / hour // dollars per joule current_wholesale= 1.38889e-08 : // Ratio of prices: solar photovoltaic versus current wholesale: : spv_ratio = spv_unit_price / current_wholesale spv_ratio= 2.28159 : : // So if we cover an area 250 miles on a side with solar : // cells we can supply the entire US energy demand. : // (This disregards inefficiencies associated with : // load-levelling across the 24-hour cycle, which could : // be considerable.) : nv_area = 109806 * mile * mile // total area of the state nv_area= 2.84396e+11 : // Land area from: http://www.50states.com/nevada.htm : spv_nv_frac = spv_area_required / nv_area spv_nv_frac= 0.497847 : // i.e. this is something like half the land area of Nevada : us_spv_capital = spv_install * us_rate us_spv_capital= 3.24467e+13 : us_defense = 379e9 // dollars per year us_defense= 3.79e+11 : : // Electric energy output is only about 12% of US energy : // consumption. This is output, downstream of generation : // inefficiencies. : elec_side_mi = side_mi * sqrt(0.12) elec_side_mi= 80.9938 : // So a much smaller area would suffice to cover all : // the demand for _electrical_ energy. : : : // Solar thermal -> salt -> steam turbine : // http://www.eere.energy.gov/power/pdfs/solar_tower.pdf : // (Predicted to cost about $1.00 per PEAK watt in 2010) : // Better analysis: : tower_power = 1139e9 * hour / year // watts tower_power= 1.29937e+08 : tower_life = 10*year tower_life= 3.15569e+08 : tower_unit_capital = 2.605 // dollars per NAMEPLATE watt tower_unit_capital= 2.605 : tower_nameplate = 200e6 tower_nameplate= 2e+08 : tower_capital = tower_unit_capital * tower_nameplate tower_capital= 5.21e+08 : tower_unit_price = tower_capital / tower_life / tower_power tower_unit_price= 1.27061e-08 : // Ratio of prices: solar tower versus current wholesale: : tower_ratio = tower_unit_price / current_wholesale tower_ratio= 0.914838 : // Note: possibly unrealistically, I'm ignoring cooling-water : // issues. There isn't a lot of cooling water in Nevada : : tower_persqmeter = tower_nameplate / 2.5e6 // watt per m^2 tower_persqmeter= 80 : tower_area_required = us_rate / tower_persqmeter tower_area_required= 4.05584e+10 : tower_nv_frac = tower_area_required / nv_area tower_nv_frac= 0.142612 : // : // Miscellaneous reference: https://www.nrel.gov/pv/