Magnitude of Energy Resources

Here we calculate how fast the world's energy supply would be exhausted if we stick to current projections. Of course I expect people to wise up and change their behavior before complete exhaustion occurs; for details on this see ./fossil-resources.htm In any case, though, the straight-line analysis presented here remains useful; if nothing else it establishes the timescale over which something big must happen.

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
: 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:
:
: // ============
:
: // 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://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/
```