Comments on: The Treasury’s Pre-Budget review http://www.carboncommentary.com/2007/10/15/30 A critical appraisal of issues in the move to a low-carbon economy Sat, 05 Jul 2008 01:27:03 +0000 http://wordpress.org/?v=2.3.3 By: William Ernest Schenewerk http://www.carboncommentary.com/2007/10/15/30#comment-86 William Ernest Schenewerk Sun, 25 Nov 2007 13:36:10 +0000 http://www.carboncommentary.com/2007/10/15/30#comment-86 Carbon Tax May have to be $1000/tonne Ms/sir: If goal is to arrest atmospheric CO2 at 2 times pre-industrial CO2 by 2080, then carbon tax must be at least 1.0 $/kg-C ($1000/tonne-Carbon). 1.0 $/kg-C tax doubles the price of electricity generated from fossil fuel. 1.0 $/kg-C tax does not give natural gas a price advantage over coal if natural gas costs more than $5/1000 ft^3. MHD-Coal may be competitive with natural gas regardless of the carbon tax. European auto-fuel taxes already exceed 1.0 $/kg-C ($2/gallon). Preindustrial CO2 is 0.028% by volume. Starting at 0.001% CO2 in 1850, industrial CO2 has been compounding 3%/year. 1950 CO2 is 0.0300 % (300 ppmv) and 2000 CO2 is 0.037% (370 ppmv), using Mauna Loa data. Continuing at 3% CO2 (atmospheric carbon) increase per year adds 0.028% to existing 0.028% preindustrial by 2038, giving 0.056% CO2. 0.056% minus (y 2000) 0.037% is 0.019%. The added 0.019% CO2 increase by volume represents 414 Tkg-C (414 trillion kilograms carbon). We are already 1/3 of the way toward CO2 doubling. Applying 1.0 $/kg-C carbon tax to 414 Tkg-C, collects 3% World GDP between 2000 and 2080. This assumes 3% annual economic growth and CO2 doubling by 2080. If CO2 doubles by 2038, the 1.0 $/kg-C represents 15% World GDP. Arresting CO2 at twice preindustrial by 2080 requires approximately 400 TWe-y (400,000 giga-watt-years electric) atomic generation between 2000 and 2080. After 2080 World annual atomic power requirement is 25 TWe. This assumes world population is constant after 2030. All non-nuclear scenarios double CO2 between 2038 and 2080, with exponential increase continuing thereafter. The first 60 TWe-y will have to come from 1500 +/- 500 light-water reactors (LWRs). 60 TWe-y LWRs consume 10 MtUnatural, the estimated World uranium resource base. Plutonium from spent LWR fuel, military plutonium and military HEU is used to load 2500 +/- 1000 fast breeder reactors (FBRs) by 2035. By 2080 there will be 25,000 FBRs operating and power-plant CO2 emission will cease. World energy grows 2%/year until 2080, assuming world population stops increasing before 2030. Hydrogen and ammonia will be produced by electrolysis. Aluminum cars will burn ammonia. Propeller aircraft will burn liquid hydrogen. Phosphate fertilizer, detergent and concrete will be produced in arc furnaces. 1.0 $/kg-C carbon tax increases pulverized coal power cost 0.085 $/kWh more than it increases CCGT (Combined-Cycle gas turbine) power cost. This cost differential is the minimum required to make CCGT less expensive than power generated from pulverized coal. Natural gas is 3 to 6 times as expensive as coal on a BTU basis. CCGT (Combined-Cycle Gas Turbine) needs 0.05 $/kWh profit to pay its $1500/kW plant cost within 5 years. Decontrolled natural-gas and FERC price-caps require a 5 yr payout on any new power plant that uses natural gas. A "8000 BTU" CCGT pays $5/MMBTU for natural gas. $5/MMBTU fuel adds an additional 0.04 $/kWh to the cost of electricity from the "8000 BTU" CCGT. A new CCGT must charge 0.09 $/kWh, absent the carbon tax. An existing coal-fired power plant has to pay less than $1/MMBTU for coal, putting its total generation cost at less than 0.04 $/kWh, absent the carbon tax. One Dollar/kg Carbon tax adds 0.13 $/kWh to the CCGT and adds 0.21 $/kWh to the "9000 BTU" coal plant. Under these extreme conditions the new CCGT only has a 0.03 $/kWh advantage over an existing coal plant. Electricity price is more than doubled in the process. Under the same conditions, the simple cycle gas turbine charges roughly 0.08 $/kWh, absent the carbon tax. The simple cycle carbon tax is 0.16 $/kWh, giving 0.24 $/kWh total power cost. This is only 0.01 $/kWh less than the existing coal plant. CCGT (Combined-Cycle Gas Turbine) is typically two airplane motors (Brayton Cycle) exhausting into a single steam boiler (Rankine Cycle). Airplane motors produce roughly 80% of total electric power. CCGT bottoming Rankine cycle produces roughly 20% of total electric power. A CCGT is typically an "8000 BTU" plant, using 8000 BTU heat input per kWh electric output. Resulting thermal efficiency is 3412 BTU/kWh/8000 BTU/kWh (42.65 %), based on natural-gas HHV (higher heating value). CCGT heat rates of 7000 BTU/kWh are within reach, absent blade erosion and load following. Absent cooling water, airplane motors are installed minus a bottoming Rankine cycle. Resulting simple Brayton Cycle heat rate is roughly 10,000 BTU/kWh, burning natural gas. Pulverized coal power heat rate is typically 9000 BTU/kWh, using a super-critical Rankine cycle and cooling water. Coal can also be gasified, cleaned and fired in a CCGT. Overall heat rate is roughly 10,000 BTU/kWh, because gasification loses 1/3 of the energy. Valuable liquid byproducts improve gasifier economics. A coal-fired MHD Combined Cycle (Coal-MHDCC) may reach 6000 BTU/kWh, a 57% thermal efficiency. Coal-MHDCC carbon tax would be roughly the same as for CCGT. n-octane, C8H18, is roughly 70 API gasoline at 700 kg/m^3 (5.84 lbs/US-gallon; US gallon = 231 in^3). C8H18 HHV is 5.46 GJt-HHV/kg-mole-C8H18. 1.0 $/kg-C carbon tax on gasoline translates into 2.0 $/US-gallon. Existing Carbon Mass in Earth Atmosphere Preindustrial atmospheric CO2 = 0.028% by volume Post 2008 Carbon = 5.263 Ekg-Air * (12 MW-C/29 MW-Air) * (560 ppmv - 394 ppmv)/1000,000 p) * (1.0 E+06 Tkg/1.0 Ekg) = 361 Tkg-C = 361,000 Mt-C = 361,000 Mt-C/(500 EJt/yr/0.0569 EJt-HHV/Mt-C) = 41 years CO2 doubling = 2008 + 41 = 2049 Carbon buildup 1800 to 2001 at 2.25% historic annual increase: ppmvc = 280 + Exp(0.0225 * (year - 1800)) Preindustrial, 275-284 ppm, 1550 - 1800 A.D. Carbon Dioxide Information Analysis Center http://cdiac.esd.ornl.gov C.D. Kelling and T. P. Worf, Carbon Dioxide Research Group, Scripps Institution of Oceanography, La Jolla CA 92093-0044 cdiac.esd.ornl.gov/ftp/maunaloa-co2/maunaloa.co2, Mauna Loa Observatory, Hawaii ppmvc = 280 + Exp(0.0225 * (year - 1800)) Mauna Loa Eq Mauna Loa Eq 1959 316.00 316 1960 316.91 317 1961 317.63 317 1981 339.95 339 1962 318.46 318 1982 341.09 340 1963 319.02 319 1983 342.75 341 1964 319.52 320 1984 344.44 343 1965 320.09 321 1985 345.86 344 1966 321.34 322 1986 347.14 346 1967 322.13 323 1987 348.99 347 1968 323.11 324 1988 351.44 349 1969 324.60 325 1989 351.44 350 1970 325.65 326 1990 354.19 352 1971 326.32 327 1991 355.62 354 1972 327.52 328 1992 356.36 355 1973 329.61 329 1993 357.10 357 1974 330.29 330 1994 358.86 259 1975 331.16 331 1995 360.90 360 1976 332.18 332 1996 362.78 362 1977 333.88 334 1997 363.84 364 1978 335.52 335 1998 366.58 366 1979 336.89 336 1999 368.28 368 1980 338.67 337 2000 369.39 370 2001 370.93 372 cdiac.esd.ornl.gov/ftp/trends/co2/siple2.013, Friedli et al. (1986) Siple Station Ice Core, Physics Institute, University of Bern, CH-3012, Bern, SW Year 1744 1764 1791 1816 1839 1843 1847 Bern 276.8 276.7 279.7 283.8 283.1 287.4 286.8 Curve 281 282 283 283 283 Year 1854 1869 1874 1878 1887 1899 Bern 288.2 289.3 289.5 290.3 292.3 295.8 Curve 285 285 286 287 289 Year 1903 1905 1909 1915 1921 1927 1935 1943 1953 Siple 294.8 296.9 299.2 300.5 301.6 305.5 306.6 307.9 312.7 Curve 290 291 292 293 295 397 301 305 311 Try ppmv = 280 + Exp(0.0225 * (Y - y-1800)) Justification for 1.0 $/kg-C Carbon Tax Assume: World GDP grows 3%/year, US yr-2000 GDP = 10 T$ and World GDP = 4 * US GDP: World GDP = 10 T$ USA * 4 World/USA * Exp(0.03*(yr - 2000)) Assume World must pay 1.0 $/kg-C as it releases 414 Tkg-C from 2000 to yearend 2080. Atmospheric CO2 increases from 370 ppm y-2000 to 560 ppm y-2080, adding an additional 414 Tkg-C. Carbon Tax = 1.0 $/kg-C * 414 Tkg-C = 414 T$ 414 T$ Carbon Tax/Cumulative GDP Between 2000 and 2080 = 414 T$/(Cumulative World GDP yr-2000 to yr-2080) = 414 T$/(10 T$ * 4 * [Integral{Exp(0.03 * (2080 - 2000))}]) = 414/(10 * 4 * [(1/0.03) * (Exp(0.03 *(2080 - 2000)) - 1)]) = 0.03 * 414 / (10 * 4 * (Exp(0.03 * (2080 - 2000)) - 1)) = 0.03 * 414 / (10 * 4 * (11.02 - 1)) = 0.031 [3% Carbon tax] , where [Integral{Exponential equation} limits are 2000 and 2080]. Notation and Conversions atm = atmospheric pressure = 101325 N/m^2 BTU = British Thermal Unit, energy unit Cal = calorie, energy unit (= 4.1868 Joules) g = acceleration of gravity (= 9.80665 m/sec^2) HHV = Higher Heating Value, combustion steam is condensed J = Joule, energy unit LHV = Lower Heating Value, combustion steam not condensed kWh = electric kilowatt hour = 3600,000 J MHD = Magneto-Hydrodynamic MMBTU = Million BTU, MM is Roman Numeral 1000 times 1000 MMBTU = 1055.06 MJ NM = Nautical Mile = 1852 m = 1 degree/60 at equator scf = standard cubic natural gas at 60 F and 30" Hg t = metric ton = 1000 kg = long ton = tonne k = kilo = 1.0E+03 (thousand) M = mega = 1.0E+06 (million) G = giga = 1.0E+09 (billion) T = tera = 1.0E+12 (trillion) E = exa = 1.0E+18 (ecto) Z = zetta = 1.0E+21 (zillion) 1 BTU = ((lb-H2O-F) * (1000 g/kg/2.2046226 lb/kg) * (C/1.8 F) * Cal/gm-H2O-C * 4.1868 J/Cal = 1055.056 J Air Molecular Weight = 29 kg/kg-mole H Molecular Weight = 1.00797 kg/kg-mole C Molecular Weight = 12.01115 kg/kg-mole S Molecular Weight = 32.064 kg/kg-mole Natural Gas Carbon Tax Natural gas is burned in an "8000 BTU" Combined Cycle CCGT. Natural Gas standard cubic foot (scf) is calculated at 30" Hg (101592 N/m^2) and 60 F (288.70556 K): 1 kg-mole natural gas at standard conditions = 1 kg-mole * 288.70556 K * 8314.5 J/kg-mole-K/101592 N/m^2 = 23.6283 m^3 (834.43 scf) Natural Gas volume fraction: 0.94 CH4, 0.03 C2H6, 0.01 CO2. Natural Gas HHV = (0.98 kg CH4 * 16.04303 * 50010 kJ/kg + 0.03 kg C2H6 * 30.07012 * 47470 kJ/kg + 0.01 CO2 * 0) * 1.0 MJ/kJ / (1055.056 MJ/MMBTU * 834.43 scf/kg-mole) = 0.000942 MMBTU/scf 1 $/kg-C (Natural Gas Carbon Tax) = 1 $/kg-C * 12.01115 kg-C/kg-mole-C * (0.98 * 1 + 0.03 * 2 + 0.01 * 2) kg-mole-C/kg-mole-gas / (834.43 scf/kg-mole-gas * 0.000942 MMBTU/scf) = 15.9 $/MMBTU-natural gas "8000 BTU" Combined Cycle Gas Turbine (CCGT) carbon tax = (8000 BTU/kWh * 15.9 $/MMBTU) / 1000,000 BTU/MMBTU = 0.13 $/kWh "10000 BTU" Simple Cycle Gas Turbine (SSGT) carbon tax = (10000 BTU/kWh * 15.9 $/MMBTU) / 1000,000 BTU/MMBTU = 0.16 $/kWh Pulverized Coal Power Plant Carbon Tax (Rankine Cycle) Pulverized coal is burned in an "9000 BTU" pulverized coal steam plant. Overall thermal efficiency is 38%, based on fuel HHV (higher heating value). Coal is assumed to be 80% (C-H-S0.01). 0.01 sulfur in the formula give 2.4% sulfur coal. The remaining 20% coal mass is incombustible water, bound oxygen, bound nitrogen and ash. Coal thermal energy is based on 1 kg-mole Carbon: Coal mass/kg-mole-C = (12.0115 kg-C/kg-mole-C + 1.00797 kg-H/kg-mole-H * 1.0 kg-mole-H/kg-mole-C + 32.064 kg-S/kg-mole-S * 0.01 kg-mole-S/kg-mole-C) / 0.80 kg-fuel/kg-coal = 16.675 kg-coal/kg-mole-C Coal HHV/kg-mole-C = 393 MJ/kg-mole-C + 142 MJ-HHV/kg-mole-H * 1.0 kg-mole-H/kg-mole-C + 301 MJ/kg-mole-S * 0.01 kg-mole-S/kg-mole-C = 538 MJ-HHV/kg-mole-C (= 13,800 BTU/lb-coal) Coal HHV/kg-C = 538 MJ-HHV/kg-mole-C/12.01115 kg-C/kg-mole-C = 44.8 MJ/kg-C 1.0 $/kg-C (Coal Carbon Tax) = (1 $/kg-C/44.8 MJ/kg-C) * 1055.56 MJ/MMBTU = 23.6 $/MMBTU "9000 BTU" Pulverized-Coal Power Plant Carbon Tax = (9000 BTU/kWh * 23.6 $/MMBTU) / 1000,000 BTU/MMBTU = 0.21 $/kWh "6000 BTU" Coal-MHDCC Power Plant Carbon Tax = (6000 BTU/kWh * 23.6 $/MMBTU) / 1000,000 BTU/MMBTU = 0.14 $/kWh 4.10.3 Composition of 1 kg coal, C-H-H2O-S-dirt. HHV is higher heating value, water is condensed. Heat of Reactions are from Reference 12. Ref 20, page 13-5 Illinois Bituminous Volatile B, 13388 BTU/lb is roughly: Component kg-mole MW kg HHV HHV * MJ/kg-mole kg-mole C 0.062 12 0.744 393 24.4 H 0.048 1 0.048 142 6.8 S 0.0006 32 0.019 301 Ref 20 0.2 H2O 0.0048 18 0.086 0 0.0 Bound O 0.0002 16 0.003 -197 -0.0 N 0.0001 14 0.001 Ash 0.099 0 Total 1.000 31.4 MJ/kg (13499 BTU/lb) Carbon Tax May have to be $1000/tonne

Ms/sir:
If goal is to arrest atmospheric CO2 at 2 times pre-industrial CO2 by 2080, then carbon tax must be at least 1.0 $/kg-C ($1000/tonne-Carbon). 1.0 $/kg-C tax doubles the price of electricity generated from fossil fuel. 1.0 $/kg-C tax does not give natural gas a price advantage over coal if natural gas costs more than $5/1000 ft^3. MHD-Coal may be competitive with natural gas regardless of the carbon tax. European auto-fuel taxes already exceed 1.0 $/kg-C ($2/gallon).
Preindustrial CO2 is 0.028% by volume. Starting at 0.001% CO2 in 1850, industrial CO2 has been compounding 3%/year. 1950 CO2 is 0.0300 % (300 ppmv) and 2000 CO2 is 0.037% (370 ppmv), using Mauna Loa data.
Continuing at 3% CO2 (atmospheric carbon) increase per year adds 0.028% to existing 0.028% preindustrial by 2038, giving 0.056% CO2. 0.056% minus (y 2000) 0.037% is 0.019%. The added 0.019% CO2 increase by volume represents 414 Tkg-C (414 trillion kilograms carbon). We are already 1/3 of the way toward CO2 doubling.
Applying 1.0 $/kg-C carbon tax to 414 Tkg-C, collects 3% World GDP between 2000 and 2080. This assumes 3% annual economic growth and CO2 doubling by 2080. If CO2 doubles by 2038, the 1.0 $/kg-C represents 15% World GDP.
Arresting CO2 at twice preindustrial by 2080 requires approximately 400 TWe-y (400,000 giga-watt-years electric) atomic generation between 2000 and 2080. After 2080 World annual atomic power requirement is 25 TWe. This assumes world population is constant after 2030. All non-nuclear scenarios double CO2 between 2038 and 2080, with exponential increase continuing thereafter.
The first 60 TWe-y will have to come from 1500 +/- 500 light-water reactors (LWRs). 60 TWe-y LWRs consume 10 MtUnatural, the estimated World uranium resource base. Plutonium from spent LWR fuel, military plutonium and military HEU is used to load 2500 +/- 1000 fast breeder reactors (FBRs) by 2035. By 2080 there will be 25,000 FBRs operating and power-plant CO2 emission will cease. World energy grows 2%/year until 2080, assuming world population stops increasing before 2030. Hydrogen and ammonia will be produced by electrolysis. Aluminum cars will burn ammonia. Propeller aircraft will burn liquid hydrogen. Phosphate fertilizer, detergent and concrete will be produced in arc furnaces.
1.0 $/kg-C carbon tax increases pulverized coal power cost 0.085 $/kWh more than it increases CCGT (Combined-Cycle gas turbine) power cost. This cost differential is the minimum required to make CCGT less expensive than power generated from pulverized coal. Natural gas is 3 to 6 times as expensive as coal on a BTU basis.
CCGT (Combined-Cycle Gas Turbine) needs 0.05 $/kWh profit to pay its $1500/kW plant cost within 5 years. Decontrolled natural-gas and FERC price-caps require a 5 yr payout on any new power plant that uses natural gas. A “8000 BTU” CCGT pays $5/MMBTU for natural gas. $5/MMBTU fuel adds an additional 0.04 $/kWh to the cost of electricity from the “8000 BTU” CCGT.
A new CCGT must charge 0.09 $/kWh, absent the carbon tax. An existing coal-fired power plant has to pay less than $1/MMBTU for coal, putting its total generation cost at less than 0.04 $/kWh, absent the carbon tax. One Dollar/kg Carbon tax adds 0.13 $/kWh to the CCGT and adds 0.21 $/kWh to the “9000 BTU” coal plant. Under these extreme conditions the new CCGT only has a 0.03 $/kWh advantage over an existing coal plant. Electricity price is more than doubled in the process. Under the same conditions, the simple cycle gas turbine charges roughly 0.08 $/kWh, absent the carbon tax. The simple cycle carbon tax is 0.16 $/kWh, giving 0.24 $/kWh total power cost. This is only 0.01 $/kWh less than the existing coal plant.
CCGT (Combined-Cycle Gas Turbine) is typically two airplane motors (Brayton Cycle) exhausting into a single steam boiler (Rankine Cycle). Airplane motors produce roughly 80% of total electric power. CCGT bottoming Rankine cycle produces roughly 20% of total electric power.
A CCGT is typically an “8000 BTU” plant, using 8000 BTU heat input per kWh electric output. Resulting thermal efficiency is 3412 BTU/kWh/8000 BTU/kWh (42.65 %), based on natural-gas HHV (higher heating value). CCGT heat rates of 7000 BTU/kWh are within reach, absent blade erosion and load following.
Absent cooling water, airplane motors are installed minus a bottoming Rankine cycle. Resulting simple Brayton Cycle heat rate is roughly 10,000 BTU/kWh, burning natural gas. Pulverized coal power heat rate is typically 9000 BTU/kWh, using a super-critical Rankine cycle and cooling water.
Coal can also be gasified, cleaned and fired in a CCGT. Overall heat rate is roughly 10,000 BTU/kWh, because gasification loses 1/3 of the energy. Valuable liquid byproducts improve gasifier economics. A coal-fired MHD Combined Cycle (Coal-MHDCC) may reach 6000 BTU/kWh, a 57% thermal efficiency. Coal-MHDCC carbon tax would be roughly the same as for CCGT.
n-octane, C8H18, is roughly 70 API gasoline at 700 kg/m^3 (5.84 lbs/US-gallon; US gallon = 231 in^3). C8H18 HHV is 5.46 GJt-HHV/kg-mole-C8H18. 1.0 $/kg-C carbon tax on gasoline translates into 2.0 $/US-gallon.

Existing Carbon Mass in Earth Atmosphere
Preindustrial atmospheric CO2 = 0.028% by volume

Post 2008 Carbon = 5.263 Ekg-Air * (12 MW-C/29 MW-Air)
* (560 ppmv - 394 ppmv)/1000,000 p) * (1.0 E+06 Tkg/1.0 Ekg)
= 361 Tkg-C = 361,000 Mt-C
= 361,000 Mt-C/(500 EJt/yr/0.0569 EJt-HHV/Mt-C) = 41 years
CO2 doubling = 2008 + 41 = 2049

Carbon buildup 1800 to 2001 at 2.25% historic annual increase:
ppmvc = 280 + Exp(0.0225 * (year - 1800))

Preindustrial, 275-284 ppm, 1550 - 1800 A.D.

Carbon Dioxide Information Analysis Center
http://cdiac.esd.ornl.gov
C.D. Kelling and T. P. Worf, Carbon Dioxide Research Group,
Scripps Institution of Oceanography, La Jolla CA 92093-0044
cdiac.esd.ornl.gov/ftp/maunaloa-co2/maunaloa.co2,
Mauna Loa Observatory, Hawaii
ppmvc = 280 + Exp(0.0225 * (year - 1800))
Mauna Loa Eq Mauna Loa Eq
1959 316.00 316
1960 316.91 317
1961 317.63 317 1981 339.95 339
1962 318.46 318 1982 341.09 340
1963 319.02 319 1983 342.75 341
1964 319.52 320 1984 344.44 343
1965 320.09 321 1985 345.86 344
1966 321.34 322 1986 347.14 346
1967 322.13 323 1987 348.99 347
1968 323.11 324 1988 351.44 349
1969 324.60 325 1989 351.44 350
1970 325.65 326 1990 354.19 352
1971 326.32 327 1991 355.62 354
1972 327.52 328 1992 356.36 355
1973 329.61 329 1993 357.10 357
1974 330.29 330 1994 358.86 259
1975 331.16 331 1995 360.90 360
1976 332.18 332 1996 362.78 362
1977 333.88 334 1997 363.84 364
1978 335.52 335 1998 366.58 366
1979 336.89 336 1999 368.28 368
1980 338.67 337 2000 369.39 370
2001 370.93 372
cdiac.esd.ornl.gov/ftp/trends/co2/siple2.013,
Friedli et al. (1986)
Siple Station Ice Core, Physics Institute,
University of Bern, CH-3012, Bern, SW
Year 1744 1764 1791 1816 1839 1843 1847
Bern 276.8 276.7 279.7 283.8 283.1 287.4 286.8
Curve 281 282 283 283 283

Year 1854 1869 1874 1878 1887 1899
Bern 288.2 289.3 289.5 290.3 292.3 295.8
Curve 285 285 286 287 289

Year 1903 1905 1909 1915 1921 1927 1935 1943 1953
Siple 294.8 296.9 299.2 300.5 301.6 305.5 306.6 307.9 312.7
Curve 290 291 292 293 295 397 301 305 311

Try ppmv = 280 + Exp(0.0225 * (Y - y-1800))
Justification for 1.0 $/kg-C Carbon Tax
Assume: World GDP grows 3%/year, US yr-2000 GDP = 10 T$ and
World GDP = 4 * US GDP:

World GDP = 10 T$ USA * 4 World/USA * Exp(0.03*(yr - 2000))

Assume World must pay 1.0 $/kg-C as it releases 414 Tkg-C
from 2000 to yearend 2080. Atmospheric CO2 increases from
370 ppm y-2000 to 560 ppm y-2080, adding an additional
414 Tkg-C.

Carbon Tax = 1.0 $/kg-C * 414 Tkg-C = 414 T$

414 T$ Carbon Tax/Cumulative GDP Between 2000 and 2080
= 414 T$/(Cumulative World GDP yr-2000 to yr-2080)
= 414 T$/(10 T$ * 4 * [Integral{Exp(0.03 * (2080 - 2000))}])
= 414/(10 * 4 * [(1/0.03) * (Exp(0.03 *(2080 - 2000)) - 1)])
= 0.03 * 414 / (10 * 4 * (Exp(0.03 * (2080 - 2000)) - 1))
= 0.03 * 414 / (10 * 4 * (11.02 - 1))
= 0.031 [3% Carbon tax] , where

[Integral{Exponential equation} limits are 2000 and 2080].

Notation and Conversions
atm = atmospheric pressure = 101325 N/m^2
BTU = British Thermal Unit, energy unit
Cal = calorie, energy unit (= 4.1868 Joules)
g = acceleration of gravity (= 9.80665 m/sec^2)
HHV = Higher Heating Value, combustion steam is condensed
J = Joule, energy unit
LHV = Lower Heating Value, combustion steam not condensed
kWh = electric kilowatt hour = 3600,000 J
MHD = Magneto-Hydrodynamic
MMBTU = Million BTU, MM is Roman Numeral 1000 times 1000
MMBTU = 1055.06 MJ
NM = Nautical Mile = 1852 m = 1 degree/60 at equator
scf = standard cubic natural gas at 60 F and 30″ Hg

t = metric ton = 1000 kg = long ton = tonne
k = kilo = 1.0E+03 (thousand)
M = mega = 1.0E+06 (million)
G = giga = 1.0E+09 (billion)
T = tera = 1.0E+12 (trillion)
E = exa = 1.0E+18 (ecto)
Z = zetta = 1.0E+21 (zillion)

1 BTU = ((lb-H2O-F) * (1000 g/kg/2.2046226 lb/kg)
* (C/1.8 F) * Cal/gm-H2O-C * 4.1868 J/Cal = 1055.056 J

Air Molecular Weight = 29 kg/kg-mole
H Molecular Weight = 1.00797 kg/kg-mole
C Molecular Weight = 12.01115 kg/kg-mole
S Molecular Weight = 32.064 kg/kg-mole

Natural Gas Carbon Tax
Natural gas is burned in an “8000 BTU” Combined Cycle CCGT.

Natural Gas standard cubic foot (scf) is calculated at
30″ Hg (101592 N/m^2) and 60 F (288.70556 K):

1 kg-mole natural gas at standard conditions
= 1 kg-mole * 288.70556 K * 8314.5 J/kg-mole-K/101592 N/m^2
= 23.6283 m^3 (834.43 scf)

Natural Gas volume fraction: 0.94 CH4, 0.03 C2H6, 0.01 CO2.
Natural Gas HHV = (0.98 kg CH4 * 16.04303 * 50010 kJ/kg
+ 0.03 kg C2H6 * 30.07012 * 47470 kJ/kg + 0.01 CO2 * 0)
* 1.0 MJ/kJ / (1055.056 MJ/MMBTU * 834.43 scf/kg-mole)
= 0.000942 MMBTU/scf

1 $/kg-C (Natural Gas Carbon Tax)
= 1 $/kg-C * 12.01115 kg-C/kg-mole-C
* (0.98 * 1 + 0.03 * 2 + 0.01 * 2) kg-mole-C/kg-mole-gas
/ (834.43 scf/kg-mole-gas * 0.000942 MMBTU/scf)
= 15.9 $/MMBTU-natural gas

“8000 BTU” Combined Cycle Gas Turbine (CCGT) carbon tax
= (8000 BTU/kWh * 15.9 $/MMBTU) / 1000,000 BTU/MMBTU
= 0.13 $/kWh

“10000 BTU” Simple Cycle Gas Turbine (SSGT) carbon tax
= (10000 BTU/kWh * 15.9 $/MMBTU) / 1000,000 BTU/MMBTU
= 0.16 $/kWh

Pulverized Coal Power Plant Carbon Tax (Rankine Cycle)
Pulverized coal is burned in an “9000 BTU” pulverized coal steam plant. Overall thermal efficiency is 38%, based on fuel HHV (higher heating value).
Coal is assumed to be 80% (C-H-S0.01). 0.01 sulfur in the formula give 2.4% sulfur coal. The remaining 20% coal mass is incombustible water, bound oxygen, bound nitrogen and ash. Coal thermal energy is based on 1 kg-mole Carbon:

Coal mass/kg-mole-C
= (12.0115 kg-C/kg-mole-C
+ 1.00797 kg-H/kg-mole-H * 1.0 kg-mole-H/kg-mole-C
+ 32.064 kg-S/kg-mole-S * 0.01 kg-mole-S/kg-mole-C)
/ 0.80 kg-fuel/kg-coal
= 16.675 kg-coal/kg-mole-C

Coal HHV/kg-mole-C = 393 MJ/kg-mole-C
+ 142 MJ-HHV/kg-mole-H * 1.0 kg-mole-H/kg-mole-C
+ 301 MJ/kg-mole-S * 0.01 kg-mole-S/kg-mole-C
= 538 MJ-HHV/kg-mole-C (= 13,800 BTU/lb-coal)

Coal HHV/kg-C
= 538 MJ-HHV/kg-mole-C/12.01115 kg-C/kg-mole-C
= 44.8 MJ/kg-C

1.0 $/kg-C (Coal Carbon Tax)
= (1 $/kg-C/44.8 MJ/kg-C) * 1055.56 MJ/MMBTU
= 23.6 $/MMBTU

“9000 BTU” Pulverized-Coal Power Plant Carbon Tax
= (9000 BTU/kWh * 23.6 $/MMBTU) / 1000,000 BTU/MMBTU
= 0.21 $/kWh

“6000 BTU” Coal-MHDCC Power Plant Carbon Tax
= (6000 BTU/kWh * 23.6 $/MMBTU) / 1000,000 BTU/MMBTU
= 0.14 $/kWh

4.10.3 Composition of 1 kg coal, C-H-H2O-S-dirt. HHV is higher
heating value, water is condensed. Heat of Reactions are
from Reference 12. Ref 20, page 13-5 Illinois Bituminous
Volatile B, 13388 BTU/lb is roughly:
Component kg-mole MW kg HHV HHV *
MJ/kg-mole kg-mole
C 0.062 12 0.744 393 24.4
H 0.048 1 0.048 142 6.8
S 0.0006 32 0.019 301 Ref 20 0.2
H2O 0.0048 18 0.086 0 0.0
Bound O 0.0002 16 0.003 -197 -0.0
N 0.0001 14 0.001
Ash 0.099 0
Total 1.000 31.4 MJ/kg (13499 BTU/lb)

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