Problem Set #3 Solutions 1. Combined-Cycle Power Plant a. Cogeneration is the combined production of power and heat. In cogeneration facilities, the waste heat from the engine is put into use instead of being dumped into the environment. By providing an additional service with practically the same amount of consumed energy, cogeneration facilities increase their first law efficiency (η I = Energy useful / Energy in). Cogen s η I = Electricity + Additional heat service / Energy in Non-cogen s η I = Electricity / Energy in => Cogen s (η I) > Non-cogen s (η I) b. From 20 C to 100 C, the specific heat of water is 4.184 J/g- C, so heating the 1.00 kg of water to the boiling point takes: 1 kg x 4.184 kj/kg- C x 80 C = 0.3347 MJ The heat of vaporization for water is 2258 kj/kg, so the phase change from water to vapor takes 1 kg x 2258 kj/kg = 2.258 MJ The specific heat of steam at 1 bar is 2.027 kj/kg- C, so heating the final 20 degrees takes 1 kg x 2.027 kj/kg- C x 20 C = 0.0405 MJ The total energy required to heat one kilogram of water is 2.63 MJ Based on the energy required to heat one pound, we can calculate the total power output represented by the steam production: 84.0ton hr 1000kg ton 1hr 2.63MJ = 61.37MW 3600sec kg Total useful energy produced = Electricity + Steam = 21.35 MW + 5.0 MW + 61.37 MW = 87.72 MW Energy from the fuel (natural gas) input = Wout/ηI = 87.72/0.76 = 115.42 MW 115.42 MJ/s / (39MJ/m 3 ) = 2.96 m 3 /s 3.0 m 3 /s c. Distance from central plant to campus (VLSB) is roughly 1.1 miles so say ~5800 ft. Temperature difference of steam to air is 120 C (248 F) minus the 40 F weather is 208 F. Interpolate between 200 F and 225 F for 2 pipe on the table. So heat loss rate in y btu/(hr.ft) is y 346 = 208 200 410 346 225 200 Heat loss rate is 366 btu/(hr.ft) Power loss in the pipe: 5800 ft * 366 btu/(hr.ft) * 1 hr/3600s * 1055 J/ btu * 1 MJ/1x10^6 J = 1
0.622 MW or 0.62 MW 0.622 MW / 61.37 MW is 1.0% (1.01%) loss. Note: much more heat is lost once it is delivered to buildings and there are more bends and turns in the pipes, which create inefficiencies and losses. d. 2.00 x10 5 MWh/yr = (21.35 MW + 5.0 MW) x 8760 hr/yr x cf cf = 0.866 or 87% 2. Thermodynamics of Energy Systems a. Brayton: 2
Combined Rankine and Brayton: Compressor: Gases be compressed to high pressure; increases the temperature; requires work; no heat loss. (Isentropic) Combustor: Increases the temperature at a constant pressure; constant-pressure heat addition; no work. (isobaric) Turbine: Decreases in pressure and temperature; produces work; no heat loss. (isentropic) Exhaust/Heat Exchanger: Decrease in temperature at a constant pressure; heat is lost to environment or used for other service; no work is applied or extracted. (isobaric) Pump: Pumps water to high pressure; increases the temperature; requires work; no heat loss. (isentropic) Heat exchanger: Increases the temperature at a constant pressure; heat addition; no work. (isobaric) Turbine: Decreases in pressure and temperature; produces work; no heat loss. (isentropic) Condenser: Vapor turns into liquid; temperature drops at a constant pressure; no work required, heat is lost. (isobaric) b. 3
η C = 1 T C = 1 T 1 (273 + 32.0)K = 1 T H T 3 (273 + 873)K = 1 305K = 73. 4% 1146K Note that temperatures should be converted from C to Kelvin c. Power input to the older generators: 11080 106 btu hour η I = P out P in = 1290MW e 3247MW th = 39.73% 39.7% 1055J btu 1hr 3600sec = 3247 MW th d. η II = η I = 39.73% = 54.12% 54.1% η c 73.4% e. η overall = η Brayton + (1 η Brayton ) η Rankine = 39.73% + (1 39.73%) 28.0% = 56.60% 56.6% f. 2330MW e 8760hours 64% = 13.06 TWh 13 TWh year g. Energy balance from the 1 st Law, waste heat rate is Q out = Q in W out = 3247MW th 1290MW e = 1957MW th Recall that Q = mc T, where Q is the input of waste heat into water. Because Q is given as a rate (energy per time), the mass m should also be a rate (mass per time). Thus: Note that c is the specific heat, which for water is 4.184 J/(g C). The power input for 2 0 C increase in water temperature per 1m 3 /s of water flow: 1m 3 s 1 103 kg m 3 4.184kJ kg 0 C 2 0 C = 8.368MW The 1957 MWth of waste heat would require a water flow rate: 1957MW th 8.368MW th m 3 /sec = 234 m 3 /sec 230 m 3 /s 3. History of the U.S. Electric Power Sector a) It became was clear that electric utilities operated best as a natural monopoly. Among other things, this prevented infrastructural redundancies that would have increased overall costs of operation. In the early 1900s generation companies began buying transmission and distribution companies leading to vertical integration. With increasing consolidation, they became predominant giant centralized electric power corporations: GE, Westinghouse, the Consolidated Gas Company. At the same time there were huge improvements in generation technologies (Power Loss, p. 57). This was enabled by movement along the learning curve and reduced the cost of 4
operation to utility managers. Also demand was encouraged by both promotional campaigns (Gold Medallion Homes) and improved and expanded end-uses. The companies increased load factor by expanding beyond residential and commercial users to industrial users (such as steel and ice making companies). Electricity soon became a necessity. Together these factors led to electricity providers being classed them with other utility providers - such as railroad companies - as public necessities and public demons in that if a monopoly existed, this would lead to uncontrolled price gouging of the public, especially since technological advances in generator units made it increasingly possible to supply more demand at less cost. [eg Chief investigator with New York Government, Charles Hughes, found in 1907 that New York Gas and Electric Light owned by Consolidated Gas was producing at 3.7c and selling at 15 c.] As such, a utility consensus was arrived at in which utility companies were allowed to operate as natural monopolies but where some regulatory body could control prices. This is the time around which a number of states established utility commissions and passed legislation for regulation. Each state established a utility commission that governed rate setting, allowing a reasonable rate of return on investment to utilities and ensuring fair rates for the consumer (in California the CPUC). Everyone was made better off by the system that developed. Customers enjoyed improved standard of living at diminishing costs, utilities made money, governments promoted progress. This lasted for more than two decades after World War 11 into the 1970s. b) Technological stasis approached thermodynamic limits to improvements; metallurgical limits to how hot boilers could get (less efficient plants were more reliable); learning-by-doing was replaced with doing-by-doing. Energy crisis utilities had a difficult time getting access to enough fuel and equipment to meet demand; oil shocks of the 70s (in 1970, 14% of US electricity came from oil); increased fuel prices lead to an increase in electricity prices The environmental movement increased awareness of the environmental impact of energy extraction and use (smog, thermal pollution, etc.); compliance with new standards (Clean Air Act, Clean Water Act, etc.) increased costs; anti-nuclear sentiment and litigation These factors meant that there was undermined faith in consuming as much power as possible, and that the cost of producing electricity was unlikely to continue to decline as it had through the 1960s. This contributed to the passage of PURPA in 1978. 4. Estimating US Petroleum Reserves a. Since 1970 was the peak year, this would mean that 90 Gbbl was half of US ultimate production. Therefore, ultimate production would equal 2 x 90 Gbbl or 180 Gbbl => 200 Gbbl (sf). b. BP s Statistical Review of World Energy 2014 : cumulative production through 2013 5
Cost per barrel Energy and Society (ER100/PP184/ER200/PP284) Fall 2014 BP data indicates that production for 1971-2013 is 141 Gbbl for the US. This means total cumulative production equals 141 + 90 = 231 Gbbl => 230 Gbbl (sf). This is larger than the total extractable that we would expect from a symmetrical curve (as in part a). c. Find the area under the curve. Hubbert Curve with Oil Sands 1940 1960 1980 2000 2020 2040 2060 Years Regular Hubbert's Curve Hubbert Curve including Oil Sands d. two features for this graph: the increase in peak production, and the shift of peak production time into the future. 600 Prediction of cost per barrel per year based on Hubbert's Curve 500 400 300 200 100 0 1940 1960 1980 2000 2020 2040 2060 2080 Years e. The declining cost is likely to arise from economies of scale, while the rising cost is expected when the oil reserves are depleting and becoming more costly to extract. 6
5. Economic Analysis a. 70 mi/day x 4 day/wk x 48 wk/yr = 13,440 mi/yr CRF (6 yr, 3%) = 0.1846 Vehicle Option Toyota Camry Toyota Prius C Nissan Leaf S Purchase price $22,235 $19,080 $29,010 Fuel cost $4.22/gal * 1 gal/30 miles * 13440 miles = $1891/year $4.22/gal * 1 gal/50 miles * 13440 miles = $1134/year $0.15/kWh *34 kwh/ 100 miles * 13440 miles = $685/year Other costs $1,000/yr + $65/yr + $375/yr $1,000/yr + $65/yr + $500/yr $1,000/yr + $65/yr + $300/yr Total annual $3331/yr $2699/yr $2050/yr costs NPV of annual costs (annual costs / CRF) $3331/yr / 0.1846 = $18044 $2699/yr / 0.1846 = $14,621 PV of Resale value $6,000 / $1.03^6 = $5025 $5,000 / $1.03^6 = $4187 Total NPV of -$22235 - $18044 + $5025 -$19080 - $14621 + $4187 car ownership = -$35,254-35,000 = -$29,514-30,000 The Prius C has the lowest total cost of ownership for a 6 year period. $2050/yr / 0.1846 = $11,105 $8,000 / $1.03^6 $6700 -$29010 - $11105 + $6700 = -$33415-33,000 b. The Nissan Leaf has a $7500 tax credit. The after-subsidy NPV is -$33,415+$7500 = -$25,915-26,000. This would make it a more attractive option than the Prius C, assuming you pay more than $7500 in taxes, though the credits can be rolled over between years to capture all of the value. The federal government supports this tax credit because they know that the higher upfront cost of an electric vehicle is a deterrent for car buyers. By offering this incentive, they hope to jumpstart the electric vehicle industry, which is seen as a key industry for economic growth in the U.S. 7
6. The Environmental Impacts of the Oil Transition a. Equation used: Oil Production (t) = ( peak production) e -0.5 æ ç ç ç è t - peak year 24 yr 2 ö ø b. c. 8
Note that Ethanol today has a value of about 88 gco2/mj, and this is equivalent to 24 gc/mj. gc/mj Proportion in Alternate scenario Proportion in BAU scenario Tar sands 32 0.4 0 GTL synfuels 29 0.05 0 Average grams Carbon per Megajoule Oil shale 52 0.25 0 34.45 Alternate "Ethanol today" 24 0.3 0 25 Bau Conventional oil 25 0 1 The gap in curve B in 2025 was 9.764 x 10^9 bbl 9.8 x 10^9 bbl of oil. (9.764 x 10^9 bbl) * (5.6 x 10^9 J/ 1bbl) * ([34.45 25] gc/ 1 x 10^6 J) * (1 ton C/ 1 x 10^6 gc) * (1Gt C/ 1x 10^9 ton C) = 0.5167 Gt C 0.52 Gt of carbon emissions. 9
According to WRI - CAIT, the world s transportation carbon emissions in 2011 were 5.8 GtCO2 or 1.6 GtC, which is about three times larger than the difference between our scenarios. In another words, the effect of these more carbon intensive unconventional fuels are equivalent of carbon emissions from transportation increase from 1.6 GtC to 2.1 GtC or a roughly 30% increase, so it is quite significant. d. gc/mj Proportion in Alternate scenario Proportion in BAU scenario Tar sands 32 0.4 0 Efficiency 0 0.05 0 Average grams Carbon per Megajoule Extra biofuels 30 0.25 0 27.5 Alternate "Ethanol today" 24 0.3 0 25 BAU Conventional oil 25 0 1 (9.764 x 10^9 bbl) * (5.6 x 10^9 J/ 1bbl) * ([27.5 25] gc/ 1 x 10^6 J) * (1 ton C/ 1 x 10^6 gc) * (1Gt C/ 1x 10^9 ton C) = 0.1367 Gt C 0.14 Gt of carbon emissions. The combination of efficiency improvements and replacement of oil shale with biofuels achieve an important reduction in the emissions associated to the gap created by the decrease production and increased demand in 2025. e. Hybrid 10,000 miles/year * 1 gallon/70 miles * 1 bbl/42 gal = 3.40 bbl /year per hybrid vehicle 10,000 miles/year * 1 gallon/35 miles * 1 bbl/42 gal = 6.80 bbl /year per standard vehicle So each hybrid leads to savings of 3.40 barrels per year. 0.15 * 9.764 x 10^9 bbl / (3.40 bbl gasoline saved / hybrid) = 4.3 x 10^8 hybrids (or 430 million hybrid cars) Which is about 40% of the current fleet of vehicles. Even when the fleet of vehicles is likely to increase by 2025, it seems slightly too optimistic to expect that ~40% of vehicles worldwide will be as efficient as 70 miles per gallon by 2025. 10