a) Why is cogeneration 1 more efficient than conventional power generation methods? [3 points]

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1 To facilitate returning graded problems more efficiently, please write on your submitted problem sets: Name (as on bcourse), Student ID, Course # (ER100 etc), Discussion Section ( ) Combined-Cycle Power Plant 1. UC Berkeley s campus features a combined heat and power (CHP) energy system. This power (electricity) station is a combined-cycle: a MW natural gas turbine (Brayton cycle) and a 5.0 MW steampowered, bottoming-cycle generator (Rankine cycle). Waste heat from this system feeds into a steam loop that serves to heat central campus and several peripheral buildings; at peak output, the plant generates 84.0 tons of steam each hour. It has been claimed that the overall efficiency of this facility is 76%. [16 points total] a) Why is cogeneration 1 more efficient than conventional power generation methods? [3 points] b) How much energy does it take to raise 1.00 kg of water from 20.0 C to C? Assume the specific heat of water is kj/kg. 0 C, and the specific heat of steam at 1 bar is kj/kg. 0 C (Don t forget the heat of vaporization of water: 2258 kj/kg). If the steam produced by the power station has been heated over this range of temperatures, at what rate does this CHP system consume fuel (assume the energy content of natural gas is 39MJ/m 3 )? Give your answer in units of m 3 /s with two significant digits. [5 points] c) Assume the steam produced at UC Berkeley s physical plant (2000 Carleton St) is then transported via 2 inch uninsulated pipe to Berkeley campus. Assume all the steam is transported to a central location on Berkeley campus such as Valley Life Sciences Building, which is about 1.1 mile away, and it s a cold winter morning in Berkeley (40 F). According to the table below, how much power is lost in the process (answer in MW)? What percentage loss is this in comparison to the power of the original steam produced? Note: the h in btu/h per ft is hour. [4 points] 1 Another term for CHP Page 1 of 6

2 d) In 2013, campus used roughly 200. GWh of electricity. What would the capacity factor of the CHP have to be in order to generate that much electricity? [4 points] Thermodynamics of Energy Systems 2. Dynegy s Moss Landing Power Plant (Monterey), a natural gas fired plant, is California s largest electric generator with a total installed capacity of approximately 2,330 MWe. Out of this, two newly built generators (1,040 MWe total) are combined cycle (Brayton and Rankine cycles), whereas the older two generators (1,290 MWe total) run on gas turbines only (the Brayton cycle). When operating at full capacity, the rate of energy added to both older generators together during the combustion of fuel (not taking into account cycle efficiency) is 11,080 million Btu/hr. The power plant s capacity factor (percentage of plant s capacity used over time) is about 64%. [40 points total] a) Draw the schematic of the major components (not the thermal cycle diagrams) showing the ideal Brayton Cycle and the ideal Combined Cycle, respectively. Label all components, the associated work input/output or the heat input/output, the temperature of the working fluid before/after each component. In thermodynamic terms, explain briefly the function of each component, such as the changes in pressure, temperature, work, and heat. [10 points] b) Calculate the Carnot efficiency of a system operating at the following temperatures. [4 points] T1 = temp at exit of the exhaust heat exchanger and inlet of the compressor = 32.0ºC T2 = temp at exit of the compressor and inlet of the combustor = 360.0ºC T3 = temp at the exit of the combustor and the inlet of the turbine = 873ºC T4 = temp at the exit of the turbine and the inlet of the exhaust heat exchanger = 395.0ºC c) Calculate the 1st law efficiency of the older generators that use the Brayton cycle. [4 points] d) What is the second law efficiency of the generators that use the Brayton cycle? (Use the Carnot efficiency calculated in part b).) [4 points] e) Consider the combined-cycle generators. Assume that the performance of the gas turbines in these generators is the same as the older generators which use only the Brayton cycle. If the thermal efficiency for the steam turbine system (the Rankine cycle) is 28.0%, calculate the overall efficiency for the combined cycle. [4 points] f) What is the total power (electricity) output from the Moss Landing Power Plant in a typical year (in TWh)? [4 points] g) For the 1,290 MWe Brayton cycle described above, estimate the volumetric flow rate (in m 3 /sec) of cooling water for 2.0 ºC of temperature rise while the power plant is at full power. Assume that water has a specific heat capacity of kj/(kg ºC) and a density of 1.0 g/cm 3 and that there is no external heat lost from the system comprising the power plant and the water. [10 points] Page 2 of 6

3 History of the U.S. Electric Power Sector 3. Drawing on Richard Hirsh s Power Loss and the content presented in lecture, respond to the following prompts. [20 points total] a) What were the political, technological, and economic factors that played into the emergence of the utility consensus in the first decades of the 20 th century and that persisted until the 1970s? [10 points] b) Explain the major trends and significant events that contributed to the erosion of the utility consensus in the 1970s and presaged the passage of PURPA in [10 points] Estimating US Petroleum Reserves 4. In 1956 M. K. Hubbert of Shell oil predicted that US oil production would peak around 1970 and that US oil production would follow a Gaussian or normal curve over time. [13 points total ER 100/PP 184; 17 total points ER 200/PP 284] a) BP cites 1970 as the year of peak US oil production (BP, Statistical Review of World Energy 2014 ) 2. Combining BP data with USGS data, we find that cumulative US oil production until 1970 was approximately 90 gigabarrels (Gbbl). If Hubbert was correct, what would we expect to be the total amount of oil recoverable in the US over all time? [2 points] b) Access the production data in BP s Statistical Review of World Energy Given our data from part a) (that 90 Gbbl was produced before the end of 1970), what is the cumulative production for the US through 2013? How does this compare with your results from part a)? [4 points] Parts c, d, and e are on the next page! 2 You can access the report here: 3 A spreadsheet can be found here: /BP-Statistical_Review_of_world_energy_2014_workbook.xlsx Page 3 of 6

4 c) In words, describe how to find the total stock (i.e., the size of the entire resource) using this graph. [3 points] d) How would a Hubbert s Curve for conventional oil change if we were to add oil sands to the graph? Redraw the curve to include oil sands. [4 points] e) [ER 200/PP 284 only] Draw a cost curve based on Hubbert s Curve to describe the cost of oil extraction. Put time (year) on the x-axis and cost/barrel on the y-axis. [4 points] Page 4 of 6

5 Economic Analysis 5. [ER 100/PP 184 Students Only] Elon Musk s mission is to make the electric vehicle an object of desire and he has had some initial success as sales for both Tesla vehicles as well as electric vehicles in general are growing rapidly. In this question, you ll compare the costs of owning a standard non-hybrid vehicle versus a hybrid vehicle versus an electric vehicle with the information given below. Neglect the effect of inflation. [20 points total] Vehicle Option Toyota Camry Toyota Prius C Nissan Leaf S Purchase price $22,235 $19,080 $29,010 Fuel consumption 30. mi/gal 50. mi/gal 34. kwh/100 miles Fuel cost $4.22/gal $4.22/gal $0.15/kWh Insurance $1000./year $1000./year $1000./year License and fees $65/yr $65/yr $65/yr Maintenance/repairs $375/yr $500./yr $300./yr Resale value (in six years) $6,000. $5,000. $8,000. EV range per charge n/a n/a 100. miles (according to Nissan) Interest rate 3.00% 3.00% 3.00% a) Consider someone who plans to use their vehicle to commute to work. They live 35 miles from work. Which car has the most favorable net present value (cost) if this person will be commuting 4 days per week, 48 weeks per year, for six years? Assume that the purchased vehicle will be sold at the end of six years. Show the calculations for all three cars. [12 points] b) Search online to see if there are any US federal tax credits for the Nissan Leaf and how much it is worth. Write a short note (along with a simple calculation) on how this could change the purchase decision (maximum 2 sentences)? Why does the government offer tax credits for electric vehicles? [8 points] Page 5 of 6

6 The Environmental Impacts of the Oil Transition 6. [For ER 200/PP 284 Students Only] We will now look quantitatively at the CO 2 implications of a transition to oil substitutes. We will use stylized equations to estimate roughly the impacts of this transition. (Hint: You should build models that are easily reconfigurable for different input values, as they are in, for example, Excel.) [27 points] a) Generate and plot two curves projecting future conventional oil production (Curves A and B). Curve A assumes less oil. It follows predictions of K. Deffeyes of Princeton, who states that the peak in conventional production already passed in late 2005 or early Curve B assumes the peak is postponed until Use a Gaussian curve in both cases, and plot over the years 2000 to [8 points] Curve A: Peak year = 2005, Maximum prod = 30. Gbbl, = 25 years Curve B: Peak year = 2015, Maximum prod = 33. Gbbl, = 25 years b) Assume in both cases that demand for liquid hydrocarbons increases at 2.0% per year from the level seen in the year of peak oil production. Plot the resulting gap between conventional oil production and demand for liquid hydrocarbons for both cases (A and B) until [5 points] c) Let s work with case B. Assume that in 2025 the gap in case B is filled with 30.% biofuels as characterized in Farrell et al (2006); 4 and 40.% tar sands, 5.0% gas-to-liquids synfuels, and 25.% oil shale as characterized in Farrell and Brandt (2006) fig 1. 5 How much larger (in gigatons) are carbon emissions in this case than in a case where conventional oil production can meet all demand (in gigatonnes C)? Assume each bbl of crude or crude substitute has an energy content of 5.6 x10 9 J (Harte, 1988), and the average carbon emission factor for each fuel can be found in the reference. Comment on the magnitude of these emissions in comparison to global anthropogenic carbon emissions (See WRI CAIT for current statistics ). [6 points] d) Now let s be more optimistic. Assume that instead of GTL synfuels, 5% of the gap in the year 2025 is met by increasing light-duty vehicle efficiency. Also, assume that instead of oil shale, biofuels with a carbon intensity of 30 gc/mj are used (keep the other biofuels too). (Simply plug new carbon intensities into your calculation from above!) What are the carbon implications in this case? [3 points] e) Calculate the number of hybrids that would be required to fill 15% of the gap in Assume hybrid cars with real-world mileage of 70. miles per gallon (hopefully an attainable goal for 2025) replace cars that get 35 miles per gallon. Assume all cars travel 10,000. miles per year. Although only 46% of the oil can be refined to gasoline, assume demand for 42 gallons of gasoline is equivalent to 1.00 barrel of oil in this question. How does this figure compare to the current number of global automobiles? (A recent report by Ward s Auto 6 estimated a global vehicle population in 2010 of about one billion.) And is this optimistic case too optimistic? [5 points] 4 Farrell et al. 2006, Ethanol Can Contribute to Energy and Environmental Goals. Science 311(5760). Use ethanol today number from Figure 1. 5 Farrell and Brandt. 2006, Risks of the oil transition. Environmental Research Letters Use the average of high and low values of carbon intensity for each fuel from this paper fig. 1. E.g. if the range of carbon intensities for a fuel run from 30 to 70 g C/MJ, use a value of 50 g/mj to compute emissions from that fuel. 6 Page 6 of 6