NAME KEY Allowed: Writing utensil, calculator and the provided formula sheet. Books, notes and collaboration (friends) are not allowed! Clearly indicate your answer and show your work. I do give partial credit. Answer as much as possible on the test sheets provided. 1. (6 points) Obstacles to future energy sources. Indicate which of the alphabetized items on the right side of the table below are considered obstacles to the use of Fossil fuels, Nuclear and Renewables in the future, by putting the alpha-designator in the appropriate left-column box. Each alpha-designator can reside in only ONE box and all must be designated in order to receive full credit. Fossil Fuel Energy a, b, g, j Nuclear Energy c, d, h, i, k Renewables e, f, l, m a. Environmental impact of mining b. Inefficient combustion c. Capital cost of construction d. Waste disposal/storage e. Non-dispatchable f. Investment g. Geographical distribution h. Water use i. Access to and enrichment of fuel j. Limit supply k. Public perception l. Location (the sunshine and wind) m. Lower density Problems 2-9 are worth 2 points each. Circle T or F as appropriate for problems 6-9. 2. How do fuel resources differ from fuel reserves? Be specific and clearly indicate in your answer which is larger. Resources are estimates of potential supply, where reserves are known deposits. Resources are believed to be as much as 5 times the known reserves. 3. The US consumes about what percentage of the global energy budget (within 5%)? 4. How much is a quad of energy in BTUs? 25% 10 15 BTUs 5. Assuming about 4 Trillion gallons of actual recovery, approximately what year is the worldwide production of petroleum expected to peak? Full credit if within ±5 years. 2025
6. T F Super critical power generation stations employ nuclear fuel to create high pressure steam to generate electricity. 7. T F Combined cycle systems include at least two electromechanical generators. 8. T F Combined cycle power generation is more efficient than either the Brayton cycle or the Rankine cycle power generation, given similar operation conditions. 9. T F Coal, natural gas, oil and nuclear fuel are used to create heat in order to generate electricity. The bad thing is that they all emit CO 2 into the atmosphere. 10. (15 points) The fictitious nation of NIBROC has an Average Life Expectancy of 72 years and has Gross Enrollment Rates of 70, 55 and 30 percent in its primary, secondary and tertiary schools respectively. Presuming the Adult Literacy Index is 55% and the Gross Domestic Product per Capita is $29,000, what is the Human Development Index of NIBROC? (Hint: HDI is the sum of three indices divided by three.) GDP Index = (log(29000) log(100)) (log(40000) log(100)) = 0.946 CGER = 1 3 (. 7 +.55 +.3) = 0.517 Education Index = 2 3 (0.55) + 1 (0.517) = 0.539 3 Life Expectancy Index = 72 25 85 25 = 0.783 HDI = 1 (GDPI + EI + LEI) = 0.756 3 11. (3 points) How does the HDI differ from the Gross Domestic Product? By including education and life expectancy, the HDI is intended to measure the prosperity of a population better than does the GDP, which measures the productivity of the entity (nation or other geographical or corporate grouping). Test 1, 2/7-8/18 ELEC 427, Energy Systems Engineering page 2 of 6
12. An ideal Rankine cycle in which pump work is assumed to be negligible and expansion is isentropic is depicted in the schematic below. Some possibly helpful equations follow: a. (5 points) Draw a representative closed cycle on the T-S diagram provided. Clearly label all vertices of the cycle with the number corresponding to that of the schematic. b. (15 points) Given that the maximum pressures are 5 MPa at the turbine entry and 101.325 kpa (atmospheric) in the condenser, and using the saturated water-pressure tables provided, calculate the thermal efficiency for this cycle. Using the saturated water-pressure table provided, look up and record the h (enthalpy) values for the points that land on the curve. Neglecting the work of the pump means that h 2 = h 1, and are at atmospheric pressure, while h 3 is at the stated high pressure. h 4 is not on the curve and will require the computation and application of a quality factor. Thus h 1 and h 2 = 419.06 kj/kg (101.325 kpa) and h 3 = 2794.2 kj/kg (5000 kpa) h 4 is not on the curve but s 3 is and s 4 = s 3 (isentropic, as shown by the vertical line connecting s 3 and s 4 on the phase diagram). This can be used to calculate the quality factor, x which is a gas to fluid ration at point 4 on the cycle. This ratio will be the same for entropy as for enthalpy for given values. Knowing x will in turn allow us to calculate h 4. x = s 4 s f s g s f Test 1, 2/7-8/18 ELEC 427, Energy Systems Engineering page 3 of 6
Back to the table: s 3 (saturated steam at 5000 kpa) = 5.9737 = s 4. The atmospheric gas and steam values of entropy are on the table as s f = 1.3069 and s g = 7.3545 kj/kg K. Now we can calculate x. 5.9737 1.3069 x = 7.3545 1.3069 = 0.772 Now use the same formula, but with enthalpy instead of entropy values. Since the ratios are the same, the same x factor applies, letting us solve for h 4. x = h 4 h f h g h f h 4 = x(h g h f ) + h f h 4 = 0.772(2675.6 419.06) + 419.06 = 2161.11 WAHOO! We can now computer the efficiency. Remember that pump work is negligible, making heat in h 3 h 1. η th = Work Out (pump negligible) Heat In = h 3 h 4 2794.2 2161.11 = h 3 h 1 2794.2 419.06 = 26.25% c. (10 points) Calculate the Carnot efficiency of this cycle. We need the intake and exhaust (low and high) temperatures of the cycle in Kelvin to calculate Carnot (theoretical) thermal efficiency. These are the temperatures at atmospheric pressure and at 5MPa. T L = 99.97 C = 372.97 K and T H = 263.94 C = 536.94 K Carnot Efficiency = η C = T H T L 536.94 372.97 = = 30.5% T H 536.94 Test 1, 2/7-8/18 ELEC 427, Energy Systems Engineering page 4 of 6
13. A Brayton cycle operates with isentropic compression and expansion, with a compression ratio of 6:1. Air enters the compressor at 101.325 kpa and 32ºC and exits the combustion chamber at 1527ºC. The combustion products are then expanded in and drive the turbine. d. (5 points) Draw the Temperature-Entropy Diagram for an ideal Brayton Cycle. e. (15 points) Calculate the thermal efficiency of the cycle. This time we use the Ideal Gas Properties of Air table. We also have inlet and exhaust temperatures to work with. At 305 K (32ºC + 273ºC), p r1 = 1.4686 and h 1 = 305.22 kj/kg Six times p r1 = p r2 =8.8116, which falls between the 500 and 510K values. An interpolation factor, f = p r2 p r500 = 8.8116 8.411 = 0.646 p r510 p r500 9.031 8.411 Adding 0.646 of the difference between the h values of 500 and 510K to the h value at 500K will give us h 2. h 2 = 503.02 + 0.646(513.32 503.02) = 509.67kj/kg At 1800 K (1527ºC + 273ºC), p r3 = 1310 and h 3 = 2003.3 kj/kg One-sixth of p r3 = p r4 = 218.33 kj/kg, which falls between the 210 and 220K values. Find an interpolation factor as we did for h 2 and apply it to find h4 = 1245.1 kj/kg. Work Out Work in η th = = (h 3 h 4 ) (h 2 h 1 ) Heat In h 3 h 2 (2003.3 1245.1) (509.67 305.22) = = 37.48% 2003.3 509.67 Test 1, 2/7-8/18 ELEC 427, Energy Systems Engineering page 5 of 6
f. (10 points) Calculate the Carnot efficiency of this cycle. Use the intake and exhaust (low and high) temperatures of the cycle in Kelvin to calculate Carnot (theoretical) thermal efficiency. Carnot Efficiency = η C = T H T L 1800 305 = = 83.06% T H 1800 Education Index = 2 3 (ALI) + 1 3 (CGER) GPD Index = (log(gdppc) log(100)) (log(40000) log(100)) CGER = 1 3 (GER Primary + GER Second + GER Tertiary) Life Expectancy Index = LE 25 85 25 Test 1, 2/7-8/18 ELEC 427, Energy Systems Engineering page 6 of 6