Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

POWER PRODUCTION FROM RENEWABLE ENERGY AY 2021-22 19 th July 2022 Prof. Silva Time: 1.5 hours Instructions for the examination: 1) Clearly indicate your name on all the sheets you will deliver. 2) The score refers to exercises done in a comprehensive manner with exact numerical results. Numerical results correct but not accompanied by explanations will not be taken into account. The final score can be normalized according to the average results. 3) Talking with colleagues and / or cheating will cause the cancellation of the exam. 4) All the needed data for the resolution of exercises lies on this paper. It is NOT ALLOWED to use material other than this (e.g. books, clipboard etc.). Exercise 1 (15 points) A geothermal source has the following characteristics at the outlet of the well: temperature 180°C, enthalpy 1050 kJ/kg. CASE A Consider a single flash direct steam cycle cogenerative plant, based on a cooling tower condenser with a condensation pressure of 0.075 bar. The flash pressure is 3.3 bar. Design the lay-out of the plant (i) with all the components (1 point), considering that the cogenerative heat exchanger is fed by the separated liquid from the flash chamber. Neglecting the presence of non-condensable gases and considering a reinjection temperature of 50°C, calculate (ii) the mass flow rate of the geothermal fluid that should be extracted from the well to obtain a net electric power output of 8 MW, knowing that the electric power consumption of all the auxiliary components of the steam cycle is 440 kW, and that the isentropic efficiency and the organic-electric efficiency of the turbogenerator are respectively equal to 80% and 93% (4 points). Then determine (iii) the vapor fraction at the outlet of the steam turbine (1 point) and (iv) the net electrical efficiency of the plant (2 points), assuming a minimum temperature of reinjection equal to 45°C (c p of the ge- othermal fluid in the liquid phase equal to 4.4 kJ/kgK). Calculate also (v ) the cogenerative thermal power output (1 point), and (vi) the first-law efficiency at nominal conditions (1 point). CASE B Consider an "all electric" plant scheme in which the liquid output from the flash chamber feeds an ORC binary cycle by means of a heat exchanger which cools it to the same exit temperature as CASE A (for the rest of the system take the same assumptions). Compute (vii) the total net electric power output of the plant, knowing that second law efficiency of the ORC cycle is 50% and the condensing temperature is the same as the direct steam cycle (5 points). Thermodynamic properties of water at saturation Liquid Vapor P sat [bar] T sat [°C] h liq.sat. [kJ/kg] s liq.sat. [kJ/kgK] v liq.sat. [m3/kg] h vap.sat [kJ/kg] s vap.sat. [kJ/kgK] v vap.sat. [m3/kg] 3.3 136 .8 575 .5 1.7059 0.00100 2729. 0 6.9589 0.553 8 0.075 40.3 168 .8 0.5763 0.00101 2574 .9 8.2523 19.2391 Exercise 2 for Energy Engineering students (15 points) A CSP plant based on parabolic trough collectors adopts molten salts as Heat Trasfer Fluid (Tmin 290°C - Tmax 550°C) and a steam cycle for the conversion of thermal power into electricity. The power plant charac- teristics are reported in the table below: Steam cycle net power 46 MW Piping thermal losses 1.5 MW Second law efficiency 52% Receiver specific thermal losses (per square meter of mirror aperture) 70 W/m 2 Ambient Temperature 25°C Collector Optical Efficiency 75% Solar Multiple 2 Design DNI 800 W/m 2 Aperture of solar collector 5.75 m Distance between parallel rows 2.5 x Aperture Loop lenght 800 m Concentration factor (Aperture colle ctor/ Dglass _envelope ) 65 Calculate (i) the area of the solar collectors (3 points), (ii) the size of the solar field (2 points) and (iii) the solar collector thermal efficiency (2 points). Compute (iv) the receiver glass envelope average temperature knowing the receiver specific thermal losses (see above table) and assuming the convective/radiative heat transfer coefficient with the environment equal to 15 W/m 2K (3 points). Present any simplifying hypothesis used in the calculations. Assuming an average ann ual DNI of 710 W/m 2, compute (v) the yearly electricity yield (4 points) and (vi) the average sun-to-electricity efficiency of the plant (1 point), assuming the average values reported in the follow- ing table: Average incidence angle 30° Solar field working hours 2800 IAM=IAM(θ) with θ in degrees 1 - 5·10 -4·θ Receiver/piping thermal losses as in the design case Auxiliaries average consumption 2 MW Power Block efficiency 90% of the design case Exercise 2 for Management and Mechanical Engineering students (15 points) Determine the annual generated electricity, the levelized cost of electricity (LCOE) and the cost of avoided CO 2 for the renewable power plants considered in the following. The cost of avoided CO 2 is the additional cost of electricity production to avoid the emission of one ton of CO 2 into the atmosphere, considering for a con- ventional reference plant a LCOE of 65 €/MWh and a specific emission of 380 gCO 2/kWh. In all cases the Capital Carrying Charge is equal to 12% (CCC is the share of investment costs related to an average year). • A biomass plant fed by 22 t/h of solid biomass (LHV dry basis = 18 MJ/kg) with 40% moisture content (∆h evaporation,H2O = 2440 kJ/kg). The boiler is coupled to a Rankine steam cycle with a gross electric effi- ciency of 30% and the boiler efficiency is 91%, while the auxiliary consumptions are 850 kW. The plant is running for 8000 equivalent hours per year and specific CO 2 emissions are 10% with respect to the reference plant (biomass exploitation is not exactly ‘carbon neutral’). Total plant cost is 40 million €, variable costs are 1.3 million € per year, and the biomass cost is 22 €/t. (6 points) • A wind farm consisting of 20 turbines with a diameter of 115 m, a nominal wind speed of 13 m/s, fluid- dynamic efficiency of 80% and mechanical-electrical efficiency 94.5% (ρ air = 1.225 kg/m 3). Consider an average annual production of 3000 equivalent hours, a total investment cost for the wind farm of 150 million € and an annual O&M cost of 2.6 million €. (4 points) • A geothermal plant based on a direct steam cycle, where the CO 2 content in the fluid is 0.1% by weight. The mass flow rate of the geothermal fluid is equal to 40 kg/s, and the enthalpy at the inlet and the outlet of the turbine are respectively 2750 kJ/kg and 2450 kJ/kg. The mechanical-electric conversion efficiency is 95%, the auxiliary consumptions are 1000 kW and the system is operated for 7300 equivalent hours a year. Total plant cost is 45 million € and variable costs are 2 million € per year (5 points). Results Exercise 1 CASE A Xv is 0,832 h is 2169,5 kJ/kg Dh is 559,5 kJ/kg Dh 447,6 kJ/kg h 2281,4 kJ/kg P el 8440 kW m vap. 20,28 kg/s Xv 0,2204 m geothermal 92,02 kg/s m liq 71,7 kg/s Xv 0,878 Q th cog 27405 kW hmin 189,4 kJ/kg Q th max 79191 kW Eta el net 10,10% Eta th 34,6% Eta I 44,7% CASE B T m, ln 91,7 °C Eta Lorentz 14,1% Eta binary cycle 7,04% P el net ORC 1929,5 kW P el net tot 9929 kW Exercise 2 for Energy Engineering students Temp. ML 684,95 K eta lorentz 56,47% eta first law 29,36% power PB 156,65 MW power PB + storage 313,30 MW solar field power 314,80 MW Solar collectors surface 593961 m^2 Linear lenght of solar collectors 103298 m Number of loops 129,1 Number of loops (integer) 129,0 Solar field width 2582 m Solar field size 2065400 m^2 Thermal losses 41,58 MW Q sun 475,17 MW Eta th 66,25% Eta th (other definition) 88,3% Specific thermal losses 1448,3 W/m2 T glass 121,6 °C IAM ( θ) 98,50% cos ( T) 86,60% K ( T) = cos ( T) * IAM ( T) 85,30% Eta optical 63,98% annual DNI 1988,0 kWh/m^2 Annual radiation over tube 755,44 GWh Net annual Qth solar field 634,83 GWh Annual electricity 162,17 GWh Annual Eta el 13,73% Exercise 2 for Management and Mechanical Engineering students Case A (biomass) Case B (wind) biomass flow rate 6,111 kg/s eta 47,4 % LHV as received 9824 kJ/kg area 10387 m2 power LHV 60036 kW power 6262 kW Gross power 16390 kW tot power 125236 kW Net power 15540 kW Energy 375708 MWh Energy 124318 MWh annual total cost 20600000 € annual total cost 10,0 M€ LCOE 54,8 €/MWh LCOE 80,2 €/MWh cost of avoided CO2 -26,8 €/tCO2 cost of avoided CO2 44,5 €/tCO2 Case C (geothermal) delta H 300 kJ/kg power 11400 kW net power 10400 kW specific cost 4327 €/kW Energy 75920 MWh CO2 14 kg/MWh annual total cost 7,4 M€ LCOE 97,5 �/MWh cost of avoided CO2 88,7 �/tCO2