Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

POWER PRODUCTION FROM RENEWABLE ENERGY AY 20 21-22 4th February 20 22 Prof. Silva Time: 1 ,5 hour s Instructions for the examination: 1) Clearly indicate your name on all the files 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 cancell ation 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 (1 7 points) CASE A Consider a binary cogenerative geothermal plant fed by a geothermal brine that provides a flow rate of 700 t/h at a temperature of 1 75°C. The geothermal plant works with a saturated iso -pentane Rankine cycle described by the thermodynamic points in the table and relative graph below. Point 2 corresponds to the outlet of the feed pump, Point 5 corresponds to the turbine outlet in real conditions and Point 6 is saturated vapor. Point T [°C] P [bar] h [kJ/kg] 1 35,0 1,286 221,40 2 35,0 8,214 222,17 3 109,0 8,719 409,6 4 109,0 8,719 675,99 5 65,7 1,286 615,6 6 35,0 1,286 559,8 The following data are given:  Geothermal water average heat capacity 4,4 kJ/kgK  Sub -cooling T at the economizer outlet 2°C  Pinch point at the evaporator 4°C  Organic -electric efficiency of the generator 95.5%  Auxiliary power consumption (including feed pump) 500 kW  Minimum re -injection temp erature 45 °C The thermal power is recovered by cooling down the geothermal fluid from the economizer outlet temperature to the minimum reinjection temperature. It is re quested to (i) draw the plant layout ( 1 point ) and calculate the following quantities: (ii) the mass flow rate of iso -pentane circulating in the ORC (2 point s), (iii) net electrical power output (3 points ), (iv) the net electric efficiency of the plant ( 1 point ), and (v) the first law efficiency ( 1 point ) (consider a constant value for the liquid heat capacity of iso -pentane). CASE B Consider the introduction of a regenerative heat exchanger. In this component the hot fluid discharged from the turbine is cooled down, heating up the pressurized liquid from Point 2 before entering the economizer , so that t he economizer heat duty is reduced to 260 00 kW . Assume that the thermodynamic cycle remains the same and the thermal power is obtained as in the previous case by cooling the geothermal fluid exiting the economizer down to the minimum reinjection temperature. Calculate (v i) the regenerator effectiveness (3 points ), (vi i) the thermal power generated (2 points ) and (vi ii) the first law efficiency of the system (1 point ). Finally determine ( ix) the specific cost (€/t) of the avoided CO 2 that would allow to pay back the plant upgrade (introduction of the regeneration) in one year ( 3 points ). Use the following assumptions: - 4000 equivalent hours of thermal power re covery; - cost of the additional regenerator = 1’ 300’000 € - selling price of the thermal energy = 2. 6 c€/kWh - reference CH 4–to-heat generation efficiency = 90% - reference CO 2 emissions for CH 4 = 200 g/kWh (LHV ) Exercise 2 (1 3 points) A three -bladed horizontal axis wind turbine is equipped with a variable speed and variable pitch regulation system. The turbine has a rotor diameter of 1 41 m, a rated wind speed of 1 2 m/s and is designed for an optimal λtip equal to 7.8. Knowing that the machine fluid -dynamic performance is equal to 8 0.8% (ratio between the real Cp and the Betz Cp), that the efficiency of the gearbox is equal to 97% and the mechanical -electric gen- erator efficiency is equal to 97.8 %, comput e (i) the rated electric power developed in the design condition at sea level, 1 atmosphere and 25°C (the air density in these conditions is equal to 1.225 kg/m3) (2 points). Calculate (ii) the rotational speed at design conditions (1 point). Assuming the validity of the Betz theorem, calculate (iii) the pitch angle at the blade tip knowing that the optimal incidence angle is equal to 8° (3 points). The electrical power developed by the turbine at the cut -in speed is equal to 1 85 kW. Assuming that the turbi ne has no lower limitations for rotational speed and considering the same mechanical and electrical efficiency of the design condition, determine (iv) the wind speed in cut -in conditions (2 points), (v) the machine rotational speed (1 point) and (vi) the v ariation of the pitch angle with respect to the design conditions ( 1 point ). After that, evaluate the performance of the machine when installed at 4 400 m altitude a.s.l. (above sea lev -el) with a reference ambient temperature of 5°C (pressure gradient with alt itude equal to 10 Pa/m), in par ticular calculate (vii) the corrected values respectively of the rated wind speed (2 points), and (viii) the cut -in wind speed (1 points). RESULTS Exercise 1 case A case B Q eva 53044,4 kW Q max rig 10812 kW m isopentano 195,42 kg/s T liquid out reg. 54,5 °C P el TV 11352 kW Q rig 9641,1 kW P el netta 10852 kW e reg 89,2% Cp isop. 2,53 kJ/kgK T geot. Out ECO 82,6 °C T @ outlet of evaporator 113,00 °C Eta el CV 13,7% Q eco 35641 kW Eta el net 9,8% T geot. out ECO 71,3 °C Q cog. geot. 32178 kW Eta CV 12 % Q cog. geot. 128711 MWh Eta sorg. Th 79,7 % Eta th. Net 28,9% Eta el net 9,8% Eta I princ. 38,7% Q max 111222 kW spec. Emissions boiler 222,2 g/kWh Q cog. geot. 22537 kW Avoided emissions case A 20032,6 t/y Q cog. geot. 90147 MWh Avoided Emiss. th 28602 t/y Eta th net 20,3% Delta emissions 8570 t/y Eta I 30,0% CF case A thermal € 2.343.818 €/y CF case B thermal € 3.346.489 €/y Delta CF thermal € 1.002.671 €/y CF from CO2 € 297.329 €/y Carbon tax CO2 34,69 €/t Exercise 2 AD 15615 m2 WID nom 16526,4 kW W Betz 9793,4 kW Wpale 7913 kW W el 7507 kW Cp 0,479 omega 1,328 rad/s 12,68 rpm u [m/s] vD [m/s] w [m/s] Teta [rad] Teta [°] Gamma [°] tip 93,60 8,00 93,94 0,0852629 4,9 -3,11 W rotor 197,1 kW W Betz 244,0 kW WID 411,7 kW v cut-in 3,50 m/s omega cut -in 3,70 rpm 0,388 rad/s omega cut -in 0,388 rad/s No pitch variation! P 56000 Pa ro' 0,735 kg/m3 v1' cut -in 4,15 m/s v1' nom 14,23 m/s