Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

POW ER PRODUCTION FROM RENEW ABLE ENERGY AY 2020-21 17 th June 2021 Prof. Silva Time: 1,5 hours 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 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 (17 points) CASE A Consider a binary cogenerative geothermal plant fed by a geothermal brine that provides a flow rate of 800 t/h at a temperature of 175°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 is 60,0 1,286 604,9 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 3°C  Pinch point at the evaporator 4°C  Organic-electric efficiency of the generator 95.5%  Auxiliary power consumption (including feed pump) 585 kW  Minimum re-injection temperature 50°C The thermal power is recovered by cooling down the geothermal fluid from the economizer outlet temperature to the minimum reinjection temperature. It is requested 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 points), (iii) net electrical efficiency of the plant (2 points), (iv) first law efficiency (1 point) and (v) second law efficiency (2 points) (consider a constant value for the liquid heat ca- pacity 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 the economizer heat duty is reduced to 28500 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 (vi) the regenerator effectiveness (3 points), (vii) the thermal power generated (2 points) and (viii) 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 recovery; - cost of the additional regenerator = 1’350’000 € - selling price of the thermal energy = 2.2 c€/kWh - reference CH 4–to-heat generation efficiency = 90% - reference CO 2 emissions for CH 4 = 200 g/kWh (LHV) Exercise 2 for Management and Mechanical Engineering students (13 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 60 €/MWh and a specific emission of 400 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 20 t/h of solid biomass (LHV dry basis = 18 MJ/kg) with 40% moisture content (∆h evaporation,H2O = 2440 kJ/kg). The thermal efficiency of the grate boiler is 90% and it is coupled to a Rankine steam cycle with a gross electric efficiency of 30%, while the auxiliary consumptions are 800 kW. The plant is running for 8000 equivalent hours per year and specific CO 2 emissions are 5% with respect to the reference plant (biomass exploitation is not exactly ‘carbon neutral’). Total plant cost is 40 million €, variable costs are 1 million € per year, and the biomass cost is 20 €/t. (5 points) • A wind farm consisting of 20 turbines with a diameter of 110 m, a nominal wind speed of 11.5 m/s, fluid- dynamic efficiency of 79% 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 110 million € and an annual O&M cost of 1.9 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 44 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 1100 kW and the system is operated for 7500 equivalent hours a year. Total plant cost is 45 million € and variable costs are 2 million € per year (4 points). Exercise 2 for Energy Engineering students (13 points) You have to design a stand-alone system based on a horizontal axis wind turbine to power an isolated user, characterized by the consumptions reported in the table below. The location is described by the wind availa- bility shown in the table, divided according to the seasons over the year: Winter (Dec-Feb) Middle season (Mar-May and Sep-Nov) Summer (Jun-Ago) Daily average wind speed [m/s] 7.5 11 6.5 Daily average wind availability [h/day] 8 9 7 Daily consumption [kWh/day] 15 20 25 In order to guarantee the electricity to the user even in the worst conditions, an electrochemical storage system is used, which can satisfy the consumption for an entire week even in the complete absence of wind, while the energy amount is supposed to be produced by the turbine during a single day. Moreover the wind turbine is oversized (security factor equal to 35%) with respect to the sizing value at worst conditions. It is required to determine (i) the power output of the turbine in the sizing conditions (3 points), and (ii) the power output at the nominal wind speed of 9 m/s (4 points) considering the following data: • Coefficient of performance of the wind turbine: 44% (constant between 4 m/s and 9 m/s) • Organic-electric efficiency of the generator: 94% • Air density: 1.225 kg/m 3 • Electrochemical storage efficiency (round-trip efficiency): 80% Assuming that the production of the wind turbine and the construction of the power plant require 4400 MJ of electricity for each installed kW, calculate (iii) the energy pay-back time of the plant, with respect to the actual energy consumption of the user (3 points). Finally, in the hypothesis of a future connection to the national grid, calculate again (iv) the energy pay-back time (2 points) and (v) the plant equivalent hours (1 point). Exercise 1 Results Results case A case B Cp isop. 2,53 kJ/kgK Q max rig 12242 kW T @ outlet of evaporator 113,00 °C T liquid out reg. 55,2 °C Q eva 60622,2 kW Q rig 11295,5 kW m isopentano 221,27 kg/s 2 punti e reg 92,3% Q eco 39796 kW T geot. Out ECO 83,9 °C T geot. out ECO 72,3 °C Eta el CV 13,8% P el TV 12853 kW Eta el net 10,0% P el netta 12268 kW Q cog. geot. 33100 kW Eta CV 12,2 % Q cog. geot. 132400 MW h Eta sorg. Th 82,2 % Eta th. Net 27,1% Eta el net 10,0% 2 punti Eta I princ. 37,1% Q max 122222 kW spec. Emissions boiler 222,2 g/kWh Q cog. geot. 21804 kW Avoided emissions case A 19381,7 t/y Q cog. geot. 87218 MW h Avoided Emiss. th 29422 t/y Eta th net 17,8% Delta emissions 10040 t/y Eta I 27,9% 1 punto CF case A thermal € 1.918.792 €/y T cond 308,2 K CF case B thermal € 2.912.800 €/y T m logaritmic 109,1 °C Delta CF thermal € 994.008 €/y T m logaritmic 382,1 K CF from CO2 € 355.992 €/y Eta Lorentz 19,4% Carbon tax CO2 35,46 �/t Eta II 51,8% 2 punti Exercise 2 (Manag and Mech. Eng. Students) Case A (biomass) Case B (wind) biomass flow rate 5,556 kg/s eta 46,8 % LHV as received 9824 kJ/kg area 9503 m2 power LHV 54578 kW power 3916 kW Gross power 14736 kW tot power 78329 kW Net power 13936 kW Energy 234986 MWh Energy 111488 MWh annual total cost 15100000 € annual total cost 9,0 M€ LCOE 64,3 €/MWh LCOE 80,7 €/MWh cost of avoided CO2 10,6 €/tCO2 cost of avoided CO2 54,5 €/tCO2 Case C (geothermal) delta H 300 kJ/kg power 12540 kW net power 11440 kW specific cost 3934 €/kW Energy 85800 MWh CO2 14 kg/MW h annual total cost 7,4 M€ LCOE 86,2 €/MWh cost of avoided CO2 68,0 €/tCO2 Exercise 2 (Energy Eng. Students) Results 8 days sizing (*) 7 days sizing Daily production (summer) 250,00 kW h 218,75 kW h Average daily power (summer) 35,71 kW 31,25 kW Power considering security factor 48,21 kW 42,19 kW Turbine diameter 29,71 m 27,79 m Nominal Power 127,99 kW 111,99 kW Yearly energy need 7310 kW h 7310 kW h Yearly energy need 26316 MJ 26316 MJ Turbine energy content 563139 MJ 492747 MJ EPBT 21,4 years 18,7 years Yearly electricity production (grid -connected) 295171 kW h 258275 kW h h eq grid -connected 2306 h 2306 h Yearly electricity production (grid -connected) 1062615 MJ 929788 MJ EPBT grid -connected 0,53 years 0,53 years (*) the correct sizing of the wind turbine should consider that in a single day it must produce the amount of energy for the same day and for the following week in the absence of wind IN ANY CASE BOTH SOLUTIONS HAVE BEEN CONSIDERED AS CORRECT