Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

POW ER PRODUCTION FROM RENEW ABLE ENERGY AY 2021-22 14 th January 2022 Prof. Silva Time: 1.5 hours Ins truc tions for the examinati on: 1) Clearl y indicate your name on all the files you will deliver. 2) The scor e r efers to exercises done in a c ompr ehensi ve manner with exac t numerical res ults . Numeric al res ults corr ect but not accom panied by expl anati ons will not be taken into account. The final sc or e c an be normali zed accor ding to the average r esults . 3) Talking with c olleagues and / or c heati ng will c aus e the cancellation of the exam. 4) All the needed data for the res olution of exercis es lies on this paper . It is NOT ALLOW ED to use materi al other than this ( e.g. books , cli pboar d etc.) . Exercise 1 (17 points) A geothermal source has the following characteristics at the outlet of the well: pressure 12 bar, v apor fraction 75%, mass flowrate 21 kg/s. Draw the power plant lay-out in a configuration without the atmospheric vessel (1 point) and determine the net power output (4 points), considering a condensing pressure of 0,1 bar and assuming a steam turbine isentropic efficiency of 88% and a generator organic-electric efficiency of 97.5%. Calculate the net electric efficiency considering a minimum reinjection temperature of 40°C and an overall auxiliary consumption of 700 kW (2 points). In order to increase the power output, the geothermal fluid is further heated to 400°C in a biomass boiler (series configuration and neglecting pressure drops, biomass is oak at harvest conditions described in the table be- low). The biomass boiler consists of an ev aporator, a super-heater and a regenerativ e air pre-heater fed by the exhaust gases. Determine the net electric power output assuming an overall plant auxiliary consumption of 950 kW (2 points) and the biomass flowrate on as received basis (consider ∆h evaporation,water = 2450 kJ/kg) assuming an overall net plant efficiency (geothermal+biomass) equal to 22.4% (2 points). Calculate the effi- ciency of the boiler section and the stack temperature (3 points). Determine the pre-heater efficacy assuming dry biomass, an ambient air temperature of 15°C, Cp of exhaust gas 1.15 kJ/kgK, Cp of air 1 kJ/kgK, air mass flow rate 43 kg/s, evaporator pinch point 10°C, unburnt carbon and ashes losses equal to 2% of thermal power input (3 points). THERMODYNAMIC PROPER TIES OF WATER AT SAT URATION AND SUPER -HE ATED STEAM liquid vapor PRESSURE [BAR] Temperature [°C] h liq.sat. [kJ/kg] s liq.sat. [kJ/kgK] h vap.sat [kJ/kg] s vap.sat. [kJ/kgK] 12 198.3 798.4 2.216 2782.7 6.519 12 400.0 3261 .3 7.379 0.1 45.8 191.83 0.65 2584.78 8.15 oak (harvest conditions) %, weight dry basis C 48,80 H 6,09 O 45,00 ash 0,11 LHV, kJ/kg, dry basis 17769 HHV, kJ/kg, dry basis 19107 Moisture content, % 50 Density (as received), kg/m 3 850 Exercise 2 (13 points) Determine the annual generated electricity, the levelized cost of electricity (LCOE) and the cost of av oided 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 av oid 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 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 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. Consider biomass exploitation as carbon neutral. Total plant cost is 40 million €, variable costs are 1.3 million € per year, and the biomass cost is 23 €/t. (5 points) • A wind farm consisting of 20 turbines with a diameter of 110 m, a nominal wind speed of 13.5 m/s, fluid- dynamic efficiency of 80% and mechanical-electrical efficiency 94.5% (ρ air = 1.225 kg/m 3). Consider an av erage annual production of 2860 equivalent hours, a total inv estment cost for the wind farm of 159 million € and an annual O&M cost of 2.94 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 respectiv ely 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 7300 equivalent hours a year. Total plant cost is 50 million € and variable costs are 2.5 million € per year (4 points). Exercise 1 Pressure 12 bar Mechanical power 17053 kW enthalpy liq 798,4 kJ/kg Electrical power 16627 kW enthalpy vap 2782,7 kJ/kg Net electric power 15677 kW enthalpy 2286,7 kJ/kg thermal power input 69986 kW titolo 0,75 biomass thermal power input 25484 kW entropia 6,52 kJ/kg K flowrate dry 1,434 kg/s flowrate 15,75 kg/s water 0,5481 pressure 0,1 bar HHV as received 9554 kJ/kg isentropica 2064,3 kJ/kg LHV as rec 7661 kJ/kg entalpiaout 2150,5 kJ/kg flowrate as received 3,33 kg/s Mechanical power 9958 kW Electrical power 9709 T pinch 10 °C Net electric power 9009 kW unburnt 2,0% Q in max 44501 kW m air 43 kg/s eta el 20,2 % cp exhaust gases 1,15 kJ/kgK T air 15 °C T out 400 °C boiler efficiency 80,3 % p out 12 bar T out stack 103,2 °C moisture 50% T in exhaust gas 208,3 °C LHV dry 17769 kJ/kgdry delta T air 124,9 °C HHV dry 19107 kJ/kgdry efficacy 64,6 % overall efficiency 22,4 % Q HE 5370,2 kW Enthalpy 3261,3 kJ/kg entropia 7,379 kJ/kg K H 0,0609 p out 0,1 bar isentropica 2339 kJ/kg entalpia out 2449 kJ/kg Exercise 2 Case A (biomass) Case B (wind) biomass flow rate 6,111 kg/s eta 47,4 % LHV as received 9824 kJ/kg area 9503 m2 power LHV 60036 kW power 6416 kW Gross power 16210 kW tot power 128319 kW Net power 15410 kW Energy 366992 MWh Energy 123277 MWh annual total cost 22020000 € annual total cost 10,1 M€ LCOE 60,0 €/MWh LCOE 82,3 €/MWh cost of avoided CO2 0,0 €/tCO2 cost of avoided CO2 58,7 €/tCO2 Case C (geothermal) delta H 300 kJ/kg power 12540 kW net power 11440 kW specific cost 4371 €/kW Energy 83512 MWh CO2 14 kg/MW h annual total cost 8,5 M€ LCOE 101,8 �/MWh cost of avoided CO2 114,1 �/tCO2