Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

Wind, Hydro and Geothermal Power Generation AY 2021-22 8 th February 2022 Prof. Paolo Silva Time: 90 minutes Instructions for the examination: 1) Clearly indicate your name on all the sheets you will deliver. 2) Give a synthetic and clear answer to as many questions as possible. The final score will be normalized according to the average results. 3) Talk with colleagues and / or cheating will cause the cancellation of the exam. 1. Consider a three-bladed horizontal axis wind turbine installed on a site with a high roughness factor, resulting in a significant wind speed gradient over the area swept by the blades. Explain the effects on the velocity triangle at the tip, for a blade respectively positioned at the top (vertical up position), middle (horizontal) and bottom (vertical down) of its path during the rotation. What could be the consequences on the turbine operation? (5 points) 2. Explain the methodology for evaluating the primary energy savings and the avoided pollutant emissions for a cogenerative geothermal power plant. With particular reference to CO2 emis- sions, can geothermal plants make a positive contribution? (5 points) 3. Discuss the strategic importance of hydroelectric power plants with respect to the increasing dispatching requirements of the electricity grid. What is the role of different kinds of hydro plants in the electric system? (5 points) 4. Discuss the different types of foundations and mooring systems used for floating offshore wind technology. What are the most promising technologies in your opinion? (5 points) Exercise (10 points) Consider a binary ORC geothermal plant fed by a geothermal brine that provides a flow rate of 700 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 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 temperature 45°C 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) (consider a constant value for the liquid heat capacity of iso- pentane), (iii) net electrical power output (1 point), (iv) the cycle efficiency (1 point), and (v) the net electric efficiency of the plant (1 point). Now consider the introduction of a cogenerative heat exchanger after the ORC economizer: the thermal power is recovered by cooling down the geothermal fluid from the economizer outlet temperature to the minimum reinjection temperature. Determine (vi) the first law efficiency of the cogenerative plant (1 point) and (vii) the specific cost (€/t) of the avoided CO 2 that would allow to pay back the cogenerative heat exchanger in one year (3 points). Use the following assumptions: - 4000 equivalent hours of thermal power recovery; - cost of the additional cogenerative heat exchanger = 1’000’000 € - selling price of the thermal energy = 0.5 c€/kWh - reference CH 4–to-heat generation efficiency = 90% - reference CO 2 emissions for CH 4 = 200 g/kWh (LHV) Results Q eva 53044,4 kW m ORC fluid 195,42 kg/s P el TV 11352 kW P el net 10852 kW Cp isop. 2,53 kJ/kgK T @ outlet of evaporator 113,0 °C Q eco 35641 kW T geot. out ECO 71,3 °C Eta CV 12,2 % Eta th source 79,7 % Eta el net 9,8% Q max 111222 kW Q cog. geot. 22537 kW Eta th net 20,3% Eta I 30,0% spec. Emissions boiler 222,2 g/kWh Q cog. geot. 90147 MWh Avoided emissions 20032,6 t/y CF thermal € 450.734 €/y CF from CO2 € 549.266 €/y Carbon tax CO2 27,4 €/t