090123 Problems Solution

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Department of Energy Politecnico di Milano Author Pag.1 of 12 Date 12/01/2023 Milan, 22nd December 2022 Exam – Thermoeconomics and Energy Modelling Session of 09-01-2023 Total score: 21 points (exercise 1 counts 2/3 of the total) Exercise 1. Let’s consider a part of an open gas cycle plant. As it can be seen in Figure 1, the parts under study are: the combustion chamber (CC), the first stage of the gas turbine (GT -1) and the second stage (GT -2). The inlet 1 is compressed air while flow 2 is the fuel. In the combustion chamber, a combustion takes place and it gives off hot flue gases. First stage of gas turbine produces power and a hot fluid used in an industrial process while stream 4, still flue gases, is reused to feed the second stage turbine. The last component produces useful power 𝑊𝑊̇ 𝐺𝐺𝐺𝐺−1. With reference to the data provided, it is required to: a. Write the exergy balance and compute exergy destruction of each component. Calculate the rational and functional exergy efficiencies. Comment on the results. b. Write the Thermoeconomic system of equations for each component and derive the analytical expressions of the cost structure of the products. Highlight the auxiliary equations needed to solve the thermoeconomic system and make sure they are coherent with the “functional” use of the components. Table 1 State Ex [MW] 1 Compressed air 22 2 Fuel 190 3 Flue gases 160 4 Flue gases 80 5 Flue gases 10 6 Flue gases 30 7 𝑊𝑊̇ 𝐺𝐺𝐺𝐺−1 40 8 𝑊𝑊̇ 𝐺𝐺𝐺𝐺−2 60 Table 2 Unit cost of Fuel [€/MWh] 60 Unit cost of Compressed air [€/MWh] 5 Z – CC (Investment, O&M) [€/h] 600 Z – GT-1 (Investment, O&M) [€/h] 900 Z – GT-2 (Investment, O&M) [€/h] 1200 FIGURE 1. CONFIGURATION 1 - COGENERATION Department of Energy Politecnico di Milano Author Pag.2 of 12 Date 12/01/2023 c. Solve the system…