Energy Engineering - Advanced Thermodynamics and Thermoeconomics

Full exam

Department of Energy Politecnico di Milano Author Emanuela Colombo Pag. 1 of 18 Date 27/06/2022 Milan, 25 th May 202 2 Exam –Thermoeconomics and Energy Modelling 13 -06 -2022 Total score: 2 1 points (exercise 1 roughly 2/3 of the total) Exercise 1. The concentrated solar power plant depicted in Figure 1 works with a water steam Rankine cycle. This is a regenerative cycle. A portion of the s team exiting from the expansion Tur bine enters a regenerative Heat Exchanger (mixing type) which la ys in between the two feeding pump s. Th e solar radiation captured by solar field is equal to 942.1 MWth while the net electric power produced by the plant is equal to 39 .1 MWel. The heat released by the condenser is discharged in the environment without any additional cost . FIGURE 1: PLANT SCHEME Table 1 State Description Exergy [ MW] 0 Solar radiation 942 .1 1 Outlet solar field 109 .5 2 Inlet HP turbine 69 .9 Whp Power output HP turbine 28 .4 3 Outlet HP turbine 41.0 4 Inlet LP turbine 59 .9 Wlp Power output LP turbine 39 .1 5 Outlet LP turbine 4.7 SOLAR FIELD Heat Exchanger 1 HPturbine LP turbine WHP WLP Feed pump II Feed pump I Condenser 1 3 2 4 5 10 9 8 6 7 Wp1 Wp2 11 0 Heat Exchanger 2 Department of Energy Politecnico di Milano Author Emanuela Colombo Pag. 2 of 18 Date 27/06/2022 6 Outlet condenser 0.1 Wp1 Power supply Feedpump 1 0.1 7 Outlet Feedpump 1 0.1 8 Inlet Feedpump 2 0.9 Wp2 Power supply Feedpump 2 0.8 9 Outlet Feedpump 2 1.5 10 Bleeding 10.6 11 Condenser discharge 0 Consider T0 and P 0 to be respectively 2 98.15 K and 1 bar and the following table as additional data . With reference to the data provided , it is required to: a. Write the exergy balance computing exergy destruction for the whole plant . Check the result with the summation of the destructions for each component provided in Table 3 . b. Write all the auxiliary equations needed to characterize the thermoeconomic system of equation for this plant. Clearly explain the reason why each auxiliary equation is assigned and make sure that they are coherent with the functional use of the components. Then, compute the total capital cost rate [€/h] for each component of the plant. c. Write the thermoeconomic system of equations for each component to obtain the analytical expressions of the cost structure of the products. Table 2 Total Cost of Investments [M€] 67 Total cost of Operation & maintenance [M€/y] 6.7 Electricity cost [€/kWh] 0.25 Capacity factor [ -] 0.25 Solar field [%] 30 Heat exchanger 1 [%] 13 HP turbine [%] 15 LP turbine [%] 15 Condenser [%] 13 Feedpump 1 [%] 2 Heat exchanger 2 [%] 10 Feedpump 2 [%] 2 Interest rate on capital [%] 1 Plant operative lifetime [years] 25 Table 3: Exergy destructions [MW] Solar field 861.1 Heat exchanger 1 22.3 HP turbine 0.4 LP turbine 5.5 Condenser 4.6 Feedpump 1 0.1 Heat exchanger 2 9.8 Feedpump 2 0.2 Department of Energy Politecnico di Milano Author Emanuela Colombo Pag. 3 of 18 Date 27/06/2022 d. Calculate the unit costs of the products for each component [€ /kWh]. Collect all the numerical results into a table giving separate evidence to the value of the three constituents of the cost structure for each component. e. Explain the effect of an improvement in the concentrating system for the solar field. Sustain your consideration with quantitative analysis by referring to termoeconomic parameters such as the relative cost difference and the exergoeconomic factor. Now comment on possible i mprovements also for the condenser. Department of Energy Politecnico di Milano Author Emanuela Colombo Pag. 4 of 18 Date 27/06/2022 Exercise 1. (Solution) a. Write the exergy balance computing exergy destruction for the whole plant. Check the result with the summation of the destructions for each component provided in Table 3. Exergy Balance for each components are here reported for the sake of completeness: 01,, 19 3 2 4 ,1 ,1 23 Solar Field) 942.1 28.4 109.5 861.0 Heat Exchanger 1) 109.5 1.5 41.0 69.9 59.9 22 .2 High Pressure Turbine) hp DSF Dsf Dhe Dhe hp Ex W Ex Ex Ex MW Ex Ex Ex Ex Ex Ex Ex MW Ex Ex W E +=+ → = + − = ++ = ++ → = ++ − − = =++          ,, 4510 , , 5611 , , 6 69.9 41.0 28.4 0.5 Low Pressure Turbine) 59.9 10.6 4.7 39.1 5.5 Condenser) 4.7 0 0.1 4.6 Feed Pump 1) Dhp Dhp lp D lp Dlp Dcond Dcond p xEx MW Ex Ex Ex W Ex Ex MW Ex Ex Ex Ex Ex MW Ex W →=−−= =+ ++ → = − −− = =+ + → =−−= +         17 ,1 ,1 710 8 ,2 ,2 82 9 ,2 ,2 012 0.1 0.1 0.1 0.1 Heat Exchanger 2) 0.1 10.6 0.9 9.8 Feed Pump 2) 0.9 0.8 1.5 0.2 Total) Dp Dp Dhe Dhe p Dp Dp pp LP Ex Ex Ex MW Ex Ex Ex Ex Ex MW Ex W Ex Ex Ex MW Ex W W W E =+ → =+−= +=+ → =+−= +=+ → =+−= ++ = +          11 , , , 942.1 0.1 0.8 39.1 0 903.9 861 22.2 0.5 5.5 4.6 0.1 9.8 0.2 903.9 Dtot Dtot Dtot xEx Ex MW Ex MW +→ =++−−= =+ ++++++=   Rational and functional exergy e fficiencies for each component are here reported for the sake of completeness : - Solar Field : 1 0 109.5 0.11 942.1 28.4 0.11 r hp fr Ex Ex W η ηη == = + + ==   - Heat Exchanger 1: 24 319 243 19 69.9 59.9 0.85 41.0 109.5 1.5 69.9 59.9 41.0 0.80 109.5 1.5 r f Ex Ex Ex Ex Ex Ex Ex Ex Ex Ex η η + + = = = ++ ++ +− +− = = = + +     - High Pressure Turbine : 3 2 23 28.4 41.0 0.99 69.9 28.4 0.98 69.9 41.0 hp r hp f WEx Ex W Ex Ex η η + + == = == = − −     - Low Pressure Turbine : 510 4 4510 39.1 4.7 10.6 0.91 59.9 39.1 0.88 59.9 4.7 10.6 lp r lp f WExEx Ex W Ex Ex Ex η η ++ ++ = = = = = = −− −−      Department of Energy Politecnico di Milano Author Emanuela Colombo Pag. 5 of 18 Date 27/06/2022 - Condenser: 11 6 5 6 5 0 0.1 0.02 4.7 0.1 0.02 4.7 r f Ex Ex Ex Ex Ex η η + + === ===     - Feed Pump 1: 7 61 0.1 0.50 0.1 0.1 0.50 r p fr Ex Ex W η ηη === + + ==   - Heat Exchanger 2 : 8 710 0.9 0.08 0.1 10.6 0.08 r fr Ex Ex Ex η ηη === + + ==   - Feed Pump 2: 9 82 0.9 0.40 1.5 0.8 0.40 r p fr Ex Ex W η ηη === + + ==   b. Wri te all the auxiliary equations needed to characterize the thermoeconomic system of equation for this plant. Clearly explain the reason why each auxiliary equation is assigned and make sure that they are coherent with the functional use of the components. T hen, compute the total capital cost rate [€/h] for each component of the plant . The system is composed by 16 streams and 8 components, therefore, in order to define and close the thermoeconomic system of equations, ( n-m) numbers of auxiliary relations are required: n: Number of exergy flows = 16, m: number of components = 8: n-m = 16 - 8 = 8. Auxiliary equations: 0 11 1 2 23 34 45 10 5 1) 0 2) 0 3) 4) 5) 6) 7) 8) pel pel c c cc cc cc cc cc cc = = = = = = = = Computation of total capital cost rate for each component (