Energy Engineering - Advanced Thermodynamics and Thermoeconomics

Full exam

Department of Energy Politecnico di Milano Author Pag.1 of 12 Date 23/06/2020 Milan, 06 th June 2020 Exam – Advanced Thermodynamic and Thermoeconomics 15-06-2020 Exercise 1. Let’s consider an innovative biomass-fed steam cycle. The thermal energy required by the steam cycle to generate the steam is provided by a dedicated combustion chamber supplied by biomass feedstock. Biomass is pre-treated (PT) by reducing water content and increasing the temperature thanks to a contribution coming from the combustion chamber (stream 4) at steady conditions. The combustion chamber (CC) takes in input the pre-treated feedstock (stream 1), ambient air (stream 2) and produces useful heat for the steam cycle ( Q̇`mgjcp ) at 2000 K. Flue gases (stream 3) are then treated before being given off by means of a flue gases treatment (FGT) system which investment costs are reported in Table 2. The steam cycle gets in input the heat required to vaporize water. The condenser of the steam cycle discharges Q̇amlb to the environment. Consider that the water coming from the turbine enters into the condenser at 44°C and exits at 42°C. The overall work produced by the steam cycle is Ẇlcr . Consider that T 0 and P 0 are respectively: 298 K and 1 atm. Abbreviations: PT – pre-treatment; CC – combustion chamber; FGT – flue gases treatment; SC – steam cycle. Table 1 State Exergy [MW] 0 Input feedstock 100 1 Treated feedstock 105 2 Ambient air 0 3 Treated flue gases 18 4 Treatment heat 15 Quantity Energy [MW] Q̇`mgjcp 80 Q̇amlb 40 Ẇlcr Net power 45 Table 2 Unit cost of feedstock [€/MWh] 20 Z – PT (Investment, O&M) [€/h] 50 Z – CC (Investment, O&M) [€/h] 150 Z – SC (Investment, O&M) [€/h] 1000 Z – FGT (Investment, O&M) [€/h] 350 FIGURE 1. PLANT CONFIGURATION pre-treatment combustion chamber Steam cycle 0 3 1 4 2 Department of Energy Politecnico di Milano Author Pag.2 of 12 Date 23/06/2020 With reference to the data provided, it is required to: a. Compute the exergy streams of energy quantities. Write the exergy balance and compute exergy destruction of each component. Calculate the rational and functional exergy efficiencies. Comment on the results obtained. 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. Make comments on them c. Solve the system of equations made by the cost balances of the three components and provide the unit costs of the products for each of them [€/MWh] (as suggestion you can start the procedure solving the cost balance of pre-treatment and combustion chamber). Then collect all the numerical results into a table giving evidence to the three components of the cost structure for each component. Comment on the results obtained . d. Apply the design evaluation calculating for each component the relative cost difference and the exergoeconomic factor. Collect the data into a table and provide suggestions for reducing the costs of the products. e. Write the analytical expressions of the chemical and physical exergy related to the flue gases (Stream 3). Flue gases compositions are collected in Table 3. Then compute the chemical and physical exergy given that P=P 0 and T=340 K. Use proper assumptions about the application of formulas. Compute also the mass flow rate of gases at the stack. Reference Environment: ������������������ ������������������������������ �������������������������������������������������������������������� = {�������6 = 0.76; ���������6 = 0.20; ���������6� = 0.03; ���������� = 0.01 } Specific heat for substances: �������� � .= 4 ������ = 33.26 ������������ /������������������������ ������ ��������.� = 4.186 ������������ /������������������ ��������.= 7 2������ = 29.10 ������������ /������������������������ ������ Table 3 Compounds Volume composition CO 2 44% H2O 1% N2 55% Department of Energy Politecnico di Milano Author Pag.3 of 12 Date 23/06/2020 Exercise 1. (Solution) a. Compute the exergy streams of energy quantities. Write the exergy balance and compute exergy destruction of each component. Calculate the rational and functional exergy efficiencies. Comment on the results obtained. Calculation of exergy streams: ������������̇������ = ������̇������ l1 − ������4 ������ p= 80 ������������ ∙ l1 − 298 ������ 2000 p= 68.08 ������������ ��������� = �������� − ��������� ln @�������� ��������� A = (44 + 273.15) − (42 + 273.15) ln @44 + 273.15 42 + 273.15 A = 316 ������ = 43 ° ������ ������������̇���� = ������̇���� l1 − ������4 ��������� p= 40 ������������ ∙ l1 − 298 ������ 316 ������ p= 40 ������������ ∙ 0.057 = 2.28 ������������ ������̇��� = ������������̇���� = 45 ������������ Exergy Balance for the components: 0 4 1 , PT , PT 1 2 3 4 ,CC , CC , ,SC ) 10 ) 3.92 ) 20.8 D D boiler D D boiler condenser net D SC D PT Ex Ex Ex Ex Ex MW CC Ex Ex Ex Ex Ex Ex Ex MW SC Ex Ex W Ex Ex MW                                   Rational and functional exergy efficiencies: - PT: 1 , 0 4 1 , 0 4 105 0.913 100 15 105 0.913 100 15 r PT f PT Ex Ex Ex Ex Ex Ex                   - CC: 3 4 , 1 2 4 , 1 2 18 15 68.08 0.963 105 0 15 68.08 0.791 105 0 boiler r CC boiler f CC Ex Ex Ex MW MW Ex Ex Ex Ex MW MW Ex Ex                            - SC: , , 2.28 45 0.694 68.08 45 0.661 68.08 condenser net r SC boiler net f SC boiler Ex W Ex W Ex                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. Make comments on them Department of Energy Politecnico di Milano Author Pag.4 of 12 Date 23/06/2020 The system is composed by 8 streams and 3 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 = 8, m : number of components = 3: n-m = 8 - 3 = 5. Auxiliary equations: 0 2 4 _ _ 3 _ 3 _ 1) 2) 0 null exergy content 3) co-products 4) environmental cost 5) 0 loss Q boiler env inv inv env Q cond c given c c c Z c c Ex c               Auxiliary equations have to be consistent with the formulations of functional exergy efficiencies. In this case, all efficiencies result to be coherent with the auxiliary equations listed above. Indeed, Stream 3 in CC and Qcond in the Steam Cycle are losses. For each component it is required to write economic cost balance and substituting exergy cost relation as follows; ; ; in component out in out C Z C Economic cost balance C c Ex Exergy cost relation                PT: 0 4 1 , PT 0 0 4 4 1 1 0 0 4 4 , PT 0 4 D PT in Ex Ex Ex Ex c Ex c Ex Z c Ex c Ex c Ex c Ex Ex                          The cost structure is:   , PT 1 , PT ,PT 1 1 D PT in in inlet Investment Cost ExergyDestruction Ex Z c c c Ex Ex          CC: 1 2 3 4 , CC 1 1 2 2 3 3 4 4 1 1 2 2 , CC 1 2 _ 3 3 boiler D CC boiler boiler in env inv Ex Ex Ex Ex Ex Ex c Ex c Ex Z c Ex c Ex c Ex c Ex c Ex c Ex Ex Z c Ex                                       The cost structure is:  _ , CC 3 4 ,CC , CC 4 4 ( ) ( ) ( ) CC env inv D boiler in in boiler boiler inlet ExergyDestruction Losses Investment Cost Z Z Ex Ex c c c c Ex Ex Ex Ex                     SC: The costs structure results to be as follows: Department of Energy Politecnico di Milano Author Pag.5 of 12 Date 23/06/2020 , boiler condenser net D SC boiler boiler SC cond condenser W net Ex Ex W Ex c Ex Z c Ex c W                  The cost structure results to be:   ,SC cond D SC W boiler boiler net net inlet Investment Cost ExergyDestruction Ex Ex Z c c c W W            c. Solve the system of equations made by the cost balances of the three components and provide the unit costs of the products for each of them [€/MWh] (as suggestion you can start the procedure solving the cost balance of pre-treatment and combustion chamber). Then collect all the numerical results into a table giving evidence to the three components of the cost structure for each component. Comment on the results obtained. 0 0 4 4 1 1 1 1 2 2 _ 4 4 PT CC env inv boiler boiler boiler boiler SC cond condenser W net c Ex c Ex Z c Ex c Ex c Ex Z Z c Ex c Ex c Ex Z c Ex c W                               Unknowns (c 1 , c 4 = c boiler , c W). From the cost balances of PT and CC, the values of c 1 and c 4 = c boiler can be computed: 0 0 4 4 1 1 1 1 2 2 _ 4 4 PT CC env inv boiler boiler c Ex c Ex Z c Ex c Ex c Ex Z Z c Ex c Ex                       0 0 4 4 1 1 1 1 2 2 _ 4 4 1 1 2 2 _ 0 0 4 1 1 4 2 2 _ 0 0 4 ( ) ( ) ( PT CC env inv boiler CC env inv PT boiler CC env inv boiler c Ex c Ex Z c Ex c Ex c Ex Z Z c Ex Ex c Ex c Ex Z Z c Ex Ex Z c Ex Ex Ex c Ex Z Z c Ex Ex Ex                                                             4 4 4 1 1 1 1 1 1 4 4 2 2 _ 0 0 4 4 1 4 1 4 1 ) ( ) ( ) 20 ( ) 1 ( ) PT boiler boiler CC env inv PT boiler boiler Ex Ex Ex Z c Ex c Ex c Ex Ex Ex Ex Ex c Ex Z Z c Ex Ex Z Ex Ex c Ex Ex Ex Ex                                                                                  0 0 150 350 100 15 50 (15 68.08) 24.87€ / 15 105 1 (15 68.08) MWh                     Department of Energy Politecnico di Milano Author Pag.6 of 12 Date 23/06/2020 1 1 2 2 _ 4 4 24.87 105 0 0 150 350 37.46€ / (15 68.08) ( ) CC env inv boiler c Ex c Ex Z Z c MWh Ex Ex                    Cost Structures: PT: 0 0 4 4 , PT 0 4 20 100 37.46 15 22.28€ / 100 15 in c Ex c Ex c MWh Ex Ex               , PT 1 , PT , PT 1 1 10 50 22.28 22.28 22.28 2.12 0.48 24.87€ / * 105 105 D PT in in Ex Z c c c MWh Ex Ex                 CC: ,CC 24.87 105 0 0 24.87€ / 105 0 inc MWh        _ , CC 3 4 , CC , CC 4 4 ( ) (3.92 18) 150 350 24.87 24.87 (15 68.08) (15 68.08) ( ) ( ) 24.87 6.56 6.02 37.46€ / * CC env inv D boiler in in boiler boiler Z Z Ex Ex c c c c Ex Ex Ex Ex MWh                               SC: ,SC 4 4 (2.28 20.8) 1000 37.46 37.46 37.46 19.21 22.22 78.89€ / 45 45 cond D SC W net net Ex Ex Z c c c MWh W W                    Cost structure components are collected in the following table. component fuel destruction + losses investment total €/MWh €/MWh €/MWh €/MWh PT 22.28 2.12 0.48 24.87 CC 24.87 6.56 6.02 37.46 SC 37.46 19.21 22.22 78.89 d. Apply the design evaluation calculating for each component the relative cost difference and the exergoeconomic factor. Collect the data into a table and provide suggestions for reducing the costs of the products. To perform the design evaluation of the system it is necessary to compute the cost of the exergy destructions, the exergoeconomic factors and the relative cost differences. Exergoeconomic factor is computed as: , , , inv j j inv j des loss j c f c c    Relative cost difference is computed as: , , , des loss j inv j j fuel j c c r c    In the following table, all the results are collected Department of Energy Politecnico di Milano Author Pag.7 of 12 Date 23/06/2020 component fuel destruction + losses investment total C des+loss C inv C des+loss+inv r f €/MWh €/MWh €/MWh €/MWh €/h €/h €/h - - PT 22.28 2.12 0.48 24.87 223 50 273 0.117 0.183 CC 24.87 6.56 6.02 37.46 545 500 1045 0.506 0.478 SC 37.46 19.21 22.22 78.89 864 1000 1864 1.106 0.536 Comments: Applying the Design Evaluation approach, the first step requires to conjunctly analyse two indicators: - the extensive summation of destruction, losses and investment costs; - the value of relative cost difference. A joint analysis is needed since the destruction + investment cost rate refers to the extensive values but can be affected by high specific costs of the fuel. While relative cost difference represents the margin for improving a component. High values of both exergy destruction and investment costs and r suggest that the component can be further improved. Exergoeconomic factor indicates whether the capital and O&M expenses ( Ż) is the major source of economic cost increase. The range of values for this indicator is between zero and one: high values indicate that investments ( Ż) are the major cost source and the primary aim is to reduce cost of the products by reduction the investment and O&M costs conversely exergy destruction ( ĊH>P ) cost are higher than investments and an increase of efficiency (and investment cost usually) is recommended. - Considering the summation of exergy destruction cost rates and investments, it stands out that the steam cycle reckons the higher value followed by the combustion chamber and the biomass pre- treatment. It reflects the higher complexity of the steam cycle system joint to the higher losses that can emerge when heat transfer come to play. - Considering the relative cost difference, the trends are similar to the ones related to investment and destruction cost rates. The first two components, in terms of investments and destruction, do not affect that much the overall cost of the products. Conversely, the steam cycle presents higher product costs due to higher inefficiencies and higher investment costs - Considering the exergoeconomic factor, the last two components result to have indicators’ values very close to 0.5, that means the inefficiencies and investment costs are balanced. No further design change are suggested according to this indicator. While pre-treatment system shows high losses costs and very low configuration costs. An increase in efficiency (with probably a consequent rise in costs) is suggested to decrease component losses. e. Write the analytical expressions the chemical and physical exergy related to the flue gases (Stream 3). Flue gases compositions are collected in Table 3. Then compute the chemical and physical exergy given that P=P0 and T=340 K. Use proper assumptions about the application of formulas. Compute also the mass flow rate of gases at the stack. ������������������ ������������������������������ �������������������������������������������������������������������� = {�������6 = 0.76; ���������6 = 0.20; ���������6� = 0.03; ����������6 = 0.01 } Flues gases contains same molecular species present also in the reference environment. It can allow us to use the simplified formula for ideal gases that is: ������������ �� ,��� = ������4������ � ������� � ln F������4,� ������44 ,� G ������������ �� ,��� = ������4������ � ������� � ln F������4,� ������44 ,� G = 298 ������ ∙ 8.314 ������������������������������������ ?5 ������?5 ∙ l0.44 ln 0.44 0.01 + 0.01 ln 0.01 0.03 + 0.55 ln 0.55 0.76 p= = 3657.4 ������������ /������������������������ ��� Department of Energy Politecnico di Milano Author Pag.8 of 12 Date 23/06/2020 Compounds Volume composition Environment composition ex_ch MM - - kJ/kmol kg/kmol CO 2 44% 1% 4125.3 44.0 H2O 1% 3% -27.2 18.0 N2 55% 76% -440.7 28.0 mixture 3657.4 34.9 ������������ ��� = ������������ �∙�������= (0.44 ∙ 44 + 0.01 ∙ 18 + 0.55 ∙ 28 )= 34.9 ������������ ������������������������ Specific heat for substances: �������� � .= 4 ������ = 33.26 ������������ /������������������������ ������ ��������.� = 4.186 ������������ /������������������ ��������.= 7 2������ = 29.10 ������������ /������������������������ ������ The physical exergy of flue gases is: ������������ �� ,��� = � ������� � [(ℎ − ℎ 4)− ������4(������− ������4)] =�.�. � ������� � d�������,�(������5− ������4)− ������4 l�������,�ln ������5 ������4 − ������ln ������5 ������4 p h ������������ �� ,GS .= d�������∗(�������− ������4) − ������4 l�������∗ ln ������� ������4 − ������ln ������� ������4 p h= = d33.26 ⋅ (340 − 298) − 298 ⋅ l33.26 ⋅ ln 340 298 − 8.314 ⋅ ������������ 1 1 p h= 90.1 ������������ ������������������������ � � . ������������ �� ,L.� = [�������∗(�������− ������4)]= d4.186 ������������ ������������������ ∙ 18 ������������ ������������������������ ⋅ (340 − 298)K h= 3164.6 ������������ ������������������������ �.� ������������ �� ,R.= d�������∗(�������− ������4) − ������4 l�������∗ ln ������� ������4 − ������ln ������� ������4 p h= = d29.10 ⋅ (340 − 298) − 298.15 ⋅ l36.14 ⋅ ln 340 298 − 8.314 ⋅ ������������ 1 1 p h= 78.8 ������������ ������������������������ �. ������������ �� ,��� = � �������∙������������ �� ,�= 0.44 ∙ 90.1 + 0.01 ∙ 3164.6 + 0.55 ∙ 78.8 = 114.6 ������������ ������������������������ ��� ������������ ��� = ������������ �� ,��� + ������������ �� ,��� = (3657.4 + 114.6 ) ������������ ������������������������ ��� = 3772.0 ������������ ������������������������ ��� → ������������ ���� ����� = 3772.0 ������������ ������������������������ ��� 34.9 ������������ ������������������������ ��� = 108.0 ������������ ������������ Department of Energy Politecnico di Milano Author Pag.9 of 12 Date 23/06/2020 ������̇���� ����� = ������̇������7 ������������ ���� ����� = 18 000 ������������ 108 ������������ ������������ = 166.7 ������������ ������ (*) at the end of calculations indicates minimal inconsistencies ascribed to rounding errors. Note: the energy balance over the Steam Cycle appears not to be respected. This is due to additional flows that were present in the complete formulation of the problem, but were removed to simplify the system layout. Department of Energy Politecnico di Milano Author Pag.10 of 12 Date 23/06/2020 Exercise 2. Let’s consider the Brazilian economy in 2017. Relying on the IEA data provided by the table, it is required to: a. Evaluate the electric energy Import/Export, Express all the results in Mtoe; b. Starting from the value of final electricity consumption, evaluate the gross electric energy production. Express all the results in TWh; c. Derive the electricity production from hydro, nuclear and other RES starting from their primary energy requirements. Finally, derive the electricity production from Biomass. Express all the results in TWh; d. Evaluate the electric penetration of renewable sources only (hydro, biomass, other RES); e. Evaluate the overall efficiency of the electricity system. Please give the definition and explain it. Brazil 2017 Mtoe Total Primary Energy Supply 290.1 coal 16.8 oil 94.2 oil products 16.5 natural gas 32.5 nuclear 4.1 hydro 31.9 biomass 86.5 other RES 4.5 electricity Import-Export TWh Gross electricity production coal 25.3 oil 15.9 natural gas 65.6 nuclear hydro biomass other RES TWh Final electricity consumption 498.5 Energy indutry own use 29.1 Losses 98.1 Department of Energy Politecnico di Milano Author Pag.11 of 12 Date 23/06/2020 Exercise 3. Solution a. Evaluate the electric energy Import/Export, Express all the results in Mtoe. The changes in electric energy Import/Export can be derived by subtracting the total primary energy supply of all the voices in the table form the TPES. in absence of specific data assume that the net energy import/export is due only to electricity transaction.   / , 2013 290.1 16.8 94.2 16.5 32.5 4.1 31.9 86.5 4.5 3.1                 I E i i EE TPES TPES Mtoe Mtoe b. Starting from the value of final electricity consumption, evaluate the gross electric energy production. Express all the results in TWh. The electric energy production results as the sum of the final electricity consumption, plus the electricity losses/own uses, minus the positive net value of electricity import/export (the last term should be properly converted from Mtoe to TWh dividing by 0.086 Mtoe/TWh): _ / 1 498.5 29.1 98.1 3.1 589.6 0.086 gross net own use loss I E gross EE EE EE EE EE EE TWh           c. Derive the electricity production from hydro, nuclear and other RES starting from their primary energy requirements. Finally, derive the electricity production from Biomass. Express all the results in TWh; The electric energy production by nuclear, hydro and other RES can be calculated considering the IEA conventions for the conversion from primary energy: 1 4.1 0.33 15.7 0.086 NU NU NU EE TPES TWh        1 31.9 371.0 0.086 H H EE TPES TWh     1 4.5 52.3 0.086 RES RES EE TPES TWh     Hydro, other RES and Nuclear electric energy production can be computed from the values of primary energy (these terms should be properly converted from Mtoe to TWh dividing by 0.086 Mtoe/TWh), while the electric energy production from biomass can be derived indirectly, by subtracting all the known values of electricity production from the gross electric energy production: 589.6 15.7 371 52.3 106.8 43.8 B gross H NU otherRES i i EE EE EE EE EE EE TWh             d. Evaluate the electric penetration of renewable sources only (hydro, biomass, other RES); The electric penetration of renewables is derived by dividing the primary energy requirements of renewables by the TPES: 31.9 86.5 4.5 0.42 290.1 H B others RES PE PE PE EP TPES        Department of Energy Politecnico di Milano Author Pag.12 of 12 Date 23/06/2020 f. Evaluate the overall efficiency of the electricity system. Please give the definition and explain it 498.5 0.84 589.6 net overall gross E E     The efficiency of the electricity system is the ratio between the net amount of electricity available for the final consumption (discounted by plants own uses and transmissions losses) and the gross electricity production. This value measure how efficient the electricity system is in term of transmission infrastructures and Plant self- consumptions. It is different from the average value of efficiency of the power conversion plant.