Homework 3 solution

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Iowa State University *

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Mechanical Engineering

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Apr 3, 2024

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© 2023 Kenneth Bryden 1 ME 433 Homework 3 - Carbon emissions 1. Consider an 800 MW coal and corn stover co-fired Rankine cycle power plant with a capacity factor of 86.0% and an availability of 97.0%. The coal used to fuel the power plant has a carbon content of 54.0% (wt), a higher heating value of 8800 Btu/lbm, and costs $46.00/t. The plant is considering co-firing coal with 10% corn stover based on input energy. The corn stover consists of 30.0% carbon (wt) and has a higher heating value of 6000 Btu/lbm, and costs $62.00/t. The corn stover is considered a carbon neutral fuel. The plant has a heat rate of 9400 Btu/kWh. a. How many tons of coal are needed annually to fuel the co-fired power plant (10 6 t/y)? 800 MW 1 × 8760 h y × 0.86 MWh !"#$"# MWh %&#’( × 10 ) kWh MWh × 9400 Btu #* kWh ’ = 56.65 × 10 +, Btu -. y 0.90 1 × 56.65 × 10 !" Btu #$ y × lbm %&’( 8800 Btu × t 2000 lbm = 2.897 × 10 ) t %&’( /y = 2.90 × 10 ) t %&’( /y b. How many tons of corn stover are needed annually to fuel the co-fired power plant (t/y)? 0.10 1 × 56.65 × 10 +, Btu -. y × lbm /#!0’% 6000 Btu × t 2000 lbm = 472.1 × 10 ) t /#!0’% /y = 472 × 10 ) t /#!0’% /y c. What is the annual fuel cost of the co-fired power plant (10 6 $/y)? : 2.897 × 10 1 t 2!&3 y × $46 t 2!&3 < + : 472.1 × 10 ) t /#!0’% y × $62 t /#!0’% < = $162.5 × 10 1 y = $163 × 10 1 /y d. How many metric tons of CO 2 are generated annually by the power plant (10 6 Mg/y)? 2.897 × 10 1 t 2!&3 y × Mg 1.102 t 2!&3 × 0.54 Mg 4 Mg 2!&3 × 44 Mg 45 ! 12 Mg 2 = 5.205 × 10 1 Mg 45 ! y = 5.21 × 10 1 Mg 45 ! /y e. How many metric tons of CO 2 are generated per MWh of electricity output (Mg CO2 /MWh)? 800 MW 1 × 8760 h y × 0.86 MWh (’3-0’%’( MWh %&#’( = 6.027 × 10 1 MWh y 5.205 × 10 1 Mg 45 ! y × y 6.027 × 10 1 MWh = 0.864 Mg 45 ! / MWh

© 2023 Kenneth Bryden 2 2. Consider a 100 kW combined heat and power fuel cell power plant. The plant is fueled with natural gas that has a lower heating value of 48.3 MJ/kg. Based on the lower heating value of the fuel, the combined heat and power efficiency is 80.0%. Assume natural gas has a carbon content of 72.0% (wt). How much CO 2 is produced per MWh of combined heat and power (kg CO2 /MWh CHP )? ࠵? 45 ! ࠵? ’3’2 = MJ 78 0.80 MJ 49: ∙ kg 78 48.3 MJ 78 ∙ 0.72 kg 4 kg 78 ∙ 3.667 kg 45 ! kg 4 ∙ MJ MW ∙ s ∙ 3600 s h = 246.0 kg 45 ! MWh 49: = 246 kg 45 ! /MWh 49: 3. Consider a 100 kW fuel cell power plant that is fueled with natural gas that has a lower heating value of 48.3 MJ/kg. Based on the lower heating value of the fuel, the power plant has a heat rate of 7500 Btu/kWhe. The fuel cell is a combined heat and power (CHP) plant which produces 200,000 Btu/h of heat energy at rated power. Assume natural gas has a carbon content of 70.0% (wt). How much CO 2 is produced per MWh e if only the electrical power is used and the heat is discarded (kg CO2 /MWh e )? ࠵? 45 ! ࠵? ;<;= = 7500 Btu 78 kWh ;<;= × MJ 947.8 Btu × kg 78 48.3 MJ × 0.70 kg 4 kg 78 ∙ 3.667 kg 45 ! kg 4 ∙ 10 ) kWh MWh ࠵? 45 ! ࠵? ;<;= = 420.5 kg 45 ! MWh = 421 kg 45 ! /MWh 4. A 200 MW combined cycle gas turbine (CCGT) power generation station is considering the addition of a carbon capture and storage (CCS) system. The power generation station has a capacity factor of 90.0% and a heat rate of 8530 Btu/kWh (higher heating value). The CCS system will remove and stores 85.0% of the CO 2 produced by the power generation station. However, the CCS system will reduce the efficiency of the plant by 6.00%. For example, a plant with 32.0% efficiency without a CCS system would have 26.0% efficiency with a CCS system. The rated capacity of the plant will remain at 200 MW after the installation of the CCS. Assume the natural gas used to fuel the CCGT power generation station is composed of 95.0% methane (CH 4 ) and 5.0% nitrogen (N 2 ) on a volumetric basis and has a higher heating value of 52.8 MJ/kg. It is purchased for $3.50/MBtu. a. What is the mass fraction of carbon (C) in the natural gas (Kg C /Kg NG )? The question is ࠵? 4 = ࠵? 4 ࠵? 78 = ? The easiest way to approach this question is to first choose a basis (in this case 1 mole of natural gas works well). Recalling that volume fraction is the same as mole fraction. We can determine the mass of one mole of natural gas (NG). This is of course the molecular weight of the natural gas. MW 78 = ࠵? 78 kgmol 78 = 0.95 kgmol 49 " kgmol 78 × 16.04 kg 49 " kgmol 49 " + 0.05 kgmol 7 ! kgmol 78 × 28.01 kg 7 ! kgmol 7 ! = 16.64 kg 78 kgmol 78 We now need to find the mass of the carbon in a mole of natural gas

© 2023 Kenneth Bryden 3 ࠵? 4 kgmol 78 = 0.95 kgmol 49 " kgmol 78 × 12.01 kg 4 kgmol 49 " = 11.41 kg 4 kgmol 78 Combining ࠵? 4 = ࠵? 4 ࠵? 78 = kgmol 78 16.64 kg 78 × 11.41 kg 4 kgmol 78 = 0.6857 kg 4 kg 78 = 0.686 kg 4 /kg 78 b. What is the CO 2 emission factor for the natural gas fuel (kg CO2 /MBtu NG )? ࠵?࠵? 45 ! = 0.6857 kg 4 kg 78 × kg 78 52.8 MJ × MJ 947.8 Btu × 10 1 Btu MBtu × 3.667 kg 45 ! kg 4 = 50.25 kg 45 ! MBtu 78 = 50.3 kg 45 ! /MBtu 78 c. What are the CO 2 emissions per MWh of electricity delivered for the current power generation station (Mg CO2 /MWh)? 50.25 kg 45 ! MBtu 78 × MBtu 10 1 Btu × 8530 Btu kWh × Mg 45 ! 10 ) kg 45 ! × 10 ) kWh MWh = 0.4286 Mg 45 ! MWh = 0.429 Mg 45 ! /MWh d. What are the annual CO 2 emissions of the current generating station (Mg CO2 /y)? 200 MW 1 × 8760 h y × 0.90 MWh (’3 MWh %&#’( = 1.577 × 10 1 MWh/y 1.577 × 10 1 MWh y × 0.4286 Mg 45 ! MWh = 675.8 × 10 ) Mg 45 ! y = 676 × 10 ) Mg 45 ! /y e. What would be the CO 2 emissions per MWh of electricity delivered if the CCS were installed (Mg CO2 /MWh)? ࠵? >/44? = K kWh ’ 8530 Btu #* × 3412 Btu kWh L − 0.06 = 34.00% ࠵?࠵? >/44? = K Btu -. 0.3400 Btu !"# × 3412 Btu kWh ’ L = 10,040 Btu/kWh ’ 50.25 kg 45 ! MBtu 78 × MBtu 10 1 Btu × 10,040 Btu kWh × Mg 45 ! 10 ) kg 45 ! × 10 ) kWh MWh × 0.15 Mg 45 ! (%&’() Mg 45 !(*+,-./%-) = 0.07567 Mg 45 ! MWh = 0.0757 Mg 45 ! /MWh f. What would be the annual CO 2 emissions if the CCS is installed (Mg CO2 /y)? 1.577 × 10 1 MWh y × 0.07567 Mg 45 ! MWh = 119.3 × 10 ) Mg 45 ! y = 119 × 10 ) Mg 45 ! /y g. How many metric tons of CO 2 emissions would be avoided annually if the CCS is installed (Mg CO2 /y)?

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© 2023 Kenneth Bryden 4 675.8 × 10 ) Mg 45 ! y − 119.3 × 10 ) Mg 45 ! y = 556.5 × 10 ) Mg 45 ! y = 556 × 10 ) Mg 45 ! /y h. What is the increased cost of fuel per year of electricity generated as a result of the CCS system (10 6 $/y)? ࠵? 2"%%’.# = 1.577 × 10 1 MWh ’ y × 10 ) kWh MWh × 8530 Btu kWh ’ × MBtu 10 1 Btu × $3.50 MBtu = $47.08 × 10 1 /y ࠵? >/22/ = 1.577 × 10 1 MWh ’ y × 10 ) kWh MWh × 10,040 Btu kWh ’ × MBtu 10 1 Btu × $3.50 MBtu = $55.42 × 10 1 /y ∆ @ = $55.42 × 10 1 y − $47.08 × 10 1 y = $8.340 × 10 1 /y = $8.34 × 10 1 /y i. What is the increased cost of fuel per metric ton of CO 2 avoided ($/Mg CO2 )? ࠵? 45 ! = $8.340 × 10 1 y × y 556.5 × 10 ) Mg 45 ! = $14.99/Mg 45 ! = $15.0/Mg 45 !