Gestão de Sistemas Energéticos 2017/2018 Exergy Analysis Prof. Tânia Sousa taniasousa@tecnico.ulisboa.pt
Conceptualizing Chemical Exergy C a H b O c enters the control volume at T 0, p 0. O 2 and CO 2, H 2 O(g) enter and exit the control volume at T 0 and their respective partial pressures. The ideal gas model applies to O 2, CO 2, and H 2 O(g).
Conceptualizing Chemical Exergy Negligible kinetic and potential energy effects Heat transfer between the control volume and environment occurs only at temperature T 0 Steady state The chemical exergy per mole of C a H b O c, e ch, is the maximum theoretical value of W cv /n F
Conceptualizing Chemical Exergy
Evaluating Gibbs Function for Reacting Systems The specific Gibbs function g is given by g h Ts Gibbs function is a property because it is defined in terms of other properties.
Conceptualizing Chemical Exergy The logarithmic term typically contributes only a few percent to the chemical exergy magnitude
Compute the exergy of pure CO 2, when T 0 = 298.15K, p 0 = 1 atm.
Compute the exergy of CO 2, when T 0 = 298.15 K, p 0 = 1 atm. Standard Molar Chemical Exergy, e ch (kj/kmol), of Selected Substances at 298 K and p 0 Substance Formula Model I a Model II b Oxygen O 2 (g) 3,950 3,970 Carbon dioxide CO 2 (g) 14,175 19,870 Water H 2 O(l) 45 900 Hydrogen H 2 (g) 235,250 236,100 Methane CH 4 (g) 824,350 831,650 Octane C 8 H 18 (l) 5,413,100 Ethanol C 2 H 5 OH(l) 1,342,085 1,357,700 e e ch ch RT 0 20,108 ln ( y kj kmol 1 e CO 2 ) Applies also to other gases in the environment
Evaluating Gibbs Function for Reacting Systems The specific Gibbs function of a compound (in this datum) at a state where temperature is T and pressure is p is determined from In an ideal gas mixture, the specific Gibbs function is evaluated at P i
Evaluating Gibbs Function for Reacting Systems TABLE A25 Thermochemical Properties of Selected Substances at 298K and 1 atm Enthalpy of Gibbs Function Heating Values Absolute Formation, of Formation, Entropy, o o Higher, Lower, h g o Molar Mass, f f s HHV LHV Substance Formula M (kg/kmol) (kj/kmol) (kj/kmol) (kj/kmol K) (kj/kg) (kj/kg) Carbon C(s) 12.01 0 0 5.74 32,770 32,770 Hydrogen H2(g) 2.016 0 0 130.57 141,780 119,950 Nitrogen N2(g) 28.01 0 0 191.50 Oxygen O2(g) 32.00 0 0 205.03 Carbon Monoxide CO(g) 28.01 110,530 137,150 197.54 Carbon dioxide CO2(g) 44.01 393,520 394,380 213.69 Water H2O(g) 18.02 241,820 228,590 188.72 Water H2O(l) 18.02 285,830 237,180 69.95 Hydrogen peroxide H2O2(g) 34.02 136,310 105,600 232.63 Ammonia NH3(g) 17.03 46,190 16,590 192.33 Oxygen O(g) 16.00 249,170 231,770 160.95 Hydrogen H(g) 1.008 218,000 203,290 114.61 Nitrogen N(g) 14.01 472,680 455,510 153.19 Hydroxyl OH(g) 17.01 39,460 34,280 183.75 Methane CH4(g) 16.04 74,850 50,790 186.16 55,510 50,020 Acetylene C2H2(g) 26.04 226,730 209,170 200.85 49,910 48,220
Evaluating Gibbs Function for Reacting Systems A Gibbs function datum for the study of reacting systems is established by: Assigning a value of zero to the Gibbs function of C, H 2, N 2, O 2, and other stable elements at the standard reference state defined by T ref = 298.15 K (25 o C) and p ref = 1atm. The Gibbs function of a compound at the standard state o equals its Gibbs function of formation o g f is the change in the Gibbs function for the reaction in which the compound is formed from its elements, the compound and elements all being at the standard state. g f
Compute the exergy of methane, CH 4, when T 0 = 298.15 K (25 o C), p 0 = 1 atm.
Compute the exergy of methane, CH 4, when T 0 = 298.15 K (25 o C), p 0 = 1 atm. 2 e O H e CO 2 e O 0 O(g) H CO O F ch 2 2 2 2 2 2 ln 2 2 y y y RT g g g g e
Compute the exergy of methane, CH 4, when T 0 = 298.15 K (25 o C), p 0 = 1 atm. g o f, CH 4 50,790 kj/kmol g o f, CO 2 394,380 kj/kmol g o f, O 2 0 kj/kmol g o f, H2O(g) 228,590 kj/kmol
Compute the exergy of methane, CH 4, when T 0 = 298.15 K (25 o C), p 0 = 1 atm. Standard Molar Chemical Exergy, e ch (kj/kmol), of Selected Substances at 298 K and p 0 Substance Formula Model I a Model II b Oxygen O 2 (g) 3,950 3,970 Carbon dioxide CO 2 (g) 14,175 19,870 Water H 2 O(l) 45 900 Hydrogen H 2 (g) 235,250 236,100 Methane CH 4 (g) 824,350 831,650 Octane C 8 H 18 (l) 5,413,100 Ethanol C 2 H 5 OH(l) 1,342,085 1,357,700 kj e ch 830,174 kmol
What about the exergy of H 2 O, when T 0 = 298.15 K, p 0 = 1 atm?
What about the exergy of H 2 O, when T 0 = 298.15 K (25 o C), p 0 = 1 atm?
Heating Values of Hydrocarbon Fuels The heating value of a fuel is the difference between the enthalpy of the reactants and the enthalpy of the products when the fuel burns completely with air, reactants and products being at the same temperature T and pressure p. n ihi R R n i P n e h e o o hf h i ne hf h P e
Heating value & chemical exergy
What are the HV of methane at T 0 = 298.15 K (25 o C), p 0 = 1 atm? =831,680kJ/kmol=51980kJ/kg Substance Model for HHV LHV e ch Liquid octane Gasoline 47,900 44,430 47,390 Liquid ethanol Biofuel gasoline substitute a 29,670 26,800 29,470 b Gaseous methane Natural gas 55,510 50,020 51,850 a. In the U.S. today ethanol is made from the starch of corn kernels. In Brazil, which is also a major ethanol producer, sugar cane is used. b. On a mass basis, the chemical exergy of ethanol is about 2/3 of that for gasoline, thereby giving lower vehicle fuel mileage when using a blend such as E85 (85% ethanol, 15% gasoline).
Standard Chemical Exergy The chemical exergy of hydrocarbon fuels are approximated by their fuel heating values. Substance Model for HHV LHV e ch Liquid octane Gasoline 47,900 44,430 47,390 Liquid ethanol Biofuel gasoline substitute a 29,670 26,800 29,470 b Gaseous methane Natural gas 55,510 50,020 51,850 a. In the U.S. today ethanol is made from the starch of corn kernels. In Brazil, which is also a major ethanol producer, sugar cane is used. b. On a mass basis, the chemical exergy of ethanol is about 2/3 of that for gasoline, thereby giving lower vehicle fuel mileage when using a blend such as E85 (85% ethanol, 15% gasoline).
Total Exergy Total exergy is: First evaluate thermomechanical exergy (the system goes from T, P to T 0, P 0 ) and then evaluate the chemical exergy (at constant T 0, P 0 the system goes to the reference chemical composition of the environment)
Steam at 5 bar, 240ºC leaks from a line in a vapor power plant. Evaluate the flow exergy of the steam, in kj/kg, relative to an environment at T=25ºC, P=1 atm in which the mole fraction of water vapor is y e H2O=0.0303
Steam at 5 bar, 240ºC leaks from a line in a vapor power plant. Evaluate the flow exergy of the steam, in kj/kg, relative to an environment at T=25ºC, P=1 atm in which the mole fraction of water vapor is y e H2O=0.0303 Steam 5 bar 240ºC Liquid Water 1 bar 25ºC Vapour 0.0303 bar 25ºC
Steam at 5 bar, 240ºC leaks from a line in a vapor power plant. Evaluate the flow exergy of the steam, in kj/kg, relative to an environment at T=25ºC, P=1 atm in which the mole fraction of water vapor is y e H2O=0.0303
Methane gas enters a reactor and burns completely with 140% theoretical air. Combustion products exit as a mixture at temperature T and a pressure of 1 atm. For T 480 and 1560 K, evaluate the flow exergy of the combustion products, in kj per kmol of fuel.
Methane gas enters a reactor and burns completely with 140% theoretical air. Combustion products exit as a mixture at temperature T and a pressure of 1 atm. For T 480 and 1560 K, evaluate the flow exergy of the combustion products, in kj per kmol of fuel. Combustion Products yp 480K Combustion Products yp 25ºC Combustion Products at y e P 25ºC
What about an ideal mixture of gases present in the environment when T 0 = 298.15 K, p 0 = 1 atm?
Exergetic efficiency of an internal combustion engine Liquid octane enters an internal combustion engine operating at steady state with a mass flow rate of 1.810-3 kg/s and is mixed with the theoretical amount of air. Determine the exergetic efficiency. Substance Model for HHV LHV e ch Liquid octane Gasoline 47,900 44,430 47,390 a b