Gestão de Sistemas Energéticos 2015/2016 Exergy Analysis Prof. Tânia Sousa taniasousa@ist.utl.pt

Exergy Exergy is … Thermomechanical exergy: if temperature and/or pressure of a system differ from that of the environment; Chemical exergy – if there is a composition difference between the system and environment;

Evaluating Chemical Exergy The exergy reference environment (the Earth and its atmosphere) Environmental temperature T0 and pressure p0. Set of reference substances with concentrations closely corresponding to the chemical makeup of the natural environment. Reference substances may include Gaseous components of the atmosphere: N2, O2, CO2, H2O(g), and other gases. Solid substances from the Earth’s crust. Substances from the oceans.

Conceptualizing Chemical Exergy CaHbOc enters the control volume at T0, p0. O2 and CO2, H2O(g) enter and exit the control volume at T0 and their respective partial pressures. The ideal gas model applies to O2, CO2, and H2O(g).

Conceptualizing Chemical Exergy Negligible kinetic and potential energy effects Heat transfer between the control volume and environment occurs only at temperature T0 Steady state The chemical exergy per mole of CaHbOc, ech, is the maximum theoretical value of Wcv/nF

Conceptualizing Chemical Exergy The logarithmic term typically contributes only a few percent to the chemical exergy magnitude

Example Compute the exergy of methane, CH4, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example Compute the exergy of methane, CH4, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example Compute the exergy of methane, CH4, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example Compute the exergy of methane, CH4, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example What is the pure CO2 exergy, when T0 = 298.15 K (25oC), p0 = 1 atm?

Example Compute the exergy of pure CO2, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example Compute the exergy of CO2, when T0 = 298.15 K (25oC), p0 = 1 atm. Applies also to other gases in the environment

Example What about the exergy of H2O, when T0 = 298.15 K (25oC), p0 = 1 atm?

Example What about the exergy of H2O, when T0 = 298.15 K (25oC), p0 = 1 atm?

Example What about an ideal mixture of gases with gases that are present in the environment and with molar fractions of yi when T0 = 298.15 K (25oC), p0 = 1 atm?

Example What about an ideal mixture of gases present in the environment when T0 = 298.15 K (25oC), p0 = 1 atm?

Conceptualizing Chemical Exergy

Exergy Balances to Reacting Systems What is the exergy balance to the reversible steady-state combustion of CaHb?

Standard Chemical Exergy The standard exergy value of CaHb is

Example Compute the exergy of methane, CH4, when T0 = 298.15 K (25oC), p0 = 1 atm. gfo (CH4)= -50,79kJ/kmol

Example The exergy of methane, CH4, when T0 = 298.15 K (25oC), p0 = 1 atm. =831,680kJ/kmol=51980kJ/kg

Example What is the HHV of methane at T0 = 298.15 K (25oC), p0 = 1 atm? =831,680kJ/kmol=51980kJ/kg

Standard Chemical Exergy The chemical exergy of hydrocarbon fuels are approximated by …

Standard Chemical Exergy The chemical exergy of hydrocarbon fuels are approximated by their fuel heating values.

Standard Chemical Exergy “The chemical exergy of a substance is the maximum work that can be obtained from it by taking it to chemical equilibrium with the reference environment at constant temperature and pressure.” (Rivero & Garfias, 2006) The standard chemical exergy is chemical exergy at T= 298.15 K and P=1 atm For any substance the chemical exergy can be estimated using:

Total Exergy Total exergy is: First evaluate thermomechanical exergy (the system goes from T, P to T0, P0) and then evaluate the chemical exergy (at constant T0, P0 the system goes to the reference chemical composition of the environment)

Example 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 yeH2O=0.0303

Example 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 yeH2O=0.0303 Steam 5 bar 240ºC Liquid Water 1 bar 25ºC Vapour 0.0303 bar 25ºC

Example 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 yeH2O=0.0303

Example 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.

Example 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 yeP 25ºC

Exergetic efficiency of an internal combustion engine Liquid octane enters an internal combustion engine operating at steady state with a mass flow rate of 1.810-3 kg/s and is mixed with the theoretical amount of air. Determine the exergetic efficiency.

Fuel Cells Fuel (H2) and oxidizer (O2) 40 a 60 % efficiency

Example Compute the standard chemical exergy of hydrogen, H2, when T0 = 298.15 K (25oC), p0 = 1 atm.

Example Compute the standard chemical exergy of hydrogen, H2, when T0 = 298.15 K (25oC), p0 = 1 atm. H2 + 0.5O2 → H2O(l)

Standard Chemical Exergy TABLE A-25

Standard Chemical Exergy TABLE A-26

Standard Chemical Exergy TABLE A-26