Gestão de Sistemas Energéticos 2016/2017 Exergy Analysis Prof. Tânia Sousa taniasousa@tecnico.ulisboa.pt

Evaluating Enthalpy for Reactive Systems The specific enthalpy of a compound (in this datum) at a state where temperature is T and pressure is p is determined from What is the value of in the datum used to assign the enthalpies of formation? h is associated with the change in state from the standard state to the state where temperature is T and the pressure is p (obtained from any table).  

Absolute Entropy The specific absolute entropy of a compound at a state where temperature is T and pressure is P is determined from For the ideal gases in Table A-23, the absolute entropy at a state where temperature is T and pressure is p is given by For the component i of an ideal gas mixture º ref ref Partial pressure

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 Pi

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;

Conceptualizing Chemical Exergy

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

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

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.

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

Example What about an ideal mixture of gases present in the environment when T0 = 298.15 K (25oC), p0 = 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 1.8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

Forms of Energy - Primary energy

Forms of Energy - Final energy

Forms of Energy – Useful Energy

World Sankey Diagram in 2005 Overall 1st law efficiency in converting primary to final energy? 66% ? ? US – 94 EJ Portugal – 1.1 EJ IAASA – Global Energy Assessment 2012

World Sankey Diagram in 2005 Overall 1st law efficiency in converting primary to useful energy? 34% ? ? US – 94 EJ Portugal – 1.1 EJ IAASA – Global Energy Assessment 2012

Typical values of 2nd law efficiencies IAASA - Global Energy Assessment 2012 Overall 2nd law efficiency in converting primary to final is 76% and primary to useful energy is 10%

Second law efficiencies Second law efficiencies by providing information on how much you can improve your efficiency show where efforts should be made Rosen and Dincer, 1997

Energy Balance What is the overall efficiency in thermoelectricity production with and without cogeneration? Compare the values and comment What is the fraction of thermoelectricity that is renewable?

Energy Analysis: Specific Consumption of Operation & Inputs Specific Consumption of Operation A: CEA Specific Consumption of Material 1: CE1

Benefits of Cogeneration Substitution of fuel driven cogeneration with fuel driven electrical generation and fuel heating Comparison using first law efficiencies? What are the exergy efficiencies assuming that the energy and exergy of the fuel are identical? 423K 423K T0= 288K

Benefits of Cogeneration Substitution of fuel driven cogeneration with fuel driven electrical generation and electrical heating Comparison using first law efficiencies? What are the exergy efficiencies assuming that the energy and exergy of the fuel are identical? 423K 423K T0= 288K

Benefits of Cogeneration Cogeneration increases the energy and exergy efficiencies compared to separate processes The exergy efficiency is much lower than the energy efficiency for cogeneration and non-cogeneration. Why? Separate System Cogeneration Caso a) =66.2% =30.9% =92% =43% Caso c) =35.5% =16.6%