Gestão de Sistemas Energéticos 2015/2016 Exergy Analysis Prof. Tânia Sousa

Cogeneration Overall energy and exergy efficiencies Primary Energy and Exergy Savings Marginal efficiency of electricity produced Trade-offs between useful heat and electricity produced The ratio of electricity to useful heat

Primary Energy (Exergy) Savings How to compute PES? What are the PES in this case?

Primary Energy (Exergy) Savings What are the PES and PExS in this case? Heat at 80ºC 200

Marginal (or Effective) efficiency of electricity production The amount of electrical energy produced divided by the extra fuel used to produce electricity along with heat compared to the amount of fuel that would be used in producing heat alone.

Marginal efficiency of electricity production Comparison between  marginal and conventional 

Marginal efficiency of electricity production Comparison between  marginal and conventional 

Marginal efficiency of electricity production The marginal electricity generation efficiency in cogeneration is generally >> than the efficiency of a dedicated central powerplant To displace as much inefficient central electricity generation as possible when cogeneration is used to supply a given heating requirement requires that the electricity-to-heat production ratio in cogeneration be as large as possible

Trade-offs between useful heat and electricity In simple-cycle cogeneration, capturing some of the heat in the hot gas exhaust does not reduce the production of electricity, but the electrical production is already low

Cogeneration system Prime Mover (Open Cycle Gas Turbine) –Power: 500 kW to 250 MW –Produce High Temperature Heat (400ºC to 600ºC) –High back-work ratio (40% to 80%) –Electrical efficiency  35% –Energy and exergy efficiencies? Source: Williams (1989, Electricity: Efficient End-Use and New Generation Technologies and Their Planning Implications, Lund University Press)

Cogeneration system Prime Mover (Closed Cycle Gas Turbine) –Any fuel can be used

Trade-offs between useful heat and electricity In cogeneration with steam turbines, the withdrawal of steam from the turbine at a higher temperature than would otherwise be the case reduces the electricity production

Prime mover (Steam Turbine) –Power: 500 kW to 100 MW –Several types of fuel –Back-pressure steam turbine (e.g. in refineries): trade-offs between heat and work? Cogeneration system

Prime mover (Steam Turbine) –Power: 500 kW to 100 MW –Several types of fuel –Extraction condensing steam turbine (e.g. district heating systems): trade-offs between heat and work? –Flexibility in the amount of heat produced Cogeneration system

Trade-offs between useful heat and electricity The higher the temperature at which we want to take heat in a steam turbine, the more the electricity production is reduced Source: Bolland and Undrum (1999, Greenhouse Gas Control Technologies, , Elsevier Science, New York)

Combined Cycle Cogeneration Production of work and heat? Cascade of heat uses Electricity generation efficiencies of 55-60%, Economical only in sizes of MW or greater

Combined Cycle Cogeneration

Combined Cycle Power Generation Is this cogeneration? Tapada do Outeiro

Cogeneration Ratio of electricity to useful heat in cogeneration

Cogeneration Performance Parameters * taken from Cogeneration Guide, Cogen Europe

Cogeneration system Prime Mover (reciprocating internal combustion engines) –Processes occur within reciprocating piston-cylinder. –Cylinder contents do not execute a thermodynamic cycle –Displacement volume –Compression ratio, r Spark-ignition –A mixture of fuel and air is ignited by a spark plug. –Fuel: natural gas, gasoline –This type is For applications up to about 225 kW. Lightweight and relatively low cost.

Cogeneration system Compression-ignition –Air is compressed to a high pressure and temperature. –Combustion occurs spontaneously when fuel is injected. –This type is For high-power applications and when fuel economy is required.

Four-stroke cycle: Intake stroke With the intake valve open, piston stroke draws a fresh charge into the cylinder. – For spark-ignition engines, the charge includes fuel and air. – For compression-ignition engines, the charge is air alone. Spark ignition engine

Four-stroke cycle: Compression stroke With both valves closed, piston compresses charge, raising P and T and requiring W input –For spark-ignition engines, combustion is initiated by the spark plug. –For compression-ignition engines, combustion is initiated by injecting fuel into the hot compressed air.

Four-stroke cycle: Power stroke With both valves closed, the gas mixture expands and work is done on the piston as it returns to bottom dead center.

Four-stroke cycle: Exhaust stroke The burned gases are purged from the cylinder through the open exhaust valve.

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;

Properties Properties u, h and s are not measured directly but obtained from other data that is easier to measure Values are attributed to u, h and s considering arbitrary values at reference states For water, the reference state is saturated liquid at 0.018ºC. At this state, the specific internal energy is set to zero. Values of the specific enthalpy are calculated from h = u+ Pv

Energy and Entropy Balances for Reacting Systems Tables use arbitrary datums to assign enthalpy values, they must be used only to determine differences in enthalpy between two states H 2 and O 2 enter the control volume but do not exit, and liquid water exits but does not enter. For each it is necessary to assign enthalpy and entropy values in a way that the common datum cancels. H 2 + ½O 2 → H 2 O H2H2 H2OH2O O2O2

Evaluating Enthalpy for Reactive Systems An enthalpy datum for the study of reacting systems is established by: –Assigning a value of zero to the enthalpy of C, H 2, N 2, O 2, and other stable elements at the standard reference state defined by T ref = K (25 o C) and p ref = 1atm. –The enthalpy of a compound at the standard state equals its enthalpy of formation h f 0

Evaluating Enthalpy for Reactive Systems What is the meaning of the enthalpy of formation? TABLE A-25

Evaluating Enthalpy for Reactive Systems The enthalpy of formation is the energy released or absorbed when the compound is formed from its elements, all being at T ref and p ref. TABLE A-25 Q= Kj/Kmol

Evaluating Enthalpy for Reactive Systems A negative (positive) enthalpy of formation correspond to an exothermic (endothermic) reaction when the compound is formed from its elements. TABLE A-25

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).

Example Pulverized coal (assume carbon) enters a combustor at 298 K, 1 atm and burns completely with O 2 entering at 400 K, 1 atm. A stream of carbon dioxide exits at 500 K, 1 atm. For a control volume at steady state enclosing the reactor, evaluate the rate of heat transfer, in kJ per kmol of coal entering. Assume the ideal gas model for O 2 and CO 2, and neglect kinetic and potential energy effects. C CO 2 O2O2 298 K, 1 atm 400 K, 1 atm 500 K, 1 atm

Example TABLE A-23

Reacting Systems: combustion In combustion reactions, rapid oxidation of combustible elements of the fuel results in energy release as combustion products are formed. Combustion is complete when –All carbon present in the fuel is burned to carbon dioxide –All hydrogen present is burned to water –All sulfur present is burned to sulfur dioxide –All other combustible elements are fully oxidized

Reacting Systems: combustion The theoretical amount of air is the minimum amount of air that supplies sufficient oxygen for the complete combustion of all the carbon, hydrogen, and sulfur present in the fuel. For complete combustion with the theoretical amount of air, the products consist of CO2, H2O, and SO2 plus nitrogen present in the reactants. No free oxygen, O2, appears in the products. Air is considered to be 21% O2 and 79% N2 on a molar basis. What is the theoretical amount of air and the heat released in the combustion of CH4 (all being at T and P)?

Reacting Systems: combustion Simplifying assumptions: air and exhaust gases are considered a mixture of ideal gases

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.

Heating Values of Hydrocarbon Fuels The higher heating value (HHV) is obtained when all the water formed by combustion is a liquid. The lower heating value (LHV) is obtained when all the water formed by combustion is a vapor.

Heating Values of Hydrocarbon Fuels TABLE A-25

Example Evaluate the lower heating value of liquid octane at 25 o C, 1 atm, in kJ per kg of octane, and compare with the value provided in Table A-25. C 8 H (O N 2 ) → 8CO 2 + 9H 2 O(g) + 47N 2

Example Evaluate the lower heating value of liquid octane at 25 o C, 1 atm, in kJ per kg of octane, and compare with the value provided in Table A-25. This value agrees with the value (44,430 kJ/kg for C 8 H 18 ) from Table A-25, as expected. LHV = 5,074,630 kJ/kmol C 8 H 18 LHV = 44,429 kJ/kg C 8 H 18

Evaluating Entropy for Reactive Systems Absolute Entropy For reacting systems, a common datum must be used to assign entropy values to participating substances: –the entropy of a pure crystalline substance is 0 at T=0K (the third law of thermodynamics) Values of entropy determined relative to this datum are called absolute entropy values. Are the entropies given in A2 absolute entropies?

Evaluating Entropy for Reactive Systems Absolute Entropy For reacting systems, a common datum must be used to assign entropy values to participating substances: –the entropy of a pure crystalline substance is 0 at T=0K (the third law of thermodynamics) Values of entropy determined relative to this datum are called absolute entropy values. Steam tables and Tables A-7 through A-18 do not provide absolute entropy values.

Absolute Entropy TABLE A-25

Absolute Entropy TABLE A-23

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 Absolute Entropy º Partial pressure

Example Compute entropy production for complete combustion with a) theoretical amount of air and b) 400% theoretical air.

Evaluating Gibbs Function for Reacting Systems The specific Gibbs function g is given by Gibbs function is a property because it is defined in terms of other properties.

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

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 = K (25 o C) and p ref = 1atm. –The Gibbs function of a compound at the standard state equals its Gibbs function of formation – 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.