Exergy in Processes Flows and Destruction of Exergy
Exergy of Different Forms of Energy Chemical Energy Heat Energy Pressurised Gas Electricity Kinetic Energy
Oxidation of Methane ΔH = -890.1 kj/mol ΔS = -242.8 J/(mol.K) Exergy available = - ΔH + T 0 *ΔS If T 0 = 298K, then: Exergy = 817.9 kj/mol Energy quality = 92%
Heat If T 0 = 10C (283K) Heat at 2000C (2273K), energy quality = 87.5% Heat at 100C (373K), energy quality = 24.1% Heat sink at -100C?
Heat Water at 100C, reference T 10C As heat is taken from it, its temperature gradually decreases. So, the exergy of the first heat removed is that of heat at 100C (energy quality 24.1%) The exergy of the last heat removed is that of heat at just above 10C (energy quality zero) The average energy quality of all the heat can be calculated either by doing a mathematical integration or by looking up thermodynamic data and calculating the changes in H and in S. The result is 13%
Heat Steam at 100C Step 1 condense steam becomes water at 100C, about 2260 kj/kg of enthalpy, all at 100C. Exergy = 544.7 kj/kg Energy quality = 24.1% Step 2 as for water at 100C Total Exergy = 594.3 kj/kg, energy quality = 22.6%
Compressed Air 1 L volume of air at 2 atmospheres pressure, expanded into 1 L of vacuum Enthalpy of decompression.. zero! Entropy change 0.47 J/K If T 0 = 298K, then Exergy = 139 J Energy quality. 139/0????
Electricity No entropy Nothing random about it. If DC, the voltage is always the same. If AC, the voltage is completely predictable.
Kinetic Energy Movement of a body (Laminar) flow of fluid both predictable no entropy Thermal motion random entropy depends on temperature
Destruction of Exergy Irreversible events during the process leak pressure drop in flowing fluid heat transfer friction electric circuit losses combustion
Effect of Irreversibility Reversible only Endpoint Entropy With irreversible event Endpoint Entropy Reversible Reversible S Irreversible S Reversible Starting Entropy Starting Entropy
Exergy Destruction Reversible Process Only Enthalpy change ΔH Entropy change ΔS Exergy = - ΔH + T 0 * ΔS With Irreversible Event Enthalpy change ΔH Reversible entropy change ΔS ΔS irr Exergy = - ΔH + T 0 * (ΔS ΔS irr ) Exergy destroyed = T 0 * ΔS irr
Exergy Loss Irreversible event find ΔS How? Use literature information on entropy of before and after states Look at heat flow from high T to lower Look at reversible route for the same change and evaluate the integral of dq/t
Exergy Loss Example combustion Definitely irreversible, and generally no work or heat transfer take place during the event Gases react, forming combustion products Use ΔH to calculate temperature achieved Get entropy numbers for products Compare total entropy of products with entropy of the starting materials at the starting temperature Result is the entropy change it s all irreversible if there is no heat transfer Exergy loss is T 0 ΔS
Exergy Loss Example heat transfer Heat q moves from reservoir at T 1 to reservoir at T 2 Entropy of first reservoir decreases by q/t 1 Entropy of second reservoir increases by q/t 2 Increase is q(1/t 2 1/T 1 ) Exergy loss is T 0 * q(1/t 2 1/T 1 )
Exergy Loss Ideal gas expands to double its volume (leak) What is an equivalent reversible process? Isothermal expansion, doing work (heat in, work out) If n moles of gas are at pressure P, temperature T, then work out is: nrt ln(2) heat in is also nrt ln(2) So: ΔS = nr ln(2) Exergy loss = T 0 nr ln(2)
Basic Heat Power Cycle Pressure high Heat in Power in Pump Motor Power out Pressure low Heat out
Power Plant the Exergy View Air Steam Turbine Power Gas Boiler Condenser Exhaust Water Pump Cooling Water
1 - Combustion Burn methane in just sufficient air to provide the oxygen required. (Start at 25C, 298K) Temperature reaches 1950C, 2223K. Entropy increase from start is 802.0 J/(mol.K). This is an irreversible process. Exergy destruction is 239.0 kj/mol, or 29% of the starting exergy.
Combustion Methane, 25C Energy loss - nil Flame Gases, 1950C Air, 25C Exergy loss 29%
2 Heat Transfer Hot gases from combustion transfer heat to water at 25C, making steam at 538C and critical pressure (217.7 atm) Combustion gases cooled to 25C, and water condensed Gas entropy decreases by 1060.3 J/K per mol of methane Water entropy increases by 1661.4 J/K per mol of methane Net entropy increase of 601.1 J/K per mol of methane Exergy destruction 179.1 kj/mol, or 22% of the starting exergy. Total destroyed so far is 51%
Heat Transfer Gases, 1950C Steam, 538C, 217atm Heat Exchanger Gases + condensed water, 25C Water, 25C, 217atm
Turbine and Condenser A big steam turbine can extract 80-90% of the theoretically available energy In this example, the turbine might produce work equivalent to 30% of the exergy, and destroy 7%. Condensers have big heat flows, but at temperatures not much above ambient, so exergy losses there are about 3%
Power Plant Energy Flows Stack 5 Other Losses 3 Fuel 100 Boiler Steam 95 Shaft Power 32 Turbine Steam 60 Condenser Cooling Water 60
Power Plant Exergy Flows and Destruction Stack 2 Other Losses 1 Fuel 92 27 65 20 Steam 43 7 Shaft Power 32 Combustion Heat Transfer Turbine Steam 3 2 Condenser Cooling Water 1
Gas Turbine Air is compressed Natural gas is burned in the compressed air A turbine takes power from the hot compressed air There is still combustion, but no heat exchanger
Gas Turbine Gas in Turbine Inlet Temperature 1000 C Air in Shaft power Shaft power out Compressor, 15x, 85% efficient Turbine, 85% efficient
Gas Turbine Energy Flows Air in Gas in 100 59 159 Turbine Inlet Temperature 1000 C Heat out 68 Shaft power 59 Shaft power out 32 Compressor, 15x, 85% efficient Turbine, 85% efficient
Gas Turbine Exergy Flows and Destruction Gas in 92 Turbine Inlet Temperature 1000 C Air in 5 54 115 31 8 Heat out 16 Shaft power 59 Shaft power out 32 Compressor, 15x, 85% efficient Turbine, 85% efficient
Home Furnace Losses 1 st Law Exhaust 5 Fuel 100 Heat to Building 95
Home Furnace Exergy Flows and Destruction Combustion Exhaust 1 Fuel 92 27 Heat Transfer 58 Heat to Building 6
Energy Efficiency Usually defined as the fraction of energy that goes where you want it to. The denominator is the enthalpy available The numerator is the electricity produced, the heat that goes to the purpose intended, a total of the two (cogeneration)
Apples and Oranges Power generation 50% is very good House furnace 70% is very poor! It s easy to avoid energy losses It s very difficult to avoid exergy destruction.
Exergy Analysis Levels the energy playing field Consistent method to present the value of energy that is in different forms Choice of reference temperature depends on the purpose of the analysis