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Exergy Analysis Process EngineeringThermodynamics course # 424304.0 v. 2015 Exergy Analysis Commented / edited by Ron Zevenhoven Prof. Özer Arnas, visiting ÅA VST May/June 2014 from the US Military Academy Åbo Akademi University Thermal and Flow Engineering Laboratory / Värme- och strömningsteknik tel. 3223 ; [email protected] course material: http://users.abo.fi/rzevenho/kursRZ.html ÅA 424304 1.1 Exergy vs. Energy Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 2/102 Energy Conversion /1 . In a hydraulic power plant, the potential energy difference can be completely converted into work . For a thermal plant Carnot (C1824) discovered that only a portion of heat Q at temperature T1 can be converted into work, with cold T T T Pic: S05 W Q Q sink temperature T : 2 T T 11 jan 15 Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 3/102 Energy Conversion /2 . The preferable way to convert heat Q at T1 into work is to use a natural, unlimited cold sink, such as the natural environment at temperature T0. With T2 > T0 no full use of Q is made; T T T Pic: S05 for T2 < T0 a cooling W Q Q max effort is needed. T T 11 jan 15 Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 4/102 Exergy /1 . EXERGY quantifies how much of a certain amount of energy contained in an energy source can be extracted as useful work. jpg . The potential of (natural) energy resources for driving a mechanical, thermal, chemical or biological process depends on the deviation from thermodynamic equilibrium with the surrounding environment. This allows evaluation of the ability to perform maximum work under certain environmental conditions. This involves quality assessments, for example for heat Q its temperature T, relating it to temperature T0 of the surrounding environment. Picture:http://cpcclibraries.files.wordpress.com/2008/04/earth. Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 5/102 Exergy /2 . Note that work is a path function: W = ƒ(initial state, path, final state) . For maximising the work output: – The process should be reversible b1/Dead_possum.jpg/800px-Dead_possum.jpg – The end of the process should be at a dead state which is in equilbrium with the surrounding environment: temperature T0 and pressure p0 as the environment; no kinetic or potential energy relative to the environment; no chemical reactivity with the environment. org/wikipedia/commons/thumb/b/ (And no electrical, magnetic etc. effects.) . This requires a description of the state and, if chemistry is involved, the composition of the local environment for the prevailing chemical species. Picture: http://upload.wikimedia. Picture: Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 6/102 Exergy /3 . While the quantities of energy allow for ”bookkeeping” with the help of the First Law of Thermodynamics (”energy cannot be produced or destroyed”); the exergy concept follows from the Second Law of Thermodynamics, which involves the quality of energy and its degradation during energy conversion. A few useful definitions: Exergy expresses the maximum work output attainable in the natural environment, or the minimum work input necessary to realise the reverse process (Rant, 1956); Exergy expresses the amount of mechanical work necessary to produce a material in its specified state from components in the natural environment, in a reversible way, heat being exchanged only with the environment (Rickert, 1974) . During the 1940s, the term ”availability” had been introduced for a similar purpose (Keenan, 1941, K41) –seep. 9 Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 7/102 Surroundings - Environment . Some care should be considered with respect to ”the surroundings”, which is everything outside the system’s boundaries. Part of the surroundings, referred to as the ”immediate surroundings” are affected by the process, the ”environment” refers to the region beyond that. ”Normal conditions” for the reference environment: T° = 298.15 K, p°= 101.325 kPa, relative humidity 70%, atmospheric CO2 concentration 330 - 380 ppm, sea water salinity 3.5 %-wt, etc. etc. etc. Some data for air: N2 = 75.78 kPa; O2 = 20.39 kPa, Ar = 906 Pa, CO2 = 33.5 Pa , H2O = 2200 Pa, He = 1.77 Pa, and Ne, D2O, Kr, Xe < 1 Pa (SAKS04) 39.7 Pa would be better – see co2now.org Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 8/102 Notation For Exergy . In the literature, symbols like Ex, or X for exergy, or ex or x for specific exergy (i.e. exergy per mass, Ex/m = X/m = ex = x) are most common; but . Also the symbols B and b are used, especially in (and by followers of) the very important work by Szargut et al. And, in some (U.S.) literature, availability, B, is defined as BAV = H - T°·S, which can be related to exergy by Ex = BAV (T, p) – BAV (T°, p°), where BAV (T°,p°) = (H - T°·S)T°, p° = GT°,p° which ≠ 0 necessarily (depends on UT°,p° in HT°,p° ) Ex (T,p) = (H - T°·S)T,p - (H - T°·S)T°,p° (SAKS04) Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 9/102 ÅA 424304 1.2 Reversible Work-Irreversibility Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 10/102 Exergy and Work Potential . Thus: a system will deliver the maximum possible work in a reversible process from a specified initial state to the state of its environment, i.e. the dead state. This useful work potential is called exergy. It is also the upper limit of work from a device without violating the Laws of Thermodynamics. The part of the energy that cannot be converted into work is called unavailable energy or anergy: energy = exergy + anergy . Since exergy depends on the surrounding environment, it is not a state variable like U, H, S, V, p, G. In some special cases a changing environment can be considered, for example when analysing air flight, or large seasonal or daily changes (day/night). Unlike energy, exergy is consumed or destroyed. Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 11/10 2 Surroundings Work . During the expansion of a work W producing closed system, with volume change ΔV = Vfinal –Vstart > 0, work Ws is done on the surroundings at pressure p°: W = p°·ΔV Note: here W > 0 defined s as work done by the system . Similarly, ΔV < 0 is possible. In many cases this surroundings work cannot be recovered, reducing the useful work Wu of the process: Wu = W - Ws = W - p°·ΔV . This has no significance for 1) cyclic processes and 2) systems with fixed boundaries, but is important for constant pressure processes with large volume changes (for example: combustion furnaces, engines) Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 12/102 Reversible Work . Reversible work Wrev is the maximum amount of work that can be obtained from a process; it is equal to exergy if the final state is the dead state (which usually is not so!) . The difference between Wrev and Wu is referred to as the irreversibibility: I = Wrev -Wu which is equal to the amount of exergy that is destroyed. The irreversibility represents ”lost opportunity” to do work. If I = 0, no entropy is generated. For work consuming devices, W ≤ W rev u Pic: ÇB98 Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 13/102 Example: Irreversibility 1/1 . A heat engine (HE) receives Qin = 500 kW heat at TH = 1200 K and rejects waste heat at TL = 300 K. The power output of the engine is 180 kW. Calculate the reversible power Wrev and irreversibility rate I, in kW. Wrev follows from the Carnot efficiency ηcarnot = 1-TL/TH = 0.75 Wrev = ηcarnot ·Qin = 375 kW. The actual power output Wu = 180 kW, thus I = Wrev -Wu = 195 kW . Note that the 500 kW - 375 kW = 125 kW Pic: ÇB98 rejected to the sink was not available for work Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 14/102 Example: Irreversibility 1/2 . The 125 kW rejected to the sink follows from Q 500 kW Carnot efficiency; this is T 1200 K the anergy part of the in 417 J/(K s) input energy: energy = anergy + exergy 500 kW = 125 kW + 375 kW Q 125 kW . The entropy part of the T out 300 K energy cannot be 417 J/(K s) converted into useful work. Pic: ÇB98 11 jan 15 Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 15/102 Turku Example: Irreversibility 2/1 . A block of iron (m = 500 kg) is cooled from TH = T1 = 200°C to TL = 27°C by transferring heat to the surrounding air (T0 = 27°C). Calculate reversible work Wrev and irreversibility I, in kJ . The maximum work equals (assuming a series of reversible heat engines): TL T δWrev ηc δQin ( ) δQin ( ) δQin TH T where δQin m c avg dT which gives T T W δW m c (T T ) T ln 8191 kJ rev rev avg T T Pic: ÇB98 Åbo Akademi Univ - Thermal and Flow Engineering, Piispankatu 8, 20500 Turku 11 jan 15 16/102 Example: Irreversibility 2/2 . Here, cavg is an average value for the specific heat of iron, ~ 450 J/(kg·K) . In the result, the first part (m·cavg·ΔT) is the heat transferred from the iron block which equals 38925 kJ.
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