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CHAPTER 4 – EXERGY AND EXERGY ANALYSISInstructor:Prof. Dr. Uğur Atikol

Chapter 4Exergy and Exergy AnalysisOutline Fundamentals on Exergy Exergy Associated with KE and PE Irreversibility (Exergy Destruction) Second Law Efficiency Nonflow Exergy Exergy of a Flow stream Exergy by Heat, Work and Mass Exergy Balance

Exergy: Work Potential of Energy The exergy of a system is defined as the maximumshaft work that can be achieved by both the systemand a specified reference environment Therefore exergy is a property of both the system andthe environmentHeat Source at TQCarnotHeatEngineExergy transfer by heat𝑋ℎ𝑒𝑎𝑡 𝑜𝑟 𝑋𝑄𝑇0 1 𝑄𝑇Xheat Wmax (1 - T0/T ) x QQ0Dead StateEnvironmentat T0 at T0

Revision of Fundamentals Work f (initial state, process path, final state)The specified initial state is constantMaximum work is obtained from reversible processTo maximize the work output, final state dead stateDead state means thermodynamic equilibrium of thesystem with the environment Exergy is destroyed whenever an irreversible process occurs Exergy transfer associated with shaft work is equal to theshaft work Exergy transfer associated with heat transfer is dependenton the temperature of process in relation to thetemperature of the environment

Exergy Associated with KE and PE Kinetic and potential energies are forms of mechanicalenergy Hence they can be converted to work entirely, i.e. Thework potential or exergy are themselves:exergy of kinetic energy : xke k e 22exergy of potential energy : x pe p e g zV2xke ke 2x pe pe g z

Exergy Associated with Electricity Just like shaft work, exergy associated with electricity isequal to electric energy itself. Hence, electric energy 𝑊𝑒𝑙 and power 𝑊𝑒𝑙 can beconverted directly to 𝑋𝑒𝑙 and 𝑋𝑒𝑙 respectively:exergy of electric energy : xel welexergy power : x el w elV2xke ke 2x pe pe g z

Surroundings Work Work produced by a work producing device (that involvemoving boundary) is not always completely usable Work done by or against the surroundings is known assurroundings work, Wsurr In a piston-cylinder device some work is used to push theatmospheric air out of the wayAtmospheric airAtmospheric air In this example:P0P0Wsurr P0 (V2 V1 ) Useful work:Wu W Wsurr W P0 (V2 V1 )SystemV1SystemV2

Irreversibility (exergy destruction) Reversible work (Wrev) is defined as the maximumuseful work that can be generated (or the minimum workthat needs to be supplied) during a process When the final state of the process is the dead state thenWrev Exergy X The useful work (Wu) obtained in work producingdevices is less than Wrev due to the irreversibilities Irreversibility is viewed as the lost opportunity to dowork Irreversibilities (I) cause exergy destruction I Xdes Wrev,out – Wu,out or Wu,in – Wrev, in

I or Xdes from a Heat SourceHigh Temperature Reservoir at THQHCarnotHeatEngineQ0IrreversibilitiesDead State (Environment) at T0Lost available work, 𝑊𝑙𝑜𝑠𝑡orExergy destruction, 𝑋𝑑𝑒𝑠

Example:I or Xdes of a Heat Engine1200K500-kJ/s180-kW TL QinWrev th ,rev Qin 1 TH 300K W rev 1 (500kW ) 375 kW 1200K The rate of irreversibility or exergy destruction:X des I W rev W u 375 180 195 kW300KQ L ,total Q H W u 500 180 320 kWQ L ,rev Q H W rev 500 375 125 kWI 320 125 195 kWExample taken from Çengel 7th Ed. p.425This is not available forconverting to workQ L ,totalI or X desQ L ,rev

Example:Xdes from a Hot Water Tank When the water is not used the work potential iscompletely wasted0Exergy stored in the tank is completely destroyed, I Xdes Wrev – Wu WrevHot Water Tank at TH 80oCVout 0QHOutlet valveclosedHot water80oC10oCCarnotHeatEngineWu 0Q0InletEnvironment at T0 10oC

Example:Xdes from a Hot Water Tank When the water is used the Xdes can be expressed as:Exergy destroyed, I Xdes Wrev – Wu Xst – XoutHot Water Tank at TH ent at T0 10oC

Second-Law Efficiency, ηII Second-law efficiency is defined as the ratio of the actualthermal efficiency to the maximum possible (reversible)thermal efficiency under the same conditions: th For heat engines: II th,revWu For work producing devices: II WrevWrev For work consuming devices: IIWuCOP For refrigerators and heat pumps: II COPrev

Example:Hot Water Usage from a TankXoutX out II X stOutletwhere Xout is the useful exergy extracted from the tankand Xst is the exergy stored in the tankXstInletAlso note that:X des II 1 X stIf all the stored exergy is destroyed, then ηII 0If no exergy destruction takes place (reversible case)then ηII 1 (maximum). This means that Wu Wrev

Nonflow Exergy: Exergy of a fixed mass Any useful work is due to pressure above atmospheric pressure : W P dV ( P P0 ) dV P0 dV Wb ,useful Work potential due to heat transfer : WHE 1 T0 Q T T Q 0 Q T T0 dS Q WHE T0 d SNote that : Wtotal useful WHE Wb ,usefulSubstitute Q and W in the energy equation : Q W dU ( WHE T0 d S ) ( Wb ,useful P0 dV ) dU Wtotal useful T0 d S P0 dV dU Wtotal useful dU P0 dV T0 d S

Nonflow Exergy: Exergy of a fixed massEquation obtained : Wtotal useful dU P0 dV T0 d SIntegrating from given state to dead state (0 subscript) : Wtotal useful (U U 0 ) P0 (V V0 ) T0 ( S S0 ) Availability or ExergyOn a unit mass basis the nonflow exergy can be expressed as : (u u0 ) P0 (v v0 ) T0 ( s s0 )Including the kinetic energy and potential energy terms :1 (u u0 ) P0 (v v0 ) T0 ( s s0 ) 2 g z2where g is gravitational acceleration, is velocity and z is elevation.The exergy change of a nonflow system (from state 1 to 2) :1 2 1 (u2 u1 ) P0 (v2 v1 ) T0 ( s2 s1 ) ( 22 12 ) g ( z2 z1 )2 (e2 e1 ) P0 (v2 v1 ) T0 ( s2 s1 )where e is (u 2 2 gz )

Nonflow Exergy: Exergy of a fixed massFor incompressible substances it is recalled that :cdTTFor example, the nonflow exergy of a full tank of hot waterdu cdT , dv 0 and ds can be evaluated from :0 (u u0 ) P0 (v v0 ) T0 ( s s0 ) (u u0 ) T0 ( s s0 )where u is the total specific internal energyand s is the total specific entropy in the tank.Note 1 : Suffix "0" denotes the dead state.Note 2 : Nonflow exergy is the exergy stored in thetank, therefore X st 𝑋𝑠𝑡 𝜙

Flow Exergy: Exergy of a flow streamFor flowing fluids flow energy or flow work was defined before.This is the energy needed to maintain flow in a control volume,such that wflow Pv.The flow work is done against the fluid upstream in excess of theboundary work against the atmosphere such that exergy associatedwith this flow work:xflow Pv – P0v (P – P0)vThe exergy associated withflow energy is the usefulwork that would bedelivered by an imaginarypiston in the flow section.

Flow Exergy: Exergy of a flow streamExergy of a flow stream :xflowing fluid xnonflowing fluid xflow1 (u u0 ) P0 (v v0 ) T0 ( s s0 ) 2 g z ( P P0 )v21 (u Pv) (u0 Pv0 ) T0 ( s s0 ) 2 g z21 (h h0 ) T0 ( s s0 ) 2 g z2Therefore exergy for a flow stream :1 (h h0 ) T0 ( s s 0 ) 2 g z2The exergy change of a fluid stream (from state 1 to 2) :1 2 1 (h2 h1 ) T0 ( s 2 s1 ) ( 22 12 ) g ( z 2 z1 )2

Example: Exergy change during acompression processRefrigerant 134a is to be compressed from 0.14 MPa and - 10 C to 0.8 MPa and 50 C.P2 0.8 MPaT2 50oCEnvironment conditions are 20 C and 95 kPa.Inlet state :P1 0.14 MPA h1 246.36 kJ/kg and s1 0.9724 kJ/kg KT1 10 C Exit state :winP1 0.8 MPA h1 286.69 kJ/kg and s1 0.9802 kJ/kg KT1 50 C The exergy change of the refrigerant is determined from :1 2 1 (h2 h1 ) T0 ( s 2 s1 ) ( 22 12 ) g ( z 2 z1 )2 (h2 h1 ) T0 ( s 2 s1 )CompressorP0 95 kPaT0 20oCRefrigerant 134aP1 0.14 MPaT1 - 10oC (286.69 246.36) kJ/kg (293 K ) (0.9802 0.9724) kJ/kg K 38.0 kJ/kgThis represents the minimum work input (win,min) required to compress the refrigerantto the specified state.

Exergy transfer by heat, XQHeat sourceTemperature: TQT0The maximum work can be obtained by a carnot engine : Exergy transfer T X Q 1 0 Q T by heat Carnot efficiencyWhen temperature is not constant : T0 X Q 1 QT

Exergy transfer by work, XWXW W Wsurr (for boundary work) (for other forms of work) WNote that Wsurr P0 (V2 V1 )Exergy transfer by mass, XmassThere is nouseful worktransferassociatedwith boundarywork when thepressure of thesystem ismaintainedconstant atatmosphericpressure.When mass, m, enters or leaves a system the amount of exergy that accompanies it:X mass m

Mechanisms of Exergy Balance Total exergy Total exergy Total Change in the enteringthe leavingthe exergy total exergy of system system destroyed the system X in Exergy enteringthe system by mass flow,heat and work transfers X out Exergy exitingthe system by mass flow,heat and work transfersX des X systemExergy destroyedduring the processXmass,inXQ,inXmass,outSystem XsystemXW,inXQ,outXW,outXdesAlso defined aslost available work, Wlost

Exergy Balance: Closed Systems Total exergy Total exergy Total Change in the enteringthe leavingthe exergy total exergy of system system destroyed the system X in Exergy enteringthe system by mass flow,heat and work transfers X out Exergy exitingthe system by mass flow,heat and work transfersX des X systemExergy destroyedduring the processA closed system does not involve any mass flowXmass,outXmass,inXQ,inXW,inSystem XsystemXdesXQ,outXW,out

Exergy Balance: Control Volumes Total exergy Total exergy Total Change in the enteringthe leavingthe exergy total exergy of system system destroyed the system X in Exergy enteringthe system by mass flow,heat and work transfers X out Exergy exitingthe system by mass flow,heat and work transfersMassenteringX des Exergy destroyedduring the processControlVolume XCVXdes X system

Procedure for Exergy Analysis Subdivide the process under consideration into sections asdesired Conduct conventional energy analysis Select a reference environment Evaluate energy and exergy values relative to theenvironment Set up the exergy balance and determine exergydestruction Define first and second law efficiencies of the system Interpretation of results and conclusions

Example: Solar Water HeatingSystem from Hepbasli*TaveTw,outHot water outletStorageTankCold water inletTw,inX output II 1 XinputX outputX des X inputX sun*Hepbasli A. Renewable and Sustainable Energy Reviews 2008;12

Solar CollectorThe instantaneous exergy efficiency of solar collector :Increased exergy of waterX u II,col Exergy of the solar radiation X colwhereX u m w [(hw, out hw,in ) T0 ( sw, out sw,in )]Tw,out(Note that s dq T CdT T C ln T ) T m wCw (T w, out Tw,in ) T0 ln w, out Tw,in Tw, outT0 ln Qu 1 Tw, out Tw,in Tw,inandX col A IT rsrad , max AreaTotal The maximumglobalexergy - to irradiance energy ratiofor radiation Tw,inAccording to Petela 4rsrad, max1 T 4 T 1 0 03 T 3 T*Petela R. Exergy of undiluted thermal radiation. Solar Energy 2003;74

Storage TankTw,outTaveTtopHot water outletStorageTankExergy from the storage tank to the end-user aspresented by Xiaowu et al*:Cold water inletTbottom Ttop TbottomT0 m wCw Ttop X output m wCw (Tave T0 ) m wCwT0 ln 1 ln T0 Ttop Tbottom Tbottom Exergy from the collector to the storage tank aspresented by Xiaowu et al*: Tw, out X col tank m wCw (Tw, out T0 ) T0 lnT0 *Xiaowu et al. Exergy analysis of domestic-scale solar water heatersRenewable and Sustainable Energy Reviews2005;9

piston in the flow section. For flowing fluids flow energy or flow work was defined before. This is the energy needed to maintain flow in a control volume, such that w flow Pv. The flow work is done against the fluid upstream in excess of the boundary work against the atmosphere such that exergy associated with this flow work: x flow Pv - P