chapter 4 exergy and exergy analysis€¦ · chapter 4 exergy and exergy analysis outline...

CHAPTER 4 – EXERGY AND EXERGY ANALYSIS

Instructor:

Prof. Dr. Uğur Atikol

Chapter 4 Exergy and Exergy Analysis Outline

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 maximum shaft work that can be achieved by both the system and a specified reference environment

Therefore exergy is a property of both the system and the environment

Exergy transfer by heat 𝑋ℎ𝑒𝑎𝑡 𝑜𝑟 𝑋𝑄

= 1 −𝑇0𝑇

𝑄

CarnotHeatEngine

Heat Source at T

Environment at T0

Q

Q0

X = W (1 - heat max = T0/T ) x Q

Dead State at T0

Revision of Fundamentals Work = f (initial state, process path, final state)

The specified initial state is constant

Maximum work is obtained from reversible process

To maximize the work output, final state = dead state

Dead state means thermodynamic equilibrium of the system with the environment

Exergy is destroyed whenever an irreversible process occurs

Exergy transfer associated with shaft work is equal to the shaft work

Exergy transfer associated with heat transfer is dependent on the temperature of process in relation to the temperature of the environment

Exergy Associated with KE and PE

Kinetic and potential energies are forms of mechanical energy

Hence they can be converted to work entirely, i.e. The work potential or exergy are themselves:

zgx

Vx

pe

ke

pe

2ke

2

zgx

x

pe

ke

ep:energypotentialofexergy

2ek:energykineticofexergy

2

Exergy Associated with Electricity

Just like shaft work, exergy associated with electricity is equal to electric energy itself.

Hence, electric energy 𝑊𝑒𝑙 and power 𝑊 𝑒𝑙 can be converted directly to 𝑋𝑒𝑙 and 𝑋 𝑒𝑙 respectively:

zgx

Vx

pe

ke

pe

2ke

2

elel

elel

wx

wx

:powerexergy

:energyelectricofexergy

Surroundings Work Work produced by a work producing device (that involve

moving boundary) is not always completely usable

Work done by or against the surroundings is known as surroundings work, Wsurr

In a piston-cylinder device some work is used to push the atmospheric air out of the way

In this example:

Useful work:

SystemV1

SystemV2

Atmospheric air

P0

Atmospheric air

P0

)( 120 VVPWsurr

)( 120 VVPW

WWW surru

Irreversibility (exergy destruction) Reversible work (Wrev) is defined as the maximum

useful work that can be generated (or the minimum work that needs to be supplied) during a process

When the final state of the process is the dead state then Wrev = Exergy = X

The useful work (Wu) obtained in work producing devices is less than Wrev due to the irreversibilities

Irreversibility is viewed as the lost opportunity to do work

Irreversibilities (I) cause exergy destruction

I = Xdes = Wrev,out – Wu,out or Wu,in – Wrev, in

I or Xdes from a Heat Source

CarnotHeatEngine

High Temperature Reservoir at TH

Dead State (Environment) at T0

QH

Q0 IrreversibilitiesIrreversibilities

Lost available work, 𝑊𝑙𝑜𝑠𝑡 or

Exergy destruction, 𝑋𝑑𝑒𝑠

Example:

I or Xdes of a Heat Engine

1200K

300K

180-kW

500-kJ/s

)kW500(K1200

K3001

1,

rev

in

H

Linrevthrev

W

QT

TQW

375 kW

180375urevdes WWIX 195 kW

The rate of irreversibility or exergy destruction:

Example taken from Çengel 7th Ed. p.425

totalLQ ,

desXI or

revLQ ,kW 195125320

kW 125375500

kW 320180500

,

,

I

WQQ

WQQ

revHrevL

uHtotalL

This is not available for converting to work

Example:

Xdes from a Hot Water Tank When the water is not used the work potential is

completely wasted

CarnotHeatEngine

Hot Water Tank at TH = 80 Co

Environment at T0 = 10 Co

QH

Q0

Wu = 0

Inlet

Outlet valveclosed

Hot water80 C 10 C

o

o

V = out 0

Exergy stored in the tank is completely destroyed, I = Xdes = Wrev – Wu = Wrev

0

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 – Xout

Inlet

Outlet

Xst

Xout

CarnotHeatEngine

QH

Q0

Hot Water Tank at TH = 80 Co

Environment at T0 = 10 Co

Second-Law Efficiency, ηII Second-law efficiency is defined as the ratio of the actual

thermal efficiency to the maximum possible (reversible) thermal efficiency under the same conditions:

For heat engines:

For work producing devices:

For work consuming devices:

For refrigerators and heat pumps:

revth

thII

,

rev

uII

W

W

rev

IICOP

COP

u

revII

W

W

Example: Hot Water Usage from a Tank

Inlet

Outlet

Xst

Xout st

outII

X

X

where Xout is the useful exergy extracted from the tank and Xst is the exergy stored in the tank Also note that: If all the stored exergy is destroyed, then ηII = 0 If no exergy destruction takes place (reversible case) then ηII = 1 (maximum). This means that Wu = Wrev

st

desII

X

X1

Nonflow Exergy: Exergy of a fixed mass

dVPdVPP

dVPW

usefulbW

00

,

)(

:pressure catmospheri

above pressure todue is work usefulAny

SdTWQ

QT

TQ

QT

TW

HE

dST

HE

0

0

0

0

1

:ferheat trans todue potentialWork

SdTdVPdUW

dUdVPSdTW

dUdVPWSdTW

dUWQ

WQ

WWW

usefulbHE

usefulbHE

00useful total

00useful total

0,0

,useful total

)()(

:equationenergy in the and Substitute

: thatNote


)2( is where

)()()(

)()(2

1)()()(

:2) to1 state (from system nonflow a of changeexergy The

elevation. is and velocity is on,accelerati nalgravitatio is where2

1)()()(

:msenergy ter potential andenergy kinetic theIncluding

)()()(

:as expressed becan exergy nonflow thebasis massunit aOn

)()()(

:subscript) (0 state dead tostategiven from gIntegratin

:obtainedEquation

2

12012012

12

2

1

2

21201201212

2

00000

00000

00000

Exergyor ty Availabili

useful total

00useful total

gzue

ssTvvPee

zzgssTvvPuu

zg

zgssTvvPuu

ssTvvPuu

SSTVVPUUW

SdTdVPdUW


stX

s

u

ssTuu

ssTvvPuu

dTT

cdsdvcdTdu

therefore tank,

in the storedexergy theisexergy Nonflow :2 Note

state. dead thedenotes "0"Suffix :1 Note

tank.in theentropy specific total theis and

energy internal specific total theis where

)()(

)()()(

:from evaluated becan

hot water of tank full a ofexergy nonflow theexample,For

and 0 ,

: thatrecalled isit substances ibleincompressFor

000

00000

𝑋𝑠𝑡 = 𝜙

0

Flow Exergy: Exergy of a flow stream

The exergy associated with flow energy is the useful

work that would be delivered by an imaginary 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 wflow = 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:

xflow = Pv – P0v = (P – P0)v

Flow Exergy: Exergy of a flow stream

flowfluid nonflowingfluid flowing

:stream flow a ofExergy

xxx

zgssThh

zgssTPvuPvu

vPPzgssTvvPuu

2

000

2

0000

0

2

00000

2

1)()(

2

1)()()(

)(2

1)()()(

)()(2

1)()(

:2) to1 state (from stream fluid a of changeexergy The

2

1)()(

:stream flow afor exergy Therefore

12

2

1

2

21201212

2

000

zzgssThh

zgssThh

Example: Exergy change during a compression process

kJ/kg 38.0

KkJ/kg )9724.09802.0()K 293( kJ/kg )36.24669.286(

)()(

)()(2

1)()(

:from determined ist refrigeran theof changeexergy The

KkJ/kg 9802.0 and kJ/kg 69.286C50

MPA 8.0

:stateExit

KkJ/kg 9724.0 and kJ/kg 36.246C10

MPA 14.0

:stateInlet

kPa. 95 and C20 are conditionst Environmen

C.50 and MPa 0.8 toC10- and MPa 0.14 from compressed be tois 134at Refrigeran

12012

12

2

1

2

21201212

11

1

1

11

1

1

ssThh

zzgssThh

shT

P

shT

P

This represents the minimum work input (win,min) required to compress the refrigerant to the specified state.

Compressor

Refrigerant 134a P1 = 0.14 MPa T1 = - 10oC

P2 = 0.8 MPa T2 = 50oC

P0 = 95 kPa T0 = 20oC

win

Exergy transfer by heat, XQ

QT

TX

QT

TX

Q

Q

0

efficiencyCarnot

0

1

:constantnot is ratureWhen tempe

heatby

nsfer Exergy tra1

:enginecarnot aby obtained becan work maximum The

Heat source Temperature: T

Q T0

Exergy transfer by work, XW

)( that Note

work)of formsother (for

ork)boundary w(for

120 VVPW

W

WWX

surr

surr

W

There is no useful work transfer associated with boundary work when the pressure of the system is maintained constant at atmospheric pressure.

Exergy transfer by mass, Xmass When mass, m, enters or leaves a system the amount of exergy that accompanies it:

mX mass

Mechanisms of Exergy Balance

Xmass,in

XQ,in

XW,in

Xmass,out

XQ,out

XW,out

systemdesoutin XXXX

process theduringdestroyedExergy

sfers work tranandheat flow, massby system the

exitingExergy


enteringExergy

system the

ofexergy total

in the Change

destroyed

exergy

Total

system

theleaving

exergy Total

system

theentering

exergy Total

Also defined as lost available work, Wlost

Xdes

System

Xsystem

Exergy Balance: Closed Systems

System

Xsystem

Xdes

XQ,in

XW,in

XQ,out

XW,out

systemdesoutin XXXX



exitingExergy


enteringExergy

system the

ofexergy total

in the Change

destroyed

exergy

Total

system

theleaving

exergy Total

system

theentering

exergy Total

A closed system does not involve any mass flow

Xmass,in Xmass,out

Exergy Balance: Control Volumes

systemdesoutin XXXX



exitingExergy


enteringExergy

system the

ofexergy total

in the Change

destroyed

exergy

Total

system

theleaving

exergy Total

system

theentering

exergy Total

Control

Volume

XCV

Xdes

Mass entering

Procedure for Exergy Analysis

Subdivide the process under consideration into sections as desired

Conduct conventional energy analysis

Select a reference environment

Evaluate energy and exergy values relative to the environment

Set up the exergy balance and determine exergy destruction

Define first and second law efficiencies of the system

Interpretation of results and conclusions

Example: Solar Water Heating System from Hepbasli*

Tave Tw,out

Tw,in

*Hepbasli A. Renewable and Sustainable Energy Reviews 2008;12

sun

output

input

des

input

output

IIX

X

X

X

X

X

1

Storage Tank

Cold water inlet

Hot water outlet

Solar Collector

and

ln1

ln)(

)ln that (Note

)]()[(

where

radiationsolar theofExergy

waterofexergy Increased

:collectorsolar of efficiencyexergy ousinstantane The

radiationfor ratioenergy

-to-exergy maximum The

max,

irradianceglobalTotalArea

,

,

,,

0

,

,

0,,

,,0,,

colII,

sradTcol

inw

outw

inwoutw

u

inw

outw

inwoutwww

inwoutwinwoutwwu

col

u

rIAX

T

T

TT

TQ

T

TTTTCm

TCTCdTTdqs

ssThhmX

X

X

T

T

T

Trsrad,

0

4

0max

3

4

3

11

Petela toAccording

*Petela R. Exergy of undiluted thermal radiation. Solar Energy 2003;74

Tw,out

Tw,in

Storage Tank

bottom

top

bottomtop

wwbottomtop

wwavewwoutputT

T

TT

CmTT

T

TTCmTTCmX ln1ln)( 0

0

00

Tave

Storage Tank

Cold water inlet

Hot water outlet

Exergy from the storage tank to the end-user as presented by Xiaowu et al*:

Ttop

Tbottom

*Xiaowu et al. Exergy analysis of domestic-scale solar water heatersRenewable and Sustainable Energy Reviews 2005;9

Exergy from the collector to the storage tank as presented by Xiaowu et al*:

0

,

00,tank ln)(T

TTTTCmX outw

outwwwcol

Tw,out

chapter 4 exergy and exergy analysis€¦ · chapter 4 exergy and exergy analysis outline...

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