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 + T0 *ΔS

If T0 = 298K, then:

Exergy = 817.9 kJ/mol

Energy quality = 92%

Heat

If T0 = 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 T0 = 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

Starting Entropy

S

Endpoint Entropy

Reversible

Reversible

Endpoint Entropy

Starting Entropy

Irreversible

Reversible

Reversible only With irreversible event

S

Exergy DestructionReversible Process Only

Enthalpy change ΔH

Entropy change ΔS

Exergy = - ΔH + T0 * ΔS

With Irreversible Event

Enthalpy change ΔH

Reversible entropy change ΔS – ΔSirr

Exergy =- ΔH + T0 * (ΔS – ΔSirr )

Exergy destroyed = T0 * ΔSirr

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 T0 ΔS

Exergy Loss

Example – heat transfer

Heat q moves from reservoir at T1 to reservoir at T2

Entropy of first reservoir decreases by q/T1

Entropy of second reservoir increases by q/T2

Increase is q(1/T2 – 1/T1 )

Exergy loss is T0 * q(1/T2 – 1/T1 )

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 = T0 nR ln(2)

Basic Heat Power Cycle

Heat in

Heat out

Power out

Power inPump Motor

Pressure high

Pressure low

Power Plant – the Exergy View

Boiler

Turbine

Pump

Condenser

Power

Cooling Water

Gas

Air

Exhaust Water

Steam

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

Flame

Air, 25C

Gases, 1950CMethane, 25C

Exergy loss 29%

Energy loss - nil

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

HeatExchanger

Gases, 1950CGases + condensedwater, 25C

Water, 25C, 217atmSteam, 538C, 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

Cooling Water 60

BoilerFuel 100

Stack 5

Steam 95 Shaft Power 32

Steam 60

Other Losses 3

TurbineCondenser

Power Plant Exergy Flows and Destruction

27Fuel 92

Stack 2

Steam 43

7Shaft Power 32

2Steam 3

Other Losses 1

Cooling Water 1

Turbine

Condenser

Combustion

2065

HeatTransfer

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

Air in

Compressor, 15x, 85% efficient

Gas in

Shaft power Shaft power out

Turbine Inlet Temperature 1000 C

Turbine, 85% efficient

Gas Turbine – Energy Flows

Air in

Compressor, 15x, 85% efficient

Gas in 100

Shaft power 59 Shaft power out 32

Turbine Inlet Temperature 1000 C

Turbine, 85% efficient

Heat out 6859 159

Gas Turbine – Exergy Flows and Destruction

Air in

Compressor, 15x, 85% efficient

Gas in 92

Shaft power 59 Shaft power out 32

Turbine Inlet Temperature 1000 C

Turbine, 85% efficient

Heat out 1654 115

531

8

Home Furnace Losses – 1st Law

Fuel 100

Exhaust 5

Heat to Building 95

Home Furnace Exergy Flows and Destruction

27 Heat Transfer58

Fuel 92

Combustion

Heat to Building 6

Exhaust 1

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