3.1 Drying Fundamentals(2)

5/25/2018 3.1 Drying Fundamentals(2)

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CHG 3111

Unit Operation

Chapter 9

Drying3.1 Drying Fundamentals


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Drying: Removal of relatively small amount of water or other liquid from material.

Types of Drying:

Mechanical:presses, filters, centrifuges, etc.

Thermal : hot air

Methods of Drying:

Based on process: i) Batch, ii) Continuous

Based on physical condi t ions:

Direct heating by contact with hot air at atmospheric pressures where waterremoved by air.

Indirect heating by contact with a metal wall or by radiation, at low pressures(vacuum drying)

Freeze-drying where water sublimed from the frozen material.

Applications:

Chemical Industry, e.g. mineral sand, Ammonium Sulphate, Sodium sulphate, etc

Pharmaceuticals

Food & Dairy, e.g. fruit pellets, salt, milk powder, grains and cereal, etc

Introduction


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Rate processes in drying

Evaporation of water vapor from wet solid to dry gas (air) mass transfer processcharacterized by water vapor flux (N)

Evaporation of water vapor requires heat which is supplied from hot gas (air) heattransfer processcharacterized by heat flux (q)

Drying-Fundamentals

Solid

Gas (H, T)Heat Transfer Mass Transfer

Drying force for mass transfer difference between the water vapor pressure inequilibrium with wet solid and that in air.

Driving force for heat transfer difference between the air temperature and thetemperature of solid

Question:How do we call the process opposite to that shown on the diagram above?

Question:Is it possible to have the heat and mass transfer processes in the same direction?

G Sq

q h T T A

" 2 2 2H O H O H OG S G

N k p p , ,


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Drying-Fundamentals

Important properties of water vapor

Phase diagram of water

Steam tables

Thekey properties for us to use are: the latent heat of evaporation, and the relationship between the

temperature and the vapor pressureof water at a given temperature


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Drying-Fundamentals

Humidity

Humidity Hof air-water mixture is the kg of water vaporcontained in 1 kg of dry air.

H depends on the partial pressure (pA)of water vapor in the air and on the totalpressure (P).

Saturation Humidity

Air is saturated when the water vapor is in equilibrium with liquid water at the given

conditions of pressure and temperature, i.e.pA= pAS.

Equilibrium vapor pressures of water (pAS) is tabulated inAppendix; alternatively it can be evaluated from:

5132 1730 6320 386 8 07131

233 426

o

.mmHg exp . or Antoine Eq: log mmHg .

K . CAS ASp p

T T

118 02

28 97

2 2 2

2

kg H O kg mol H O kg H O kg mol air.

kg dry air kg mol dry air kg mol H O . kg air

A

A

pH

P p

18 02

28 97

.Therefore:

.A

A

pH

P p

18 02

28 97

.

.AS

S

AS

pH

P p


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Drying-Fundamentals

Percentage Humidity

HP, is the actual humidity of air (H)divided by saturation humidity (HS)at the same Tand P.

Percentage Relative Humidity

HR, amount of saturation of an air-water vapor mixture.

Dry Bulb Temperature

Temperature of air-water mixture measured by a normal thermometer (T).

Dew Point Temperature of an Air-Water Vapor Mixture

Temperature at which a given mixture of air and water vapor would be saturated (TDP)

18 02 18 02100 100 100

28 97 28 97

. .Note that:

. .A ASA AS

P RA ASS AS A

p P pH p pH H

P p P pH p P p

100 ARAS

pH

p


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Drying-Fundamentals

Humid Heat of an Air-Water Vapor Mixture

cS, heat (J or KJ) required to increase the temperature of 1 kg of dry air plus thewater vapor by 1 K (or 1C).

Air heat capacity

[kJ/kg d ry air. K]

Water vapor heat capacity

[kJ/kg water vapor.K]

Humid Volume of an Air-Water Vapor Mixture

Total volumein m3of 1 kg of dry air plus the vapor it containsat 101.325 kPa (1.0atm) abs pressure and the given temperature.

Total Enthalpy of an Air-Water Vapour Mixture

Total enthalpy of 1 kg of airplus its water vapor. Is the sensible heat of the air-watermixture plus the latent heat of water vapor at To ( reference temperature).

1 005 1 88 . . [kJ/kg dry air K]Sc H

3 322 41 1 1

2 83 10 4 56 10273 28 97 18 02

3 .m /kg dry air . . K. .

H T H H T

1 005 1 88 kJ/kg dry air . .y S o o o oH c T T H H T T H 0 1 005 1 88 2501 4 at : . . .o

o yT C H H T H



Drying-Fundamentals

Humidity Chart of Air-Water Vapor Mixtures

Shows properties of air-water vapor mixture at 1 atm (abs).

= Dry Bulb Temperature

HS

H

TDP T

HP



Drying-Fundamentals

Adiabatic Saturation Temperature (TS)

Gas of air-water vapor mixture is contacted with a spray of liquid water.

(Equation of an adiabatic humidification curve)

If the contact between the entering gas and liquid reaches equilibrium, the outlet gaswill be saturated at TSand will have a humidity of HS.

Enthalpy balance on the system with a reference temperature of TS:

Enthalpy of the entering gas mixture = Enthalpy of the leaving gas mixture

S S S S S S S Sc T T H c T T H 1 005 1 88

. .S S

S S S

H H c H

T T


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Drying-Fundamentals

Adiabatic saturation curve

Additional parameters

= Dry Bulb Temperature

HS

H

TDP T

HP

TS

HS

1 005 1 88

. .S S

S S S

H H c H

T T


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Drying-Fundamentals

Wet Bulb Temperature

The steady-state non-equilibrium temperature achieved when a small amount ofwater is contacted with a gas under adiabatic conditions.

Measurement:A thermometer that is covered by a wet wick is placed in a stream ofair-water vapor having a temperature of T(dry bulb temperature). Water is vaporizedto the gas stream which makes the wick and water cooled to TW.

What is difference between wet bulb and adiabatic saturation temperatures?

Wet bulb temperature is a factor in the determination of relative humidity.

By knowing wet bulb and dry bulb temperature, relative humidity of an air-watervapor mixture can be determined by psychrometric charts.


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Wet Bulb Temperaturecombined mass and heat transfer

Determination of wet bulb temperature mathematically:

Heat loss, q,from the wick due to water evaporation

Drying-Fundamentals

yW, HW(at the surface)

NB: (h/MAirky)psychometric ratio 0.96-1.005 cs

2 2 2 H O W H O H O W q m M N A

Rate equation for mass transfer

2

H O y W N k y y

Expressing mole fractions in terms of humidity:

1

H O air2

air H O H O2 2

H M HMy

M H M M airH O2

H O2

y W

MN k H H

M

Thus, heat loss due to evaporation becomes: air y W W q M k A H H

Alternatively, using rate equation for heat transfer: Wq hA T T

Combining the two equations for q:

air yW S

W W W

h M kH H c

T T


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Drying-Fundamentals

Example 1: Humidity calculations, properties of humid air, humidity chart

The hot air stream has temperature of 82.2Cand a total pressure of 101.3 kPaabs; itcontains water vapor with a partial pressure pA= 9.27 kPa.

For this air stream, calculate:

(a) Humidity

(b) Saturation humidity and percentage humidity(c) Percentage relative humidity

(d) Humid heat

(e) Humid volume

(f) Enthalpy

This air stream is to be contacted in an adiabatic saturator with water. It is desired thatthe outlet air has the percentage humidity of 80%.

(g) Using the humidity chart, evaluate the outlet temperature and humidity of air

(h) Develop an analytical procedure for the determination of the outlet temperatureand humidity without using the humidity chart.


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Characterization of wet solids

Moisture content (Xt):

Drying-Fundamentals

The moisture content in excess of theequilibrium moisture content at givenrelative humidity is the free moisturecontent(X)

When drying a solid, only free moisture

content can be removed

k g t o ta l w a te r / k g d r y s o li dSt

S

W WX

W

*a n d

tX X X

w h e r e : a n d i s t h e w e i g h t o f t h e w e t s o l id a n d d r y s o l id , r e s p e c t i v e ly ;

* a n d a r e t h e e q u i l i b r iu m a n d f r e e m o i s t u r e c o n t e n ts

W W

X X

Equilibrium moisture content (X*)depend on type of the material and thehumidity.

Bound and unbound water in solids.

The equilibrium moisture content at the relative humidity of 100% is called bound water.

Bound water in the solid exerts vapor pressure less than that of liquid at the same temperature

Unbound water in solids exertsvaporpressure of ordinary water at the same temperature


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Drying Curves

Drying-Fundamentals

Initial free moisture content

AB: Evaporation rate increase

BC: Slope and rate constant

CD: Drying rate decrease

E:X*

XC: Critical moisture content

Drying rate: 22[ k g H O / h m ] w h e r e : i s t h e m a s s o f d r y s o l i d a n d i s d r y in g a r e a

S

S

L d XR L A

A d t


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Drying-Fundamentals

Drying in the Constant-Rate Period

BC:

Rate of evaporation is independent of the

type of solid.

Rate of evaporation is the same as the

rate from a free liquid surface.

Drying in the Falling-Rate Period

CD:

Starts fromXC,critical free moisture content. There is no continuous film of water on the surface.

Rate will decrease until the surface is dry.

DE:

At point D, surface is completely dry.

Vaporized water moves through the solid into the air.

Amount of moisture removed is small, and drying will

take a long time.

Drying gas Drying gas

Drying gas

Drying gas

Heat transfer

controlled

Masstransfer

controlled

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3.1 Drying Fundamentals(2)