cooling tower selection and sizing

7/21/2019 COOLING TOWER SELECTION AND SIZING

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Chapter VI Cooling tower design

Lecturer: Chakkrit Umpuch

Department of Chemical Engineering

Faculty of Engineering

Ubon Rachathani University

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What you will learn in this chapter ishere.

5.1 Introduction to cooling tower

5.2 Vapor pressure of water and humidity

5.3 Cooling tower theory5.4 Cooling tower design

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5.1Introduction

Cooling tower is the heat rejection device, which extracts heat waste

to atmosphere through the cooling of water stream to a lowertemperature.

The make-up water source is used to replenish water lost to evaporation.

Hot water from heat exchangers is sent to the cooling tower. The water exits

the cooling tower and is sent back to the exchangers or to other units forfurther cooling.

Figure 1: Closed Loop Cooling Tower System

What is cooling tower?

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Types of Cooling Towers

Figure 2: Mechanical Draft Counterflow Tower Figure 3: Mechanical Draft Crossflow Tower

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5.2 Vapor Pressure of Water and Humicdity

Vapor Pressure ofWater

Pure water can exist in three different physical states: solid ice, liquid

and vapor. The physical state in which it exists depends on thepressure and temperature.

AB line is liquid and vapor coexist in

equilibrium.

AC line is ice and liquid coexist in

equilibrium.

AD line is ice and vapor coexist in

equilibrium.

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5.2 Vapor Pressure of Water and Humidity

Steam Table

For example: At 100C (212F) the vapor pressure of water is 101.3 kPa (1.0 atm).

At 65.6C (150F) the vapor pressure of water is 25.7 kPa (3.72 atm).

At 25.7kPa and 65.6C, water will boil.

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Humidity and Humidity Chart

1. Definition of humidity

The humidity H of an air-water vapor mixture is defined as the kg of watervapor contained in 1 kg of dry air.

where

pAis partial pressure of water vapor in the air.

P is the total pressure (101.325 kPa, 1.0 atm abs, or 760mmHg)

Saturated air is air in which the water vapor is in equilibrium with liquid water at thegiven conditions of pressure and temperature. Hence, the saturation humidity Hs is

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(6.1)

(6.2)


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2. Percentage humidity

The percent humidity Hp is defined as 100 times the actual humidity H of the

air divided by the humidity Hs if the air were saturated at the same temperature andpressure.

3. Percentage relative humidity

The amount of saturation of an air-water vapor mixture is also given aspercentage relative humidity HRusing partial pressures.

Note that HR Hp:

(6.3)

(6.4)

(6.5)

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Ex 6.1 The air in a room is at 26.7C (80F) and a pressure of 101.325

kPa and contains water vapor with a partial pressure pA= 2.76 kPa.

Calculate the following.

(a) Humidity, H.

(b) Saturation humidity, Hs, and percentage humidity, Hp.(c) Percentage relative humidity, HR.

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Solution:

(a) From the steam tables at 26.7C, the vapor pressure of water is pAS = 3.50 kPa

(0.507 psia). Also, pA = 2.76 kPa and P = 101.3 kPa (14.7 psia). For part (a), using

eq. 6.1,

kgairkgH

pP

pH

A

A /001742.0

)6.273.101(97.28

)76.2(02.18

97.28

02.182


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Solution:

(b) From part (b), using eq. 6.2, the saturation humidity is

The percentage humidity, from eq. 6.3, is

For part (c), from eq. 4, the percentage relative humidity is

kgairkgHpP

pH

As

Ass /002226.0

)05.33.101(97.28

)05.3(02.18

97.28

02.182

%3.7802226.0

)01742.0(100100

s

PH

HH

%9.7805.3

)76.2(100100 As

As

ppH


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4. Dew point of an air-water vapor mixture

The temperature at which a given mixture of air and water vapor would be

saturated is called the dew-point temperature or simply the dew point.

For example,

At 26C (80F), the saturation vapor pressure of water is pAS= 3.5 kPa (0.507 psia).

Hence the dew point of a mixture containing water vapor having a partial pressure of3.50 kPa is 26.7C.

If an air-water vapor mixture is at 37.8C and contains water vapor of p A= 3.50 kPa,

the mixture would not be saturated.On cooling to 26.7C, the air would be saturated, i.e., at the dew point..

On further cooling, some water vapor would condense, since the partial pressure

cannot be greater than the saturation vapor pressure.

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5. Humid heat of an air-water vapor mixture

The humid heat csis the amount of heat in J (or kJ) required to raise thetemperature of 1 kg of dry plus the water vapor present by 1 K or 1C.

(SI)

(English)

6. Humid volume of an air-water vapor mixture

The humid volume v His the total volume in m3 of 1 kg of dry air plus the vapor

it contains at 101.325 kPa (1.0 atm) abs pressure and the given gas temperature.

Using the ideal gas law,

(6.5)

(6.4)

(6.7)

(6.6)

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7. Total enthalpy of an air-water vapor mixture.

The total enthalpy of 1 kg of air plus its water vapor is Hy J/kg or kJ/kg dry air.

(SI)

(English)

8. Humidity chart of air-water vapor mixtures.A convenient chart of the properties of air-water vapor mixtures at 1.0 atm abs

pressure is the humidity chart. In this figure the humidity H is plotted versus the actual

temperature of the air-water vapor mixture (dry bulb temperature).

(6.9)

(6.8)

(6.10

)

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Ex 6.2Air entering a dryer has a temperature (dry bulb temperature) of60C (140F) and a dew point of 26.7C (80F). Using the humidity

chart, determine the actual humidity H, percentage humidity Hp, humidheat cs, and the humid volume vHin SI and English units.

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Solution:

The dew point of 26.7C is the temperature when the given mixture is at 100%saturation. Starting at 26.7C, Fig. of humidity chart and drawing a H = 0.0225 kg

H2O/kg dry air is read off the plot. This is the actual humidity of the air at 60C. Stated

in another way, if air at 60C and having a humidity H = 0.0225 is cooled, its dew point

will be 26.7C. In English units, H = 0.0225 lb H2O/lb dry air.

Locating this point of H = 0.0225 and t = 60C on the chart, the percentage humidity

HPis found to be 14%, by linear interpolation vertically between the 10 and 20% lines.The humidity heat of H = 0.0225 is, from eq.(6).


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The humidity volume at 60C (140F), from eq. 7 is

)0225.0(88.1005.1 sc

KkgJorKairdrykgkJ ./10047.1/047.1 3

)0225.0(45.024.0 sc

Fairdrylbbtuc ms ./250.0

)27360)(0225.01056.41083.2( 33 Hv

airdrykgm /977.0 3

In English units,

airdrylbftv mH /67.15)140460)(0225.00405.00252.0( 3


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Adiabatic Saturation Temperature

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Adiabatic Saturation Temperature

Total enthalpy of the entering gas mixture = enthalpy of the leaving gas mixture

(SI)

(English)

(6.12

)

(6.13

)

(6.11)

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Ex 6.3An air stream at 87.8C having a humidity H = 0.030 kg H2O/kgdry air is contacted in an adiabatic saturator with water. It is cooled and

humidified to 90% saturation.

(a) What are the final values of H and T?(b) For 100% saturation, what would be the values of H and T?

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Solution:For part (a), the point H = 0.030 and T = 87.8C is located on the humidity chart.

The adibatic saturation curve through this point is followed upward to the left

until it interests the 90% line at 42.5C and followed upward to the left until it

intersects the 90% line at 42.5C and H = 0.0500 kg H2O/kg dry air.

For part (b), the same line is followed to 100% saturation, where T = 40.5C andH = 0.0505 kg H2O/kg dry air.


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Wet Bulb Temperature

For air-water vapor mixture, the adiabatic saturation lines can also be used for wet bulb lines with

reasonable accuracy.

Hence, the wet bulb temperature determination is often used to determine the humidity of an air-water vapor mixture.

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Ex 6.4A water vapor-air mixture having a dry bulb temperature of T =60C is passed over a wet bulb as shown in slide 17, and the wet bulb

temperature obtained is TW= 29.5C. What is the humidity of the

mixture?

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Solution:The wet bulb temperature of 29.5C can be assumed to be the same as the

adiabatic saturation temperature TS, as discussed. Following the adiabaticsaturation curve of 29.5C until it reaches the dry bulb temperature of 60C, the

humidity is H = 0.0135 kg H2O/kg dry air.


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Theory and Calculation of Water-CoolingTowers

Pressure gradient

Water vapor diffuses from the

interface to the bulk gas phase with a

driving force in the gas phase:

HiHGkg H2O/kg dry air

No driving force in liquid phase, sincewater is pure liquid

Temperature gradient

The temperature driving force is TLTiin the liquid phase and TiTGK or C in gas

phase.

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L = water flow , kg water/s.m2(lbm/h.ft2)TL= temperature of water, C or K (F)

G = dry air flow, kg/s.m2(lbm/h.ft2)TG = temperature of air, C or K (F)

H = humidity of air, kg water/ kg dry air (lb water/ lb dry air)

Hy= enthalpy of air-water vapor mixture, J/kg dry air (btu/lbmdry air)

(English)

(SI)

(6.15

)

(6.14

)

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Total heat balance for the dash line box

(6.17

)

(6.16

)

(6.18

)

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Design of water-cooling tower UsingFilm Mass transfer Coefficients

The tower design is done using the following steps.

1. The enthalpy of saturated air Hy1is plotted versus Tion an H versus T plot as shown in Fig. in

slide 24 This enthalpy is calculated with eq. using the saturation humidity from the humidity chartfor a given temperature, with 0C (273K) as a base temperature. Calculated values are tabulated

in Table in slide 27

2. Knowing the entering air conditions TG1

and H1, the enthalpy of this air H

y1is calculated from eq.

6.8. The point Hy1and TL1(desired leaving water temperature) is plotted in Fig. in slide 24 as one

point on the operating line. The operating line is plotted with a slope Lc L/G and ends at point TL2,

which is the entering water temperature. This gives Hy2 . Alternatively, Hy2can be calculated from

eq. 6.16.

3. Knowing hLa and kGa, lines with a slope of hLa/kGaMBP are plotted as shown in Fig. in slide 24.

From eq. 6.18 point P represents Hyand TL on the operating line, and point M represents Hyi and

Ti, the interface conditions. Hence, line MS or Hyi -Hyrepresents the driving force in eq. 6.17.

4. The driving force Hyi - Hy is computed for various values of TL between TL1 and TL2. Then by

plotting 1/(Hyi -Hy) versus Hy from Hy1 to Hy2, a graphical integration is performed to obtain thevalue of the integral in eq. 6.17. Finally, the height z is calculated from eq. 6.17.

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Ex 6.5 A packed countercurrent water-cooling tower using a gasflow rate of G = 1.356 kg dry air/s.m2 and a water flow rate ofL=1.356 kg water/s.m2is to cool the water from TL2= 43.3 C (110

F) to TL1=29.4 C (85 F). The entering air at 29.4 C has a wet

bulb temperature of 23.9 C. The mass-transfer coefficient kGa is

estimated as 1.207x10-7 kgmol/s.m3.Pa and hLa/kGaMBP as4.187x104J/kg/K (10.0 btu/lbm. F). Calculate the height of packed

tower z. The tower operates at a pressure of 1.013x105Pa.

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cooling tower selection and sizing

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