HUMIDIFICATION HUMIDIFICATION FUNDAMENTALSFUNDAMENTALS

COOLING TOWER COOLING TOWER DESIGNSDESIGNS

http://www.picture-newsletter.com/nuclear/cooling-tower-ub4.jpg

COOLING TOWER OPERATION

• EVAPORATION OF A PORTION OF ENTERING HOT WATER INTO UNSATURATED AIR

• COOLING OF THE WATER STREAM• PACKED BED CONTACTOR• SEE FIGURE 10.5-2 FOR FLOWSHEET

http://www.ges-inc.com/CoolingTower.gif

PROCESS PROCESS TEMPERATURE AND HUMIDITY PROFILES

•FIGURE 10.5-1

TOP OF TOWER BOTTOM OF TOWER

i i

G

GWATERVAPOR WATER

VAPOR

TL

WATERVAPOR

TL

TGTGLIQ. SENS.

HEAT

LIQ. SENS. HEAT

LATENT HT IN GASLIQ. SENS. HEATLIQ. SENS. HEAT

LATENT HT IN GAS

GAS SENS. HT

GAS SENS. HT

DIFFERENTIAL BALANCES IN THE TOWER

•DIFFERENTIAL CROSS-SECTION OF THE TOWER, Sdz– ENTHALPY BALANCE IS GydHy = d (LHL)

– dL≈ 0, GydHy = LcLdTL (10.5-3)

•HEAT TRANSFER RATE FROM LIQUID TO INTERFACE– LdHL = LcLdTL = hLa(TL - Ti)dz = GydHy

(10.5-4)

DIFFERENTIAL BALANCES IN THE TOWER

•HEAT TRANSFER RATE FROM INTERFACE TO GAS– G’ycsdTy = hya(Ti - Ty)dz (A)

•MASS TRANSFER RATE OF VAPOR FROM INTERFACE TO GAS– G’ydĤ = kyMBa(Ĥi - Ĥ)dz (B)

DIFFERENTIAL BALANCES IN THE TOWER

• INTEGRATION TO OBTAIN REQUIRED INTEGRATION TO OBTAIN REQUIRED HEIGHT OF PACKED SECTIONHEIGHT OF PACKED SECTION

• (A) CAN BE REARRANGED

)(CdzLc

ah

TT

dT

L

L

iL

L

)('

DdzcG

ah

TT

dT

Sy

y

yi

y

DIFFERENTIAL BALANCES IN THE TOWER

• DIFFERENTIAL MASS BALANCE:DIFFERENTIAL MASS BALANCE:

• DIFFERENTIAL ENTHALPY BALANCE:DIFFERENTIAL ENTHALPY BALANCE:

)('ˆˆ

ˆEdz

G

aMk

HH

Hd

y

By

i

)('

FG

Lc

dT

dH

y

L

L

y

DIFFERENTIAL BALANCES IN THE TOWER

• GAS PHASE ENTHALPY TO MASS GAS PHASE ENTHALPY TO MASS TRANSFER RATE:TRANSFER RATE:

•GAS PHASE ENTHALPY TO LIQUID PHASE TEMPERATURE

)125.10('

dzG

aMk

HH

dH

y

BG

yyi

y

)145.10(

PaMk

ah

TT

HH

BG

L

Li

yyi

DIFFERENTIAL BALANCES IN THE TOWER

• AND FOR aAND FOR ahh = a = amm::

• PACKED HEIGHT:PACKED HEIGHT:

y

LL

BG

L

Li

yyi

h

ch

PaMk

ah

TT

HH

)135.10(2

10

y

y

H

H yyi

y

GB

z

HH

dH

aPkM

Gzdz

DESIGN EQUATIONSDESIGN EQUATIONS

•REQUIRES INTEGRATION OF EQUATIONS (C), (D), (E) OR (10.5-13)

•RESULTS HAVE THE GENERAL FORM Zi = (HTU)i(NTU)I

– HTU ≡ HEIGHT OF A TRANSFER UNIT– NTU ≡ NUMBER OF TRANSFER UNITS– TRANSFER UNIT≡ Δ VARIABLE/AVERAGE

DRIVING FORCE

L2

L1

L

y2

y1

y

2

1

y2

y1

y

T

T LiL

LT

T

T yyi

yT

H

H iH

H

H yyi

yH

TT

dTN

TT

dTN

HH

HdN

HH

dHN

ˆ

ˆˆ ˆˆ

ˆ

TRANSFER UNITSTRANSFER UNITS• NTU ARE EVALUATED ASNTU ARE EVALUATED AS

• HTU ARE EVALUATED ASHTU ARE EVALUATED AS

ah

cGH

ah

cG'H

aMk

G'HH

L

LLT

y

SyT

BG

y

HH

Ly

y

ˆ

TRANSFER UNIT DESIGNTRANSFER UNIT DESIGN• EVALUATION OF NTU’S REQUIRES

– EQUILIBRIUM DATA NORMALLY OBTAINED FROM PSYCHROMETRIC CHARTS

– OPERATING LINE DATA• INTERGRATE (10.5-13) FOR NTU

EQUILIBRIUM LINE

O PE RA T ING LINE

LIQUID TEMPERATURETi1

TL2

H*y2

H*y1

Hy2

Hy1

Hy2i

Hy1i

TL1 Ti2

TRANSFER UNIT DESIGNTRANSFER UNIT DESIGN

• SLOPE OF OPERATING LINE IS SLOPE OF OPERATING LINE IS LcL/Gy

•SLOPE OF DRIVING FORCE LINE IS -hLa/kGaMBP

•SEE EXAMPLE 10-5-1INVERSE DRIVING FORCE VS TL

0.00E+00

1.00E-05

2.00E-05

3.00E-05

4.00E-05

5.00E-05

28.0 32.0 36.0 40.0 44.0

LIQUID TEMP (C)

1/(H

yi -

Hy

)

TL 1/(Hyi - Hy)

29.4 4.41E-05

32.2 4.02E-05

35.0 3.39E-05

37.7 2.83E-05

40.5 2.29E-05

43.3 1.82E-05

MINIMUM AIR FLOWMINIMUM AIR FLOW

• LIMITING VALUE BASED ON INFINITE LIMITING VALUE BASED ON INFINITE PACKING HEIGHTPACKING HEIGHT