Treybal Cooling Tower

Cooling Tower Application according Treibal

Index

1 Data

2 Tower height

3 NTU and HTU

4 Tower area

5 Compensation water

6 Operaqting diagram

7 Cooling tower schematic


Rev cjc 30012014

Index

Data for cooling tower application

Main equations and results

Cooling Tower height NTU and HTU

Free-cross sectional surface of tower

Compensation elimination evaporation and entrainment fow rates

Equilibrium curve and operation lines

Schema

Cooling Tower Application Data

This application will be realized with following numerical data (Note 1)

Data for numerial exampleWater flow rate entering the tower L1 = 15 kg aguas

Temperature of water entering the tower at the top (2) 45 ordmC

Dry bulb temperature of air entering the tower 30 ordmC

Wet bulb temperature of air entering the tower 24 ordmC

Local height above sea level H = 0 mMaacuteximum cooling temperature will be defined with

5 K

Air to water flow rates ratio shall be r times its

minimum possible value r = 15

temperature 10 degC

and will have a hardness 500 ppm

hardness 2000 ppm

Mass transfer coefficient in the air 62E-05

Air molecular mass 2896 kgkmol

Tower effective heat or mass transfer surface a = 500 msup2msup3

Liquid unit mass flow rate 27

Air unit mass flow rate 20

Note 1Basic data has been taken from [1] pages 278-281

tL2

=

tdbG1 =

twbG1

a differential temperature ∆t above air wet bulb temp ∆t =

The compensation water entering the system wil havetcomp =

da_c

=

The in system circulating water sould have a maximum da

_M =

ky_kmol = kmol ( m2s)

Mair =

Lu = kg(sm2)

Gu = kg(sm2)

Help Variables Cooling Tower Schema

State L1

Water leaving the tower

L2 =

24

5 K

29 ordmCCompensation water

State G1 10 ordmC

Ambient air entering the tower 2000 ppm

30 ordmC

24 ordmC

H = 00 m

h = Psychro_Enthalpy_tdb_twb_H Qh = VALUE kJkg

x = Psychro_AbsoluteHumidity_tdb_twb_H

x = VALUE kglg

Mass transfer coefficient

Mass transfer coefficient in the air

62E-05Air molecular mass

2896 kgkmol

Mas transfer per kilogram

62E-05

2896 kgkmol

00018

Product Kya

Kya

00018a = 500 msup2msup3

090

Q = 270 W

tL1

= twbG1

+ ∆t

tbhG1 tL2 =

∆t =

tL1

=

tacomp

=

dac =

tbsG1

=

tbhG1

ky_kmol

= kmol ( m2s)

Mair

=

daM =

ky = k

y_kmol M

air

ky_kmol

= kmol ( m2s)

Mair

=

ky = kg ( m2s)

Kya =

ky = kg ( m2s)

Kya = kg ( m3s)

W

Blowdown water B

Rev cjc 30012014

Cooling Tower Schema

15 kg s

45 ordmC Air

Water

30 ordmC

24 ordmC

Water

Air

2000 ppm

Rev cjc 30012014

tdbG1 =

twbG1

L1G1

Torreenfriadora

G22

Blowdown water B

G1

L2

Cooling Tower height

Tower packing height [2] Number of Transfer Units

The packing height (l) of a tower can be calculated as The number of transfer units (NTU)is calculated by numerical integtation

[1] eq (753) page 276 Sheet 2- NTU presents a calculationexample of the NTU

withResult of NTU example (sheet NTU)

NTU =NTU =

and [1] eq (754) page 277 Height of Transfer Unit HTU

Z Tower packing height [m]

flow rate of dry air (is a constat) [kgs] HTU =molar mass of air [kgkmol] HTU =mass transfer coefficient in the air [kmol(msup2s)]

a effective heat or mass transfer surface [msup2msup3] Tower packing heightA free cross-sectional surface of the tower [msup2] Z =

enthalpy in the air phase = enthalpy of humid air [Jkg] HTU =(in the bulk phase) NTU =enthalpy in the air phase (i at ther boundary [Jkg] Z =that is in saturated condition)

HTU Height of Transfer Unit

NTU Number of Transfer Units

Subscripts

B dry air

y air phase = humid air

a top of the tower

b bottom of the tower

i corresponds to the boundary (ie saturated state)

QS =V

MB

ky

Iy

Iyi

NTUHTUZ sdot=

AakMQ

HTUyB

S

sdotsdotsdot=

( )int sdotminus

=ay

by

I

I

yyiy

dIII

1NTU

AakMQ

HTUyB

S

sdotsdotsdot=

Rev cjc 30012014

Number of Transfer Units

The number of transfer units (NTU)is calculated by numerical integtationSheet 2- NTU presents a calculationexample of the NTU

Result of NTU example (sheet NTU)

VALUE -

Height of Transfer Unit HTU

VALUE m

Tower packing heightHTU NTU

VALUE mVALUE -VALUE m

(hL_a - hL_b) N Σf(x)

GS (M

B k

y a A)

AakMQ

HTUyB

S

sdotsdotsdot=

NTU and HTU calculations column 1 column 2

Equilibrium curve for saturated airWater temperature at inlet of tower This curve is

45 ordmC f(t)

Water temperature at tower outlet where the function

29 ordmC hairsat = Psychro_Enthalpy_tdb_HumRel_H

Range has been used

The curve strats at point

Number of sections 3 (29964) The range will be divided in a number Nand ends at point

of sections 4 (452182)N = 6

column 3

Between both temperatures N-1 Operation line for r = 1

temperatures are inserted to define where r is the ratio between the actual

the N sections All section are defined mass flow rate and the minimum flow

with the same temperature differential rate

The line strts at a point defined by the

Temperature differential inlet air properties (point 1 in operating

ordmC diagram) also called state G1

45 ordmC

29 ordmC State G1 (Point 1)

16 K 29 ordmC

24 ordmCSection temperature increment H = 0 m

Psychro_AbsoluteHumidity_tdb_twb_H

16 K VALUE kgkgN = 6 -

267 K VALUE kJkg

Temperature at point i+1

Table 1 Tower packing height calculation1 2 3 3a 4 5

Equilibrium Operation Operation curve for line for line for

saturated air r = 1 r = 15

tL2

= hairsat

=

tL1 =

tL2 - tL1

Column 1 starts with temperature tL2

and ends with temperature tL1

∆tL = t

L2 - t

L1

tL2

=

tL1 =

∆tL = tdbG1 =

twbG2

=

∆tL_Sect

= ∆tL N x

G1 =

∆tL = xG1 =

∆tL_Sect

= hG1

=

ti+1

= ti + ∆t

L_sect

∆h = ∆h =

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

kJkg kJkg kJkg kJkg kJkg25 VALUE

255 VALUE

Top(2) 45 VALUE VALUE VALUE VALUE VALUE

4233 VALUE VALUE VALUE VALUE VALUE3967 VALUE VALUE VALUE VALUE VALUE3700 VALUE VALUE VALUE VALUE VALUE3433 VALUE VALUE VALUE VALUE VALUE3167 VALUE VALUE VALUE VALUE VALUE

Bottom (1) 29 VALUE VALUE VALUE VALUE VALUE

In Operating diagram (sheet 6)t H

degC kJkgPoint 1 29 VALUEPoint 2 45 VALUE Line 1-2 Operation line for r = 1Point 2 45 VALUE Line 1-2 Operation line for r = 15Point 3 29 VALUEPoint 4 45 VALUE Line 3-4 Equilibrium (saturation) line

From column 3a is possible to see that the differences between the Equilibriumcurve and the operation line for r = 1 are very small (053 kJkg) at a certain temperature (3967 degC) Thus this operation line is near enough a minimumflow rate line In the operating diagram figure (sheet 6) the operating line for r = 1 appearsto be tangent with the Equilibrium curve This fact visualizes that this line is close enough to the real minimum flow rateThe condition of tangency between these two curves is due to the fact that ifthe operating line would cross the equilibrium line it would not be possible to have mass transfer in this region

Height of tower packing Number of Transfer Units NTU

From Treibal Equation (7-51)

(751a)

(751b)

The numerial integration of NTU is

performed by means of the trapezoidal

integration method

the air-water mixture for the actual case According this method the integration

where H2 and H1 are the enthalpies of

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

int minus=

2

1

H

H i HHdH

NTU

[ ]mHH

dHak

GZ

H

H iy

S int minussdot

sdot=

2

1

that is in this case for r = 15 is realized as it is shown in the columns6 7 and 8

The final evaluation is done according(751c) following equation

(751d)

NTU =Also where

VALUE

VALUEN = 6

VALUE

Numerical results shown are from next NTU = VALUEcalculation sheets

Treybal [2] result isNTU = 325

The difference comes from the values ofthe psychrometric properties Treybal takes its values from graphics and inthe example are taken form psychrometricfunctios Also the numerical integrationmethod is not indicated

Comparison between the example calculation table and the tabvle from Treibal

Calculation table using psychrometric functions1 2 3 4 5 6

Curva de Liacutenea de Liacutenea de equilibrio para operacioacuten operacioacutenaire saturado para r = 1 para r = 15

tkJkg kJkg kJkg kJkg 1(kJkg)

25 VALUE255 VALUE

29 VALUE 72 72 VALUE VALUE3167 VALUE 96 877 VALUE VALUE

3433 VALUE 119 1034 VALUE VALUE

3700 VALUE 143 1191 VALUE VALUE3967 VALUE 166 1349 VALUE VALUE4233 VALUE 190 1506 VALUE VALUE4500 VALUE 213 16627 VALUE VALUE

Table from Treybal [1] page 2801 2 3 4 5 6

Curva de Liacutenea de Liacutenea de

(hL_a

- hL_b

) (2 N)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

Z=HTUsdotNTU [m ]

HTU=GS

k ysdota[m ]

HTU=GS

M Bsdotk ysdotasdotA

equilibrio para operacioacuten operacioacutenaire saturado para r = 1 para r = 15


25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

The line ends in a point defined by the Slope of line with r = 15 Air flow rateproperties of the leaving satutared air S = m = L Cpw Gs (754)Point 2 L = 15 kgs From heat balance

Estado G2 Cpw = 41868 kJ(kgK)

45 ordmC Gs = VALUE kg ass

f = 100 S = VALUE (kJkg)K

H = 0 m Exit enthalpy

S =

VALUE kJkgThe operation linefor r = 1 is the

VALUE JkgSlope of operation line witrh r = 1 S = VALUE (kJkg)K

45 ordmC

VALUE kJkg 29 ordmC [1] Eq (754) page 277

VALUE kJkg VALUE Jkg

45 ordmC

29 ordmC column 5

VALUE (kJkg)K Driving enthalpy difference at a point i

(754)

m = L liquid flow rate [kg s] (assumed constant)

VALUE (kJkg)K column 6

m = VALUE Reciproc of driving enthalpy difference

L = 15 kg aguas

Cpw = 41868 kJ(kgK) column 7

VALUE kg ass Coefficients for numerical integration

1 at both endscolumn 4 2 in the other elements

Operation line for r = 15

The line starts from the same point 1 column 8the properties at the inlet defined as the Numerical integration elements

state G1

Gs =r = 15

VALUE kg assGs = VALUE kg ass

Table 1 Tower packing height calculation6 7 8

Numerical Air conditions in the towerfor r = 1integration Conditions at the bottom of the tower (point 1 in diagram)coefficient Point 1

f(x) 290 ordmC (Column 1)

tbsG2

=

hG2

= Psychro_Enthalpy_tdb_HumRel_H (hG2

- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)

straight line 12 where r = G Gcon r = G Gmin hG1 =

Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1

= GS gas flow rate [kg as s]

Sr=1

= hG2

exit air enthalpy (top) [kJkg]

GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h

G1 inlet air enthalpya (bottom) [kJkg]

Sr=1

Sr=1 = cpw liquid specific heat [kJ(kgK)]

tL2

inlet water temperature (top) [degC]

tL1

exir water temperature (bottom) [degC]

Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=

minussdotsdot=minussdot

∆=∆

12

12

12

12

1212

1

2

1(kJkg) VALUE kJkg (Column 3)Conditions at the top of the tower (point 2 in diagram)Point 2

VALUE 1 VALUE 45 ordmC (Column 1)

VALUE 2 VALUE VALUE kJkg (Column 3)VALUE 2 VALUEVALUE 2 VALUEVALUE 2 VALUEVALUE 2 VALUEVALUE 1 VALUE

VALUE

Number of Transfer Units NTU Height of Transfer Unit HTU Height of Transfer Unit HTU


HTU =withGs = VALUE

The numerial integration of NTU is 2896

performed by means of the trapezoidal HTU = 62E-05

20 kg(msup2s) a = 500

According this method the integration 09 A = VALUE

hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =

GS ( ky a) ky_kmol =

GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS


is realized as it is shown in the columns HTU = 22 m HTU = VALUE Treybal [2] result is

The final evaluation is done according HTU = 22 m flow rate of dry air (is a constat)

molar mass of air

Height of packing tower mass transfer coefficient in the air

a effective heat or mass transfer surface

A free cross-sectional surface of the tower

Z = HTU NTU

HTU = 22 mNTU = VALUE

kJkg Z = VALUE m

kJkgTreybal [2] result is

Z = 722 m

-

-The difference comes from the values ofthe psychrometric properties Treybal takes its values from graphics and inthe example are taken form psychrometricfunctios Also the numerical integration

Comparison between the example calculation table and the tabvle from Treibal Trapezoidal numerical integration rule

Calculation table using psychrometric functions7 8

Numericalintegrationcoefficient

f(x)

1 VALUE NTU =2 VALUE where

2 VALUE 1663 kJkg

2 VALUE 720 kJkg2 VALUE N = 62 VALUE VALUE1 VALUE

VALUE NTU = VALUE -

Table from Treybal [1] page 2807 8

Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====

sdotsdotminusasympsdot sumint

=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU

integrationcoefficient

f(x) Treybal table differs from the calculationtable in the values of the psichrometricpropertiesAdditionaly Treibal uses a different

1 003575 numerical integration method where 1 004545 the numerical integration coefficienst are

1 0042921 003846 The numerical integration used is not1 003195 indicated and Treybal gives as a1 002410 final result a NTU value1 001905

023767 NTU = 325 -

Ci

not required (or Ci = 1)

Σf(x) =

Rev cjc 30012014

of 4

L liquid flow rate [kg s] (assumed constant)

Rev cjc 30012014

Page 2 of 4

Table 1 Tower packing height calculation

Conditions at the bottom of the tower (point 1 in diagram)

gas flow rate [kg as s]


inlet air enthalpya (bottom) [kJkg]

liquid specific heat [kJ(kgK)]



( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m

flow rate of dry air (is a constat) [kgs]

molar mass of air [kgkmol]

mass transfer coefficient in the air [kmol(msup2s)]

effective heat or mass transfer surface [msup2msup3]

free cross-sectional surface of the tower [msup2]

Page 4 of 4

Microsoft Editor de ecuaciones 30


HTU TreibalEquation (7-51)

HTU = V (MB ky a A)withV = 5684 kg ass

MB = 2896 kgkmol

ky_kmol = 62E-05 kmol ( m2s)

a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m

Tower height l = NTU HTU

NTU = 425 -HTU = 119 m

l = 504 mV = G AG = 1066 kg as(smsup2)

533 msup2

5684 kg ass

GS ( ky a)2 kg(msup2s)



Area of cross sectional surface Seleted area

From borh results the smallest value

L = should be selected to ensure that the

L liquid flow rate [kgs]

the indicated value ofsectional surface) [kg ( msup2s)]

A area of cross section 090So

A = L Lu A = VALUEL = 15 kgs

27 kg(msup2s)A = 556 msup2

Using the gas flow rate

A =G gas rate [kgs]

sectional surface) [kg ( msup2s)]A area of cross section

Gs = VALUE kg ass

2 kg(msup2s)A = VALUE msup2

Lu A

value of the product kya has at least

Lu unit flow rate (for unit of cross

kya =

Lu =

GS G

Su

Gu unit flow rate (for unit of cross

GSu

=

Rev cjc 30012014


should be selected to ensure that the

msup2


kg ( m3s)

Compensation water

Cosidering a compensation and a Entrainment loss rate W water that is Applicationcontinuous elimination the mass being transported with the exit airbalance is leaving from de top of the tower as a Evaporation rate E

(a) loss of water1- Absolute humidity of exit air

Evaporation rate E water that is Assuming that the leaving air is basicallyA water hardness balance is evapotated in the air flow producing saturated at Point O

de cooling of the water flow(b) From equation (d) The enthalpy at this point from the

calculation Table 1 is

and thereforeAssuming initially a temperature value

(c) the corresponding enthalpy for thisassumed temperature is with

Eliminating M from (a) and (c)H =h =

(d) Now using Solver find a value of the

With calculated exit air temperature

M compensation rate [kgh] the corresponding absolute humidity

B elimination rate [kgh] can be be calculatedE evaporation rate [kgh] t =

W entrainment loss rate [kgh]

H =

circulating water [kgkg] or [ppm]

compensation water [kgkg] or [ppm] 2- Absolute humidity of inlet air

From sheet 2

Elimination rate B required to replace

water with a maximum allowable salts

content with fresh water with the in this 3- Humidity change

water existing salt content This is

called the compensation rate

(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC

hardness weight fraction of

xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=

( ) CM daWBdaM sdot+=sdot

( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=sdotminus

sdot+sdot=++

1

11

11

1

1

Entrainment water

E =Dry air flow rate (sheet 2)

Evaporation rate E Gs = VALUE kg ass Water

VALUE kgkg1- Absolute humidity of exit air E = VALUE kgs Assuming that the leaving air is basically saturated at Point O Entrainment loss W

100 To estimate the entrainment lossesThe enthalpy at this point from the one assumes that these losses are calculation Table 1 is a percentage ampW of the water flow rate

VALUE kJkg ampL = 02 Assuming initially a temperature value The water flow rate is

30 degC L = 15 kgsthe corresponding enthalpy for this W = L ampL Compensation waterassumed temperature is with L = 15 kgs

400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl

VALUE kJkg Elimination rate BNow using Solver find a value of the B =

E = VALUE kgsWith calculated exit air temperature W = 0030 kgs

the corresponding absolute humidity 500 ppm

can be be calculated 2000 ppm400 degC B = VALUE kgs

100

0 masl Compensation rate M

VALUE kgkg M =

B = VALUE kgs2- Absolute humidity of inlet air W 0030 kgs

From sheet 2 2000 ppm

VALUE kgkg 500 ppm

M = VALUE kgs3- Humidity change

kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =

E ( daM (daC - daM) ) - W

temperature tO to obtain that h = hO

da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram

1 2 3 3a 4 5 6Curva de Liacutenea de Liacutenea de


kJkg kJkg kJkg kJkg kJkg 1(kJkg)250 VALUE255 VALUE

290 VALUE VALUE VALUE VALUE VALUE VALUE317 VALUE VALUE VALUE VALUE VALUE VALUE343 VALUE VALUE VALUE VALUE VALUE VALUE370 VALUE VALUE VALUE VALUE VALUE VALUE397 VALUE VALUE VALUE VALUE VALUE VALUE423 VALUE VALUE VALUE VALUE VALUE VALUE

450 VALUE VALUE VALUE VALUE VALUE VALUE

∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120

Operation Diagram of Cooling Tower

Equilibrium curveColumn EOp L r = 15

Liquid temperature [degC]

En

tha

lpy

air

-va

po

r [

kJk

g d

a]

Equilibrium curve for saturated air

Operating line with r = 1


2

1

2

3

4

7 8Numerical Hintegration (gas-vapor mixture)coefficient kJkg as

f(x)

4

1 VALUE2 VALUE2 VALUE2 VALUE2 VALUE2 VALUE

1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1

Liquid temperature t

tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2

Liquid temperature tL degC

Cooling tower schematic [3]

[1] Operaciones de transferencia de masa 2eRobert E TreybalMcGraw Hill2003

Page 274 Enfriamiento de agua con aire


[1] Operaciones de transferencia de masa 2eRobert E TreybalMcGraw Hill 2003

[2]

[3]

httplibrarykfupmedusaISI20065-2006pdf

1- Packing heightThe packing height of a tower can be calculated according [2] equation (65)

Z = I Tower packing height

flow rate of dry air (is a constat)

molar mass of air

Naming the first term as Height of Transfer mass transfer coefficient in the air Unit (HTU) a effective heat or mass transfer surface


enthalpy in the air phase = enthalpy of humid air (in the bulk phase)

enthalpy in the air phase (i at ther boundaryand the second term as the Numbert of Transfer that is in saturated condition)Units (NTU)

HTU Height of Transfer UnitNTU Number of Transfer Units

Subscripts

B dry airthe packinh height becomes y air phase = humid air

a top of the towerb bottom of the toweri corresponds to the boundary (ie saturated state)

Packing height and free-cross sectional surface of a tower [2]

QS =V

MB

ky

Iy

Iyi

Z=(QS

M Bsdotk ysdotasdotA )sdotintI y b

I y a1

( I y iminusI y )iquest dI y

AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU

Tower packing height [m]



mass transfer coefficient in the air [kmol(msup2s)]effective heat or mass transfer surface [msup2msup3]free cross-sectional surface of the tower [msup2]

enthalpy in the air phase = enthalpy of humid air [Jkg](in the bulk phase)

enthalpy in the air phase (i at ther boundarythat is in saturated condition)

Height of Transfer UnitNumber of Transfer Units

air phase = humid airtop of the towerbottom of the towercorresponds to the boundary (ie saturated state)


Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area

5- Compensation water

6- Operating diagram

7- Cooling tower schematic

Ref 1

Ref

Ref 2


Rev cjc 30012014

Index

Data for cooling tower application

Main equations and results

Cooling Tower height NTU and HTU


Compensation elimination evaporation and entrainment fow rates

Equilibrium curve and operation lines

Schema








5 K



temperature 10 degC


hardness 2000 ppm







tL2

=

tdbG1 =

twbG1



da_c

=


_M =


Mair =

Lu = kg(sm2)

Gu = kg(sm2)


State L1


L2 =

24

5 K


State G1 10 ordmC


30 ordmC

24 ordmC

H = 00 m



x = VALUE kglg




2896 kgkmol


62E-05

2896 kgkmol

00018

Product Kya

Kya

00018a = 500 msup2msup3

090

Q = 270 W

tL1

= twbG1

+ ∆t

tbhG1 tL2 =

∆t =

tL1

=

tacomp

=

dac =

tbsG1

=

tbhG1

ky_kmol

= kmol ( m2s)

Mair

=

daM =

ky = k

y_kmol M

air

ky_kmol

= kmol ( m2s)

Mair

=

ky = kg ( m2s)

Kya =

ky = kg ( m2s)

Kya = kg ( m3s)

W

Blowdown water B

Rev cjc 30012014


15 kg s

45 ordmC Air

Water

30 ordmC

24 ordmC

Water

Air

2000 ppm

Rev cjc 30012014

tdbG1 =

twbG1

L1G1

Torreenfriadora

G22

Blowdown water B

G1

L2






NTU =NTU =








Subscripts

B dry air


a top of the tower



QS =V

MB

ky

Iy

Iyi

NTUHTUZ sdot=

AakMQ

HTUyB

S

sdotsdotsdot=

( )int sdotminus

=ay

by

I

I

yyiy

dIII

1NTU

AakMQ

HTUyB

S

sdotsdotsdot=

Rev cjc 30012014




VALUE -


VALUE m




GS (M

B k

y a A)

AakMQ

HTUyB

S

sdotsdotsdot=



45 ordmC f(t)



Range has been used




column 3








45 ordmC


16 K 29 ordmC




267 K VALUE kJkg





tL2

= hairsat

=

tL1 =

tL2 - tL1



∆tL = t

L2 - t

L1

tL2

=

tL1 =

∆tL = tdbG1 =

twbG2

=

∆tL_Sect

= ∆tL N x

G1 =

∆tL = xG1 =

∆tL_Sect

= hG1

=

ti+1

= ti + ∆t

L_sect

∆h = ∆h =

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15


255 VALUE









(751a)

(751b)



integration method



( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

int minus=

2

1

H

H i HHdH

NTU

[ ]mHH

dHak

GZ

H

H iy

S int minussdot

sdot=

2

1



(751d)

NTU =Also where

VALUE

VALUEN = 6

VALUE








25 VALUE255 VALUE






(hL_a

- hL_b

) (2 N)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

Z=HTUsdotNTU [m ]

HTU=GS

k ysdota[m ]

HTU=GS




25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2








5 K



temperature 10 degC


hardness 2000 ppm







tL2

=

tdbG1 =

twbG1



da_c

=


_M =


Mair =

Lu = kg(sm2)

Gu = kg(sm2)


State L1


L2 =

24

5 K


State G1 10 ordmC


30 ordmC

24 ordmC

H = 00 m



x = VALUE kglg




2896 kgkmol


62E-05

2896 kgkmol

00018

Product Kya

Kya

00018a = 500 msup2msup3

090

Q = 270 W

tL1

= twbG1

+ ∆t

tbhG1 tL2 =

∆t =

tL1

=

tacomp

=

dac =

tbsG1

=

tbhG1

ky_kmol

= kmol ( m2s)

Mair

=

daM =

ky = k

y_kmol M

air

ky_kmol

= kmol ( m2s)

Mair

=

ky = kg ( m2s)

Kya =

ky = kg ( m2s)

Kya = kg ( m3s)

W

Blowdown water B

Rev cjc 30012014


15 kg s

45 ordmC Air

Water

30 ordmC

24 ordmC

Water

Air

2000 ppm

Rev cjc 30012014

tdbG1 =

twbG1

L1G1

Torreenfriadora

G22

Blowdown water B

G1

L2






NTU =NTU =








Subscripts

B dry air


a top of the tower



QS =V

MB

ky

Iy

Iyi

NTUHTUZ sdot=

AakMQ

HTUyB

S

sdotsdotsdot=

( )int sdotminus

=ay

by

I

I

yyiy

dIII

1NTU

AakMQ

HTUyB

S

sdotsdotsdot=

Rev cjc 30012014




VALUE -


VALUE m




GS (M

B k

y a A)

AakMQ

HTUyB

S

sdotsdotsdot=



45 ordmC f(t)



Range has been used




column 3








45 ordmC


16 K 29 ordmC




267 K VALUE kJkg





tL2

= hairsat

=

tL1 =

tL2 - tL1



∆tL = t

L2 - t

L1

tL2

=

tL1 =

∆tL = tdbG1 =

twbG2

=

∆tL_Sect

= ∆tL N x

G1 =

∆tL = xG1 =

∆tL_Sect

= hG1

=

ti+1

= ti + ∆t

L_sect

∆h = ∆h =

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15


255 VALUE









(751a)

(751b)



integration method



( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

int minus=

2

1

H

H i HHdH

NTU

[ ]mHH

dHak

GZ

H

H iy

S int minussdot

sdot=

2

1



(751d)

NTU =Also where

VALUE

VALUEN = 6

VALUE








25 VALUE255 VALUE






(hL_a

- hL_b

) (2 N)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

Z=HTUsdotNTU [m ]

HTU=GS

k ysdota[m ]

HTU=GS




25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2


State L1


L2 =

24

5 K


State G1 10 ordmC


30 ordmC

24 ordmC

H = 00 m



x = VALUE kglg




2896 kgkmol


62E-05

2896 kgkmol

00018

Product Kya

Kya

00018a = 500 msup2msup3

090

Q = 270 W

tL1

= twbG1

+ ∆t

tbhG1 tL2 =

∆t =

tL1

=

tacomp

=

dac =

tbsG1

=

tbhG1

ky_kmol

= kmol ( m2s)

Mair

=

daM =

ky = k

y_kmol M

air

ky_kmol

= kmol ( m2s)

Mair

=

ky = kg ( m2s)

Kya =

ky = kg ( m2s)

Kya = kg ( m3s)

W

Blowdown water B

Rev cjc 30012014


15 kg s

45 ordmC Air

Water

30 ordmC

24 ordmC

Water

Air

2000 ppm

Rev cjc 30012014

tdbG1 =

twbG1

L1G1

Torreenfriadora

G22

Blowdown water B

G1

L2






NTU =NTU =








Subscripts

B dry air


a top of the tower



QS =V

MB

ky

Iy

Iyi

NTUHTUZ sdot=

AakMQ

HTUyB

S

sdotsdotsdot=

( )int sdotminus

=ay

by

I

I

yyiy

dIII

1NTU

AakMQ

HTUyB

S

sdotsdotsdot=

Rev cjc 30012014




VALUE -


VALUE m




GS (M

B k

y a A)

AakMQ

HTUyB

S

sdotsdotsdot=



45 ordmC f(t)



Range has been used




column 3








45 ordmC


16 K 29 ordmC




267 K VALUE kJkg





tL2

= hairsat

=

tL1 =

tL2 - tL1



∆tL = t

L2 - t

L1

tL2

=

tL1 =

∆tL = tdbG1 =

twbG2

=

∆tL_Sect

= ∆tL N x

G1 =

∆tL = xG1 =

∆tL_Sect

= hG1

=

ti+1

= ti + ∆t

L_sect

∆h = ∆h =

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15


255 VALUE









(751a)

(751b)



integration method



( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

int minus=

2

1

H

H i HHdH

NTU

[ ]mHH

dHak

GZ

H

H iy

S int minussdot

sdot=

2

1



(751d)

NTU =Also where

VALUE

VALUEN = 6

VALUE








25 VALUE255 VALUE






(hL_a

- hL_b

) (2 N)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

Z=HTUsdotNTU [m ]

HTU=GS

k ysdota[m ]

HTU=GS




25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

Rev cjc 30012014


15 kg s

45 ordmC Air

Water

30 ordmC

24 ordmC

Water

Air

2000 ppm

Rev cjc 30012014

tdbG1 =

twbG1

L1G1

Torreenfriadora

G22

Blowdown water B

G1

L2






NTU =NTU =








Subscripts

B dry air


a top of the tower



QS =V

MB

ky

Iy

Iyi

NTUHTUZ sdot=

AakMQ

HTUyB

S

sdotsdotsdot=

( )int sdotminus

=ay

by

I

I

yyiy

dIII

1NTU

AakMQ

HTUyB

S

sdotsdotsdot=

Rev cjc 30012014




VALUE -


VALUE m




GS (M

B k

y a A)

AakMQ

HTUyB

S

sdotsdotsdot=



45 ordmC f(t)



Range has been used




column 3








45 ordmC


16 K 29 ordmC




267 K VALUE kJkg





tL2

= hairsat

=

tL1 =

tL2 - tL1



∆tL = t

L2 - t

L1

tL2

=

tL1 =

∆tL = tdbG1 =

twbG2

=

∆tL_Sect

= ∆tL N x

G1 =

∆tL = xG1 =

∆tL_Sect

= hG1

=

ti+1

= ti + ∆t

L_sect

∆h = ∆h =

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15


255 VALUE









(751a)

(751b)



integration method



( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

int minus=

2

1

H

H i HHdH

NTU

[ ]mHH

dHak

GZ

H

H iy

S int minussdot

sdot=

2

1



(751d)

NTU =Also where

VALUE

VALUEN = 6

VALUE








25 VALUE255 VALUE






(hL_a

- hL_b

) (2 N)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

Z=HTUsdotNTU [m ]

HTU=GS

k ysdota[m ]

HTU=GS




25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2






NTU =NTU =








Subscripts

B dry air


a top of the tower



QS =V

MB

ky

Iy

Iyi

NTUHTUZ sdot=

AakMQ

HTUyB

S

sdotsdotsdot=

( )int sdotminus

=ay

by

I

I

yyiy

dIII

1NTU

AakMQ

HTUyB

S

sdotsdotsdot=

Rev cjc 30012014




VALUE -


VALUE m




GS (M

B k

y a A)

AakMQ

HTUyB

S

sdotsdotsdot=



45 ordmC f(t)



Range has been used




column 3








45 ordmC


16 K 29 ordmC




267 K VALUE kJkg





tL2

= hairsat

=

tL1 =

tL2 - tL1



∆tL = t

L2 - t

L1

tL2

=

tL1 =

∆tL = tdbG1 =

twbG2

=

∆tL_Sect

= ∆tL N x

G1 =

∆tL = xG1 =

∆tL_Sect

= hG1

=

ti+1

= ti + ∆t

L_sect

∆h = ∆h =

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15


255 VALUE









(751a)

(751b)



integration method



( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

int minus=

2

1

H

H i HHdH

NTU

[ ]mHH

dHak

GZ

H

H iy

S int minussdot

sdot=

2

1



(751d)

NTU =Also where

VALUE

VALUEN = 6

VALUE








25 VALUE255 VALUE






(hL_a

- hL_b

) (2 N)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

Z=HTUsdotNTU [m ]

HTU=GS

k ysdota[m ]

HTU=GS




25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

Rev cjc 30012014




VALUE -


VALUE m




GS (M

B k

y a A)

AakMQ

HTUyB

S

sdotsdotsdot=



45 ordmC f(t)



Range has been used




column 3








45 ordmC


16 K 29 ordmC




267 K VALUE kJkg





tL2

= hairsat

=

tL1 =

tL2 - tL1



∆tL = t

L2 - t

L1

tL2

=

tL1 =

∆tL = tdbG1 =

twbG2

=

∆tL_Sect

= ∆tL N x

G1 =

∆tL = xG1 =

∆tL_Sect

= hG1

=

ti+1

= ti + ∆t

L_sect

∆h = ∆h =

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15


255 VALUE









(751a)

(751b)



integration method



( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

int minus=

2

1

H

H i HHdH

NTU

[ ]mHH

dHak

GZ

H

H iy

S int minussdot

sdot=

2

1



(751d)

NTU =Also where

VALUE

VALUEN = 6

VALUE








25 VALUE255 VALUE






(hL_a

- hL_b

) (2 N)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

Z=HTUsdotNTU [m ]

HTU=GS

k ysdota[m ]

HTU=GS




25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2



45 ordmC f(t)



Range has been used




column 3








45 ordmC


16 K 29 ordmC




267 K VALUE kJkg





tL2

= hairsat

=

tL1 =

tL2 - tL1



∆tL = t

L2 - t

L1

tL2

=

tL1 =

∆tL = tdbG1 =

twbG2

=

∆tL_Sect

= ∆tL N x

G1 =

∆tL = xG1 =

∆tL_Sect

= hG1

=

ti+1

= ti + ∆t

L_sect

∆h = ∆h =

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15


255 VALUE









(751a)

(751b)



integration method



( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

int minus=

2

1

H

H i HHdH

NTU

[ ]mHH

dHak

GZ

H

H iy

S int minussdot

sdot=

2

1



(751d)

NTU =Also where

VALUE

VALUEN = 6

VALUE








25 VALUE255 VALUE






(hL_a

- hL_b

) (2 N)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

Z=HTUsdotNTU [m ]

HTU=GS

k ysdota[m ]

HTU=GS




25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2


255 VALUE









(751a)

(751b)



integration method



( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

int minus=

2

1

H

H i HHdH

NTU

[ ]mHH

dHak

GZ

H

H iy

S int minussdot

sdot=

2

1



(751d)

NTU =Also where

VALUE

VALUEN = 6

VALUE








25 VALUE255 VALUE






(hL_a

- hL_b

) (2 N)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

Z=HTUsdotNTU [m ]

HTU=GS

k ysdota[m ]

HTU=GS




25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2



(751d)

NTU =Also where

VALUE

VALUEN = 6

VALUE








25 VALUE255 VALUE






(hL_a

- hL_b

) (2 N)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

Z=HTUsdotNTU [m ]

HTU=GS

k ysdota[m ]

HTU=GS




25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2



25 VALUE255 VALUE29 1000 72 72 280 00357

3167 1140 96 920 220 00455

3433 1298 119 1065 233 004293700 1470 143 1210 260 003853967 1668 166 1355 313 003194233 1910 190 1495 415 002414500 2160 213 16350 525 00190

∆h = 1∆h

hairsat

hoper_r=1

hoper_r=15

hairsat

-hop_r=15






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2






S =



45 ordmC



45 ordmC

29 ordmC column 5


(754)




L = 15 kg aguas






state G1

Gs =r = 15





tbsG2

=

hG2


- hG1

) (tbsG2

- tbsG1

)

hG2

= hG2

= hG1

+ S (tbsG2

- tbsG1

)


Sr=1

= (hG2

- hG1

) (tL2

- tL1

) tbsG2

=

hG2

= tbsG1

=

hG1

= hG2

=

tL2

=

tL1


Sr=1

= hG2


GS = G

r=1 = 1m L c

pw ∆hi = h

airsat_i -h

op_r=15_i h


Sr=1


tL2


tL1


Gr=1 =

Ci =

f(xi) = C

i (1∆h

i)

r Gr=1

Gr=1

=

1∆h

Ci tbs1 =

( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2




VALUE



HTU =withGs = VALUE



20 kg(msup2s) a = 500


hG1

=

tbs2 =

h2 =

Σf(x) =

GS (M

B k

y a A)

MB =


GS

kya kg ( m3s)

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

HTU=GS

k ysdotaHTU=

GS




molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2



molar mass of air




Z = HTU NTU


kJkg Z = VALUE m


Z = 722 m

-





f(x)


2 VALUE 1663 kJkg


VALUE NTU = VALUE -


Numerical

QS

MB

ky

L_a - h

L_b) (2 N) Σf(x)

Ci

NTU=(hL2

- hL1)

2N (f(x1) + 2f(x

2) + 2f(x

3) + hellip+ 2f(x

N-1) + f(x

N) )

(hL_a

- hL_b

) (2 N) Σf(x)

hL_in_r=15

=

hL_out=r=15

=

Σf(x) =

Σf(x) =

sumsdotsdotminus

= )(2

__xf

N

hhNTU

bLaL

)1(22

11

2)(

1

minus====


=

Niparag

Nyiparag

fgN

abdxxf

i

i

k

N

ki

b

a

Z=HTUsdotNTU





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2





023767 NTU = 325 -

Ci


Σf(x) =

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

Rev cjc 30012014

Page 1 of 4


Rev cjc 30012014

Page 2 of 4









( ) ( )( )

( )

( )

m

cLG

tt

hhm

hh

ttcLG

ttcLhhG

bottom

top

HH

pwS

LL

GG

GG

LLpwS

LLpwGGS

Liquidair

sdot=

minusminus=

minusminussdotsdot=


∆=∆

12

12

12

12

1212

1

2

Page 3 of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

of 4


kg ass

kgkmol

msup2msup3

msup2

S (M

B k

y a A)

kmol ( m2s)

HTU=GS


m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

m






Page 4 of 4





MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2




MB = 2896 kgkmol


a = 500 msup2msup3

A = 533 msup2

AakM

VHTU

yB sdotsdotsdot=

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

HTU = 119 m


NTU = 425 -HTU = 119 m


533 msup2

5684 kg ass













A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2











A =G gas rate [kgs]


Gs = VALUE kg ass


Lu A



kya =

Lu =

GS G

Su


GSu

=

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

Rev cjc 30012014



msup2


kg ( m3s)

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

Compensation water














H =



From sheet 2






(e)

φO =

hO =

tO =

tO =

φO =

temperature t

φO =

daC


xa2

=

daM


xa1

=

∆x2-1

=

xa2

=

xa1 =

∆x2-1

=

WEBM ++=


( )M

C

da

daWBM

sdot+=

( )M

C

da

daWBWEB

sdot+=++

Wdada

daEB

MC

M minusminus

sdot=

Wdada

daEB

dadada

EWB

da

dadaE

WB

dadaE

WB

Eda

daW

da

daB

Eda

daW

da

daB

Eda

daW

da

daW

da

daB

dada

WEdada

Wdada

B

WEdada

Wdada

BB

dada

Wdada

BWEB

MC

M

M

MC

M

CM

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

M

C

minusminus

sdot=

minus+minus=

minusminusminus=

minusminusminus=

minus

minussdotminus=

minussdot

minus

minussdot=

minussdot

minusminussdot=

minussdot

minusminussdot=

minussdot


sdot+sdot=++

1

11

11

1

1

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

Entrainment water







400 degC ampL = 0002 -

100 W = 0030 kgs 0 masl





100


VALUE kgkg M =



VALUE kgkg 500 ppm


kgkg

VALUE kgkg

VALUE kgkg

VALUE kgkg

GS ∆x

2-1

∆x2-1 =



da_M

=

da_c

=

(B + W) daC da

M

da_c

=

da_M

=

xa2

- xa1

M daM

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

Rev cjc 30012014

Entrainment water

Air

Elimination water


L1 G1

Cooling tower

G2

E

W daC

B daC

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

Operation Diagram






∆h = ∆h = 1∆h

tL

hairsat

hoper_r=1

hairsat

-hop_r=1

hoper_r=15

hairsat

-hop_r=15

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




2

1

2

3

4


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2




4 Enfriamiento de agua con aire



[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2


f(x)

4


1 VALUE 3

VALUE

1

Ci

H2

H2

H1

Σf(x) =

H1


tL1

tL2

250 300 350 400 450 50000

20

40

60

80

100

120




En

tha

lpy

air

-va

po

r [

kJk

g d

a]




R

ST

U( )HtL

( )acuteHtL

( ) ii Ht

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

Rev cjc 30012014

2







[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2






[2]

[3]





molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2




molar mass of air






Subscripts




QS =V

MB

ky

Iy

Iyi

Z=(QS


I y a1


AakM

VHTU

yB sdotsdotsdot=

( ) yyiy

I

I

dIII

NTU

ay

by

sdotminus

= int

1

Z=HTUsdotNTU










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2










Index

1- Data

2- Tower height

3- NTU amp HTU

4- Tower area




Ref 1

Ref

Ref 2

Treybal Cooling Tower

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Transcript of Treybal Cooling Tower