Chemical Engineering
Humidification
Reviewer for Chemical Engineering
Licensure Examination, 2nd Edition
THEORY AND EQUATIONS
This topic involves the GOntact of a pure liquid with a gas for the purpose of changing the
vapor content of the gas and/or adding or removing heat from the contacting phases for
purposes of cooling or heating. The operation may be· classified as . Humidification,
Dehumidification, Air-Conditioning and Water Cooling. The concern of a chemical
engineer is to design the various equipment used in the gas-liquid contact operations.
Phase Equilibria
The operation involves two components and two phases, Based on the Gibb's phase rule,
the number of degrees of freedom to define equilibrium conditions is two. Thus, i( the total
pressure is fixed, specifying the temperature fixes the concentration. of the vapor in the gas
phase. It .is important therefore to define the var.ious properties of the gas-vapor systet~l
both under equilibrium and non-equilibrium conditions that are used in the analysis and
design of the equipment.
Definitions
1.
Absolute Humidity, H lb. vapor . This refers to the ratio of the mass of vapor per
/b.d.g
.
.unit mass of vapor-free gas. This may be determined from the partial pressure
exerted by the vapor (A) in the gas (B).
2.
Saturation Humidity, H s . This refers to the maximum amount of vapor that. a
gas can contain which is in equilibrium with the liquid at a given temperature. The
partial pressure of the vapor is in effect equal to the vapor pressure.
H =
p~
~ . Pr- p~
3.
X
MA
MB
Relative Humidity; RH or HR. This refers to the ratio of the partial pressure to
the vapor pressure at a specified temperature of the gas-vapor mixture.
PA
HR = X 100
PJ
4.
Percentage Saturation or Percentage Humidity;-H A ~
100 -- H R X P.r -PJ
X
Hs
Pr - PA
Humid Volume, vH , ft?/Ib dry gas. This is the volume occupied by one pound of
dry gas plus whatever vapor it contains at a given pressure and temperature.
H A -- - H
5.
vH =vs +VA= RT (ns +nA)
.
p
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Chemical Engineering
Humidification
Reviewer for Chemical Engineering
Licensure Examination, 2nd Edition
or
VH = 0.73 T
p
(-I-+_!!_)·
MB
MA
6. Saturated Volume, Vs . The specific volume ifthe gas is saturated with the vapor.
V s = 0.73T
P
7.
(-)-+
MB
H5 )
MA
Humid Heat, c5 BTU/lb-6 F: This is the heat needed to raise the temperature of
one pound of dry gas and the vapor it contains by I °F.
For air-water system: c5 =cp8 +cpA H
C5 =0.24 + 0.46 H
8. Enthalpy of Mixture, Hy, BTU/lb dry gas. This refers to the total enthalpy content
of I lb of dry gas and its vapor at a given temperature.
Hy = HYB +HYA
If the reference temperature for the gas is taken as T R and for the liquid as T~ , we
9.
get
i[y = cp. (rY -TR )+c~. H (rY- T~) + H:tr~
If T~ =TR
Hy ~c 5 (Ty- TR)+HArR
Adiabatic Saturation Temperature, T..•. This refers to the steady state temperature
attained by a gas-vapor mixture when saturated with vapor by spraying under
adiabatic conditions. An Enthalpy Balance around the spray chamber gives
., 1 :~.,· "-.::~
. . ~- ~--~_-..v.:
•
..... ..:;,.
H -Hs
C5
'i·
~y - Ts
As
t- f A~- L
The above is known as the equation ofthe Adiabatic Humidification Line (AHL).
I 0. Wet Bulb Temperature, Tw . This refers to the steady state temperature attained
by a small mass of liquid immersed in a large body of gas. Application of mass
· and heat transfer equation around this small mass of liquidyieids
H - Hw
'fk l,,
..
kyMB~
Ty -Tw
For air-water system:
.. .. ·.::.>
~ :.~ ~t, :>.·,_·t ":··f.. -~- ~ r ·1.
r ,~ •.~
~"" 0.26 . This is known as the Lewis Relation. Since
kyMB
II.
0.26 is very near the value of c5 , for air-water system the wet bulb temperature
becomes identical with the adiabatic saturation temperature, Tw = T5 •
Dew Point, Td . This is the steady temperature attained when a vapor-gas mixture
becomes saturated when cooled at constant humidity, that is PA = P;
I2. Humidity Chart. Many of the above properties for air-water system can be
obtained fromthe humidity chart' at I atffi pressure. Humidity charts for other gasvapor mixtures are also available.
209
Chemical Engineering
Reviewer for Chemical Engineering
Licensure Examination, 2nd Edition
Humidification
Design Equations
Consider a gas-liquid contact equipment with the gas and liquid are in counter-current flow
with L =as the mass flow rate of the liquid; w =as the mass flow rate of the vapor-free
gas; S =free cross-sectional area; and Z = as the height of the contact tower, the following
equations may be generated:
l.
Tx 2
Tx 1
H,
Ty ,
Material Balance: Me = wdH = dL
Enthalpy Balance: wdHy = Lc~.dTx
Heat Balance: w (c_,dTy + MH ) = LC LdTx
Mass Transfer Equation (gas phase only}: wdH = K~a (H -Hi)Sd Z
Heat Transfer Equation:
Gas Phase: we5 dTY = h0 a (ry -7;) Sd Z
Liquid Phase: . Lc L dTx = hL a (7; --' T,) Sd Z
Enthalpy Transfer Equation (air-water system only):
wdHY = K>(Hy- HYi )sd z
The above equations may be solved and applied to describe the various types of gas-liquid
contact operations.
I.
Adiabatic Humidification
In order for humidification to be considered adiabatic, the following conditions must
bernet:
f
H;
/
//
/
I
I ·
I
H
Tv
I
I
'
1. Tx 1 = Tx2 = Tx = constant
2. TWJ = T.W z = TX =constant
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------------------------------------------~------~
Reviewer for Chemical Engineering
Licensure Examination, 2nd Edition
Chemical Engineering
Humidification
That is, the temperature of the water is constant and equal to the wet-bulb temperature
of the gas which is also constant. This, of course, is a simplification which may not be
achieved in reality. Solving the differential design equations forthis case, we get
1.
Material Balance. e = w (H 2 - H 1) = L 2 - L 1
2.
Heat Balance. A general heat balance can be derived by an energy
accounting around the tower. Let TR = Ty 2 , then
[wcsi(Tyi-Tyz)+wHI ..try2 ] + ~cr(Tx 2 -Ty 2 )=
air inlet
air outlet
For adiabatic humidification, since: Tx 1 = Tx 2 = Tx, the above equation may
be simplified to the form
Hz-!4 =_3_
TY2- TYI
ArY2
which is similar to the equation of Adiabatic Humidification Line
3.
Mass Transfer Equation. Since Hi =H s =constant, integration of the mass
transfer equation yields w ( H 2 - H 1) = K~ a (H s- H)1n.SZ
4.
Heat Transfer Equation. Since the temperature of the liquid is constant only
gas phase heat transfer is involved. With Tx = T; =constant, the heat transfer
equation gives w~s (rYI - rY2 )= hoa (rY - rx )In sz
Note that h0 a = U0 a, the over-all heat transfer coefficient, since there is no
resistance to heat transfer in the liquid phase.
II. Dehumidification or Air-Conditioning
gas
liquid
H---
- - - - S.H.
I.
2.
Integration of the general design equations gives,
Material Balance. ± & = L1 - L2 = w ( H 1 - Hz)
Enthalpy Balance. LcL (Tx 1 - Tx 2 )= w ( H yi- Hyz)
Heat Balance is the same as that derived under adiabatic humidification.
211
Chemical Engineering
Reviewer for Chemical Engineering
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3.
Humidification
Mass Transfer Equation. Since the interfacial humidity is not usually known,
integration can be approximated by assuming H; = HT • Thus,
.
X
w ( H 1-Hz) = K~ a (H- H T )Jn SZ
4.
Heat Transfer Equation. Likewise, since the interfacial temperature is not
readily known and since the heat transfer resistance in the liquid phase is small,
T;-:o;;Tx
w~s(Ty -TY2)=Vaa(Ty-Tx) nSZ
.
1
1
III. Water Cooling
For water cooling, the air undergoes a non-adiabatic humidification process. Thus, the
integrated design equations used are similar to that of dehumidification except that the
limits are reversed.
·
More Accurate Design Equations
Due to the approximate nature of the mass and heat transfer equations generated for water
cooling and dehumidification, it is necess,ary to seek for better working design equations. If
the system is limited to air-water system, the design can be based on the enthalpy driving
force as given by the Merkel's Equation.
Water Cooling
From the enthalpy transfer equation given by
wd H y = K>(Hy; -Hy)SdZ
integration yields
where Ha is the height of a transfer unit (HTU) and N G , the number of transfer units
(NTU). Na may be evaluated by graphical integration if the interfacial enthalpy Hy, is
known. To get values of H y, vs H Y, the following steps can b~ used:
212
r-
I
Chemical Engineering
Humidification
· Reviewer for Chemical Engineering
Licensure Examination, 2nd Edition
1.
2.
Plot the ·Equilibrium Curve which consists of the enthalpy of air at saturation as a
function of the temperature of water: Hys vs. Tx. This may be obtained from the
humidity chart.
Plot the Operating Line which is generated using the Enthalpy Balance.
L
H
-H
w
TX2 -TXI
Y2
YI = Slope of O.L.
The ratio !:.. is the slope of the operating line.
w
3.
Determine · the Slope of the Tie Line obtained by dividing the enthalpy transfer
equation by the liquid phase Heat Transfer Equation, that is
H. -H
Yt
T.·l -TX
Y
=
h
-+
= Slope ofT.L.
K a
a
y
With the slope known, several values of H Yi versus Hy can be generated from the plot
which can be used in the graphical integration for N 0 .
If the operating line ~d the equilibrium curve are practically linear within the limits of
integration, Namay be evaluated using the logarithmic mean driving force,
Hyz -Hyt
No== (Hyi -HY)In
If the resistance to heat transfer in the liquid phase can be neglected, the slope of the
.tie line becomes infinite, reducing the interfacial conditions to become equal to the
equilibrium condition based on the liquid temperature. Usually if hLa is not known
and difficult to evaluate this leads to the assumption that hi a>> K Ya.
•
f
dHY
Thus, H Yi ~ H Y and N G ~ N 00 = ---=.,..--'Hy-Hy
For Dehumidification or Air-Conditioning - equations used are similar to water cooling
except that the limits are reversed and the operating line is above the equilibrium curve.
To determine the temperature profile of the air as it flows from bottom to top of the tower
may be evaluated graphically using Mickley's Method (see Foust). This involves the finite
difference plotting of the differential equation obtained from the enthalpy transfer equation
and the gas-phase heat transfer equation
·
dHy = Hy; -Hy
dTY
Ty; -Ty
The limiting flow rates of liquid and gas may be determined from the slope of the operating
line when it intersects the equilibrium curve in the Enthalpy-Temperature Diagram.
213
~'
Reviewer for Chemical Engineering
Licensure Examination, 2nd Edition
Chemical Engineering
Humidification
. REVIEW QUESTIONS AND PROBLEMS
1.
This is the temperature at which a vapor-gas mixture becomes saturated when cooled
at constant humidity.
c. saturation temperature
a. wet-bulb temperature
b. dew point temperature
· d. dry-bulb temperature
2.
This is the temperature of a vapor-gas mixture as ordinarily determined by immersion
of a thermometer in the mixture.
a. wet-bulb temperature
c. saturatiqn temperature
b. dew point temperature
d. dry-bulb temperature
3.
If the partial pressure of the vapor in a gas-vapor mixture is, for any reason, less than
the equilibrium vapor pressure of the liquid at the same temperature, the mixture is
a. saturated
c. supersaturated
b. unsaturated
d. sub-cooled
4.
This is a steady-state temperature reached by a small am.ount of liquid evaporating into
a large amount of unsaturated vapor-gas mixture.
c. saturation temperature
a. wet-bulb temperature
b. dew point temperature
d. dry-bulb temperature
5.
For the air-water vapor system, the Lewis relation, hyfkyc., takes a value of
a. less than unity
c. essentially equal to unity
b. greater than unity
d. none of these
6.
In order for the 15as to be dehumidified, as in the water vapor~air mixture, the humidity
of the gas must be
a. greater than the gas-liquid interface
c. less than the gas-liquid interface
b. equal with the gas-liquid interface
d. saturated
7.
In dehumidification, where the Lewis Number is equal to one, the operating line on the
gas-enthalpy-liquid temperature graph
a. is below the equilibrium curve
c. is above the equilibrium curve
b. coincides with the equilibrium curve
d. intersects the equilibrium
8.
The process which illustrates the principle of adiabatic humidification is
a. cooling tower
c. packed tower
b. spray chamber
d. heated dryer
9.
Fogging is a result of a condition whereby the gas becomes
a. saturated with vapor
c. supersaturated with vapor
b. unsaturated with vapor
d. liquid due to cooling
I
10. Air conditioning involves
a. stripping
b. humidification
c. dehumidification
d. evaporative cooling
214
Chemical Engineering
Humidification
Reviewer for Chemical Engineering
Licensure Examination, 2nd Edition
11. Air, supplied at the rate of 1200 cfrn to a refrigerated coil has a relative humidity of
20% and dry bulb temperature of 150°F. The mass flow rate of dry air entering per
minute is
c. 78.50
a. 74J
d. 75.26
b. 75.0
12. A sling psychrometer is whirled on a fast spin when measuring the wet bulb
temperature of ambient air
a. since centrifugal force helps in stabilizing the mercury level in the thermometer
b. to remove excess water in the cloth wrapped around the mercury bulb
c. to minimize the effect of radiation on the temperature reading
d. to minimize the effect of convection on the temperature reading
13. In an air-water contact equipment, the individual gas-phase mass transfer coefficient is
equal to the over-all mass transfer coefficient since
·
a. the mass transfer resistance in the liquid-phase is small
b. the mass transfer resistance in the gas-phase is small
c. there is no co~centration gradient in the gas-phase
d. there is no concentration gradient in the liquid-phase
14. The enthalpy transfer equation based on Merkel's procedure of determining the
volume of a cooling tower is a convenient way of
a. eliminating the complications introduced by the effect of sensible and latent
heats
·
b. eliminating the determination of interfacial temperature and humidity
c. eliminating the complications of a non-adiabatic dehumidification of air
d. eliminating the effect of the resistance to heat transfer in the liquid phase
1,5. In adiabatic humidification, it is possible to maintain the temperature of water constant
since
a. according to the phase-rule, the degrees of freedom is 3
b. the system can be well insulated from the surroundings
c. the temperature of the air can also be maintained constant
d. the increase in the humidity of the air is very small
16. Besides measuring the dry bulb and wet bulb temperatures in determining the humidity
of air, another methqd may be used. This is by
a. measuring the specific heat of the air
b. measuring the enthalpy of the air
c. measuring the dew point of the air
d. measuring the specific volume of the air
17. In terms of heat transfer, the. use of a cooling tower is said to be more efficient and
more economical compared to an ordinary heat exchanger since
a. large volume of air is available and free
b. temperature profiles of air and water can cross each other
c. large amount of water can be processed
d. a cooling tower is much smaller and cheaper than a heat exchanger
215
ChemiCal Engineering
Humidification
Reviewer for Chemical Engineering
Licensure Examination, 2nd Edition
18. For an air flow rate of 5000 lb!hr and a water flow rate of 7500 lblhr, the temperature
of the cold water is 80°F using air with temperature of 90°F dry bulb and
70°F wet bulb. The estimated inlet temperature of water for these conditions is
(see Figure 12-13 Perry)
c. 88°F
a. 84°F
d. none ofthese
b. 98°F
19. Given a forced· draft cooling tower with the following operating data: hot water
temperature= ll0°F, cooling range= 18°F, wet bulb temperature= 75°F, water flow
rate = 500 gal/min. The estimated fan horsepower for this tower is
a. 2 hp
c. 8 hp
b.5hp
d.lOhp
20. For dehumidification, when the top liquid flow rate is fixed and the top conditions of
water temperature and air enthalpy are known, the limiting flow rate is considered to
be
c. minimum water flow rate
a. minimum air flow rate
b~ maximum air flow rate
d. none of these
21. The height to diameter ratio of a cooling tower is much less compared to that of a gas
absorber because
a. the liquid flow rate is larger compared to a gas absorber
· b. the liquid flow rate is smaller
c. the gas flow rate is larger
d. the gas flow rate is smaller
22. For a cooling tower with a circulating water flow of 5000 gpm, an inlet and outlet
water temperatures of 100°F and 80°F, respectively and a 0.5% drift loss, the
estimated make-up water is
a: 85 gpm
c. 110 gpm
b. 25 gpm
d. none of these
23. An air-carbon tetrachlo,ride-vapor mixture at 100°F dry bulb and 60°F wet bulb is
heated until the temperature reaches 180°F. The final percentage relative humidity is
about
c. 2%
a. 10%
d. none of these
b. 5%
f
24. The enthalpy entering and leaving a cooling tower is 52.0 and 75 BTU/lb, respectively.
If the inlet and outlet water temperature are 120°F and 100°F, respectively, the
estimated overall numberoftransfer units is approximately
a. 0.8
c. 2.2
b. 1.2
d. none ofthese
I
25 . If the air flow rate is 1000 lb!hr, the ·maximum water rate needed for the tower in
Problem 24 is about ·
c. 3400 lb!hr
a. 1200 lb!hr
b. 6000 lb!hr
d. none of these
I
t
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·- --- - · ~ -- - - -
Chemical Engineering
Humidification
Reviewer for Chemical Engineering
Licensure Examination, 2nd Edition
26. If the temperature of the air entering the tower of Problem 24 is 100°F, the exit
temperature of the air is estimated to be (use Mickley's graphical method)
a. ll0°F
c. 105°F
b. ll5°F
d. none ofthese
27. The temperature at which the moisture in humid air exerts a partial pressure equal to
its vapor pressure is called the
a. dry bulb temperature
c. critical temperature
b. ambient temperature
d. dew point
28. An indication of the moisture content of ambient air is its
a. dry-bulb temperature
c. ambient pressure
b. wet~bulb temperature
d. vapor pressure
29. The ratio between partial pressure of water vapor in air and the vapor pressure of the
water at the air temperature multiplied by I 00 is
a. absolute humidity
c. percentage saturation humidity
b. percentage absplute humidity
d. percentage relative humidity
30. The relative humidity of air at a given temperature is the
a. pounds of water vapor in one pound of dry air
b. the ratio between the actual temperature of the air and its dew point
·c. the ratio between the volume of the water vapor in the air and the humid
volume
d. the ratio of the partial pressure of the water vapor and the vapor pressure of
water
31. The dew point of air indicates
a. the actual temperature of the air
b. the temperature at which its volume per unit weight of dry air is calculated
c. the temperature at which its enthalpy is calculated
d. the temperature at which its water content will start to condense
32. lfthe mass transfer coefficient, Kya = 230 lbs water/hr~fe-atm, then the MTC in lbs
water!hr-ft3 -absolute humidity is
a. 142.8
c. 370.6
b. 7.93
d. 12.8
33. The relative humidity of unsaturated air-water vapor mixture is always
a. equal
c. less than
b. greater than
d. can not be determined
compared to the relative or percentage saturation.'
34. In an air-water contact operation, when the temperature and humidity of the air both
decrease the process is
a. dehumidification
c. non-adiabatic humidification
d. water cooling
b. adiabatic humidification
217
Chemical Engineering
Humidification
Reviewer for Chemical Engineering
Licensure Examination, 2nd Edition
35. The enthalpy transfer equation as proposed by Merkel is applicable to air-water system
only because the ratio of he, convective heat transfer coefficient and the mass transfer
coefficient, ky M8 is
a. constant
c. equal to the enthalpy
b. equal to humid heat
d. equal to unity
36. The tons refrigeration needed to supply air in a room 20 ft by 20 ft by 10 ft charged
every 5 min at 70°F dry bulb and 65°F wet bulb by cooling outside air at 120°F db and
l00°F wb is
a. 20.2
c. 50.8
b. 12.2
d. 7.6
37. If 100 lb of dry air at 50°F db and 50°F wb is mixed with 300 lb of dry air at ll0°F db
and 80°F wb, the resulting mixture will have a dry bulb temperature of
a. 80°F
c. 90°F
b. 85°F
d. 95°F
38. The wet bulb temperature of the resulting mixture for the mixed air of Problem 37 is
a. 65°F
c. 75°F
b. 70°F
d. 80°F
39. For a dehumidifier, the slope of the tie line is 2.5 for a liquid to gas ratio of 1.0. Air
enters the dehumidifier at 80°F db and 78°F wb while water leaves at 76°F. Estimate
the interfacial temperature at a point where the enthalpy of the air is 30 BTU/lb.
a. 63.5°F
c. 70.2°F
b. 58.2°F
d. 73.5°F
40. For air-benzene vapor mixture at I atm, the dry bulb temperature is 100°F and wet
bulb temperature of 90°F. The absolute humidity at this condition is
a. 0.35
c. 0.50
b. 0.26
d. 0.62
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