df
ABSORPTION OF GASES 701
Mass per cent of air = [0.9 ~ 29/(0.1 ~ 17 + 0.9 ~ 29)] ~ 100 = 93.8.
Thus: mass flowrate of air = (0.938 ~ 0.95) = 0.891 kg/m2s
and: Gm = (0.891/29) = 0.0307 kmol/m2s
Lm = 0.65/18 = 0.036 kmol/m2s
A mass balance between a plane in the tower where the compositions are X and Y and the top
of the tower gives:
Gm(Y . Y2) = Lm(X . X2)
But: X2 = 0
Thus: 0.0307(Y . 0.001) = 0.036X, or Y = 1.173X + 0.001
This is the equation of the operating line in terms of mole ratios.
The given equilibrium data may be converted to the same basis since:
PG = yP =
YP
1 + Y
and: Y =
PG
P . PG
Using these equations, the following data are obtained:
kmol NH3/kmol H2O 0.021 0.031 0.042 0.053 0.079 0.106 0.159
Partial pressure PG (mm) 12 18.2 24.9 31.7 50.0 69.6 114.0
P . PG = 760 . PG (mm) 748 741.8 735.1 728.3 710 690.4 646
Y = PG/(P . PG) 0.016 0.0245 0.0339 0.0435 0.0704 0.101 0.176
These data are plotted in Figure 12.24.
From a mass balance over the column, the height Z is given by:
Z =
Gm
kGaP
Y1
Y2
(1 + Y)(1 + Yi)
(Y . Yi)
dY (equation 12.45)
Figure 12.25 may be used to evaluate the integral as follows:
Y Yi (1 + Y)(1 + Yi)
(1 + Y)(1 + Yi)
(Y . Yi)
0.111 0.089 1.21 55.0
0.10 0.078 1.185 53.8
0.08 0.059 1.14 54.3
0.06 0.042 1.11 61.4
0.04 0.027 1.067 82.0
0.02 0.013 1.035 148
0.01 0.006 1.016 254
0.005 0.0026 1.010 421
0.001 0 1.0 1000
702 CHEMICAL ENGINEERING
0
0.05
0.15
0.10
Equilibrium curve
Operating line
0.20
0.05 0.10 0.15
kmol NH3/kmol air
kmol NH3/kmol H2O
Figure 12.24. Operating and equilibrium lines for Example 12.5
The area under the curve in Figure 12.25 is 12.6. For a very soluble gas kGa kGa so that:
Z =
0.0307
(0.001 ~ 101.3) ~ 12.6 = 3.82 m
If the equilibrium line is assumed to be straight, then:
Gm(Y2 . Y1) = KGaZ.Plm
Top driving force = .Y2 = 0.022. Bottom driving force = .Y1 = 0.001.
Thus: .Ylm = 0.0068, .Plm = 0.688 kN/m2
and: Z =
(0.0307 ~ 0.11)
(0.001 ~ 0.688) = 4.91 m.
12.8. PLATE TOWERS FOR GAS ABSORPTION
Bubble-cap columns or sieve trays, of similar construction to those described in Chapter 11
on distillation, are sometimes used for gas absorption, particularly when the load is more
than can be handled in a packed tower of about 1 m diameter and when there is any
ABSORPTION OF GASES 703
0 0.05 0.10
100
200
300
400
500
600
700
800
900
1000
Area under curve = 12.6
Y
(1 + Y ) (1 + Yi)/(Y . Yi)
Figure 12.25. Determination of column height for Example 12.5
likelihood of deposition of solids which would quickly choke a packing. Plate towers are
particularly useful when the liquid rate is sufficient to flood a packed tower. Since the
ratio of liquid rate to gas rate is greater than with distillation, the slot area will be rather
less and the downcomers rather larger. On the whole, plate efficiencies have been found
to be less than with the distillation equipment, and to range from 20 to 80 per cent.
The plate column is a common type of equipment for large installations, although when
the diameter of the column is less than 2 m, packed columns are more often used. For
the handling of very corrosive fluids, packed columns are frequently preferred for larger
units. The essential arrangement of such a unit is shown in Figure 12.26, where:
Lm is the molar rate of flow per unit area of solute free liquid,
Gm is the molar rate of flow per unit area of inert gas,
n refers to the plate numbered from the bottom upwards (and suffix n refers to
material leaving plate n),
x is the mole fraction of the absorbed component in the liquid,
y is the mole fraction of the absorbed component in the gas, and
s is the total number of plates in the column.
It may be assumed that dilute solutions are used so that mole fractions and mole ratios
are approximately equal. Each plate is taken as an gidealh unit, so that the gas leaving of
composition yn is in equilibrium with the liquid of composition xn leaving the plate.
704 CHEMICAL ENGINEERING
Gas
ys
ys
yn
y1
y0
x2
x1
xs +1
ys +1
yn +1
xn +1
xs
xn
n + 1
n . 1
n
Liquid
Top plate
Gas Liquid
Bottom plate
Figure 12.26. Plate tower.nomenclature for fluid streams
A material balance for the absorbed component from the bottom to a plane above plate
n gives:
Gmyn + Lmx1 = Gmy0 + Lmxn+1 (12.84)
or: yn =
Lm
Gm
xn+1 + y0 .
Lm
Gm
x1 (12.85)
This is the equation of a straight line of slope Lm/Gm, relating the composition of the
gas entering a plate to the liquid leaving the plate, and is known as the operating line. As
shown in Figure 12.27, such a line passes through two points B(xs+1, ys) and A(x1, y0),
representing the terminal concentrations in the column. The equilibrium curve is shown
in this figure as PQR.
Point A represents conditions at the bottom of the tower. The gas rising from the bottom
plate is in equilibrium with a liquid of concentration x1 and is shown as point 3 on the
operating line. Then point 4 indicates the concentration of the liquid on the second plate
from the bottom. In this way steps may be drawn to point B, giving the gas ys rising
from the top plate and the liquid xs+1 entering the top of the absorber.
12.8.1. Number of plates by use of absorption factor
If the equilibrium curve can be represented by the relation ye = mx, then the number of
plates required for a given degree of absorption can conveniently be found by a method
due to KREMSER(56) and SOUDERS and BROWN(57). The same treatment is applicable for
concentrated solutions provided concentrations are expressed as mole ratios, and if the
equilibrium curve can be represented approximately by Ye = mX.
ABSORPTION OF GASES 705
Figure 12.27. Diagrammatic representation of changes in a plate column
A material balance over plate n gives:
Lm(xn . xn+1) = Gm(yn.1 . yn) (12.86)
For an ideal plate, yn = mxn;
and:
Lm
mGm
(yn . yn+1) = yn.1 . yn (12.87)
This group Lm/mGm, which will be taken as constant, is called the absorption
factor A.
Thus: yn =
yn.1 +Ayn+1
1 +A
(12.88)
Applying this relation to the bottom plate and taking y0 as the mole fraction of absorbed
component in the gas entering the column, then:
y1 =
y0 +Ay2
1 +A
And for the second plate from the bottom:
y2 =
y1 +Ay3
1 +A
=
A(1 +A)y3 +Ay2 + y0
(1 +A)2
Simplifying: y2 =
y0(1 +A) +A2y3
A2 +A+ 1
706 CHEMICAL ENGINEERING
And for the third plate from the bottom:
y3 =
y0(1 +A+A2) +A3y4
A3 +A2 +A+ 1
which may be written as:
y3 =
[(A3 . 1)/(A. 1)]y0 +A3y4
(A4 . 1)/(A. 1)
=
(A3 . 1)y0 +A3(A. 1)y4
A4 . 1
Proceeding thus until plate n is reached:
yn =
(An . 1)y0 +An(A. 1)yn+1
An+1 . 1
y0 =
(An+1 . 1)yn .An(A. 1)yn+1
An . 1
Thus: y0 . yn =
(An+1 .An)yn .An(A. 1)yn+1
An . 1
and: y0 . yn+1 =
(An+1 . 1)yn . (An+1 . 1)yn+1
An . 1
Dividing:
y0 . yn
y0 . yn+1 =
(An+1 .An)yn .An(A. 1)yn+1
(An+1 . 1)yn . (An+1 . 1)yn+1
=
An(A. 1)(yn . yn+1)
(An+1 . 1)(yn . yn+1)
or:
y0 . yn
y0 . yn+1 =
An+1 .A
An+1 . 1
Applying this relation over the whole column and putting n = s gives:
(y0 . ys) = actual change in composition of gas, and
(y0 . ys+1) = maximum possible change in composition of gas, that is if the gas leaving
the absorber is in equilibrium with the entering liquid (or ys = mxs+1).
Then:
y0 . ys
y0 . mxs+1 =
(Lm/mGm)s+1 . (Lm/mGm)
(Lm/mGm)s+1 . 1
(12.89)
This equation is conveniently represented, as suggested by SOUDERS and BROWN(57),
by Figure 12.28, and it is easy to use such a diagram to determine the number of
plates required.
A high degree of absorption can be obtained, either by using a large number of plates,
or by using a high absorption factor Lm/mGm. Since m is fixed by the system, this means
that Lm/Gm must be large if a high degree of absorption is to be obtained, although this
ABSORPTION OF GASES 707
Figure 12.28. Graphical representation of the effect of the absorption factor and the number of plates on the
degree of absorption
will result in a low value of x for the liquid leaving at the bottom. This problem is to
some extent met by recirculating the liquid over the tower, although the advantages of
a countercurrent flow system are then lost. A value of mGm/Lm of about 0.7.0.8 is
probably the most economic, that is Lm/mGm 1.3.
It is important to note that, if Lm/mGm is less than 1, then a very large number of
plates are required to achieve a high recovery, and even an infinite number will not give
complete recovery. Lm/mGm is the ratio of the slope of the operating line Lm/Gm to
the slope of the equilibrium curve m, so that if Lm/Gm < m, or Lm/mGm < 1, then the
operating line will never cut the equilibrium curve and the gas leaving the top of the
column will not therefore reach equilibrium with the entering liquid.
12.8.2. Tray types for absorption
It has already been noted that trays which are suitable for distillation may be used for
absorption duties though in general lower efficiencies will be obtained. In Chapter 11, the
design of trays for common contacting devices is considered and the methods presented
in that chapter are generally applicable. The most commonly used tray types are shown
in Figure 11.50a with the crossflow tray being the most popular.
At high liquid flowrates, the liquid gradient on the tray can become excessive and
lead to poor vapour distribution across the plate. This problem may be overcome by the
shortening of the liquid flow-path as in the case of the double-pass and cascade trays.
The whole design process is discussed in Volume 6.
708 CHEMICAL ENGINEERING
Example 12.6
A bubble-cap column with 30 plates is to be used to remove n-pentane from a solvent oil by means
of steam stripping. The inlet oil contains 6 kmol of n-pentane per 100 kmol of pure oil and it is
desired to reduce the solute content to 0.1 kmol per 100 kmol of solvent. Assuming isothermal
operation and an overall plate efficiency of 30 per cent, find the specific steam consumption, that
is the kmol of steam required per kmol of solvent oil treated, and the ratio of the specific and
minimum steam consumptions. How many plates would be required if this ratio were 2.0?
The equilibrium relation for the system may be taken as Ye = 3.0X, where Ye and X are expressed
in mole ratios of pentane in the gas and liquid phases respectively.
Solution
Number of theoretical plates = (30 ~ 0.3) = 9.
At the bottom of the tower:
Flowrate of steam = Gm (kmol/m2s)
Mole ratio of pentane in steam = Y1, and
Mole ratio of pentane in oil = X1 = 0.001
At the top of the tower:
exit steam composition = Y2, inlet oil composition = X2 = 0.06,
flowrate of oil = Lm (kmol/m2s)
The minimum steam consumption occurs when the exit steam stream is in equilibrium with the
inlet oil, that is when:
Ye2 = (0.06 ~ 3) = 0.18
Lmin(X2 . X1) = Gmin(Y2 . Y1)
If Y1 = 0, that is the inlet steam is pentane-free, then:
Lmin(0.06 . 0.001) = (Gmin ~ 0.18)
and: (G/L)min = (0.06 . 0.001)/0.18 = 0.328
The operating line may be fixed by trial and error as it passes through the point (0.001, 0), and
9 theoretical plates are required for the separation. Thus it is a matter of selecting the operating
line which, with 9 steps, will give X2 = 0.001 when X1 = 0.06. This is tedious but possible, and
the problem may be better solved analytically since the equilibrium line is straight.
Use may be made of the absorption factor method where
Y1 . Y2
Y1 . mX2 =
AN+1 .A
AN+1 . 1
(equation 12.89)
where A is the absorption factor = Lm/mGm and N is the number of theoretical plates.
The corresponding expression for a stripping operation is:
X2 . X1
X2 . Y1/m =
(1/A)N+1 . (1/A)
(1/A)N+1 . 1
ABSORPTION OF GASES 709
In this problem, N = 9,X2 = 0.06,X1 = 0.001, and Y1 = 0
Thus:
(0.06 . 0.001)
0.06 = 0.983 =
(1/A)10 . (1/A)
(1/A)10 . 1
from which (1/A) = 1.37
Thus:
mGm
Lm = 1.37,
Gm
Lm =
1.37
3 = 0.457
and:
actual Gm/Lm
minimum Gm/Lm =
0.457
0.328 = 1.39
If (actual Gm/Lm)/(min Gm/Lm) = 2, actual Gm/Lm = 0.656.
Thus: 1/A = mGm/Lm = 1.968
and: 0.983 =
(1.968)N+1 . 1.968
(1.968)N+1 . 1
from which N = 4.9
The actual number of plates = (4.9/0.3) = 16.3 (say 17).
12.9. OTHER EQUIPMENT FOR GAS ABSORPTION
12.9.1. The use of vessels with agitators
A gas may be dissolved in a liquid by dispersing it through holes in a pipe immersed
in the liquid which is stirred with some form of agitator, as shown in Figure 12.29.
Although this type of equipment will give only one theoretical stage per unit, but it often
provides a useful method of saturating a liquid with a gas. COOPER et al.(58) have studied
the absorption of oxygen from air in an aqueous solution of sodium sulphite using simple
vessels of 0.15 to 2.44 m diameter fitted with four simple baffles. Air was just below the
agitator which was a vaned-disc or flat-paddle. It was found that the absorption coefficient
KGa varied almost directly with PV , the power input per unit volume. For constant values
of PV , the following relation was obtained:
KGa å u0.67
s (12.90)
where us is the superficial gas velocity based on the volume of gas at inlet and the crosssection
of tank. A general correlation was obtained by plotting KGa/u0.67
s against the
power input per unit volume PV , as shown in Figure 12.30 taken from this investigation.
AYERST and HERBERT(59) have given some data on the use of this type of unit for the
absorption of carbon dioxide into ammoniacal solutions.
The interfacial area, a, was the subject of an investigation by WESTERTERP et al.(60)
though the correlations proposed are complex. Maximum values of a are about
1000 m2/m3. Further work on the interfacial area in agitated vessels has been
reviewed and summarised by SRIDAR and POTTER(61) who found that the correlation of
CALDERBANK(62) was applicable for most situations. Calderbank proposed that, for pure
710 CHEMICAL ENGINEERING
Figure 12.29. Vessel fitted with vaned-disc agitator
Figure 12.30. General correlation of data for a vessel (height = diameter) with vaned-disc agitator
liquids, the specific interfacial area, that is the surface area per unit volume of aerated
suspension, a(m2/m3) is given by:
a = 24,200 (PV )0.4
ƒÏ0.2
L
ƒÐ0.6
us
u0
0.5
(12.91)
ABSORPTION OF GASES 711
where surface aeration is negligible, that is when:
Nd2
t ƒÏL
ƒÊL
0.7
Ndi
us
0.3
< 25, 000 (12.92)
When the surface aeration is significant, then the interfacial area is:
a
a = 10.4
ýþ
ÿ
.
Nd2
i ƒÏL
ƒÊL
0.7
Ndt
us
0.2
.
. . 25, 000
..
. (12.93)
In these equations, a is the specific interfacial area for a significant degree of surface
aeration (m2/m3), PV is the agitator power per unit volume of vessel (W/m3), ƒÏL is the
liquid density, ƒÐ is the surface tension (N/m), us is the superficial gas velocity (m/s), u0
is the terminal bubble-rise velocity (m/s), N is the impeller speed (Hz), di is the impeller
diameter (m), dt is the tank diameter (m), ƒÊL is the liquid viscosity (Ns/m2) and d0 is the
Sauter mean bubble diameter defined in Chapter 1, Section 1.2.4.
The effects of gas hold-up and bubble diameter have also been studied by Sridhar and
Potter and, again, the correlations obtained by Calderbank are recommended.
The liquid-phase mass transfer coefficient, kL, in agitated vessels has been measured
and data correlated by several workers. SIDEMAN et al.(63) and VALENTIN(64) have presented
reviews of the early work and more recent work has been published by YAGI and
YOSHIDA(65), ZLOKARNIK(66), VANfT RIET(67) and HOKER, LANGER and UDO(68). For small
bubbles (< 2.5 mm diameter) produced in well-agitated vessels, CALDERBANK(62) suggests
the following correlation for bubbles in agitated electrolytes:
kL = 0.31
.ƒÏƒÊLg
ƒÏ2
L
1/3
(Sc).2/3 (12.94)
where: .ƒÏ = density difference between gas and liquid,
ƒÏL,ƒÊL = density and viscosity of the liquid, and
Sc = Schmidt number for transport in the liquid.
JOSHI and SHARMA(69) and FUKADA et al.(70) have investigated the performance of vessels
with multiple impellers on horizontal shafts.
Several investigations have been carried out into the power requirements for agitation
of aerated liquids including those of YUNG et al.(71) and LUONG and VOLESKY(72) and it
is generally concluded that the power required is less for an aerated system than for a
non-aerated system.
Although, as described by BJERLE et al.(73), liquid jet-type absorbers are also used, one
relatively recent application of mass transfer in agitated tanks with chemical reaction is
the absorption of pollutants from flue gases and, in particular, the scrubbing of sulphur
dioxide by a slurry containing fine limestone particles. In this case, the concentration of
sulphur dioxide is usually very low and the mechanism of the absorption is complicated
due to the presence of solids in the liquid phase where the rate of solid dissolution may
significantly affect the absorption rate.
712 CHEMICAL ENGINEERING
Studies on the dissolution of solids in the liquid phase include that of HIXSON and
BAUM(74) whose correlation of data in terms of Reynolds, Sherwood and Schmidt numbers,
discussed in detail in Section 10.2 in connection with mass transfer during leaching, is
one of the most frequently used methods for calculating the mass transfer coefficient for
the solid dissolution.
Further work on the absorption of sulphur dioxide by UCHIDA et al.(75) has shown that
the absorption rate changes with the surface area of the limestone particles which in turn
varies with the size and the number of particles, and that the rate of dissolution plays a
very important role on the absorption. It was further found the absorption rate does not
vary significantly with temperature and that the reactions involved may be considered as
being instantaneous.
12.9.2. The centrifugal absorber
In an attempt to obtain the benefits of repeated spray formations, a centrifugal type
absorber has been developed from the ideas of Piazza for a still head. The principle of
the unit is shown in Figure 12.31. A set of stationary concentric rings intermeshes with
a second set of rings attached to a rotating plate. Liquid fed to the centre of the plate
Figure 12.31. The centrifugal absorber
is carried up the first ring, splashes over to the baffle and falls into the through between
the rings. It then runs up the second ring and in a similar way passes from ring to ring
through the unit. The gas stream can be introduced at the top to give cocurrent flow,
or at the bottom if countercurrent flow is desired. Some of the features of this unit are
discussed by AHMED(76) who found that the depth of the ring was not very important and
that most of the transfer took place as the gas mixed with the liquid spray leaving the top
of the rings. CHAMBERS and WALL(77) have given some particulars of the performance of
the 510 mm diameter unit shown in Figure 12.32, for the absorption of carbon dioxide
ABSORPTION OF GASES 713
from air containing 10.15 per cent of carbon dioxide, using mono-ethanolamine solution.
Some values of absorption rates are given in Table 12.7.
Figure 12.32. Details of a 510 mm diameter centrifugal absorber
Table 12.7. Results for absorption in a 510 mm diameter absorber
Gas flow Liquid flow per cent CO2 in gas Absorption rate
(m3/s) (m3/s) in out (kg/s)
0.016 1.07 ~ 10.4 16.3 2.3 0.0044
0.024 1.07 ~ 10.4 15.8 4.5 0.0055
0.031 1.07 ~ 10.4 14.3 6.6 0.0051
0.039 1.07 ~ 10.4 16.3 8.7 0.0065
12.9.3. Spray towers
In the spray tower, the gas enters at the bottom and the liquid is introduced through a series
of sprays at the top. The performance of these units is generally rather poor, because the
droplets tend to coalesce after they have fallen through a few metres, and the interfacial
surface is thereby seriously reduced. Although there is considerable turbulence in the gas
phase, there is little circulation of the liquid within the drops, and the resistance of the
equivalent liquid film tends to be high. Spray towers are therefore useful only where the
714 CHEMICAL ENGINEERING
Figure 12.33. Centrifugal spray tower(78)
main resistance to mass transfer lies within the gas phase, and have consequently been
used with moderate success for the absorption of ammonia in water. They are also used
as air humidifiers, in which case the whole of the resistance lies within the gas phase.
Centrifugal spray tower
Figure 12.33, taken from the work of KLEINSCHMIDT and ANTHONY(78), illustrates a spray
tower in which the gas stream enters tangentially, so that the liquid drops are subjected
to centrifugal force before they are taken out of the gas stream at the top.
12.10. FURTHER READING
HOBLER, T.: Mass Transfer and Absorbers (Pergamon Press, Oxford, 1966).
MCCABE, W. L.,SMITH, J. C. andHARRIOTT, P.: Unit Operations of Chemical Engineering, 4th edn. (McGraw-
Hill, New York, 1984).
NORMAN, W. S.: Absorption, Distillation and Cooling Towers (Longmans, London, 1961).
SHERWOOD, T. K. and PIGFORD, R. L.: Absorption and Extraction (McGraw-Hill Book Co., New York, 1952).
SHERWOOD, T. K., PIGFORD, R. L. andWILKE, C. R.: Mass Transfer (McGraw-Hill Book Co., New York, 1975).
SMITH, B. D.: Design of Equilibrium Stage Processes (McGraw-Hill Book Co., New York, 1963).
TREYBAL, R. E.: Mass Transfer Operations, 3rd edn. (McGraw-Hill Book Co., New York, 1980).
ABSORPTION OF GASES 715
WANKAT, P. C.: Equilibrium Staged Separations: Separations for Chemical Engineers (Elsevier, New York,
1988).
ZARZYCKI, R. and CHACUK, A.: Absorption. Fundamentals and Applications (Pergamon Press, Oxford, 1993).
ZENZ, F. A.: Design of Gas Absorption Towers. In SCHWEITZER, P. A.: Handbook of Separation Techniques for
Chemical Engineers 2nd edn. (McGraw Hill, New York, 1988).
12.11. REFERENCES
1. WHITMAN, W. G.: Chem. Met. Eng. 29 (1923) 147. The two-film theory of absorption.
2. HIGBIE, R.: Trans. Am. Inst. Chem. Eng. 31 (1935) 365. The rate of absorption of pure gas into a still liquid
during short periods of exposure.
3. DANCKWERTS, P. V.: Ind. Eng. Chem. 43 (1951) 1460. Significance of liquid-film coefficients in gas
absorption.
4. DANCKWERTS, P. V. and KENNEDY, A. M.: Trans. Inst. Chem. Eng. 32 (1954) S49. Kinetics of liquid-film
processes in gas absorption.
5. LYNN, S., STRAATEMEIER, J. R., and KRAMERS, H.: Chem. Eng. Sci. 4 (1955) 49, 58, 63. Absorption studies
in the light of the penetration theory. I. Long wetted-wall columns. II. Absorption by short wetted-wall
columns. III. Absorption by wetted-spheres, singly and in columns.
6. DAVIDSON, J. F., CULLEN, E. J., HANSON, D., and ROBERTS, D.: Trans. Inst. Chem. Eng. 37 (1959) 122. The
hold-up and liquid film coefficient of packed towers. Part I. Behaviour of a string of spheres.
7. DAVIDSON, J. F.: Trans. Inst. Chem. Eng. 37 (1959) 131. The hold-up and liquid film coefficient of packed
towers. Part II: Statistical models of the random packing.
8. DANCKWERTS, P. V. and KENNEDY, A. M.: Chem. Eng. Sci. 8 (1958) 201. The kinetics of absorption of
carbon dioxide into neutral and alkaline solutions.
9. ROBERTS, D. and DANCKWERTS, P. V.: Chem. Eng. Sci. 17 (1962) 961. Kinetics of CO2 absorption in
alkaline solutions. I. Transient absorption rates and catalysis by arsenite.
10. DANCKWERTS, P. V., KENNEDY, A. M. and ROBERTS, D.: Chem. Eng. Sci. 18 (1963) 63. Kinetics of CO2
absorption in alkaline solutions. II. Absorption in a packed column and tests of surface renewal models.
11. CULLEN, E. J. and DAVIDSON, J. F.: Trans. Faraday Soc. 53 (1957) 113. Absorption of gases in liquid jets.
12. RAIMONDI, P. and TOOR, H. L.: A.I.Ch.E.Jl. 5 (1959) 86. Interfacial resistance in gas absorption.
13. STERNLING, C. V. and SCRIVEN, L. E.: A.I.Ch.E.Jl. 5 (1959) 514. Interfacial turbulence: Hydrodynamic
instability and the Marangoni effect.
14. GOODRIDGE, F. and ROBB, I. D.: Ind. Eng. Chem. Fundamentals 4 (1965) 49. Mechanism of interfacial
resistance.
15. GARNER, F. H. and KENDRICK, P.: Trans. Inst. Chem. Eng. 37 (1959) 155. Mass transfer to drops of liquid
suspended in a gas stream. Part I.A wind tunnel for the study of individual liquid drops.
16. GARNER, F. H. and LANE, J. J.: Trans. Inst. Chem. Eng. 37 (1959) 162. Mass transfer to drops of liquid
suspended in a gas stream. Part II: Experimental work and results.
17. KING, C. J.: A.I.Ch.E.Jl. 10 (1964) 671. The additivity of individual phase resistances in mass transfer
operations.
18. GILLIAND, E. R. and SHERWOOD, T. K.: Ind. Eng. Chem. 26 (1934) 516. Diffusion of vapours into air
streams.
19. HOLLINGS, H. and SILVER, L.: Trans. Inst. Chem. Eng. 12 (1934) 49. The washing of gas.
20. CHILTON, T. H. and COLBURN, A. P.: Ind. Eng. Chem. 26 (1934) 1183. Mass transfer (absorption) coefficients.
prediction from data on heat transfer and fluid friction.
21. MORRIS, G. A. and JACKSON, J.: Absorption Towers (Butterworths, London, 1953).
22. KOWALKE, O. L., HOUGEN, O. A., andWATSON, K. M.: Bull. Univ. Wisconsin Eng. Sta. Ser. No. 68 (1925).
Transfer coefficients of ammonia in absorption towers.
23. BORDEN, H. M. and SQUIRES, W.: Massachusetts Institute of Technology, S. M. thesis (1937). Absorption
of ammonia in a ring-packed tower. (cited in Reference 30).
24. NORMAN, W. S.: Trans. Inst. Chem. Eng. 29 (1951) 226. The performance of grid-packed towers.
25. FELLINGER, L. L.: Massachusetts Institute of Technology. D.Sc. thesis (1941). Absorption of ammonia by
water and acids in various standard packings.
26. PERRY, R. H., GREEN, D. W., andMALONEY, J. O. (eds.): Perryfs Chemical Engineersf Handbook. 7th edn.
(McGraw-Hill Book Company, New York, 1997).
27. MOLSTAD, M. C., MCKINNEY, J. F. and ABBEY, R. G.: Trans. Am. Inst. Chem. Eng. 39 (1943) 605. Performance
of drip-point grid tower packings, III. Gas-film mass transfer coefficients: additional liquid-film
mass transfer coefficients.
716 CHEMICAL ENGINEERING
28. VAN KREVELEN, D. W. and HOFTIJZER, P. J.: Rec. Trav. Chim 67 (1948) 563. Kinetics of gas.liquid
reactions. Part I. General theory.
29. SEMMELBAUER, R.: Chem. Eng. Sci. 22 (1967) 1237. Die Berechnung der SchNutthNohe bei Absorptionsvorg
Nangen in FNullkNorperkolonnen. (Calculation of the height of packing in packed towers.)
30. SHERWOOD, T. K. and HOLLOWAY, F. A. L.: Trans. Am. Inst. Chem. Eng. 36 (1940). Performance of packed
towers. 21.Experimental studies of absorption and desorption, 39, 181.liquid film data for several
packings.
31. COOPER, C. M., CHRISTL, R. J., and PEERY, L. C.: Trans. Am. Inst. Chem. Eng. 37 (1941) 979. Packed tower
performance at high liquor rates.The effect of gas and liquor rates upon performance in a tower packed
with two-inch rings.
32. NONHEBEL, G.: Gas Purification Processes for Air Pollution Control, 2nd edn. (Newnes.Butterworth,
London, 1972).
33. HIXSON, A. W. and SCOTT, C. E.: Ind. Eng. Chem. 27 (1935) 307. Absorption of gases in spray towers.
34. WHITMAN, W. G., LONG, L., and WANG, H. Y.: Ind. Eng. Chem. 18 (1926) 363. Absorption of gases by a
liquid drop.
35. PIGFORD, R. L. and PYLE, C.: Ind. Eng. Chem. 43 (1951) 1649. Performance characteristics of spray-type
absorption equipment.
36. NORMAN, W. S.: Absorption, Distillation and Cooling Towers (Longmans, London, 1961).
37. HATTA, S.: Tech. Repts. Tohoku Imp. Univ. 10 (1932) 119. On the absorption velocity of gases by liquids.
II. Theoretical considerations of gas absorption due to chemical reaction.
38. NIJSING, R. A. T. O., HENDRIKSZ, R. H. and KRAMERS, H.: Chem. Eng. Sci. 10 (1959) 88. Absorption of
CO2 in jets and falling films of electrolyte solutions, with and without chemical reaction.
39. TEPE, J. B. and DODGE, B. F.: Trans. Am. Inst. Chem. Eng. 39 (1943) 255. Absorption of carbon dioxide
by sodium hydroxide solutions in a packed column.
40. CRYDER, D. S. and MALONEY, J. O.: Trans. Am. Inst. Chem. Eng. 37 (1941) 827. The rate of absorption of
carbon dioxide in diethanolamine solutions.
41. STEPHENS, E. J. and MORRIS, G. A.: Chem. Eng. Prog. 47 (1951) 232. Determination of liquid-film
absorption coefficients. A new type of column and its application to problems of absorption in presence of
chemical reaction.
42. DANCKWERTS, P. V. and MCNEIL, K. M.: Trans. Inst. Chem. Eng. 45 (1967) 32. The absorption of carbon
dioxide into aqueous amine solutions and the effects of catalysis.
43. DANCKWERTS, P. V. and SHARMA, M. M.: Chem. Engr. London No. 202 (Oct. 1966) CE244. The absorption
of carbon dioxide into solutions of alkalis and amines (with some notes on hydrogen sulphide and carbonyl
sulphide).
44. SAHAY, B. N. and SHARMA, M. M.: Chem.Eng. Sci. 28 (1973) 41. Effective interfacial areas and liquid and
gas side mass transfer coefficients in a packed column.
45. ECKERT, J. S.: Chem. Engg. 82 (14 April 1975) 70. How tower packings behave.
46. SHERWOOD, T. K., PIGFORD, R. L., and WILKE, C. R.: Mass Transfer (McGraw-Hill Book Company, New
York, 1980).
47. TREYBAL, R. E.: Mass Transfer Operations, 3rd edn. (McGraw-Hill Book Co., New York, 1980).
48. POLL, A. and SMITH, W.: Chem. Engg. 71 (26 Oct. 1964) 111. Froth contact heat exchanger.
49. COGGAN, C. G. and BOURNE, J. R.: Trans. I. Chem. E. 47 (1969) T96, T160. The design of gas absorbers
with heat effects.
50. SHULMAN, H. L., ULLRICH, C. F., PROULX, A. Z. and ZIMMERMAN, J. O.: A.I.Ch.E.Jl. 1 (1955) 2, 253.
Interfacial areas.gas and liquid phase mass transfer rates.
51. EASTHAM, I. E.: Private communication (1977).
52. CHILTON, T. H. and COLBURN, A. P.: Ind. Eng. Chem. 27 (1935) 255. Distillation and absorption in packed
columns.
53. RACKETT, H. G.: Chem. Eng. Albany 71 (21 Dec. 1964) 108. Modified graphical integration for determining
transfer units.
54. Norton Chemical Process Products Div., Box 350, Akron, Ohio; Hydronyl Ltd., King St., Fenton, Stokeon-
Trent, U.K.
55. COLBURN, A. P.: Trans. Am. Inst. Chem. Eng. 35 (1939) 211. The simplified calculation of diffusional
processes. General consideration of two-film resistances.
56. KREMSER, A.: Nat. Petroleum News 22 (21 May 1930) 43. Theoretical analysis of absorption processes.
57. SOUDERS, M. and BROWN, G. G.: Ind. Eng. Chem. 24 (1932) 519. Fundamental design of high pressure
equipment involving paraffin hydrocarbons. IV. Fundamental design of absorbing and stripping columns
for complex vapours.
58. COOPER, C. M., FERNSTROM, G. A., and MILLERS, S. A.: Ind. Eng. Chem. 36 (1944) 504. Performance of
agitated gas.liquid contactors.
59. AYERST, R. R. and HERBERT, L. S.: Trans. Inst. Chem. Eng. 32 (1954) S68. A study of the absorption of
carbon dioxide in ammonia solutions in agitated vessels.
ABSORPTION OF GASES 717
60. WESTERTERP, K. R., VAN DIERENDONCK, L. L. and DE KRAA, J. R.: Chem. Eng. Sci. 18 (1963) 157. Interfacial
areas in agitated gas.liquid contactors.
61. SRIDHAR, T. and POTTER, O.E: Chem. Eng. Sci. 35 (1980) 683. Interfacial areas in gas.liquid stirred vessels.
62. CALDERBANK, P. H.: Chem. Engnr. No. 212 (Oct. 1967) CE 209. Gas absorption from bubbles.
63. SIDEMAN, S. O., HORTACSU, O., and FULTON, J. W.: Ind. Eng. Chem. 58 (July 1966) 32. Mass transfer in
gas.liquid contacting systems.
63. SIDEMAN, S. O., HORTACSU, O. and FULTON, J. W.: Ind. Eng. Chem. 58 (July 1966) 32. Mass transfer in
gas.liquid contacting systems.
64. VALENTIN, F. H. H.: Brit. Chem. Eng. 12 (1967) 1213. Mass transfer in agitated tanks.
65. YAGI, H. and YOSHIDA, F.: Ind. Eng. Chem. Proc. Des. Dev. 14 (1975) 488. Gas absorption by Newtonian
and non-Newtonian fluids in sparged agitation vessels.
66. ZLOKARNIK, M.: Adv. Biochem. Eng. 8 (1978) 133. Sorption characteristics for gas.liquid contacting in
mixing vessels.
67. VANfT RIET, K.: Ind. Eng. Chem. Proc. Des. Dev. 18 (1979) 357. Review of measuring methods and results
in nonviscous gas.liquid mass transfer in stirred tanks.
68. HON CKER, H., LANGER, G. and UDO, W.: Germ. Chem. Eng. 4 (1981) 51. Mass transfer in aerated Newtonian
and non-Newtonian liquids.
69. JOSHI, J. B. and SHARMA, M. M.: Can. J. Chem. Eng. 54 (1976) 460. Mass transfer characteristics of
horizontal agitated contactors.
70. FUKUDA, H., IDOGAWA, K., IKEDA, K. and ENDOH, K.: J. Chem. Eng. Japan 13 (1980) 298. Volumetric
gas-phase mass transfer coefficients in baffled horizontal stirred tanks.
71. YUNG, C. H.,WONG, C. W. and CHANG, C. L.: Can. J. Chem. Eng. 59 (1979) 672. Gas holdup and aerated
power consumption in mechanically stirred tanks.
72. LUONG, H. T. and VOLESKY, B.: AIChE Jl. 25 (1970) 893. Mechanical power requirements of gas.liquid
agitated systems.
73. BJERLE, I., BENGTSSON, S. and FAN RNKVIST, K.: Chem. Eng. Sci. 27 (1972) 1853. Absorption of SO2 in
CaCO3-slurry in a laminar jet absorber.
74. HIXSON, A. W. and BAUM, S. J.: Ind. Eng. Chem. 33 (1941) 478. Agitation: heat and mass transfer coefficients
in liquid-solid systems.
75. UCHIDA, S., MORIGUCHI, H., MAEJIMA, H., KOIDE, K. and KAGEYAMA, S.: Can. J. Chem. Eng. 56 (1978)
690. Absorption of sulphur dioxide into limestone slurry in a stirred tank reactor.
76. AHMED, N.: University of London, Ph.D. thesis (1949). Design of gas scrubber based upon thin films and
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77. CHAMBERS, H. H. and WALL, R. C.: Trans. Inst. Chem. Eng. 32 (1954) S96. Some factors affecting the
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of Pease.Anthony gas scrubber.
12.12. NOMENCLATURE
Units in Dimensions
SI System in M, L, T Į
A Cross-sectional area of column m2 L2
A Absorption factor . .
a Surface area of interface per unit volume
of column
m2/m3 L.1
a1, a2 . . . Constants in equation 12.39 . .
a Specific surface area (equation 12.94) m.1 L.1
B A constant in equation 12.23 . .
B A constant in equation 12.24 . .
C Molar concentration kmol/m3 NL.3
CA, CB Molar concentrations of A, B kmol/m3 NL.3
CAL, CBL Molar concentrations of A, B in bulk of
liquid phase
kmol/m3 NL.3
CAe Molar concentration of A in liquid phase
in equilibrium with partial pressure
PAG in gas phase
kmol/m3 NL.3
718 CHEMICAL ENGINEERING
Units in Dimensions
SI System in M, L, T Į
CAi Molar concentration of A at interface kmol/m3 NL.3
CAL Molar concentration of A in bulk
of liquid
kmol/m3 NL.3
CT Total molar concentration kmol/m3 NL.3
c Constant term in equation of equilibrium
line
. .
cG Gas mixture constant (ƒÏr/ƒÊr )0.25/
(DV r)0.5 in cgs units
[(cm2/s).3/4] L.3/2T3/4
DL Liquid phase diffusivity m2/s L2T.1
DV Vapour phase diffusivity m2/s L2T.1
d Column diameter m L
di Impeller diameter m L
d0 Sauter mean diameter m L
dp Packing size m L
dt Tank diameter m L
e Voidage . .
F Fractional conversion (equation 12.39) . .
f Fraction of surface renewed per unit time s.1 T.1
Gm Molar rate of flow of inert gas per unit
cross-section
kmol/m2s NL.2T.1
G Gas flowrate (mass) per unit cross-section kg/m2s ML.2T.1
H Height of transfer unit m L
h Heat transfer coefficient W/m2K MT.3Į.1
hD Mass transfer coefficient (DV /zG) m/s LT.1
hp Height of packing m L
H Henryfs constant (N/m2)/(kmol/m3) MN.1L2T.2
i Number of mole of B reacting with
1 mole of A
. .
jd j -factor for mass transfer . .
KG Overall gas-phase transfer coefficient s/m L.1T
KL Overall liquid-phase transfer coefficient m/s LT.1
K G Overall gas-phase transfer coefficient in
terms of mole fractions
kmol/m2s NL.2T.1
K L Overall liquid-phase transfer coefficient in
terms of mole fractions
kmol/m2s NL.2T.1
k Thermal conductivity W/m K MLT.3Į.1
kG Gas-film transfer
coefficient (DV P/RT zGPBm)
s/m L.1T
kG Gas-film transfer coefficient (DV /RT zG) s/m L.1T
k G Gas-film transfer coefficient in terms of
mole fractions
kmol/m2s NL.2T.1
kL Liquid-film transfer coefficient m/s LT.1
k L Liquid-film transfer coefficient in terms of
mole fractions
kmol/m2s NL.2T.1
k2 Reaction rate constant for second-order
reaction
m3/kmols N.1L3T.1
Lm Molar rate of flow of solute-free liquor
per unit cross-section
kmol/s m2 NL.2T.1
Lv Volumetric liquid rate m3/s L3T.1
L Liquid flowrate (mass) per unit
cross-section
kg/s m2 ML.2T.1
m Slope of equilibrium line . .
NA, NB Molar rate of diffusion of A, B per unit
area
kmol/s m2 NL.2T.1
ABSORPTION OF GASES 719
Units in Dimensions
SI System in M, L, T Į
NA , NB Molar rate of absorption of A, B per unit
area
kmol/s m2 NL.2T.1
N A Molar rate of absorption of A per unit
area with chemical reaction
kmol/s m2 NL.2T.1
N Number of transfer units . .
N Impeller speed s.1, (Hz) T.1
n Number of plates from bottom . .
P Total pressure N/m2 ML.1T.2
PA, PB Partial pressures of A and B N/m2 ML.1T.2
PBm Logarithmic mean value of PB N/m2 ML.1T.2
PAe Partial pressure of A in equilibrium with
concentration CAL in liquid phase
N/m2 ML.1T.2
PAG Partial pressure of A in bulk of gas phase N/m2 ML.1T.2
PAi Partial pressure of A at interface N/m2 ML.1T.2
.PAlm Log mean driving force for A N/m2 ML.1T.2
PV Power input per unit volume W/m3 ML.1T.3
R Universal gas constant J/kmol K NM.1L2T.2Į.1
r Ratio of effective film thickness for
absorption without and with chemical
reaction
. .
S Specific surface of packing m.1 L.1
s Total number of plates in column . .
T Absolute temperature K Į
t Time s T
u Gas velocity m/s LT.1
u0 Terminal rise velocity m/s LT.1
us Superficial gas velocity (based on inlet
conditions)
m/s LT.1
V Volume of packed section of column m3 L3
X Moles of solute gas A per mole of solvent
in liquid phase
. .
x Mole fraction of A in liquid phase . .
Y Molar ratio of solute gas A to inert gas B
in gas phase
. .
y Mole fraction of A in gas phase . .
Z Height of packed column m L
z Distance of direction of mass transfer m L
zG Thickness of gas film m L
zL Thickness of liquid film m L
ƒ¿ A coefficient in equation 12.28 s1.8/kg0.8m0.4 M.0.8L.0.4T1.8
ƒÀ A coefficient 1/m1.25 L.5/4
ƒÀ A coefficient (equation 12.33) . .
ƒÊ Viscosity of gas Ns/m2 ML.1T.1
ƒÊL Viscosity of liquid Ns/m2 ML.1T.1
ƒÏ Density of gas kg/m3 ML.3
ƒÏL Density of liquid kg/m3 ML.3
ƒÐ Surface tension J/m2 MT.2
ƒÓ Correction factor for concentrated
solutions
. .
Ga Galileo number . .
Pr Prandtl number . .
Re Reynolds number . .
Sc Schmidt number . .
Sh Sherwood number . .
720 CHEMICAL ENGINEERING
Units in Dimensions
SI System in M, L, T Į
Suffixes
1 denotes conditions at bottom of packed column, or at plane 1
2 denotes conditions at top of packed column, or at plane 2
A denotes soluble gas
B denotes insoluble gas
e denotes equilibrium value
f denotes film value
i denotes value at interface
G denotes gas phase
L denotes liquid phase
lm denotes logarithmic mean value
n denotes values on plate n
r denotes reference state (293 K, 101.3 kN/m2)
LG, OG, L, OL refer to gas film, overall gas, liquid film, and overall liquid transfer units