ABSORPTION PROCESS UTILIZING PACKED TOWERS
V O L 5 9 NO. 2 F E B R U A R Y 1 9 6 7
41
0
Figure 1.
Overall &ne in absorption
3 4 615 UIE fH./sd
F
he absorption process is classically regarded as one of diffusion. However, in the last fifteen years some investigators have begun to recognize that these classical theories do not explain all of the facts. Whitman [laterWiandWhitman (74,79)lisgenerally regarded as the originator of the classical two-film theory of mass transfer on which practically all work has been based, especially that related to packed towers. But subsequent experience through the yeara indicates that the two-film theory leaves a bit to be desired as a useful design concept. Higbie (72) reported further study of the two-film concept in 1935 with the added modification of a concentration gradient at each lilm, rather than the very thin film of Lewis and Whitman. This has become known as the penetration theory; and though it was an improvement on the original two-film theory, it still did not explain all the observed phenomena of gas liquid magll transfer. In 1951 Danckwerts (6),recognizing the limitations of the stagnant film concept of both the two6lm and penetration theories, postulated a rapid surface renewal theory. However, after offering a speculative philosophy, he did not attempt any experimental proof. Lewis and Whitman (74) anticipated the development of Higbie and D a n b e r t s by discovering that an agitated vessel the thicknes ofthe film will vary as the 0.8 power of the velocity of rotation. Cumnt theory regarding absorption maintains that a soluble gas moves from the gas to the liquid phase under a driving p m which is the difference in p m u r e baween the mole fraction in the gas phase and the vapor
8
~
_
-
~
- Ai
Koa
koa
m ~ L R
or: _1 = _ 1 KIP kLa
+-d o1a
Here koa and k,a are the individual film resistances and m is the slope of the operating line (Figure 1). If the operating line lies above the equilibrium line, absorption or m a s transfer from the gas to the liquid phase will take place; while if the operating l i e lies below the equilibrium line, then maw transfer from the liquid to the gas phase, or “stripping” will take place. A more useful way of expressing the 6lm constant is by mass transport rather than by resistance:
N = Koa VAy and
N=KLRVAX Koa and KLRare usually referred to as the maw transfer coefficients. Koa is most useful in designs when composition of the gas phase is of primary interest and K M where composition of the liquid phase is of primary intereat. A b s o r b are generally designed using the
INDUSTRIAL A N D ENGINEERING CHEMISTRY
~
= A,
-1= - +l -
AUrnoRS John S. Ecknt is Cfief Engineer and Earl H. Fm&,Lcrmmd R. Rollison, and h i s F. W a k me EngincCrs for U.S. Stoneware, Inc.
~
7
The rate of transfer of this gas is directly proportional to the driving force but is resisted by its diffusion rate in both the gas and liquid phases. These restrictions have come to be known as the liquid and gas film resistances. I t is purely a philosophical point whether these two films are very thin or whether they vary in concentration frum one side of the interface to the other. Several things are known about these films. Their resistances are best determined by experimental operation of the system, and they are seldom, if ever, separated for use in industrial design practice. In other words, the film mistance used in industrial design is used as a combined constant:
Tbg
~
4
pressure of the same gas in equilibrium with the liquid phase:
plex than the dfisional resistance encountered at the interface between the gas and the liquid in this review of the classical theories of this process
~
5
Figure 2. Perfmame ckaracfm’stics of packed be&
TIE absorption process is shown to be more com-
42
2
_
_
_
~
~
r
K d coefficient. Colbum (5) expresses this transport in the form of transfer units where the above expressions take this form:
The useful form of these equations, as used in designing packed absorbers, is:
Adequate methods for calculating the required area of a tower (8) are already in general use so that it will not be necessary to review these techniques here. The chief problem in designing an absorber is determining the m a s transfer coefficient (&) for a packed tower and the plate efficiencyfor a plate tower. Much more is known about packed absorbers than the plate type, since most tower research has concerned distillation. A great amount of work has been done on the use of packed beds for absorbers, both on a laboratory and plant scale. Much of this work has been published, along with a great amount of theory in the realm of mathematical models. The absorption process is complex and, therefore, has not yielded to accurate mathematical analysis. h i s (74) was dose to the truth when he found that agitation of the liquid reduced the film resistance. The further improvements of Higbie (72) and Danckwerts (6) result from their perception that the film resistance would be sensitive to agitation as first determined by Lewis. The degree of this effect is best illustrated in the distillation process, where higher pressure drop operation is more commonly encountered than in absorption (Figure 2). Work done in distillation (9, 70) holds a major key to a few of the problems. Figure 2 illustrates the controlling domains of masa transfer. I t is rather evident that the diffusional process
Figure 3.
Koa us. % ' conversion C02-NnOH-H~0
only controls at low pressure drop where gas friction is not sufficient to induce much surface turbulence in the liquid. When the pressure drop in the bed becomes as high as 0.6 inch H20/foot packed depth, it is further evident (Table I) that the mass transfer, resulting from intense mixing of the gas and liquid at the interface, is so much greater than the slower diffusional process that the effect of variables generally thought to control the slower diffusional process is almost completely lost. Table I indicates that most of the usual variables which are thought to affect mam transfer, under more or less stagnant f ilm conditions, have no noticeable effect at a pressure drop approximating 0.6 inch/foot packed depth. The properties of latent heat of vaporization, heat capacity, relative volatility, average change of concentration per plate of separation, and the diffusion coefficient have been subjected to wide variations by a selection of six different binary mixtures, only to find that the HETP is really constant at this pressure drop with the exception of the methyl chloroform-toluene system. [See (70) on method of correcting for end effects between 5 and 10 feet of packed depth.] Complex variables are needed in an equation expnse ing the mass transfer characteristics between a liquid and a gas in a packed bed where the liquid is filmed over a solid surface and agitated by the gas. The mass transfer coefficientat low pressure drop Zone A (Figure 2) is under the major influence of the Schmidt No. Ns,and is basically a diffusional operation. In Zone B the mass transfer is controlled by both the Schmidt No. and the Reynolds No., N,; and as Zone C is approached, it is controlled almost entirely by the Reynolds No. The shape of the HETP curve indicates that the relationship of these two groups of variables on the rn transfer coefficient is complex and will require complex coefficients related to the pressure drop across the packed bed. Tepe and Dodge (77) determined that for the NaOHC O r H a system, the rate of mass transfer would in-
1.5 1.4 1.3
E. 0.9
3 0.8 0.7
0.6 0.5 0.4
0.3 0.2 0.1
0
V O L 5 9 NO. 2 F E B R U A R Y 1 9 6 7 43
the designer is unable to assign sufficiently accurate values to yield worthwhile answers. Absorption systems are best designed from either pilot or existing plant data with modifications from this base. For example, the Koa values are known for most of the systems used in industry today a t specific operating conditions (Table 111). The effect of various operating conditions on this basic mass transfer coefficient is becoming more commonly known (Figures 3 and 6). The systems which Lewis preferred to call “liquid filni controlled” were gases of low solubility such as 0 and
crease by the sixth power of the absolute temperature. In general, however, it is not presently known if this effect will be the same with salts other than sodium carbonate. Much research is needed to determine the temperature effect on rate of mass transfer (on systems other than NaOH-COz-HzO). The hot carbonate system achieves a much higher mass transfer because of the higher temperature of absorption ( 3 ) . Up to the present time, generalized equations and mathematical models have had little value in actual design work because they contain relative system properties to which
TABLE I ~
I
Methyl Chloroform Toluene
I
I
Benzene Toluene
i-Octane Toluene
Methanol Water
Latent heat of vaporization, AH
156
169 156
117 156
474 1000
296 1000
220 1000
Heat capacity, cp.
0.26
0.24 0.26
0.38 0.28
0.599 1 .o
0.596 1 .ooo
0.51 1 1 .o
3.4-4.6
25
1 .4-1 . 2 (740 mm.) 1.78-1.2 (100 mm.)
21.1
11.82
4.3
i-Propanol Water
Acetone Water -
Relative volatility
1
I
I
Av., Aconcn./plate
I
HTU
1
H ET Pa a
6.66 X l o w 5
4.63
x
10.5 10-5
1.23
0.90
0.92/0.80
1.36b
1.10
0.96/0.96
x
5.96
j
1.55
10-5
x
3.87
10-5
0.60
0.35
1
0.70*
20.0-1.25 I
I
3.82 Diffusion coefficient 6.58 X lo-’
1
1 ,46-l .03
7.0-2.45
1
1.00
5.35
1 1
3.73
x
0.68 0.98
H E P T and HTU taken at 0.6 inch HzO/ft. Afi. Fine-foot packed height. All other tests were run at IO-ft. bed height.
TABLE II. KGUWITH ADDITIVES IN NAOH-CO, SYSTEM Li uid Rate,
I
Lb.fSq. Ft. Hr. -~
Gas Rate, Lb./Sq. Ft. Hr.
I
~~
Pressure Drop, In. /Ft.
Additive
Amount Additive, P.P.M.
1i :: 11
5000
760
0.15
None
5000
520
0.15
Detergent
5000
1000
0.30
None
0.30
Detergent
0.30
Detergent and antifoam A
5000
1
900
1
-
..
~
1025
5000
~
~~
.. 15
1 I
2.0 2.4 2.3 2.3
~
5000
1050
0.30
Antifoam B
2
2.3
5000
1050
0.30
Antifoam B
16
2.2
5000
1350
0.6
None
..
2.7
* *
2.7
5000
I
1030
1
0.6
Detergent
5000
1
1290
I
0.6
Detergent and antifoam A
Additives: Detergent. Alkyl benzoyl sulfonate. Antifoam A. Unsaturated monohydric alcohol. Antifoam 3. Silicone.
44
~
1 1
2.4
INDUSTRIAL A N D ENGINEERING CHEMISTRY
I ~
15
1
2.6
10-5
TABLE 1 1 1 Gas
Reagent
Ion
NaOCl
Na+OCI-
20.0
HCI
H+CI-
16.0 13.0 8.0 7.0
“+OH-
NHOH
MEA+2S03-2
MEA. SO3 DEA*S
DEA +2S-2
5.0
KzC03 MEA * C 0 3
K+C03-’
3.10
...
MEA+’COg-’
2.50
...
HzS03 HOC1 HzC03
-
a
...
Na +so,-’
HzS
HzO MEA H z 0 -DEA
7 x 10-4 1.8 X
NazS03
Na2COa
HzO * KOH HzO. NaOH
Ionization “K”
Hydrate
N~+COS-~
H+S-2 Hf S 0 3 - 2 H+OCIH +C03-’ H+OH-
KOH NaOH MEA*OH
K+OHNafOHMEA-OH-
DEA*OH
DEA-OH-
...
...
2.25
0.400 0.317 0.138 0.072 0.0072 Kaa above a t 25%
completion
1.1
x
10-7
5 . 6 X lo-* 3.2 X lo-* 5.0 X 1 . 0 x 10-14
