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Mass transfer during bubbling in single and multi-orifice absorbers
Chemhzl Eng*reering Science, Vol. 41, No. 8, pp. 1987LlW4, Printed in Great Britain.
MASS
1986.
ooo9-2509/86 Pergamon
TRANSFER DURING BUBBLING IN SINGLE MULTI-ORIFICE ABSORBERS
53.00+0.00 Journals Ltd.
AND
J. R. F. GUEDES
DE CARVALHO, F. A. N. ROCHA, M. I. VASCONCELOS, M. C. M. SILVA and F. A. R. OLIVEIRA Centro de EngenhariaQuimica, FacuIdadede Engenharia,Rua dos Bragas, 4099 Porto Codex, Portugal (Receiued
2 April
1985)
Abstract-An experimental study is described of the process of mass transfer during continuous bubbling in single and multi-orifice plates. The regions of bubble formation and bubble rise are considered separately and the values of the corresponding interfacial areas, gas side and liquid side transfer coefficients are determined. For the multi-orifice absorbers the values of these parameters per orifice are compared with the corresponding values for single orifice absorbers. This provides a reasonable test of the idea that a multiorifice absorber may be regarded as a set of single orifice absorbers operating in parallel.
INTRODUCTION
bubbling of gases or vapours through liquids is a common operation in the chemical and allied industries and it is usually associated with interphase mass transfer. The need to understand this type of operation has aroused much interest in the fields of bubble mechanics and mass transfer from bubbles, and a vast amount of literature has been published on these topics in the past 25 years. However, there seems to be a wide gap between the understanding of idealized situations (mostly isolated bubble phenomena) and the performance of real equipment. The present paper is an attempt to find out whether the theory on isolated bubbles is applicable to situations of continuous bubbling, such as are found in industrial equipment. The approach adopted borrows a lot from that developed by Rocha and Guedes de Carvalho (1984), but in the present study the geometry of the bubbling orifices is different, and consideration is given to multiorifice gas injection The type of absorber used is shown in Fig. I. Gas at a metered flow rate, tis per orifice, was fed to the gas chamber beneath a perforated plate (single or multiorifice) over which there was a layer of absorbing liquid, of height h (this height was measured in the absence of bubbling). The solute in the gas stream was partly absorbed as it bubbled through the liquid, and the rate of absorption was determined. Three different gas-liquid systems were used in order to determine separately interfacial areas, gas side and liquid side transfer coefficients. The systems used were CO1 (in air)-NaOH (aqueous solution), NH3 (in air)-HCl (aqueous solution) and O2 (in air)-water. Experimental data were interpreted in terms of a two (three in one case) region model (Rocha and Guedes de Carvalho, 1984) to be detailed. The
EXPERIMENTAL
(a)
NH3
(in airkHC1
(aqueous
METHOD
solution)
sysrem
In these experiments a metered stream of air mixed with NH3 (always less than 3 o/0 molar in NH3) was 1987
fed to the absorber where it bubbled through a given volume of an aqueous solution of HCl. The gas issuing from the absorber was then passed successively through two washing bottles where it bubbled again through HCl solutions. The fractional retention of solute in either the absorber or the washing bottles was so high (always greater than 95%) that the gas discharged to the atmosphere was virtually free of NHs. Each experiment was allowed to run for a given time, t, (usually 5-15 min), after which admission of NHs to the system was interrupted. The time t, was always such that about half the HCl in the absorber was neutralized. The number of moles of NHs retained in the first absorber, nA. was determined by titration of the absorbing solution before and after the run. As for the washing bottles, the number of moles retained there (ni and n2, respectively) was determined by means of the Nessler reagent (spectrophotometric) method on account of the low concentrations present. It should be mentioned that the direct measurement of the amount of solute not retained in the absorber (i.e. n, + n2) is important in terms of the accuracy of the data obtained. Indeed, the parameter required for
-I
1 ----z-o=-- h 0"
-02 -
*-
I
’NV, Fig. 1. Schematic diagram of the absorber.
1988
J. R. F.
GUEDES
DE
CARVALHO et ol.
Control valve Fig. 2. Flowsheetof the installationfor the study of 0, absorption by water.
theoretical treatment is not the fraction of solute retained in the absorber, X, but rather 1 -X. Since values of X are currently above 0.95 and sometimes above 0.99, a method such as that used by Mehta and Sharma (1966) for a similar study is likely to yield very inaccurate data. Those authors measured the amount of solute fed to the absorber as well as that retained in it and then calculated 1 -X from the difference between the two. (b) O2 (in airjwater system A diagram of the experimental set-up for this system is shown in Fig. 2. The absorber under study was connected with a stripper which was fed continuously, at the bottom, with Nz. A positive displacement pump drove liquid continuously at a measured flow rate, pL, from the absorber to the top of the stripper. When the steady state was reached the same flow rate was being discharged back to the absorber by gravity. A control valve was placed along the discharge pipe to allow changes in liquid height in the absorber. The liquid streams going in and out of the absorber were monitored continuously for dissolved O2 and the corresponding concentrations (Ci, and Cfr”,, respectively) were recorded when the steady state was attained. Nitrogen was also fed continuously to the gas space above the liquid in the absorber where a stirrer ensured good mixing. A continuous O2 gas analyser kept sampling gas from this space and the flow rate of N2 was adjusted so that the level of 0, in this gas space was in equilibrium with that in the liquid in the absorber (concentration CL,,). This procedure eliminated the possibility of oxygen transfer across the free surface of the liquid. The liquid in the absorber could be taken as perfectly mixed on account of the strong stirring action of the bubbling air; injection of a blob of ink indicated complete dispersion within less than 5 s. The rate of oxygen transfer to the liquid in the absorber was easily calculated as riol = vL (CL,, -Cl,,.
(c) CO2 (in air jNaOH (aqueous solution) system This system was used for the measurement of interfacial areas. Carbon dioxide was added continuously to the air fed to the absorber, which contained (approximately an aqueous solution of NaOH 1 kmol dm-‘) as the absorbing liquid. A continuous IR gas analyser was used to monitor COa levels both at the inlet and outlet and the rate of absorption was calculated easily as irco= = Vg(Ca -C&). Care was taken to use less than 1 y0 molar of CO2 in the inlet stream in order to avoid significant changes of NaOH concentration in the liquid during one run. For each system, the rate of solute absorption was determined at various gas flow rates for liquid heights between 40 and 180 mm. The body of the absorber was made of a transparent acrylic tube. The internal diameter of this tube was 0.10 m for all the experiments on O2 absorption and for the experiments with multiorifice plates. An acrylic tube of 0.07 m internal diameter was used for all the other experiments. During the experiments the absorber was always kept in a constant temperature bath at 293 IL
THEORY
FOR
A SINGLE
ORIFICE
ABSORBER
In the theoretical treatment of the absorbers studied, three distinct regions were considered for the analysis of mass transfer. Figure 1 shows the region of bubble formation (region I) which comprises bubbles while attached to the injection nozzle, followed by the region of bubble rise (region II) and the free surface (region III). At any instant the total rate of transfer of solute to the liquid may be written as ir = A, + ri,, + ri,,,; expressions for transfer rates in each region may be developed separately for the cases of pure physical absorption and absorption with chemical reaction. Physical absorption For the system used the gas side resistance could be
Mass transferduring bubbling
1989
neglected and the expressions ri, = &Jc*
-C)
(1)
and ti,, = k,A (c* -C)
(2)
define the coefficients fL for region I and @,_A) for rising bubbles. C* is the interfacial concentration of solute on the liquid side and C is its concentration in the bulk of the liquid. With the arrangement shown in Fig. 2 and described previously, the concentration of O2 in the liquid bulk is CL,, because of good mixing, and riuI = 0 because the partial pressure of O2 above the liquid free surface was always adjusted to equilibrate CL,, . Now the rate of transfer of O2 to the liquid is n1 +nrI and VI_(C h”, -c;,>
= (fL+kLA)
(c* -CL,,).
(3)
An interfacial area per unit depth of immersion, a*, may be defined as a* = A/h and eq. (3) may be rearranged to give CL + k,a* h) = vL CCL,, -Cf,)/(C*
-CL,,>.
(4)
Measurement of the variables on the right-hand side together with knowledge of C* gives (_f, + k,u* h) for each depth of immersion and gas flow rate. IffL and k,a* do not vary with the depth of immersion for each gas flow rate, a plot of V,(CL,, - Ct,)/(C* -CL,,) vs. h (at a given v,J should yield a straight line with intercept fL and slope k,a*. Figure 3 shows plots of these variables for a range of flow rates. The values offL and k,a* obtained when bubbling air from one orifice at different flow rates are shown in Fig. 4. Chemical absorption For the C02-NaOH (solution) and NHB--HCl (solution) systems the concentration of absorbed species is zero in the liquid bulk, while in the gas its concentration varies significantly between inlet and outlet. For the region of bubble formation h, = Fo(CiB,-0)
(5)
defines the coefficient Fo (and the use ofCsin is justified
Fig. 4. Variation of liquid side transfer coefficients with gas flow rate for a single orifice (N = 1, 0, a) and a multi-orifice (N = 4,0, I) absorber.
since the bubble forming is always in contact with the nozzle mouth). Also, fi, = tig CC&- Cf). which together with eq. (5) gives
(6) where Cf is the average concentration of solute in the gas bubbles upon detachment from the nozzle. For the rising bubbles - VgdCs=
K,a*dz
(Cg-0)
and this defines the coefficient K,. (7) from z = 0 to z = h yields
G
cf
=
exp C-
(7)
Integration of eq.
Woa*/pg) hl
(8)
where C! is the average solute concentration in the bubbles as they reach the free surface of the liquid. The total rate of transfer from rising bubbles is then Piu = Vg (C,p-C,“)
(9)
and upon substituting Ct from eq. (8) into eq. (9) the result is tiII = (1 -exp[-((KGa*/i’,)h]}
Cfvg.
(10)
Absorption across the.free surface (including ejected drops and wetted walls due to splashing and sloshing) may be characterized by a coefficient, E,, defined by
1
0 0
50
100
hlmm)
200
Fig. 3. Dependence ofthe rate of O1 absorption on the depth of immersion for a single orifice absorber. (0, tig = 21 cm3/s; A, Vg = 44 cm3/s; I, tis = 69 cm-‘/s.)
Ii III =
-%i
c%,
-
0)
(11)
assuming the gas space to be well mixed above the free surface.
1990
J. R. F. GUEDESDECARVALHO~~~[.
The material balance gives A III
=
vg(C28- cp,“,)
(12)
and substitution of eq. (11) into eq. (12) gives (13) The fraction of solute not retained in the absorber is (1 -X) = (C&JCL) and this may bc obtained from the product of eqs (6), (8) and (13) as ln(l -X)
= ln[(v)(&)]
- (K&z*/Pg)
h
(14)
after taking logarithms. This equation suggests a plot of In (1 -X) vs. h for each gas flow rate and from the resulting straight lines KGa* and a combination of F, and E, may be obtained. (i) NHs-HCI (solurion) system. For this system the transfer coefficients in cq. (14) refer to the gas side only; this fact will be stressed by using lower case letters for these coefficients (i.e. Jo, ko). Order of magnitude calculations indicate that eo may be neglected in the present system and therefore plots of In (1 -X) vs. h and intercept In (vs -Jo)/ tis_ have slope ( - k,o*/pg) (ii) COs-NaOH (solution) system. For this system the transfer coefficients in eq. (14) comprise liquid side as well as gas side resistance, but it may be shown that the latter is always less than 10 o/0of the total resistance. Thus it was considered a good approximation to take the overall coefficients in eq. (14) as referring to the liquid side only. Elsewhere (Rocha and Guedes de Carvalho, 1986) it is shown that for the experimental conditions considered, the reaction accompanying the absorption of CO2 in solutions of NaOH may be treated as pseudo-first order if gas-liquid contact times are in the range 0.0015-1.64s. It was also shown there that the upper limit of 1.64 s is not exceeded in practice for bubbles forming or rising, and this excludes the possibility of reagent depletion near the interface. A check on the lower limit cannot bc made based on calculations, and further discussion is left until a later section. The rate of absorption per unit interfacial area
and plots of In (1 -X) vs. h (at constant pg) constructed from the data. The slope will now yield a* and the intercept may be calculated to give the average area of forming bubbles 7i, if a good estimate of the area of transfer at the free surface, S, is available. In another study (Rocha and Guedes de Carvalho, 1986), experimental determination of S for the equipment used was attempted, but the resulting values of Ar were not very convincing. Therefore in the present study it was decided to install a conical hood above the pool of liquid to try and reduce the area of the free surface (Fig. 5). This hood was always adjusted in height to have the free surface at the entrance of the small cylindrical tube. The existence of a cloud of bubbles (not accounted for in the model) under the conical surface is bound to make S larger than just the small portion appearing in the cylindrical section. In this sense, the value of S is still unknown. However, it is reasonable to assume that for each flow rate tis, and with the hood at the same height relative to the free surface of the liquid, the value of S will not vary with height. If that were so, the slope from eq. (15) would give correct values for u*, but the intercept will give Y’& only insofar as a good estimate of S is made. EXTENSION
OF THE
THEORY
TO A MULTI-ORIFICE
ABSORBER
If gas at a flow rate NVs is fed to the plenum chamber under a plate with N equally sized orifices, and if the pressure drop across the orifices is reasonably high (compared with the hydrostatic pressure above the plate), the gas will be evenly distributed and a flow rate tis will go through each orifice. Now, for a pool of liquid above the plate which is not deep, if the orifices are sufficiently far apart, bubbles issued from each orifice will reach the free surface without interacting with bubbles issued from neighbouring orifices. The whole plate may then be regarded as a set of N
is then taken as li = mC*, where k, is the kinetic constant in the rate equation for consumption of CO2 in the liquid (i.e. r = k tC &) and D L is the diffusivity of COz in solution. In terms of gas phase concentrations, ri = (a/n)Cs,
where H is Henry’s law constant
and values of m/H (= kb) for the conditions of interest are reported by Rocha and Guedes de Carvalho (1986). Equation (14) may be rewritten for this system as
-(k&
a*/vg)
h
Fig. 5. Schematic diagram of the hood arrangement prevent sloshing of liquid in the absorption of CO,.
to
Mass transferduring bubbling single orifice absorbers in parallel (Fig. 6) and it is reasonable to expect the transfer coefficients (for bubbles forming and rising) to be the same as those observed with the single orifice absorber working at vs. This should also apply to the area a* generated per orifice. Physical absorption For the plate bubbling from N orifices, consideration of the two regions mentioned previously leads to and
(16)
n, = (f3N (C* -C) ri,, = (k,a*),
h(C* -C)
(17)
where the subscript N is included to distinguish this from the single orifice situation (which corresponds to N = 1). A line of argument similar to that used for the single , orifice absorber here leads to (&JN + %_a*),
h = vi (CL
-ClMC*
-C!,,,)
(18)
where C* is known and all the other variables on the right-hand side of eq. (18) can be measured. For each gas flow rate a plot [(f,), + (k,a*)Nh] vs. h should yield a straight line with intercept (j&i and slope (k,a*),. After division by N these values can be compared withf, and kLa*, respectively, to test the idea that an N-orifice absorber may be regarded as a set of N single orifice absorbers in parallel. Chemical absorption Experiments on chemical absorption for multiorifice plates were carried out only for the NHa-HCl (solution) system and therefore consideration is given only to this case. With a flow rate Nvs fed to the absorber, there will be a rate of transfer in region I given by
fi1 =
cf.&
(Cip,
-Cf)
1991
dz reads -N
I’s dCs = (k,a*),
dz (C* - 0)
(21)
and integration between z = 0 and z = h gives C,B = exp I - C(koa*),l(N
Cf
vg)lh1.
(22)
The argument used to obtain eq. (14) here leads to ln(1 -X)
= In
N ps-u&J N i’a
PJ h. 1-CUwf%lN (23)
It is expected that (fo), = Nfo and (k,a*), = N (k,a*) if an N-orifice absorber (run at a flow rate N tis) is equivalent to N single orifice absorbers in parallel (each at a flow rate vs). EXPERIMENTAL
RESULTS
Values offL, kLa*, fG, kGa* and a* were determined experimentally, following the methods outlined above, and the corresponding values are shown in Figs 4, 7 and 8. As for A,, experimental values based on different estimates of S are also shown in Fig. 8. Tests with orifices 2 and 3 mm in diameter showed no dependence of the transfer coefficients on this parameter, for the range of flow rates investigated. This finding is in line with the predictions of a simple theory for the bubbling process presented elsewhere (Rocha and Guedes de Carvalho, 1984, 1986). The predictions from that theory are
fL = 3.65 $‘;-’ DT5 g-o.’ kLa+ = 5.24 ~~~3D~s go.’ fG = 3.65 $‘;-’ D&? g-o.’ kGa* = 5.24 v,“-’ 0:’
go.’
(24) (25) (26) (27)
(19)
and from the mass balance tit = N vs (Ct - Cf ) there results
For the rising bubbles the material balance over height
Fig. 6. Schematicdiagram of a multi-orificeabsorber (the value of h was measuredfor zero gas hold-up).
Fig. 7. Variationof gas sidetransfercoefficients withgas flow rate for a single orifia (N = 1, 0.0) and a multi-orifice (N = 4,0,1; and N = 9,A,A) absorber.
J. R. F. GUEDES DE CARVALHO
et al.
1o-3 0
10
20
30 v, lCn+/s)
Fig. 9. Fraction of solute not retained during bubble forma-
tion(N=l,O;N=4,m;N=9,A).
Fig. 8. Variation of interfacial area with gas flow rate (Cl, S = 2 cm’ was assumed; 0, S = 50 cm’ was assumed).
a,*= 2,
5.73
vg.’
g-o.2
= 3.16
Vi.8
g-o.4
and the corresponding lines are shown in Figs 4,? and 8. It should be mentioned that eqs (23~(26) are to be preferred to the corresponding ones in Rocha and Guedes de Carvalho (1984), for in the latter values of g in c.g.s. units were substituted in the formulae. In Fig. 7 the values offo are seen to lie very close to the line& = vs, which represents complete absorption of the solute at the injection nozzle (region I). In view of this, it is more convenient to express the extent of mass transfer at the injection nozzle by means of the ratio Cf /C& for the NHs-HCI (solution) system. This ratio represents the fraction of solute not retained in region I and for each orifice and gas-liquid system it should depend only on gas flow rate vs. Equation (6) gives the relationship between Cf /C$ and fG, and a plot of experimental values is given in Fig. 9. A four-orifice absorber was used for the measurement of liquid side and gas side transfer coefficients; a nine-orifice absorber was also used but only for the measurement of gas side coefficients. All the orifices were 2 mm in diameter. The four-orifice plate had the orifices evenly placed on a circumference 55 mm in diameter; on the other plate, one hole was at the centre and the other eight holes were on a circumference 65 mm in diameter. Experimental data for multiorifice absorbers are conveniently displayed in Figs 4 and 7. Indeed, it was shown above that for the same flow rate per orifice the four equalities
fo = ( foh,IN~ ft = U&.x/N.
koa* = (k,a*),/N k,_a* = (kLa*),,,/N
should hold if the N-orifice absorber were equivalent to N single orifice absorbers in parallel The plots ‘allow several comparisons to be made. Transfer coefficients for single and multi-orifice ab-
sorbers generally fall above theoretical predictions (sometimes far above) and the more so, the higher the gas flow rate per orifice, vs_ Similar findings were reported by Rocha and Guedes de Carvalho (1984) in another study and the suggestion is that adequate theory has to be developed to predict transfer coefficients in bubble formation. Theoretical predictions of coefficients for rising bubbles are not too far out, but the dependence of these coefficients on gas flow rate is more pronounced than what is predicted by theory. Again, for rising bubbles, theoretical predictions of interfacial area are in good agreement with experiment. Interfacial areas in the region of bubble formation are considerably underpredicted, but this may be the result of great uncertainties in the estimates of S. The possibility that the reaction was slower than required to yield the interfacial areas for the region of bubble formation may not be excluded either. Indeed, values of fLare very high and if the correct estimate for S were around or above 50 cm2, experimental enhancement factors for that region would be only marginally above unity, indicating that the contact times were too short. Finally, comparison of data for multi-orifice absorbers with those for single orifice absorbers lends credit to the idea that an N-orifice absorber may be regarded as a set of N single orifice absorbers operating in parallel at the same flow rate per orifice, For the case of absorption with a very fast reaction in the liquid. For oxygen absorption in water, the transfer coefficients for Forming bubbles seem to be considerably lower in the four-orifice absorber than in the single orifice one. This is probably associated with the Fact that mass transfer From bubbles held under the surface before bursting is being counted as mass transfer in the region of bubble formation. This problem is currently being further investigated.
HEIGHT
EQUIVALENT
TO THE
INJECTION
REGION
experiments described show that mass transfer is enhanced near the injection orifices. Following the approach of Rocha and Guedes de Carvalho (1984), the height equivalent to the inlet nozzle may be defined The
Mass transferduring bubbling
(ml 0.2
0
00 0
0.0
01
o
,
20
I 60 U,(cm%)
40
Fig. 10. Height equivalentto the injectionregion for a single orifice absorber (0, gas side; 0, liquid side).
and the corresponding values calculated from &(C*
-C)
= k,a*
(30)
hkq (C* -C)
for physical absorption of sparingly soluble gases. This gives h& =
f~lW,_~*)
(31)
which is the expression for the equivalent height. Figure 10 gives h&calculated from experimental values of fL and kLa* for the single orifice absorber. The theoretical expression h& = 0.696 Vi.4 g-o.2
(32)
may be obtained from eq. (31) withy, from eq. (24) and k,a* from eq. (25). This is not plotted in Fig. 10 because it would be difficult to distinguish from the horizontal axis. For the absorption of NH3 in solutions of HCI, from Rocha and Guedes de Carvalho (1984)
range of flow rates investigated. Theoretical predictions of interfacial area for rising bubbles are also in good agreement with the values measured. Experiments with nozzles 2 and 3 mm in diameter showed no dependence of transfer coefficients or interfacial areas on that parameter over the range of flow rates investigated. For multi-orifice absorbers, the values of the transfer coefficients per orifice are similar to the corresponding values in single orifice absorbers, operating at the same flow rate per orifice, except in the case of liquid side coefficients for forming bubbles. This gives some support to the idea that an N-orifice absorber is approximately equivalent to N single orifice absorbers operating in parallel at the same flow rate per orifice. This idea has to be tested further, particularly on account of the disagreement between single orifice and multi-orifice liquid side transfer coefficients for forming bubbles mentioned above.
NOTATlON
u* A
2‘
=s C”l
Cf”?cl.1 DL eG
(33)
hg =
EG Figure 10 shows values of hg calculated from experiments with the single orifice absorber, and the theoretical line would be he”q = 0.191 x
In
v;-7
~(30.5
,$ - 3.65
obtained from eq. (33), withf, and (27) respectively.
g-O.’
fG fL
% vgo.7
0;’
g-o.’
(34) >
and kGa* from eqs (26)
CONCLUSIONS
The present study shows clearly that the extent of solute transfer near the injection plate is very significant in shallow bubbling absorbers. The division of the absorber into two regions, namely bubble formation and bubble rise, is therefore important for an adequate quantitative treatment. The experimental values of the transfer coefficients in the region of bubble formation are considerably higher than the predictions from a simple theory. This observation emphasizes the need for further theoretical treatment of the problem. For the region of bubble rise, the transfer coefficients predicted from a simple theory are in reasonable agreement with the experimental values over the
1993
FG H
k, kb k, k, kci nA?%, n2
il
N
s
interfacial area of bubbles rising, per unit depth of immersion total surface area of bubbles rising average area of bubbles forming concentration of solute in gas stream at inlet to and outlet from gas absorber, respectively concentration of dissolved oxygen in ingoing and outgoing streams, respectively diffusivity of CO, in solution gas side transfer coefficient for transfer above free surface overall transfer coefficient for transfer above the free surface [defined in eq. (11)l gas side transfer coefficient for bubbles forming liquid side transfer coefficient for bubbles forming [defined in eq. (l)] overall transfer coefficient for bubbles forming [defined in eq. (5) J Henry’s law constant gas side transfer coefficient for bubbles rising liquid side transfer coefficient for reacting solute, based on gas side concentrations kinetic constant in rate equation for consumption of CO1 in the liquid liquid side transfer coefficient for bubbles rising [defined in eq. (2)] overall transfer coefficient for bubbles rising [defined in eq. (7)] number of moles absorbed in absorber, washing bottle 1 and washing bottle 2, respectively molar rate of transfer number of bubbling orifices interfacial area at and above the free surface of liquid
J. R.F.
1994
2, rs VL
X
GUEDESDECARVALHO~~
duration of an experiment volumetric flow rate of gas per orifice volumetric flow rate of liquid fraction of solute retained in absorber REFERENCES
Mehta, V. D. and Sharma, M. M., 1966, Effect ofdiffusivity on gas side mass transfer coefficient. Chem. Engng Sci. 21, 361-365.
al.
Rocha, F. A. N. and Guedes de Carvalho, J. R. F., 1984, Absorption during gas injection through a submerged nozzle. Part I--Gas side and liquid side transfer coefficients. Chem. Engng Res. Des. 62, 303-314. Recha, F. A. N. and Guedes de Carvalho, J. R. F., 1986, Absorption during gas injection through a submerged nozzle. Part II-Interfacial areas. Chem. Engng Res. Des. (in press).
MASS
1986.
ooo9-2509/86 Pergamon
TRANSFER DURING BUBBLING IN SINGLE MULTI-ORIFICE ABSORBERS
53.00+0.00 Journals Ltd.
AND
J. R. F. GUEDES
DE CARVALHO, F. A. N. ROCHA, M. I. VASCONCELOS, M. C. M. SILVA and F. A. R. OLIVEIRA Centro de EngenhariaQuimica, FacuIdadede Engenharia,Rua dos Bragas, 4099 Porto Codex, Portugal (Receiued
2 April
1985)
Abstract-An experimental study is described of the process of mass transfer during continuous bubbling in single and multi-orifice plates. The regions of bubble formation and bubble rise are considered separately and the values of the corresponding interfacial areas, gas side and liquid side transfer coefficients are determined. For the multi-orifice absorbers the values of these parameters per orifice are compared with the corresponding values for single orifice absorbers. This provides a reasonable test of the idea that a multiorifice absorber may be regarded as a set of single orifice absorbers operating in parallel.
INTRODUCTION
bubbling of gases or vapours through liquids is a common operation in the chemical and allied industries and it is usually associated with interphase mass transfer. The need to understand this type of operation has aroused much interest in the fields of bubble mechanics and mass transfer from bubbles, and a vast amount of literature has been published on these topics in the past 25 years. However, there seems to be a wide gap between the understanding of idealized situations (mostly isolated bubble phenomena) and the performance of real equipment. The present paper is an attempt to find out whether the theory on isolated bubbles is applicable to situations of continuous bubbling, such as are found in industrial equipment. The approach adopted borrows a lot from that developed by Rocha and Guedes de Carvalho (1984), but in the present study the geometry of the bubbling orifices is different, and consideration is given to multiorifice gas injection The type of absorber used is shown in Fig. I. Gas at a metered flow rate, tis per orifice, was fed to the gas chamber beneath a perforated plate (single or multiorifice) over which there was a layer of absorbing liquid, of height h (this height was measured in the absence of bubbling). The solute in the gas stream was partly absorbed as it bubbled through the liquid, and the rate of absorption was determined. Three different gas-liquid systems were used in order to determine separately interfacial areas, gas side and liquid side transfer coefficients. The systems used were CO1 (in air)-NaOH (aqueous solution), NH3 (in air)-HCl (aqueous solution) and O2 (in air)-water. Experimental data were interpreted in terms of a two (three in one case) region model (Rocha and Guedes de Carvalho, 1984) to be detailed. The
EXPERIMENTAL
(a)
NH3
(in airkHC1
(aqueous
METHOD
solution)
sysrem
In these experiments a metered stream of air mixed with NH3 (always less than 3 o/0 molar in NH3) was 1987
fed to the absorber where it bubbled through a given volume of an aqueous solution of HCl. The gas issuing from the absorber was then passed successively through two washing bottles where it bubbled again through HCl solutions. The fractional retention of solute in either the absorber or the washing bottles was so high (always greater than 95%) that the gas discharged to the atmosphere was virtually free of NHs. Each experiment was allowed to run for a given time, t, (usually 5-15 min), after which admission of NHs to the system was interrupted. The time t, was always such that about half the HCl in the absorber was neutralized. The number of moles of NHs retained in the first absorber, nA. was determined by titration of the absorbing solution before and after the run. As for the washing bottles, the number of moles retained there (ni and n2, respectively) was determined by means of the Nessler reagent (spectrophotometric) method on account of the low concentrations present. It should be mentioned that the direct measurement of the amount of solute not retained in the absorber (i.e. n, + n2) is important in terms of the accuracy of the data obtained. Indeed, the parameter required for
-I
1 ----z-o=-- h 0"
-02 -
*-
I
’NV, Fig. 1. Schematic diagram of the absorber.
1988
J. R. F.
GUEDES
DE
CARVALHO et ol.
Control valve Fig. 2. Flowsheetof the installationfor the study of 0, absorption by water.
theoretical treatment is not the fraction of solute retained in the absorber, X, but rather 1 -X. Since values of X are currently above 0.95 and sometimes above 0.99, a method such as that used by Mehta and Sharma (1966) for a similar study is likely to yield very inaccurate data. Those authors measured the amount of solute fed to the absorber as well as that retained in it and then calculated 1 -X from the difference between the two. (b) O2 (in airjwater system A diagram of the experimental set-up for this system is shown in Fig. 2. The absorber under study was connected with a stripper which was fed continuously, at the bottom, with Nz. A positive displacement pump drove liquid continuously at a measured flow rate, pL, from the absorber to the top of the stripper. When the steady state was reached the same flow rate was being discharged back to the absorber by gravity. A control valve was placed along the discharge pipe to allow changes in liquid height in the absorber. The liquid streams going in and out of the absorber were monitored continuously for dissolved O2 and the corresponding concentrations (Ci, and Cfr”,, respectively) were recorded when the steady state was attained. Nitrogen was also fed continuously to the gas space above the liquid in the absorber where a stirrer ensured good mixing. A continuous O2 gas analyser kept sampling gas from this space and the flow rate of N2 was adjusted so that the level of 0, in this gas space was in equilibrium with that in the liquid in the absorber (concentration CL,,). This procedure eliminated the possibility of oxygen transfer across the free surface of the liquid. The liquid in the absorber could be taken as perfectly mixed on account of the strong stirring action of the bubbling air; injection of a blob of ink indicated complete dispersion within less than 5 s. The rate of oxygen transfer to the liquid in the absorber was easily calculated as riol = vL (CL,, -Cl,,.
(c) CO2 (in air jNaOH (aqueous solution) system This system was used for the measurement of interfacial areas. Carbon dioxide was added continuously to the air fed to the absorber, which contained (approximately an aqueous solution of NaOH 1 kmol dm-‘) as the absorbing liquid. A continuous IR gas analyser was used to monitor COa levels both at the inlet and outlet and the rate of absorption was calculated easily as irco= = Vg(Ca -C&). Care was taken to use less than 1 y0 molar of CO2 in the inlet stream in order to avoid significant changes of NaOH concentration in the liquid during one run. For each system, the rate of solute absorption was determined at various gas flow rates for liquid heights between 40 and 180 mm. The body of the absorber was made of a transparent acrylic tube. The internal diameter of this tube was 0.10 m for all the experiments on O2 absorption and for the experiments with multiorifice plates. An acrylic tube of 0.07 m internal diameter was used for all the other experiments. During the experiments the absorber was always kept in a constant temperature bath at 293 IL
THEORY
FOR
A SINGLE
ORIFICE
ABSORBER
In the theoretical treatment of the absorbers studied, three distinct regions were considered for the analysis of mass transfer. Figure 1 shows the region of bubble formation (region I) which comprises bubbles while attached to the injection nozzle, followed by the region of bubble rise (region II) and the free surface (region III). At any instant the total rate of transfer of solute to the liquid may be written as ir = A, + ri,, + ri,,,; expressions for transfer rates in each region may be developed separately for the cases of pure physical absorption and absorption with chemical reaction. Physical absorption For the system used the gas side resistance could be
Mass transferduring bubbling
1989
neglected and the expressions ri, = &Jc*
-C)
(1)
and ti,, = k,A (c* -C)
(2)
define the coefficients fL for region I and @,_A) for rising bubbles. C* is the interfacial concentration of solute on the liquid side and C is its concentration in the bulk of the liquid. With the arrangement shown in Fig. 2 and described previously, the concentration of O2 in the liquid bulk is CL,, because of good mixing, and riuI = 0 because the partial pressure of O2 above the liquid free surface was always adjusted to equilibrate CL,, . Now the rate of transfer of O2 to the liquid is n1 +nrI and VI_(C h”, -c;,>
= (fL+kLA)
(c* -CL,,).
(3)
An interfacial area per unit depth of immersion, a*, may be defined as a* = A/h and eq. (3) may be rearranged to give CL + k,a* h) = vL CCL,, -Cf,)/(C*
-CL,,>.
(4)
Measurement of the variables on the right-hand side together with knowledge of C* gives (_f, + k,u* h) for each depth of immersion and gas flow rate. IffL and k,a* do not vary with the depth of immersion for each gas flow rate, a plot of V,(CL,, - Ct,)/(C* -CL,,) vs. h (at a given v,J should yield a straight line with intercept fL and slope k,a*. Figure 3 shows plots of these variables for a range of flow rates. The values offL and k,a* obtained when bubbling air from one orifice at different flow rates are shown in Fig. 4. Chemical absorption For the C02-NaOH (solution) and NHB--HCl (solution) systems the concentration of absorbed species is zero in the liquid bulk, while in the gas its concentration varies significantly between inlet and outlet. For the region of bubble formation h, = Fo(CiB,-0)
(5)
defines the coefficient Fo (and the use ofCsin is justified
Fig. 4. Variation of liquid side transfer coefficients with gas flow rate for a single orifice (N = 1, 0, a) and a multi-orifice (N = 4,0, I) absorber.
since the bubble forming is always in contact with the nozzle mouth). Also, fi, = tig CC&- Cf). which together with eq. (5) gives
(6) where Cf is the average concentration of solute in the gas bubbles upon detachment from the nozzle. For the rising bubbles - VgdCs=
K,a*dz
(Cg-0)
and this defines the coefficient K,. (7) from z = 0 to z = h yields
G
cf
=
exp C-
(7)
Integration of eq.
Woa*/pg) hl
(8)
where C! is the average solute concentration in the bubbles as they reach the free surface of the liquid. The total rate of transfer from rising bubbles is then Piu = Vg (C,p-C,“)
(9)
and upon substituting Ct from eq. (8) into eq. (9) the result is tiII = (1 -exp[-((KGa*/i’,)h]}
Cfvg.
(10)
Absorption across the.free surface (including ejected drops and wetted walls due to splashing and sloshing) may be characterized by a coefficient, E,, defined by
1
0 0
50
100
hlmm)
200
Fig. 3. Dependence ofthe rate of O1 absorption on the depth of immersion for a single orifice absorber. (0, tig = 21 cm3/s; A, Vg = 44 cm3/s; I, tis = 69 cm-‘/s.)
Ii III =
-%i
c%,
-
0)
(11)
assuming the gas space to be well mixed above the free surface.
1990
J. R. F. GUEDESDECARVALHO~~~[.
The material balance gives A III
=
vg(C28- cp,“,)
(12)
and substitution of eq. (11) into eq. (12) gives (13) The fraction of solute not retained in the absorber is (1 -X) = (C&JCL) and this may bc obtained from the product of eqs (6), (8) and (13) as ln(l -X)
= ln[(v)(&)]
- (K&z*/Pg)
h
(14)
after taking logarithms. This equation suggests a plot of In (1 -X) vs. h for each gas flow rate and from the resulting straight lines KGa* and a combination of F, and E, may be obtained. (i) NHs-HCI (solurion) system. For this system the transfer coefficients in cq. (14) refer to the gas side only; this fact will be stressed by using lower case letters for these coefficients (i.e. Jo, ko). Order of magnitude calculations indicate that eo may be neglected in the present system and therefore plots of In (1 -X) vs. h and intercept In (vs -Jo)/ tis_ have slope ( - k,o*/pg) (ii) COs-NaOH (solution) system. For this system the transfer coefficients in eq. (14) comprise liquid side as well as gas side resistance, but it may be shown that the latter is always less than 10 o/0of the total resistance. Thus it was considered a good approximation to take the overall coefficients in eq. (14) as referring to the liquid side only. Elsewhere (Rocha and Guedes de Carvalho, 1986) it is shown that for the experimental conditions considered, the reaction accompanying the absorption of CO2 in solutions of NaOH may be treated as pseudo-first order if gas-liquid contact times are in the range 0.0015-1.64s. It was also shown there that the upper limit of 1.64 s is not exceeded in practice for bubbles forming or rising, and this excludes the possibility of reagent depletion near the interface. A check on the lower limit cannot bc made based on calculations, and further discussion is left until a later section. The rate of absorption per unit interfacial area
and plots of In (1 -X) vs. h (at constant pg) constructed from the data. The slope will now yield a* and the intercept may be calculated to give the average area of forming bubbles 7i, if a good estimate of the area of transfer at the free surface, S, is available. In another study (Rocha and Guedes de Carvalho, 1986), experimental determination of S for the equipment used was attempted, but the resulting values of Ar were not very convincing. Therefore in the present study it was decided to install a conical hood above the pool of liquid to try and reduce the area of the free surface (Fig. 5). This hood was always adjusted in height to have the free surface at the entrance of the small cylindrical tube. The existence of a cloud of bubbles (not accounted for in the model) under the conical surface is bound to make S larger than just the small portion appearing in the cylindrical section. In this sense, the value of S is still unknown. However, it is reasonable to assume that for each flow rate tis, and with the hood at the same height relative to the free surface of the liquid, the value of S will not vary with height. If that were so, the slope from eq. (15) would give correct values for u*, but the intercept will give Y’& only insofar as a good estimate of S is made. EXTENSION
OF THE
THEORY
TO A MULTI-ORIFICE
ABSORBER
If gas at a flow rate NVs is fed to the plenum chamber under a plate with N equally sized orifices, and if the pressure drop across the orifices is reasonably high (compared with the hydrostatic pressure above the plate), the gas will be evenly distributed and a flow rate tis will go through each orifice. Now, for a pool of liquid above the plate which is not deep, if the orifices are sufficiently far apart, bubbles issued from each orifice will reach the free surface without interacting with bubbles issued from neighbouring orifices. The whole plate may then be regarded as a set of N
is then taken as li = mC*, where k, is the kinetic constant in the rate equation for consumption of CO2 in the liquid (i.e. r = k tC &) and D L is the diffusivity of COz in solution. In terms of gas phase concentrations, ri = (a/n)Cs,
where H is Henry’s law constant
and values of m/H (= kb) for the conditions of interest are reported by Rocha and Guedes de Carvalho (1986). Equation (14) may be rewritten for this system as
-(k&
a*/vg)
h
Fig. 5. Schematic diagram of the hood arrangement prevent sloshing of liquid in the absorption of CO,.
to
Mass transferduring bubbling single orifice absorbers in parallel (Fig. 6) and it is reasonable to expect the transfer coefficients (for bubbles forming and rising) to be the same as those observed with the single orifice absorber working at vs. This should also apply to the area a* generated per orifice. Physical absorption For the plate bubbling from N orifices, consideration of the two regions mentioned previously leads to and
(16)
n, = (f3N (C* -C) ri,, = (k,a*),
h(C* -C)
(17)
where the subscript N is included to distinguish this from the single orifice situation (which corresponds to N = 1). A line of argument similar to that used for the single , orifice absorber here leads to (&JN + %_a*),
h = vi (CL
-ClMC*
-C!,,,)
(18)
where C* is known and all the other variables on the right-hand side of eq. (18) can be measured. For each gas flow rate a plot [(f,), + (k,a*)Nh] vs. h should yield a straight line with intercept (j&i and slope (k,a*),. After division by N these values can be compared withf, and kLa*, respectively, to test the idea that an N-orifice absorber may be regarded as a set of N single orifice absorbers in parallel. Chemical absorption Experiments on chemical absorption for multiorifice plates were carried out only for the NHa-HCl (solution) system and therefore consideration is given only to this case. With a flow rate Nvs fed to the absorber, there will be a rate of transfer in region I given by
fi1 =
cf.&
(Cip,
-Cf)
1991
dz reads -N
I’s dCs = (k,a*),
dz (C* - 0)
(21)
and integration between z = 0 and z = h gives C,B = exp I - C(koa*),l(N
Cf
vg)lh1.
(22)
The argument used to obtain eq. (14) here leads to ln(1 -X)
= In
N ps-u&J N i’a
PJ h. 1-CUwf%lN (23)
It is expected that (fo), = Nfo and (k,a*), = N (k,a*) if an N-orifice absorber (run at a flow rate N tis) is equivalent to N single orifice absorbers in parallel (each at a flow rate vs). EXPERIMENTAL
RESULTS
Values offL, kLa*, fG, kGa* and a* were determined experimentally, following the methods outlined above, and the corresponding values are shown in Figs 4, 7 and 8. As for A,, experimental values based on different estimates of S are also shown in Fig. 8. Tests with orifices 2 and 3 mm in diameter showed no dependence of the transfer coefficients on this parameter, for the range of flow rates investigated. This finding is in line with the predictions of a simple theory for the bubbling process presented elsewhere (Rocha and Guedes de Carvalho, 1984, 1986). The predictions from that theory are
fL = 3.65 $‘;-’ DT5 g-o.’ kLa+ = 5.24 ~~~3D~s go.’ fG = 3.65 $‘;-’ D&? g-o.’ kGa* = 5.24 v,“-’ 0:’
go.’
(24) (25) (26) (27)
(19)
and from the mass balance tit = N vs (Ct - Cf ) there results
For the rising bubbles the material balance over height
Fig. 6. Schematicdiagram of a multi-orificeabsorber (the value of h was measuredfor zero gas hold-up).
Fig. 7. Variationof gas sidetransfercoefficients withgas flow rate for a single orifia (N = 1, 0.0) and a multi-orifice (N = 4,0,1; and N = 9,A,A) absorber.
J. R. F. GUEDES DE CARVALHO
et al.
1o-3 0
10
20
30 v, lCn+/s)
Fig. 9. Fraction of solute not retained during bubble forma-
tion(N=l,O;N=4,m;N=9,A).
Fig. 8. Variation of interfacial area with gas flow rate (Cl, S = 2 cm’ was assumed; 0, S = 50 cm’ was assumed).
a,*= 2,
5.73
vg.’
g-o.2
= 3.16
Vi.8
g-o.4
and the corresponding lines are shown in Figs 4,? and 8. It should be mentioned that eqs (23~(26) are to be preferred to the corresponding ones in Rocha and Guedes de Carvalho (1984), for in the latter values of g in c.g.s. units were substituted in the formulae. In Fig. 7 the values offo are seen to lie very close to the line& = vs, which represents complete absorption of the solute at the injection nozzle (region I). In view of this, it is more convenient to express the extent of mass transfer at the injection nozzle by means of the ratio Cf /C& for the NHs-HCI (solution) system. This ratio represents the fraction of solute not retained in region I and for each orifice and gas-liquid system it should depend only on gas flow rate vs. Equation (6) gives the relationship between Cf /C$ and fG, and a plot of experimental values is given in Fig. 9. A four-orifice absorber was used for the measurement of liquid side and gas side transfer coefficients; a nine-orifice absorber was also used but only for the measurement of gas side coefficients. All the orifices were 2 mm in diameter. The four-orifice plate had the orifices evenly placed on a circumference 55 mm in diameter; on the other plate, one hole was at the centre and the other eight holes were on a circumference 65 mm in diameter. Experimental data for multiorifice absorbers are conveniently displayed in Figs 4 and 7. Indeed, it was shown above that for the same flow rate per orifice the four equalities
fo = ( foh,IN~ ft = U&.x/N.
koa* = (k,a*),/N k,_a* = (kLa*),,,/N
should hold if the N-orifice absorber were equivalent to N single orifice absorbers in parallel The plots ‘allow several comparisons to be made. Transfer coefficients for single and multi-orifice ab-
sorbers generally fall above theoretical predictions (sometimes far above) and the more so, the higher the gas flow rate per orifice, vs_ Similar findings were reported by Rocha and Guedes de Carvalho (1984) in another study and the suggestion is that adequate theory has to be developed to predict transfer coefficients in bubble formation. Theoretical predictions of coefficients for rising bubbles are not too far out, but the dependence of these coefficients on gas flow rate is more pronounced than what is predicted by theory. Again, for rising bubbles, theoretical predictions of interfacial area are in good agreement with experiment. Interfacial areas in the region of bubble formation are considerably underpredicted, but this may be the result of great uncertainties in the estimates of S. The possibility that the reaction was slower than required to yield the interfacial areas for the region of bubble formation may not be excluded either. Indeed, values of fLare very high and if the correct estimate for S were around or above 50 cm2, experimental enhancement factors for that region would be only marginally above unity, indicating that the contact times were too short. Finally, comparison of data for multi-orifice absorbers with those for single orifice absorbers lends credit to the idea that an N-orifice absorber may be regarded as a set of N single orifice absorbers operating in parallel at the same flow rate per orifice, For the case of absorption with a very fast reaction in the liquid. For oxygen absorption in water, the transfer coefficients for Forming bubbles seem to be considerably lower in the four-orifice absorber than in the single orifice one. This is probably associated with the Fact that mass transfer From bubbles held under the surface before bursting is being counted as mass transfer in the region of bubble formation. This problem is currently being further investigated.
HEIGHT
EQUIVALENT
TO THE
INJECTION
REGION
experiments described show that mass transfer is enhanced near the injection orifices. Following the approach of Rocha and Guedes de Carvalho (1984), the height equivalent to the inlet nozzle may be defined The
Mass transferduring bubbling
(ml 0.2
0
00 0
0.0
01
o
,
20
I 60 U,(cm%)
40
Fig. 10. Height equivalentto the injectionregion for a single orifice absorber (0, gas side; 0, liquid side).
and the corresponding values calculated from &(C*
-C)
= k,a*
(30)
hkq (C* -C)
for physical absorption of sparingly soluble gases. This gives h& =
f~lW,_~*)
(31)
which is the expression for the equivalent height. Figure 10 gives h&calculated from experimental values of fL and kLa* for the single orifice absorber. The theoretical expression h& = 0.696 Vi.4 g-o.2
(32)
may be obtained from eq. (31) withy, from eq. (24) and k,a* from eq. (25). This is not plotted in Fig. 10 because it would be difficult to distinguish from the horizontal axis. For the absorption of NH3 in solutions of HCI, from Rocha and Guedes de Carvalho (1984)
range of flow rates investigated. Theoretical predictions of interfacial area for rising bubbles are also in good agreement with the values measured. Experiments with nozzles 2 and 3 mm in diameter showed no dependence of transfer coefficients or interfacial areas on that parameter over the range of flow rates investigated. For multi-orifice absorbers, the values of the transfer coefficients per orifice are similar to the corresponding values in single orifice absorbers, operating at the same flow rate per orifice, except in the case of liquid side coefficients for forming bubbles. This gives some support to the idea that an N-orifice absorber is approximately equivalent to N single orifice absorbers operating in parallel at the same flow rate per orifice. This idea has to be tested further, particularly on account of the disagreement between single orifice and multi-orifice liquid side transfer coefficients for forming bubbles mentioned above.
NOTATlON
u* A
2‘
=s C”l
Cf”?cl.1 DL eG
(33)
hg =
EG Figure 10 shows values of hg calculated from experiments with the single orifice absorber, and the theoretical line would be he”q = 0.191 x
In
v;-7
~(30.5
,$ - 3.65
obtained from eq. (33), withf, and (27) respectively.
g-O.’
fG fL
% vgo.7
0;’
g-o.’
(34) >
and kGa* from eqs (26)
CONCLUSIONS
The present study shows clearly that the extent of solute transfer near the injection plate is very significant in shallow bubbling absorbers. The division of the absorber into two regions, namely bubble formation and bubble rise, is therefore important for an adequate quantitative treatment. The experimental values of the transfer coefficients in the region of bubble formation are considerably higher than the predictions from a simple theory. This observation emphasizes the need for further theoretical treatment of the problem. For the region of bubble rise, the transfer coefficients predicted from a simple theory are in reasonable agreement with the experimental values over the
1993
FG H
k, kb k, k, kci nA?%, n2
il
N
s
interfacial area of bubbles rising, per unit depth of immersion total surface area of bubbles rising average area of bubbles forming concentration of solute in gas stream at inlet to and outlet from gas absorber, respectively concentration of dissolved oxygen in ingoing and outgoing streams, respectively diffusivity of CO, in solution gas side transfer coefficient for transfer above free surface overall transfer coefficient for transfer above the free surface [defined in eq. (11)l gas side transfer coefficient for bubbles forming liquid side transfer coefficient for bubbles forming [defined in eq. (l)] overall transfer coefficient for bubbles forming [defined in eq. (5) J Henry’s law constant gas side transfer coefficient for bubbles rising liquid side transfer coefficient for reacting solute, based on gas side concentrations kinetic constant in rate equation for consumption of CO1 in the liquid liquid side transfer coefficient for bubbles rising [defined in eq. (2)] overall transfer coefficient for bubbles rising [defined in eq. (7)] number of moles absorbed in absorber, washing bottle 1 and washing bottle 2, respectively molar rate of transfer number of bubbling orifices interfacial area at and above the free surface of liquid
J. R.F.
1994
2, rs VL
X
GUEDESDECARVALHO~~
duration of an experiment volumetric flow rate of gas per orifice volumetric flow rate of liquid fraction of solute retained in absorber REFERENCES
Mehta, V. D. and Sharma, M. M., 1966, Effect ofdiffusivity on gas side mass transfer coefficient. Chem. Engng Sci. 21, 361-365.
al.
Rocha, F. A. N. and Guedes de Carvalho, J. R. F., 1984, Absorption during gas injection through a submerged nozzle. Part I--Gas side and liquid side transfer coefficients. Chem. Engng Res. Des. 62, 303-314. Recha, F. A. N. and Guedes de Carvalho, J. R. F., 1986, Absorption during gas injection through a submerged nozzle. Part II-Interfacial areas. Chem. Engng Res. Des. (in press).