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liquid interfacial area a and the coefficient kLa in a counter-current packed column
C.hemical Eng,negnng ancl . Process,ng Chemical Engineering and Processing 35 (1996) 247-253
ELSEVIER
Influence of pressure on the gas/liquid interfacial area a and the coefficient kLa in a counter-current packed column B. Benadda, M. Otterbein*, K. Kafoufi, M. Prost LCPAE, D@artement de G~nie Energ~tique, INSA de L YON, 20 av. Albert Einstein 69621, Villeurbanne,France Received 20 October 1994; accepted 25 September 1995
Abstract The effects of pressure on the volumetric coefficient k~a and the interfacial area a in a counter-current packed coiumn were studied in the pressure range 105 to 12 x 105 Pa. The method of gas/liquid absorption with chemical reaction was applied. The influence of the gas/liquid system on the interfacial area was also studied using three different chemical systems. It is shown that a and kia decrease when the total pressure is increased. The authors have attempted to explain the differences between the values of a obtained under atmospheric pressure when the chemical system is changed.
Rfisum~ En mettant en oeuvre l'absorption gaz/liquide avec r6action chimique, l'influence de la pression totaIe (105/t 12 x 105 Pa) sur le coefficient de transfert de mati~re kLa et l'aire interfaciale a ~t6 6tudi~e dans une colonne/t garnissage fonctionnant/t contre -courant. L'influence du syst~me chimique a aussi ~t~ 6tudi~e en utilisant trois syst~mes chimiques diff6rents. II a 6t6 montr6 que a et kLa diminuent quand la pression augmente et nous avons essay6 d'interpr~ter les differences entre les valeurs de i'aire interfaciale obtenues sous pression atmosph~rique quand on change de syst~me chimique. Keywords: Pressure; Gas/liquid interracial area; Counter-current packed column
Synopse Si les publications sont nombreuses pour quantifier l'influence des d6bits gazeux et liquide sur les aires interfaciales et les coefficients de transfert de mati~re, elles se font par contre tr~s rares en ce qui concerne l'influence de la pression. Le but de ce travail est de d6tenniner, par absorption avec r~action chimique, l'influence de la pression totale (105 /~ 12 x 105 Pa) sur le coefficient de transfert de mati~re kLa et l'aire interfaciale a dans une colonne garnissage en vrac fonctionnant ~. contre-courant. L'originalit~ de cette 6tude est due au manque de travaux publi~s sur l'influence de la pression sur ce type
* Corresponding author.
de contacteur. Nous avons ~tudi6 d'abord ~ pression atmosph~rique l'influence du systbme chimique sur l'aire interfaciale, objet d'une pol6mique r~guli~rement entretenue dans la litt6rature. Nous avons utilis6 les trois syst~mes chimiques suivants: (i) CO2/Na2CO3-NaHCO3 avec comme catalyseur NaCIO; (iO OJN%SO3 avec COSO4; et (iii) Q/CuC1 sans catalyseur. Les constantes cin6tiques de ces syst~mes ont 6t6 d6termin~es dans les m~mes conditions op6ratoires en utilisant un appareil de laboratoire ~ surface d'6change gaz/liquide connue. L'installation est compos6e essentiellement d'une colonne en verre r~sistant ~ 15 x 105 Pa et dont le diam~tre et la hauteur sont respectivement de 0,062 et 1 m. Elle est garnie d'anneaux Raschig 10 x 10 mm en c~ramique.
248
B. Benadda et al. / Chemical Engineering and Processing 35 (1996) 247-253
Les rdsultats obtenus sous pression atmosph6rique et dans les domaines de ddbits de 1,84 ~
The aim of this present work was to elucidate the influence of total pressure, ranging from l0 s to 12 x l0 s Pa, on the interfacial area a and on the volumetric coefficient/qa inside a counter-current packed column when gas/liquid absorption was used with chemical reaction. The originality of such a study arises from the fact that the influence of pressure in this kind of contactor has been scarcely investigated to date. We first studied under atmospheric pressure the influence of the gas/liquid system on the interracial area, a subject that often gives rise to disagree in the literature [3]. We used three different chemical systems whose kinetic constants were determined under similar experimental conditions [2-4].
2. Apparatus The experimental set-up has already been described in detail elsewhere [2]. It is mainly composed of a cylindrical column (1), the inner diameter and height of which are 0.062 m and 1 m, respectively. This column, A
Watcr
C
1. Introduction Many articles in the literature are devoted to the absorption of gas/liquid systems with chemical reaction at atmospheric pressure; references dealing with the influence of pressure are seldom encountered and are non-existant in some cases. In 1989, Oyevaar and Westerterp [1] estimated that only about 20 publications were directly or indirectly related with the influence of pressure on the hydrodynamics and mass transfer in gas liquid contactors. A recent literature survey of this topic [2] showed that the operating pressure has a significant effect on the masstransfer parameters and that most of the corresponding studies were carried out either in stirred vessels or in bubble columns. This literature review also showed that most authors seem to agree on the independence of kL towards pressure; in contrast, the results obtained for kLa and a are different and sometimes contradictory, even when the same kind of experimental device is used.
Water
V--,© Fig. 1. Schematic flow sheet of the experimental installation: I, packed column; 2, vessel; 3, gas cylinder;4, inlet pressure regulator; 5, mass flowcontroller;6, valve;7, pH meter; 8, thermometer;9, level indicator, 10, sampling valve; 11, centrifugal pump; 12, heat exchanger; 13, rotameter; 14, manometer; 15, pressure relief valve; 16, distributor; 17, outlet pressure regulator; 18, gas analyzer; 19, recorder; 20, differentialmanometer.
B. Benadda et al. / Chemical Engineer#zg and Processing 35 (1996) 247-253 Table 1 Operating conditions employed Operating pressure Temperature solution pH of solution
Molarity of catalyst Molarity of reactive species Partial pressure of solute Volume of reactant solution Specific mass flow liquid phase Specific mass flow gas phase
105 to I2 x I05 Pa 20 °C __+1 °C OjNa2SO 3 CO2/Na2CO3-NaHCO 3 O2/CuCI NaC10 CoSO 4 NazSO 3 NazCO3 CuCI 02 C02 2 × 10 -3 m 3
249
solution, respectively. Finally, the specific absorption flow cp depends on the chemical regime. 3. I. Determination of a in a fast reaction regime 8.0 9.8-8.8 1.9-1.8 0-0.1 M 5 × I0 -4 M 0.80 M 0.43 M 0.i0 M 21% 10% + 0.5%
1.84-7.36 kg m -2 s -~
The following chemical systems were employed: 02/ Na2CO3 (catalyst: COSO4) and O2/CuC1 (without catalyst). The corresponding reactions are: Co2 +
2SO 2- + 0 2
,2SO42-
02 + 4CuI + 4H +
(a)
~ 4 C u II
-1-2H20
(b)
These reactions are fast and pseudo-first order. In this case and if the gas-phase resistance to mass transfer is negligible, the specific absorption flow per unit volume of the liquid phase q~ is given by:
0.05-0.2 kg m -2 s -~
= ~oa = aC*
(2)
D,,/-~ak~
and hence: 1 a = z---~ C* D,,/~Ak~ 0~V1
packed with ceramic Raschig rings 10 x 10 mm, is made of glass capable of resisting pressure up to 15 x 105 Pa. Pressurization of the column is provided by a gas cylinder (3) and controlled by means of both inlet and outlet pressure regulators (4) and (17). A schematic flow sheet of the experimental installation is presented in Fig. 1.
In this equation the subscript A corresponds to oxygen, ~ is the slope of the plot of [SO3- ] = f(t) or of [Cu I] = f(t) according to reaction (a) or (b), and kl is the kinetic rate constant for the pseudo-first order reaction.
3. Theoretical basis
3.2. Determination of a and kLa in the intermediate regime
We assume that the hypothesis employed and the method used at atmospheric pressure remain valid at higher pressures. Column modelling was based on previously reported methods [5,6]. The authors consider the overall device as being similar to the association of a plug-flow reactor (packed column) and perfectly stirred reactor (tank, pump and feedback loop). It is assumed that [5,6]: (i) absorption with chemical reaction only takes place in the column. Since the absorption rate is low through the packing, it can be assumed to be negligible elsewhere in the device; (ii) the concentration of reactant B is a linear function of the packing height (chemical system with constant specific absorption flowrate); and (iii) both gas and liquid phases circulate under pure plug-flow conditions. A liquid distributor is installed to limit wall effects. Mass balances for the reactant B in both parts of the installation then lead to: c~--
z~oaVo V1
(1)
(3)
The following chemical system was employed: COJ Na2CO3-NaHCQ (catalyst: NaCIO). The corresponding reaction is: C O 2 + U 2 0 -]- C O 2 _ [cio-~]
2HCO3
(c)
The kinetic constant for this reaction may be written as [7]: kl -- k2[C10 - ]
(4)
Under intermediate regime conditions when the gasside resistance may be neglected, ~ can be expressed as: • = a C * x / D a k 1 -}- k 2
(5)
and combination of Eqs. (1), (4) and (5) leads to:
[
- c~Vt l 2 = a2C*2Dak2[ClO-] + ]cLa2C*A2
zVo
(6)
If [ - (c~V1/zVo)]2 is plotted versus [C10-], the resulting adjusted Danckwerts line allows the interfacial area a and the volumetric coefficient kLa to be determined. For the chemical system chosen, the subscript A represents carbon dioxide and c~ is the slope of [CO 2- ] =
f(t). where c~is the slope of the plot of [B] = f(t) and z is the stoichiometric coefficient of the reaction used. The volumes Vo and V1 are those of the packing and reactant
It should be noted that, for practical reasons, only the CQ/Na2CO3-NaHCO3 system was investigated under pressure.
B. Benadda et al, / Chemical Engineering and Processing 35 (1996) 247-253
250
Table 2 Physicochemical and kinetic parameters at atmospheric pressure System
Catalyst
C~ 10 -4 moI 1-~
DA10 -9 m 2 s -1
Kinetic constant
Ref.
O2/Na2SO a CO2/NazCO3-NaHCO3 OjCuCI
CoSO 4
1.38 265 2.52
1.6I 1.60 2.05
2746 s - I 1450 1 m o l - t s - i 21 520 Iz mo1-2 s -1
[2] [4] [2]
NaC10 None
4. Operating conditions, physicochemical and kinetic parameters Table 1 lists the various characteristics associated with the operating conditions used. The physicochemical parameters are identical with those quoted in Refs. [2] and [4]. The same references lists the kinetic constants of the reactions investigated which were investigated under atmospheric pressure using the same experimental conditions as in this work, the laboratory device used being the gas-lift bubble column. The values of these parameters are listed in Table 2. As suggested in Refs. [8] and [9], the diffusivity of CO2 in carbonate and bicarbonate solutions and the kinetic constant of reaction (c) were assumed to be independent of the pressure. In addition, the solubility of CO2 and the Henry's law constant He were corrected for pressure. The method used was that of Van Krevelen and Hoftijzer [9] as applied to electrolyte solutions which gives: log
=E
where the ionic strengths I~ of salt i and the contribution h,. of different species are considered to be independent of the pressure for a given temperature. The variation of Heo with pressure was taken from Ref. [10].
4.1. Analysis Small aliquots of the reacting solutions were sampled at different times from the feedback loop. Their molarities were then determined by titration (iodometric for 1 0 3 -" •
sulphite ions, potentiometric for carbonate ions). For the O2/Cu ~ system, [Cu~]= fit) was deduced by continuously following the redox potential. For more details regarding the analyses, the reader is referred to Ref. [2].
5. Results and discussion 5.i. At atmospheric pressure Fig. 2 shows the variations of a versus L, with G remaining constant, for the three gas/liquid systems studied. It should be noted that in all three cases the interracial area a increased with the liquid mass flowrate. However, the values for the system COJ NazCOg-NaHCO3 are 40% greater than the corresponding values for O2/NazSQ, although the latter are in good agreement with those of Onda et al. [11]. In addition, the values for the Oz/CuCl system are somewhat lower. The discrepancy in the results cannot be explained by values of the kinetic constants, as assumed by Badssi et al. [8], since they were all determined using the same experimental device and under the same operating conditions as used in this study. However, such differences may be explained when consideration is taken of the fact that the interracial area depends strongly on the ability of the gas/liquid system to generate foams [3]. Such foam formation was not observed during our experiments with the O,/CuC1 system. This aspect of the chemical method has led to many discussions in the literature; in fact some authors [12] have emphasized the chemical method as an experimental tool which allows the absolute value of a value to be 103-
021CuCl
• O2/Na2SO3 o CO2/Na2CO3 --
e~
[11] e~
o ------o
o
10::
102
I01 o
;
4
;
~
~o
L (kg m-2s-1) Fig. 2. Comparison of the values of a for three gas/liquid systems used (G=0.1 kg m - 2 s - l ) .
I0
0.05
0.1
0.15
0.20
0.25 G (kg m'2s"1)
Fig. 3. Variation of a with gas mass flowrate (L = 5.52 kg m - 2 s - ~).
B. Benadda et al. / Chemical Engineering and Processing 35 (I996) 247-253 IgLa (I0-2 s-l)
(10-2 s-i) I01
RL a
101
o This work --
251
[131
o
--
o
~
o ~
c
I0 °
10°
/
1(i1 2
4
I01
10 0
10 2 P (105 Pa)
L (kg m'2s ~I) Fig. 4. Variation of kLa with liquid mass flowrate (G = 0.1 kg m - 2 s - 1 , C O j N a z C Q _ N a H C O 3 system).
Fig. 6. Variation of kLa with total pressure ( L = 5.52 kg m - 2 s - I and G = 0 . 1 kg m - 2 s - ~ ) .
obtained independent of the nature of the reaction used. Fig. 3 depicts the variation of a versus the gas mass flowrate G for a liquid mass flowrate L -- 5.52 kg m -2 s - i. The chemical reaction studied in this case was the oxidation of sodium sulphite. It should be noted that the interfacial area is hardly affected by the gas mass flowrate G, in agreement with previous literature statements. A great deal of the results on this subject have been brough together by Laurent and Charpentier [12]. Values of the volumetric coefficient kLa, obtained by the Danckwerts method, are plotted versus liquid mass flowrates in Fig. 4. It should be noted that the variation is virtually the same as that by a correlation given by Mohunta et al. [13]. However, our own values, obtained with the CO2/Na2CO3-NaHCO 3 system, are somewhat greater.
/CLa also decreases over the same range of pressure and flow, in accord with the results of Larachi et al. [14]. These latter authors used a co-current gas/liquid trickle-bed reactor in their studies. We have chosen to compare our results with those of both latter works, because the experimental devices employed in these cases appear to be quite close to ours. With a constant gas mass flowrate G, an increase in pressure leads to a decrease in the superficial velocity of the gas via an increase in its specific gravity. But the superficial velocity of the gas has very little influence on the interfacial area under our experimental conditions, particularly below 10 x 10 .2 ms -1. This velocity was the maximal value studied by us under pressure conditions. When working up to 30 x 105 Pa, Larachi [15] came to the same conclusion, but without separating the roles of those factors influencing the pressure and the specific gravity. The influence of one or other may be explained by the decreased importance of fluid phases penetration under high pressure and by a change in the fluid distribution and flow regime. Flow under a film regime becomes more important than flow under a drop regime. We have based our determinations on the penetration theory and the Danckwerts method. As stated in
5.2. Influence of pressure For liquid and gas mass flowrates L--5.52 kg m -2 s -1 and G=0.1 kg m -2 s -1, respectively, Fig. 5 indicates that a decreases when the pressure is increased from 105 to 12 x 105 Pa, apparently in agreement with Badssi et al. [8] who worked with a laboratory column equipped with cross-flow sieve trays. Fig. 6 shows that
[
c~ V f - ~-'-~J ( [10-3 kmol.m-3min-1]2 )
103=
400
'E
t ? !!!!p~aaa [ 300 ] A 710~Pa [ 10 2.
200 I/'oZ,
I01 I0 °
.
.
.
.
.
.
.
.
j
101
.
.
.
.
.
.
.
limit of the method validity -- ---- ~ -- _ ..L_
f
-'-z'.V
- -
..........
.
102 P (105 Pa)
Fig. 5. Variation of a with total pressure (L = 5.52 kg m - 2 s - 1 and G=0.1 kgm -2s-1).
0
1
2
3
4
5
6 [NaCIO ] I0"zM
Fig. 7. Danckwerts lines for pressures of I x 105, 3 x l0 s, 5 x 105 and 7 x l0 s Pa.
B. Benadda et al. / Chemical Engineering and Processing 35 (1996) 247-253
252
4 PA
[ c~V!] ( 108 Pare3 s kmol"I)
[ c~VL'[2 ~ : • -12 -T"q-2~J([10"~kmol.m~rmn ] ) 300
~.
_-
280 260 240 220
6 • 12105Pol
•, ~
~
i
i
m
~
o
o
---27-
+ arm,pres. ]
5
3
it of the method validity
2 1
180 160 . . . . . . . . . . 0,0 0,1
0,2
. • . . , ......... 0,3 0,4
, ......... 0,5 0,6 0,7 -2 [NaCIO] 10 M
2
4
6
8
10 1
12 ( 10.3 s m'l)
4 k 2 + D A k 2 [ClO']
Fig. 8. Danckwerts lines for 10 x 10 s and 12 x 105 Pa,
Fig. 9. Verification of gas-phase resistance at 1 x l0 s and 12 x l0 s Pa,
the next section, we have verified the theoretical criteria necessary for their use at different pressure values. However, we must point out a limitation on the validity of the Danckwerts line when the pressure is increased, as shown in Figs. 7 and 8. This is probably due to a change in the reaction regime which occurs at a critical concentration of catalyst. This critical concentration decreases when the pressure is increased. Hence, the pressure interval over which the Danckwerts line may be applied become increasingly narrower. Only the linear parts of such Danckwerts curves have been taken into consideration in our discussions.
6.2. Chemical regime The condition for the intermediate chemical regime if given by Danckwerts [17] as 0.3 < H a < 3. For the limiting catalyst concentrations, we obtained 0.76 < Ha < 2.55.
6.3. Gas-phase resistance When the gas-side resistance is taken into account, the absorption flow (I~ may be expressed as: ~=
PA
1 He -~ga-~ ax/K[ + DAk2[CIO- ]
6. Verification of the utilization criteria for the Danckwerts method under pressure
Combining this relationship with Eq. (1) gives:
6.1. Pseudo-first-order criterion
PA
For the system CO2/Na2CO3-NaHCO3-NaC10, this criterion has been defined by Danckwerts and Sharma [16], and simplified by McNeill [7], as X<< Y, with X= #1 + kiDA/k 2 and Y= 1/(C* /[CO~- ] + 2CX /
[HCO- ]). Table 3 lists the results obtained for this relationship under different pressures and maximal catalyst concentrations. It is assumed that 9 << 35, according to McNeill [7] the pseudo-first order criterion is verified. Hence, from the results given Table 3, this criterion is also satisfied in this study. Table 3 Verificationof pseudo-first-order criterion at elevatedpressure P(105 Pa)
Maximal concentration of NaClO(mol 1-i)
X
Y
1 3 5 7 10 12
0.0625 0.0125 0.0125 0.063 0,003 0.0025
2.12 1.68 1.95 1.54 1.26 1.26
54 17.67 10.60 7.57 5.31 4.42
1
He
I -z--~=°:Vli=-~ga-~ax//c2+DAk~[ClO-] Thus, a straight line should be obtained when PAl[c~V1/zVo] is plotted versus 1/,/k [ +OAlq[ClO-], the intercept at the origin being 1/kga. Fig. 9 shows that this resistance is practically equal to zero both at atmospheric pressure and at 12 x 10s Pa for the range of catalyst concentration studied.
7. Conclusion
In conclusion, our study contributes to a knowledge of absorbers under pressure. It shows that the total pressure influences mass-transfer parameters such as a and kLa. Our results also confirm others quoted in the literature, which still remains very sparse on this topic. As far as the influence of the chemical system is concerned, this appears important in any extrapolation of the a values determined for one chemical system to another. Without a careful comparison of the physicochemical properties, such as the foam-formation abilities, of such systems, such extrapolation may be invalid.
B. Benadda et al. / Chemical Engineering and Processing 35 (1996) 247-253
Appendix A: Nomenclature
(p
a A B
References
C* DA G Ha
He Heo hi I,. kl
k~a kL
kLa L P PA
t Vo Vx z
interfacial area per volume unit, m - i gas solute (02 or CO2) reactive species dissolved in the liquid phase ( C O ~ - , SO 2- or Cu ~) molarity of A at equilibrium, kmol m -3 diffusivity of gas into the solution, m - : s -I specific mass flow per unit of cross-section for the gas phase, kg m -2 s -I Hatta number, Henry constant when salts are present in the solution, bar m 3 kmolHenry constant when salts are absent from the solution, bar m 3 kmol-1 salt coefficient, m 3 k m o l ionic strength, kmol m -3 kinetic constant (unit corresponding to the type of reaction) volumetric mass-transfer coefficient in the gas phase, kmol m -3 Pa -1 s -1 liquid-side mass-transfer coefficient, m svolumetric mass-transfer coefficient in the liquid phase, s- 1 specific mass flow per unit cross-section for the liquid phase, kg m -2 s -1 total pressure, Pa partial pressure, Pa time, s (min) packing volume, m 3 volume of reactant solution, m 3 stoichiometric coefficient slope of lines [B] = f(t), kmol m -3 min -1
253
specific absorption flow, kmol m -2 s -~ specific absorption flow per unit volume of liquid phase, kmol m -3 s -~
[I] M.H. Oyevaar and K.R. Westerterp, Chem. Eng. Process., 25 (1989) 85. [2] B. Benadda, ThOse, Universit6 Claude Bernard Lyon I, 1994. [3] B.M. Soulami, ThOse, Institut Polytechnique de Lorraine (Nancy), 1980. [4] B. Benadda, M. Prost, S. Ismaili, R. Bressat and M. Otterbein, Chem. Eng. Process., 33 (I994) 55. [5] A. Laurent, ThOse Doct ks-sciences, Institut National Polytechnique de Lorraine (Nancy), I975. [6] J. Andrieu and B. Claudel, Chem. Eng. Sci., 29 (I973) 1263. [7] K.M. McNeiI1, Can. J. Chem. Eng., 48 (1970) 252. [8] A. Badssi, R. Bugarel, C. Blanc, J.L. Peytavy and A. Laurent, Chem. Eng. Process., 23 (1988) 89. [9] D.W. Van Krevelen and P.J. Hoftijzer, NumOro spdcial du XXIOme Congr. Int. de Chimie Industrielle, Bruxelles, September 1948, p. 168. [I0] H. Stephen and T. Stephen, Solubilities of Inorganic and Organic Compounds, Part 1, Binary Systems, Pergamon Press, Oxford, VoI. 1, 1983. [11] K. Onda, H. Takeuchi and Y. Koyama, J. Chem. Eng. Jpn., i
(i968) 56. [12] A. Laurent and J.C. Charpentier, Chem. Eng. J. Lausanne 8, (1974) 85. [13] D.M. Mohunta, A.S. Vaidyanathan and G.S. Laddha, Indian J. Chem. Eng., 1I (I969) 73. [I4] F. Larachi, P.M. MovilIiat, A. Laurent et N. Midoux, Rdcents ProgrOs en GOnie des Proeddds, 3dine CongrOs Franfais de GOnie des ProcOdds, Compi6gne, 4-6 Septembre, I991, 5, 16, 141. [15] F. Larachi, ThOse, Institut Polytechnique de Lorraine (Nancy), 1991. [16] P.V. Danckwerts and M.M. Sharma, Chem. Eng. (NY), 202 (1966) 244. [17] P.V. Danckwerts, Gas-Liquid Reactions, McGraw-Hill, New York, I970. 270pp.
ELSEVIER
Influence of pressure on the gas/liquid interfacial area a and the coefficient kLa in a counter-current packed column B. Benadda, M. Otterbein*, K. Kafoufi, M. Prost LCPAE, D@artement de G~nie Energ~tique, INSA de L YON, 20 av. Albert Einstein 69621, Villeurbanne,France Received 20 October 1994; accepted 25 September 1995
Abstract The effects of pressure on the volumetric coefficient k~a and the interfacial area a in a counter-current packed coiumn were studied in the pressure range 105 to 12 x 105 Pa. The method of gas/liquid absorption with chemical reaction was applied. The influence of the gas/liquid system on the interfacial area was also studied using three different chemical systems. It is shown that a and kia decrease when the total pressure is increased. The authors have attempted to explain the differences between the values of a obtained under atmospheric pressure when the chemical system is changed.
Rfisum~ En mettant en oeuvre l'absorption gaz/liquide avec r6action chimique, l'influence de la pression totaIe (105/t 12 x 105 Pa) sur le coefficient de transfert de mati~re kLa et l'aire interfaciale a ~t6 6tudi~e dans une colonne/t garnissage fonctionnant/t contre -courant. L'influence du syst~me chimique a aussi ~t~ 6tudi~e en utilisant trois syst~mes chimiques diff6rents. II a 6t6 montr6 que a et kLa diminuent quand la pression augmente et nous avons essay6 d'interpr~ter les differences entre les valeurs de i'aire interfaciale obtenues sous pression atmosph~rique quand on change de syst~me chimique. Keywords: Pressure; Gas/liquid interracial area; Counter-current packed column
Synopse Si les publications sont nombreuses pour quantifier l'influence des d6bits gazeux et liquide sur les aires interfaciales et les coefficients de transfert de mati~re, elles se font par contre tr~s rares en ce qui concerne l'influence de la pression. Le but de ce travail est de d6tenniner, par absorption avec r~action chimique, l'influence de la pression totale (105 /~ 12 x 105 Pa) sur le coefficient de transfert de mati~re kLa et l'aire interfaciale a dans une colonne garnissage en vrac fonctionnant ~. contre-courant. L'originalit~ de cette 6tude est due au manque de travaux publi~s sur l'influence de la pression sur ce type
* Corresponding author.
de contacteur. Nous avons ~tudi6 d'abord ~ pression atmosph~rique l'influence du systbme chimique sur l'aire interfaciale, objet d'une pol6mique r~guli~rement entretenue dans la litt6rature. Nous avons utilis6 les trois syst~mes chimiques suivants: (i) CO2/Na2CO3-NaHCO3 avec comme catalyseur NaCIO; (iO OJN%SO3 avec COSO4; et (iii) Q/CuC1 sans catalyseur. Les constantes cin6tiques de ces syst~mes ont 6t6 d6termin~es dans les m~mes conditions op6ratoires en utilisant un appareil de laboratoire ~ surface d'6change gaz/liquide connue. L'installation est compos6e essentiellement d'une colonne en verre r~sistant ~ 15 x 105 Pa et dont le diam~tre et la hauteur sont respectivement de 0,062 et 1 m. Elle est garnie d'anneaux Raschig 10 x 10 mm en c~ramique.
248
B. Benadda et al. / Chemical Engineering and Processing 35 (1996) 247-253
Les rdsultats obtenus sous pression atmosph6rique et dans les domaines de ddbits de 1,84 ~
The aim of this present work was to elucidate the influence of total pressure, ranging from l0 s to 12 x l0 s Pa, on the interfacial area a and on the volumetric coefficient/qa inside a counter-current packed column when gas/liquid absorption was used with chemical reaction. The originality of such a study arises from the fact that the influence of pressure in this kind of contactor has been scarcely investigated to date. We first studied under atmospheric pressure the influence of the gas/liquid system on the interracial area, a subject that often gives rise to disagree in the literature [3]. We used three different chemical systems whose kinetic constants were determined under similar experimental conditions [2-4].
2. Apparatus The experimental set-up has already been described in detail elsewhere [2]. It is mainly composed of a cylindrical column (1), the inner diameter and height of which are 0.062 m and 1 m, respectively. This column, A
Watcr
C
1. Introduction Many articles in the literature are devoted to the absorption of gas/liquid systems with chemical reaction at atmospheric pressure; references dealing with the influence of pressure are seldom encountered and are non-existant in some cases. In 1989, Oyevaar and Westerterp [1] estimated that only about 20 publications were directly or indirectly related with the influence of pressure on the hydrodynamics and mass transfer in gas liquid contactors. A recent literature survey of this topic [2] showed that the operating pressure has a significant effect on the masstransfer parameters and that most of the corresponding studies were carried out either in stirred vessels or in bubble columns. This literature review also showed that most authors seem to agree on the independence of kL towards pressure; in contrast, the results obtained for kLa and a are different and sometimes contradictory, even when the same kind of experimental device is used.
Water
V--,© Fig. 1. Schematic flow sheet of the experimental installation: I, packed column; 2, vessel; 3, gas cylinder;4, inlet pressure regulator; 5, mass flowcontroller;6, valve;7, pH meter; 8, thermometer;9, level indicator, 10, sampling valve; 11, centrifugal pump; 12, heat exchanger; 13, rotameter; 14, manometer; 15, pressure relief valve; 16, distributor; 17, outlet pressure regulator; 18, gas analyzer; 19, recorder; 20, differentialmanometer.
B. Benadda et al. / Chemical Engineer#zg and Processing 35 (1996) 247-253 Table 1 Operating conditions employed Operating pressure Temperature solution pH of solution
Molarity of catalyst Molarity of reactive species Partial pressure of solute Volume of reactant solution Specific mass flow liquid phase Specific mass flow gas phase
105 to I2 x I05 Pa 20 °C __+1 °C OjNa2SO 3 CO2/Na2CO3-NaHCO 3 O2/CuCI NaC10 CoSO 4 NazSO 3 NazCO3 CuCI 02 C02 2 × 10 -3 m 3
249
solution, respectively. Finally, the specific absorption flow cp depends on the chemical regime. 3. I. Determination of a in a fast reaction regime 8.0 9.8-8.8 1.9-1.8 0-0.1 M 5 × I0 -4 M 0.80 M 0.43 M 0.i0 M 21% 10% + 0.5%
1.84-7.36 kg m -2 s -~
The following chemical systems were employed: 02/ Na2CO3 (catalyst: COSO4) and O2/CuC1 (without catalyst). The corresponding reactions are: Co2 +
2SO 2- + 0 2
,2SO42-
02 + 4CuI + 4H +
(a)
~ 4 C u II
-1-2H20
(b)
These reactions are fast and pseudo-first order. In this case and if the gas-phase resistance to mass transfer is negligible, the specific absorption flow per unit volume of the liquid phase q~ is given by:
0.05-0.2 kg m -2 s -~
= ~oa = aC*
(2)
D,,/-~ak~
and hence: 1 a = z---~ C* D,,/~Ak~ 0~V1
packed with ceramic Raschig rings 10 x 10 mm, is made of glass capable of resisting pressure up to 15 x 105 Pa. Pressurization of the column is provided by a gas cylinder (3) and controlled by means of both inlet and outlet pressure regulators (4) and (17). A schematic flow sheet of the experimental installation is presented in Fig. 1.
In this equation the subscript A corresponds to oxygen, ~ is the slope of the plot of [SO3- ] = f(t) or of [Cu I] = f(t) according to reaction (a) or (b), and kl is the kinetic rate constant for the pseudo-first order reaction.
3. Theoretical basis
3.2. Determination of a and kLa in the intermediate regime
We assume that the hypothesis employed and the method used at atmospheric pressure remain valid at higher pressures. Column modelling was based on previously reported methods [5,6]. The authors consider the overall device as being similar to the association of a plug-flow reactor (packed column) and perfectly stirred reactor (tank, pump and feedback loop). It is assumed that [5,6]: (i) absorption with chemical reaction only takes place in the column. Since the absorption rate is low through the packing, it can be assumed to be negligible elsewhere in the device; (ii) the concentration of reactant B is a linear function of the packing height (chemical system with constant specific absorption flowrate); and (iii) both gas and liquid phases circulate under pure plug-flow conditions. A liquid distributor is installed to limit wall effects. Mass balances for the reactant B in both parts of the installation then lead to: c~--
z~oaVo V1
(1)
(3)
The following chemical system was employed: COJ Na2CO3-NaHCQ (catalyst: NaCIO). The corresponding reaction is: C O 2 + U 2 0 -]- C O 2 _ [cio-~]
2HCO3
(c)
The kinetic constant for this reaction may be written as [7]: kl -- k2[C10 - ]
(4)
Under intermediate regime conditions when the gasside resistance may be neglected, ~ can be expressed as: • = a C * x / D a k 1 -}- k 2
(5)
and combination of Eqs. (1), (4) and (5) leads to:
[
- c~Vt l 2 = a2C*2Dak2[ClO-] + ]cLa2C*A2
zVo
(6)
If [ - (c~V1/zVo)]2 is plotted versus [C10-], the resulting adjusted Danckwerts line allows the interfacial area a and the volumetric coefficient kLa to be determined. For the chemical system chosen, the subscript A represents carbon dioxide and c~ is the slope of [CO 2- ] =
f(t). where c~is the slope of the plot of [B] = f(t) and z is the stoichiometric coefficient of the reaction used. The volumes Vo and V1 are those of the packing and reactant
It should be noted that, for practical reasons, only the CQ/Na2CO3-NaHCO3 system was investigated under pressure.
B. Benadda et al, / Chemical Engineering and Processing 35 (1996) 247-253
250
Table 2 Physicochemical and kinetic parameters at atmospheric pressure System
Catalyst
C~ 10 -4 moI 1-~
DA10 -9 m 2 s -1
Kinetic constant
Ref.
O2/Na2SO a CO2/NazCO3-NaHCO3 OjCuCI
CoSO 4
1.38 265 2.52
1.6I 1.60 2.05
2746 s - I 1450 1 m o l - t s - i 21 520 Iz mo1-2 s -1
[2] [4] [2]
NaC10 None
4. Operating conditions, physicochemical and kinetic parameters Table 1 lists the various characteristics associated with the operating conditions used. The physicochemical parameters are identical with those quoted in Refs. [2] and [4]. The same references lists the kinetic constants of the reactions investigated which were investigated under atmospheric pressure using the same experimental conditions as in this work, the laboratory device used being the gas-lift bubble column. The values of these parameters are listed in Table 2. As suggested in Refs. [8] and [9], the diffusivity of CO2 in carbonate and bicarbonate solutions and the kinetic constant of reaction (c) were assumed to be independent of the pressure. In addition, the solubility of CO2 and the Henry's law constant He were corrected for pressure. The method used was that of Van Krevelen and Hoftijzer [9] as applied to electrolyte solutions which gives: log
=E
where the ionic strengths I~ of salt i and the contribution h,. of different species are considered to be independent of the pressure for a given temperature. The variation of Heo with pressure was taken from Ref. [10].
4.1. Analysis Small aliquots of the reacting solutions were sampled at different times from the feedback loop. Their molarities were then determined by titration (iodometric for 1 0 3 -" •
sulphite ions, potentiometric for carbonate ions). For the O2/Cu ~ system, [Cu~]= fit) was deduced by continuously following the redox potential. For more details regarding the analyses, the reader is referred to Ref. [2].
5. Results and discussion 5.i. At atmospheric pressure Fig. 2 shows the variations of a versus L, with G remaining constant, for the three gas/liquid systems studied. It should be noted that in all three cases the interracial area a increased with the liquid mass flowrate. However, the values for the system COJ NazCOg-NaHCO3 are 40% greater than the corresponding values for O2/NazSQ, although the latter are in good agreement with those of Onda et al. [11]. In addition, the values for the Oz/CuCl system are somewhat lower. The discrepancy in the results cannot be explained by values of the kinetic constants, as assumed by Badssi et al. [8], since they were all determined using the same experimental device and under the same operating conditions as used in this study. However, such differences may be explained when consideration is taken of the fact that the interracial area depends strongly on the ability of the gas/liquid system to generate foams [3]. Such foam formation was not observed during our experiments with the O,/CuC1 system. This aspect of the chemical method has led to many discussions in the literature; in fact some authors [12] have emphasized the chemical method as an experimental tool which allows the absolute value of a value to be 103-
021CuCl
• O2/Na2SO3 o CO2/Na2CO3 --
e~
[11] e~
o ------o
o
10::
102
I01 o
;
4
;
~
~o
L (kg m-2s-1) Fig. 2. Comparison of the values of a for three gas/liquid systems used (G=0.1 kg m - 2 s - l ) .
I0
0.05
0.1
0.15
0.20
0.25 G (kg m'2s"1)
Fig. 3. Variation of a with gas mass flowrate (L = 5.52 kg m - 2 s - ~).
B. Benadda et al. / Chemical Engineering and Processing 35 (I996) 247-253 IgLa (I0-2 s-l)
(10-2 s-i) I01
RL a
101
o This work --
251
[131
o
--
o
~
o ~
c
I0 °
10°
/
1(i1 2
4
I01
10 0
10 2 P (105 Pa)
L (kg m'2s ~I) Fig. 4. Variation of kLa with liquid mass flowrate (G = 0.1 kg m - 2 s - 1 , C O j N a z C Q _ N a H C O 3 system).
Fig. 6. Variation of kLa with total pressure ( L = 5.52 kg m - 2 s - I and G = 0 . 1 kg m - 2 s - ~ ) .
obtained independent of the nature of the reaction used. Fig. 3 depicts the variation of a versus the gas mass flowrate G for a liquid mass flowrate L -- 5.52 kg m -2 s - i. The chemical reaction studied in this case was the oxidation of sodium sulphite. It should be noted that the interfacial area is hardly affected by the gas mass flowrate G, in agreement with previous literature statements. A great deal of the results on this subject have been brough together by Laurent and Charpentier [12]. Values of the volumetric coefficient kLa, obtained by the Danckwerts method, are plotted versus liquid mass flowrates in Fig. 4. It should be noted that the variation is virtually the same as that by a correlation given by Mohunta et al. [13]. However, our own values, obtained with the CO2/Na2CO3-NaHCO 3 system, are somewhat greater.
/CLa also decreases over the same range of pressure and flow, in accord with the results of Larachi et al. [14]. These latter authors used a co-current gas/liquid trickle-bed reactor in their studies. We have chosen to compare our results with those of both latter works, because the experimental devices employed in these cases appear to be quite close to ours. With a constant gas mass flowrate G, an increase in pressure leads to a decrease in the superficial velocity of the gas via an increase in its specific gravity. But the superficial velocity of the gas has very little influence on the interfacial area under our experimental conditions, particularly below 10 x 10 .2 ms -1. This velocity was the maximal value studied by us under pressure conditions. When working up to 30 x 105 Pa, Larachi [15] came to the same conclusion, but without separating the roles of those factors influencing the pressure and the specific gravity. The influence of one or other may be explained by the decreased importance of fluid phases penetration under high pressure and by a change in the fluid distribution and flow regime. Flow under a film regime becomes more important than flow under a drop regime. We have based our determinations on the penetration theory and the Danckwerts method. As stated in
5.2. Influence of pressure For liquid and gas mass flowrates L--5.52 kg m -2 s -1 and G=0.1 kg m -2 s -1, respectively, Fig. 5 indicates that a decreases when the pressure is increased from 105 to 12 x 105 Pa, apparently in agreement with Badssi et al. [8] who worked with a laboratory column equipped with cross-flow sieve trays. Fig. 6 shows that
[
c~ V f - ~-'-~J ( [10-3 kmol.m-3min-1]2 )
103=
400
'E
t ? !!!!p~aaa [ 300 ] A 710~Pa [ 10 2.
200 I/'oZ,
I01 I0 °
.
.
.
.
.
.
.
.
j
101
.
.
.
.
.
.
.
limit of the method validity -- ---- ~ -- _ ..L_
f
-'-z'.V
- -
..........
.
102 P (105 Pa)
Fig. 5. Variation of a with total pressure (L = 5.52 kg m - 2 s - 1 and G=0.1 kgm -2s-1).
0
1
2
3
4
5
6 [NaCIO ] I0"zM
Fig. 7. Danckwerts lines for pressures of I x 105, 3 x l0 s, 5 x 105 and 7 x l0 s Pa.
B. Benadda et al. / Chemical Engineering and Processing 35 (1996) 247-253
252
4 PA
[ c~V!] ( 108 Pare3 s kmol"I)
[ c~VL'[2 ~ : • -12 -T"q-2~J([10"~kmol.m~rmn ] ) 300
~.
_-
280 260 240 220
6 • 12105Pol
•, ~
~
i
i
m
~
o
o
---27-
+ arm,pres. ]
5
3
it of the method validity
2 1
180 160 . . . . . . . . . . 0,0 0,1
0,2
. • . . , ......... 0,3 0,4
, ......... 0,5 0,6 0,7 -2 [NaCIO] 10 M
2
4
6
8
10 1
12 ( 10.3 s m'l)
4 k 2 + D A k 2 [ClO']
Fig. 8. Danckwerts lines for 10 x 10 s and 12 x 105 Pa,
Fig. 9. Verification of gas-phase resistance at 1 x l0 s and 12 x l0 s Pa,
the next section, we have verified the theoretical criteria necessary for their use at different pressure values. However, we must point out a limitation on the validity of the Danckwerts line when the pressure is increased, as shown in Figs. 7 and 8. This is probably due to a change in the reaction regime which occurs at a critical concentration of catalyst. This critical concentration decreases when the pressure is increased. Hence, the pressure interval over which the Danckwerts line may be applied become increasingly narrower. Only the linear parts of such Danckwerts curves have been taken into consideration in our discussions.
6.2. Chemical regime The condition for the intermediate chemical regime if given by Danckwerts [17] as 0.3 < H a < 3. For the limiting catalyst concentrations, we obtained 0.76 < Ha < 2.55.
6.3. Gas-phase resistance When the gas-side resistance is taken into account, the absorption flow (I~ may be expressed as: ~=
PA
1 He -~ga-~ ax/K[ + DAk2[CIO- ]
6. Verification of the utilization criteria for the Danckwerts method under pressure
Combining this relationship with Eq. (1) gives:
6.1. Pseudo-first-order criterion
PA
For the system CO2/Na2CO3-NaHCO3-NaC10, this criterion has been defined by Danckwerts and Sharma [16], and simplified by McNeill [7], as X<< Y, with X= #1 + kiDA/k 2 and Y= 1/(C* /[CO~- ] + 2CX /
[HCO- ]). Table 3 lists the results obtained for this relationship under different pressures and maximal catalyst concentrations. It is assumed that 9 << 35, according to McNeill [7] the pseudo-first order criterion is verified. Hence, from the results given Table 3, this criterion is also satisfied in this study. Table 3 Verificationof pseudo-first-order criterion at elevatedpressure P(105 Pa)
Maximal concentration of NaClO(mol 1-i)
X
Y
1 3 5 7 10 12
0.0625 0.0125 0.0125 0.063 0,003 0.0025
2.12 1.68 1.95 1.54 1.26 1.26
54 17.67 10.60 7.57 5.31 4.42
1
He
I -z--~=°:Vli=-~ga-~ax//c2+DAk~[ClO-] Thus, a straight line should be obtained when PAl[c~V1/zVo] is plotted versus 1/,/k [ +OAlq[ClO-], the intercept at the origin being 1/kga. Fig. 9 shows that this resistance is practically equal to zero both at atmospheric pressure and at 12 x 10s Pa for the range of catalyst concentration studied.
7. Conclusion
In conclusion, our study contributes to a knowledge of absorbers under pressure. It shows that the total pressure influences mass-transfer parameters such as a and kLa. Our results also confirm others quoted in the literature, which still remains very sparse on this topic. As far as the influence of the chemical system is concerned, this appears important in any extrapolation of the a values determined for one chemical system to another. Without a careful comparison of the physicochemical properties, such as the foam-formation abilities, of such systems, such extrapolation may be invalid.
B. Benadda et al. / Chemical Engineering and Processing 35 (1996) 247-253
Appendix A: Nomenclature
(p
a A B
References
C* DA G Ha
He Heo hi I,. kl
k~a kL
kLa L P PA
t Vo Vx z
interfacial area per volume unit, m - i gas solute (02 or CO2) reactive species dissolved in the liquid phase ( C O ~ - , SO 2- or Cu ~) molarity of A at equilibrium, kmol m -3 diffusivity of gas into the solution, m - : s -I specific mass flow per unit of cross-section for the gas phase, kg m -2 s -I Hatta number, Henry constant when salts are present in the solution, bar m 3 kmolHenry constant when salts are absent from the solution, bar m 3 kmol-1 salt coefficient, m 3 k m o l ionic strength, kmol m -3 kinetic constant (unit corresponding to the type of reaction) volumetric mass-transfer coefficient in the gas phase, kmol m -3 Pa -1 s -1 liquid-side mass-transfer coefficient, m svolumetric mass-transfer coefficient in the liquid phase, s- 1 specific mass flow per unit cross-section for the liquid phase, kg m -2 s -1 total pressure, Pa partial pressure, Pa time, s (min) packing volume, m 3 volume of reactant solution, m 3 stoichiometric coefficient slope of lines [B] = f(t), kmol m -3 min -1
253
specific absorption flow, kmol m -2 s -~ specific absorption flow per unit volume of liquid phase, kmol m -3 s -~
[I] M.H. Oyevaar and K.R. Westerterp, Chem. Eng. Process., 25 (1989) 85. [2] B. Benadda, ThOse, Universit6 Claude Bernard Lyon I, 1994. [3] B.M. Soulami, ThOse, Institut Polytechnique de Lorraine (Nancy), 1980. [4] B. Benadda, M. Prost, S. Ismaili, R. Bressat and M. Otterbein, Chem. Eng. Process., 33 (I994) 55. [5] A. Laurent, ThOse Doct ks-sciences, Institut National Polytechnique de Lorraine (Nancy), I975. [6] J. Andrieu and B. Claudel, Chem. Eng. Sci., 29 (I973) 1263. [7] K.M. McNeiI1, Can. J. Chem. Eng., 48 (1970) 252. [8] A. Badssi, R. Bugarel, C. Blanc, J.L. Peytavy and A. Laurent, Chem. Eng. Process., 23 (1988) 89. [9] D.W. Van Krevelen and P.J. Hoftijzer, NumOro spdcial du XXIOme Congr. Int. de Chimie Industrielle, Bruxelles, September 1948, p. 168. [I0] H. Stephen and T. Stephen, Solubilities of Inorganic and Organic Compounds, Part 1, Binary Systems, Pergamon Press, Oxford, VoI. 1, 1983. [11] K. Onda, H. Takeuchi and Y. Koyama, J. Chem. Eng. Jpn., i
(i968) 56. [12] A. Laurent and J.C. Charpentier, Chem. Eng. J. Lausanne 8, (1974) 85. [13] D.M. Mohunta, A.S. Vaidyanathan and G.S. Laddha, Indian J. Chem. Eng., 1I (I969) 73. [I4] F. Larachi, P.M. MovilIiat, A. Laurent et N. Midoux, Rdcents ProgrOs en GOnie des Proeddds, 3dine CongrOs Franfais de GOnie des ProcOdds, Compi6gne, 4-6 Septembre, I991, 5, 16, 141. [15] F. Larachi, ThOse, Institut Polytechnique de Lorraine (Nancy), 1991. [16] P.V. Danckwerts and M.M. Sharma, Chem. Eng. (NY), 202 (1966) 244. [17] P.V. Danckwerts, Gas-Liquid Reactions, McGraw-Hill, New York, I970. 270pp.