Mechanism of mass transfer from bubbles in dispersions

Chemical Engineering and Processing 44 (2005) 353–361

Mechanism of mass transfer from bubbles in dispersions Part I. Danckwerts’ plot method with sulphite solutions in the presence of viscosity and surface tension changing agents V. Linek∗ , T. Moucha, M. Kordaˇc Department of Chemical Engineering, Prague Institute of Chemical Technology, Technická 5, 166 28 Prague 6, Czech Republic Received 15 December 2003; accepted 14 May 2004 Available online 2 July 2004

Abstract The paper presents physical properties and kinetics data of sodium sulphite solution, pure or with additives that change surface tension and viscosity. Sokrat44 (copolymer of acrylonitrile and acrylic acid) and short-fiber carboxymethylcellulose (CMC) for the Newtonian and long-fiber CMC for the non-Newtonian viscosity enhancement and Ocenol (cis-9-octadecen-1-ol) or polyethylenglycol (PEG) 1000 for surface tension change were used. The kinetics data are presented under the form of dependencies of oxygen absorption rate (measured in stirred cell) on catalyst (Co2+ ) concentration, oxygen concentration in gas, pH and temperature of the solution. The method based on Danckwerts’ plot for the separate determination of mass transfer coefficient kL and gas–liquid interfacial area a in gas−liquid dispersions is described using the kinetics data. Problematic features of the method both at low cobalt catalyst concentrations (deceleration of the chemical oxidation of sulphite in presence of viscosity enhancing additives and non-zero concentration of oxygen in the liquid) and at high catalyst concentrations (shrinking of bubbles in dispersion due to high absorption rates) are taken into account. The method is used in Part II for the determination of kL in gas–liquid dispersions produced in mechanically agitated vessel and bubble column. © 2004 Elsevier B.V. All rights reserved. Keywords: Oxygen absorption; Mass transfer; Sulphite oxidation; Viscosity; Surface tension; Danckwerts’ plot

1. Introduction The mechanism of mass transfer from bubbles into turbulent liquid in gas–liquid dispersions remains uncertain. Various widely different, yet partially successful, approaches exist. They predict different, often contradictory, influence of operating conditions on mass transfer coefficient kL . The most apparent contradiction concerns an effect of turbulence intensity on the mass transfer coefficient: Calderbank’s theory [1] of “small” and “large” bubbles (with rigid and completely mobile surface, respectively) predicts a decrease and the “eddy” model by Lamont and Scott [2] an increase of kL with increasing turbulence intensity. Contradictory results on the mass transfer coefficient kL determined by various authors can be partially explained by ∗ Corresponding author. Tel.: +420 2 2435 3298; fax: +420 2 3333 7335. E-mail address: [email protected] (V. Linek).

0255-2701/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2004.05.010

errors in kL a values used in its evaluation from the relation kL = kL a/a. It was shown [3,4], that kL a values measured by dynamic methods based on the inlet gas exchange at high mixing intensities are underestimated due to an incorrect flow pattern of gas phase used in the model for kL a evaluation. It was demonstrated [3] from the data of different authors [5,6] that the reported decrease of kL with increasing power input dissipation in the liquid does not reflect real phenomena but is only the result of errors in the measuring methods of kL a at high mixing intensities. Motivation of this study is to make measurements of the parameter kL in dispersions with various liquids using a well verified measuring technique to minimize further misinterpretations of the results. Thus, the study is divided in two parts. The first one contains description, verification and all physicochemical data relative to the technique, and the second one defines the effect of the liquid properties on parameter kL together with its interpretation in terms of the literature models.

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V. Linek et al. / Chemical Engineering and Processing 44 (2005) 353–361

Danckwerts’ plot method [7] with catalytic oxidation of aqueous sodium sulphite solutions by dissolved oxygen is used for the separate determination of mass transfer coefficient and interfacial area. The main advantage of the sulphite system is the low solubility of oxygen. To avoid significant depletion of the gas phase (in the case of air absorption, i.e., diluted gas) and significant shrinking of bubbles in dispersion due to high absorption rate (in the case of pure oxygen absorption), the method requires application of low cobalt catalyst concentration. The drawback is that physical properties of the batch can hardly be changed as the additives usually used for this purpose inhibit the reaction. In their review article, Linek and Vacek [8] gave only the qualitative information only on the subject. According to our findings, in the presence of the additives it is not possible to extrapolate the kinetic data measured at high catalyst concentration, but it is also necessary to measure them at low catalyst concentrations. It was shown [9] that, in presence of CMC, the reaction is decelerated so that the oxygen concentration in the batch during the absorption is not zero (as in absence of CMC) and should be determined experimentally. If the oxygen “back-pressure” was not taken into account (as it was done, e.g., by Schmitz et al. [10]) the resulting kL a values would be considerably underestimated, as shown by Linek et al. [9]. The aim of Part I is to measure the kinetic data for the sulphite oxidation in the presence of suitable viscosity and surface tension changing additives. Data are presented in the form of dependencies of oxygen absorption rate (measured under negligible influence of hydrodynamic conditions prevailing in the liquid) on cobalt catalyst concentration, oxygen concentration in gas, pH and temperature of the solu-

tions. An example of Danckwerts’ plot method is shown for the separate determination of kL and a in gas–liquid dispersions using the kinetic data in that form.

2. Theory Data on oxygen absorption in sulphite solutions are usually interpreted on the basis of the film theory. From the theory, the following relation was derived for the oxygen absorption rate, N, accompanied by nth-order irreversible reaction
2 ∗ N=c Dkn (c∗ )n−1 (1) n+1 This equation holds provided the reaction is zero-order in sulphite and all oxygen entering the liquid phase reacts completely within the liquid film (or in other words, hydrodynamic conditions prevailing in the liquid have no influence on the absorption rate). By varying the sulphite concentration and the stirrer speed, one can check whether these conditions are fulfilled or not. N can be conveniently measured in a stirred cell where the necessary conditions can be achieved and the interfacial area is known. Reith [11] derived the following relation for the over-all specific oxygen absorption rate Φ accompanied by nth-order irreversible reaction when the effects of hydrodynamics and chemical reaction on the mass transfer coefficient are comparable
2 Φ = (c∗ − cbulk )a (2) Dkn (c∗ )n−1 + kL2 n+1

relative error of approximation [%]

8 B = 100 B = 200 B = 400 B = 1000 B = 10000

6

4

2

0

Experimental range -2 0,01

0,1

1

10

Ha [-] Fig. 1. The relative difference of absorption rates calculated from Eq. (2) for second-order reaction and obtained by exact numerical solution (of the stationary mass balance of oxygen in the liquid film) plotted as a function of Hatta number. Lines represent our results; the points are taken from Reith [11].

V. Linek et al. / Chemical Engineering and Processing 44 (2005) 353–361

355

The relation approximates the exact numerical solution of the stationary mass balance of oxygen in the liquid film where it undergoes nth-order reaction with sulphite ions. This is illustrated in Fig. 1, where the relative difference of the absorption rates calculated from Eq. (2) for the second-order reaction and those obtained by numerical integration are plotted as a function of Hatta number. The parameter B represents the ratio of the bulk volume of the liquid to the film volume, B = kL /(aD). In our experiments, the B value reached up to 10,000 and the Hatta number was in the range 0.13–4.9. Thus, the error of the approximation (2) was lower than 6%. The absorption rate N is measured in a stirred cell with known interfacial area and the over-all absorption rate Φ is measured in the dispersion where the interfacial area is not known. If the measurement of N and Φ are performed in the same sulphite solution (i.e., in solutions at the same temperature, pH and cobalt catalyst concentration) we can combine Eq. (1) with Eq. (2) and obtain

enhancement, copolymers of acrylonitrile and acrylic acid in the ratio 2:1 (“Sokrat44”, product of Chemické Závody Sokolov) and short-fiber CMC TS.5 (carboxymethylcellulose “Lovosa”, product of Lovochemie) were used. As a non-Newtonian viscosity enhancing agent, long-fiber CMC TS.20 was used. For surface tension change, the addition of Ocenol (cis-9-octadecen-1-ol) or PEG 1000 (molecular weight 1000) were used. The initial pH of the solution was adjusted by addition sulphuric acid. The gas used for absorption (oxygen or air), saturated with water vapour at the temperature of absorption at atmospheric pressure, was fed above the liquid surface. The oxygen absorption rate was calculated from the decrease of sulphite concentration during the experiment using a standard iodometric titration. Effect of such variables as stirring rate, partial pressure of oxygen in the gas phase, cobalt catalyst concentration, pH of the solution, temperature and additives concentration on the oxygen absorption rate were investigated. The ranges of experimental conditions are:

Y = a2 X + (kL a)2

cNa2 SO3 cNa2 SO3 + cNa2 SO4 cCoSO4 cSokrat44 cCMC cOcenol cPEG 1000 pH pb Gas Temperature Impeller speed

where 

(c∗ )n−1 X = N 2 2∗ n+1 (ck )

(3)



 Y=

Φ c2∗ − cbulk

2 (3a)

c2∗ and ck∗ are the oxygen concentration values at the interface in the measurement of Φ and N, respectively. Plot of Y against X enables the separate determination of kL and a. The relation (3) holds under the following assumptions: (i) perfectly mixed gas phase in the dispersion (i.e., concentration c2∗ is in equilibrium with the oxygen partial pressure in the gas leaving the dispersion), (ii) constant value of the interfacial area a (i.e., changes in a are not significant in the range of absorption rates used in the plot). The kinetic data are presented in the form of oxygen absorption rate N as it provides all the necessary information for the determination of the mass transfer characteristics by the chemical method. The data in this form are not burdened with errors in the solubility and diffusivity of oxygen in the absorption solutions as it happens with kn values.

3. Experimental The apparatus used was a standard flat interface stirred cylindrical vessel (inner diameter 0.117 m) equipped with four baffles and a turbine impeller (diameter 0.06 m). The impeller shape enabled changing the impeller speed without appreciable wave motion at the surface. The vessel made of titanium and coated inside with a thermosetting silicon varnish was placed in a thermostat. At the start of each experiment, the vessel was filled with half litre of 0.8 M sodium sulphite solution in distilled water with or without physical properties changing additives. Commercial sodium sulphite of analytical grade was used. For Newtonian viscosity

0.4–0.8 kmol/m3 0.8 kmol/m3 5 × 10−6 to 5 × 10−4 kmol/m3 3 vol.% 0.2 or 0.6 wt.% 3 ppm (by volume) 100 ppm (by mass) 7.8–8.6 99.3 ± 2 kPa Air or oxygen 20, 25, 30 ◦ C 50–300 rpm

For the present experiments it was observed that a sulphite conversion up to 50% (i.e., in the interval of sulphite concentration from 0.8 to 0.4 kmol/m3 ) and stirrer speeds between 100 and 300 rpm (the maximum value at which no appreciable wave motion at the surface was observed) have no influence on the absorption rate, thus justifying validity of Eq. (1). A membrane covered polarographic oxygen probe situated at the bottom of the cell was used to check the negligible oxygen bulk concentration in experiments. Hanging-ring LAUDA Tensionmeter TE 1 C/2 and rotational viscometer RheoStress 100 were used the laboratory measurements of surface tension and viscosity. The results for all liquid batches used are given in Table 1. Diffusivity of oxygen in sulphite solution D = 1.87 × 10−9 m2 /s was calculated from Nernst–Einstein equation ηD/T = const. with D in water at 20 ◦ C is 2.01 × 10−9 m2 /s. The same value was assumed to be valid for the polymeric additives used. It is a well-known rule for a broad class of water-soluble polymers, that the variation of the diffusivity with the polymer concentration is weak. Elgozali et al. [24] verified experimentally this rule for Sokrat44 solutions in water. As a catalyst, analytical grade CoSO4 ·7H2 O was used. It is not certain that the heptahydrate form is stable under atmospheric conditions. Therefore the cobalt concentration

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V. Linek et al. / Chemical Engineering and Processing 44 (2005) 353–361

Table 1 Physical properties of 0.8 M sodium sulphite solutions with viscosity and surface tension changing additives used in this work at 30 ◦ C Solution 0.8 kmol/m3 0.8 kmol/m3 0.8 kmol/m3 0.8 kmol/m3 0.8 kmol/m3 0.8 kmol/m3 a b

sodium sodium sodium sodium sodium sodium

sulphite sulphite sulphite sulphite sulphite sulphite

+ CMC TS.5 (0.2 wt.%) + CMC TS.20 (0.6 wt.%) + Sokrat44 (3 vol.%) + Ocenol (3 ppm by volume) + PEG 1000 (100 ppm by mass)

Density (kg/m3 )

Viscosity (mPa s)

Surface tension (mN/m)

Oxygen solubility 10−9 kmol/m3 Pa

1083 1093 1093 1093 1089 1083

1.11 1.53 3.41 3.14 1.11 1.11

73.0 73.1 66.6 73.2 38.6 65.5

6.01a 6.01a 6.01a 5.83b 6.01a 6.01a

Calculated from correlation given in Ref. [8]. Experimental value measured in sulphate instead of sulphite solution.

was determined by a chelatometric titration in a concentrated base solution.

4. Results

Sulphite solution with 0.2 wt.% CMC TS.5 −(−0.0365+0.0669 log cCoSO4 )

N = 1.792 × 10−5 cCoSO4

cCoSO4 ≤ 5 × 10−5

0.485 N = 8.504 × 10−5 cCoSO 4

cCoSO4 > 5 × 10−5

Sulphite solution with 0.6 wt.% CMC TS.20 −(2.168+0.3164 log cCoSO4 )

4.1. Effect of oxygen concentration, order of reaction The reaction order of oxygen n was determined from a slope of the linear relation between the partial pressure of oxygen in gas phase and the molar absorption flux in logarithmic scale. Two different oxygen partial pressures (air and pure oxygen) were used. From the results of these experiments, given in Table 2, it can be seen that the order of reaction equals 2 either in absence or presence of the viscosity-enhancing additive Sokrat44. This agrees well with results of other authors [11–16] and with our previous finding [17] that the reaction order is two when oxygen concentration at the interface c∗ is lower than 6.3 × 10−4 kmol/m3 . In our experiments c∗ did not exceed 5.64 × 10−4 kmol/m3 .

N = 2.107 × 10−10 cCoSO4

cCoSO4 ≤ 5 × 10−5

0.519 N = 1.13 × 10−4 cCoSO 4

cCoSO4 > 5 × 10−5

−(2.061+0.325 log cCoSO4 )

N = 1.068 × 10−9 cCoSO4

cCoSO4 ≤ 5 × 10−5

0.474 N = 8.3 × 10−5 cCoSO 4

cCoSO4 > 5 × 10−5

10-6

+

O.8M Na 2SO 3 + 3ppm Ocenol O.8M Na 2SO 3

Eq.(4)

+

Line

+

10-7

(4)

the same equation fits the data for sulphite solution with 3 ppm Ocenol or 100 ppm PEG 1000, see + symbols in Fig. 2. Table 2 Order of reaction n relative to oxygen in presence and absence of additives

No No No 3 vol.% Sokrat44 3 vol.% Sokrat44

cCoSO4 (kmol/m3 ) 10−5

4.2 × 5.24 × 8.39 × 5.24 × 4.76 ×

10−5 10−5 10−5 10−6

Temperature 30 ◦ C; pH 8.5; 0.8 M Na2 SO3 .

10-6

O.8M Na 2SO 3 +0.2% CMC

10-7 10-6

O.8M Na 2 SO 3 +0.6% CMC

Eq.(6) -7

10

10-6

O.8M Na 2 SO 3 +3%Sokrat44

Eq.(7)

Order of reaction n 1.95 2.00 1.94 2.04 2.02

Eq. (4) Eq. (5) Eq. (6) Eq. (7)

Eq.(5) N [kmol/m2 s]

0.506 N = 1.033 × 10−4 cCoSO 4

(7)

In pure sulphite solution, the generally accepted value of the exponent is 0.5, i.e., a linear relation between cobalt catalyst concentration and the rate constant kn ∼ (cCoSO4 ).

+

The oxygen absorption rate as a function of cobalt catalyst concentration for sulphite solutions at pH 8.5 in presence or absence of viscosity enhancing additive are presented in Fig. 2. The data are fitted by the following relations: Pure 0.8 M Na2 SO3 solution

(6)

Sulphite solution with 3 vol.% Sokrat44

4.2. Effect of cobalt catalyst concentration

Additive

(5)

-7

10

10-5

3

cCoSO4 [kmol/m ]

10-4

Fig. 2. Effect of cobalt catalyst concentration on pure oxygen absorption rate N at pH 8.5 and 30 ◦ C.

V. Linek et al. / Chemical Engineering and Processing 44 (2005) 353–361

4.3. Effect of pH An empirical description of the influence of pH on the absorption rate proposed by Linek and Tvrd´ık [20] is used N ≈ (pH − 7.9 + 0.04t)

(8)

The relation describes a linear dependency of the oxygen absorption rate on pH at constant values of temperature, cobalt catalyst concentration and partial pressure of oxygen. The dependencies for individual cobalt concentrations intersect at the same point. The authors applied the relation successfully within the interval of pH from 7.5 to 8.5. The final equations obtained by regression of our experimental data obtained at 30 ◦ C and at oxygen partial pressure of pO2 = pb − pH2 O = (0.993 − 0.04242)·× 105 Pa are the following: For pure 0.8 M Na2 SO3 and the solution with 3ppm Ocenol (mean deviation 4.3%) 0.496 N = 4.469 × 10−5 cCoSO (pH − 6.459) 4

14 12 10

+

0.8M Na2SO3 -5

0.8M Na 2SO 3 + 3ppm Ocenol

3

cCoSO [10 kmol/m ]; T=30˚C 4

9.92 4.96 1.98 Lines Eq.(9) 0.992 0.496

8 6 4 2 0

+ + + + + ++ ++ ++

0.8M Na 2 SO 3 + 0.2% CMC

12

c CoSO [10-5 kmol/m3 ]; T=30˚C 4

10

9.51 6.63 4.75 2.80 0.951 0.475

8 6 N.107 [kmol/m2s]

At higher catalyst concentrations cCoSO4 > 5 × 10−5 kmol/m3 , the additives have negligible effect on the oxygen absorption rate N compared to pure sulphite solution. Only the addition of 3 vol.% Sokrat44 slightly increases (by 10%) the oxygen absorption rate. For CMC solutions this finding is in agreement with all authors [12,14,18,19] who used higher catalyst concentrations than 10−4 kmol/m3 and CMC concentrations from 0.5 to 2%. At lower catalyst concentrations cCoSO4 < 5× 10−5 kmol/m3 , the oxygen absorption rates were significantly reduced in the presence of viscosity enhancing additives compared to pure sulphite solution. The reduction for Sokrat44 solution reaches approximately 70% at cCoSO4 = 5 × 10−6 kmol/m3 . The reduction of N in CMC solutions depends on CMC concentration. The results clearly show that the absorption rates obtained in the presence of viscosity changing additives at high catalyst concentrations should not be extrapolated to low catalyst concentrations using the simple relation N ∼ (cCoSO4 )0.5 , valid for pure Na2 SO3 solution.

357

4 2

Lines Eq.(10)

0 0.8M Na 2SO 3 + 0.6% CMC

14 12 10 8 6 4 2 0

c CoSO [10-5 kmol/m3 ]; T=30˚C 4 2.89 19.54 14.45 + 1.93 9.63 Lines Eq.(11) 6.74 4.82

+

0.8M Na2 SO3 + 3% Sokrat c CoSO [10-5 kmol/m3 ]; T=30˚C 4 9.54 0.953 6.65 0.674 4.77 0.477 * 1.88 Lines Eq.(12) 1.52

12 10 8 6 4 2 0

*

* 6,5

7,0

7,5

8,0

+

*

* 8,5

pH

Fig. 3. Effect of pH on pure oxygen absorption rates N.

For illustration, the experimental data are compared with the correlations in Fig. 3.

(9)

For sulphite solution with 0.2 wt.% CMC TS.5 (mean deviation 4.8%) −(−0.0365+0.0669 log cCoSO4 )

N = 1.792 × 10−5 cCoSO4

(pH − 6.507) cCoSO4 ≤ 5 × 10−5

0.485 (pH − 6.507) N = 8.504 × 10−5 cCoSO 4

cCoSO4 > 5 × 10−5

(10)

For sulphite solution with 0.6 wt.% CMC TS.20 (mean deviation 7.9%) −(2.138+0.313 log cCoSO4 )

N = 1.276 × 10−10 cCoSO4

(pH − 6.575) cCoSO4 ≤ 5 × 10−5

0.54 (pH − 6.575) N = 7.144 × 10−5 cCoSO 4

cCoSO4 > 5 × 10−5

(11)

For sulphite solution with 3 vol.% Sokrat44 (mean deviation 8.3%) −(1.91+0.301 log cCoSO4 )

N = 1.0999 × 10−9 cCoSO4

0.502 (pH − 7.019) N = 7.488 × 10−5 cCoSO 4

(pH − 7.019) cCoSO4 ≤ 5 × 10−5 cCoSO4 > 5 × 10−5

(12)

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V. Linek et al. / Chemical Engineering and Processing 44 (2005) 353–361

4.4. Effect of temperature

4.6. Comparison with measurements of other workers

The Arrhenius plot of oxygen absorption rate results in an activation energy E for the absorption process. The value of E was determined for pure 0.8 M sodium sulphite solution only, which enables us to compare our experimental data with those from literature ones measured at different temperatures. The value of E was obtained by fitting Eq. (9) combined with the Arrhenius plot to the experimental data in the form

Our data on N measured in pure 0.8 M sodium sulphite solution are compared with the data of other authors, who performed their experiments also in 0.8 M sodium sulphite but at different cobalt catalyst concentrations, temperatures, pH values and oxygen partial pressures summarised in Table 3. In Fig. 4, the oxygen absorption rates measured by the authors and those calculated from Eqs. (13) and (14) are compared. Whenever the authors did not give the oxygen absorption rates in their work, the values of N were calculated from Eq. (1) using diffusivities, solubility and second-order rate constants as presented by the authors in their work. In this way differences are eliminated in N values induced by different values of oxygen solubility and diffusion coefficient, used for the evaluation of the kinetic constant k2 by the authors. The data on N given by the authors agree well with the values calculated from our correlation (see Fig. 4). The mean deviation of the author’s data from the correlation equals 8.2%. Exceptions are the data of Márquez et al. [18] and Laurent et al. [13], which are higher by 44% than the calculated ones. The differences can be explained by the different amount of catalytic impurities present in chemicals and water used by the authors. This behaviour of the sulphite system is known [12,17].

0.496 N(T) = 4.469 × 10−5 cCoSO (pH − 6.459) 4    1 E 1 − ×exp − R T 30 + 273.15

(13)

The data were measured at 30, 25 and 20 ◦ C at cCoSO4 = 4.8 × 10−5 and at pH values 7.6, 7.9, 8.3 and 8.6. The activation energy resulted in E = 19,000 kJ/kmol independent of pH. This activation energy includes activation energies for solubility and molecular diffusivity of oxygen and for the second-order rate constant k2 . The differences between experimental values and those calculated from Eq. (13) are lower than 5%. 4.5. Final correlations of the oxygen absorption rate N The absorption rates of oxygen into 0.8 M sodium sulphite solutions with and without addition of viscosity enhancing agents (Sokrat44, CMC) or surface tension changing agents (Ocenol, PEG 1000) in the regime of the fast second-order reaction as a function of cobalt catalyst concentration and pH at 30 ◦ C and at oxygen partial pressure of pO2 = pb − pH2 O = (0.993 − 0.04242) × 105 Pa are given by Eqs. (9)–(12). To include the effect of partial pressure of oxygen in gas phase, the equations should be multiplied by the following correction factor FP , which follows from Eq. (1) with n = 2:  FP =

pO2 (0.993 − 0.04242) × 105

3/2 (14)

5. Application of the kinetic data for Danckwerts’ plot method in dispersions The experiments were performed in a fully baffled (four baffles, width 1/10 of the vessel diameter) cylindrical vessel of i.d. 0.19 m equipped with a Rushton turbine of 0.075 m in diameter located 0.08 m above the bottom. Gas (pure oxygen or air) was taken from pressure flask and fed right below the impeller. The bubble column was obtained by keeping zero rotational frequency of the agitator. Detailed description of the experimental conditions is given in Part II. Over-all specific absorption rate of oxygen in dispersion Φ was measured at various cobalt catalyst concentrations ranging from 5 × 10−6 to 2 × 10−5 kmol CoSO4 /m3 for

Table 3 Experimental conditions at which the authors performed their experiments in 0.8 M sodium sulphite solution Authors Onken and Schalk [14] Ogawa et al. [22] Poggemann et al. [16] M´arquez et al. [18] Laurent et al. [13] Wesselingh and van’t Hoog [12] Waal and Okeson [23] Reith [11] Linek and Mayrhoferova [17] Sathyamurthy et al. [15]

cCoSO4 (kmol/m3 ) 10−4

2.5 × 8.48 × 10−5 to 3.4 × 10−4 2.7 × 10−4 10−4 to 2 × 10−3 10−4 to 2 × 10−3 4 × 10−4 to 2 × 10−3 3 × 10−5 to 6.89 × 10−4 1.76 × 10−5 to 6.89 × 10−4 5 × 10−6 to 5 × 10−4 5 × 10−5 to 5 × 10−4

pH

t (◦ C)

Gas

7.8–8.6 7.8–8.6 8 8.5 8.5 8.5 8–8.5 8 7.9–8.6 7.5

25 25 20 20 20 30 20, 30 20, 30 20 30

Oxygen Air Air Air Air, oxygen Air, oxygen Oxygen Oxygen Oxygen Oxygen

V. Linek et al. / Chemical Engineering and Processing 44 (2005) 353–361

Linek and Mayrhoferova (1970) [17] +

+

Wesselingh and van't Hoog (1970) [12] x

Sathyamurthy el al.(1979) [15] 10-6

359

xx

Onken and Schalk (1978) [14] Ogawa el al.(1982) [22]

xx

Reith (1968) [11] Nauthor [kmol/m2s]

x

+44%

x

x x + +

+

x

+

10-7

Márquez el al.(1994) [18] +

Laurent et al.(1974) [13] x

Waal and Okeson (1966) [23] Poggemann et al.(1983) [16]

10-7

10-6 2

Ncal [kmol/m s]

Fig. 4. Comparison of oxygen absorption rates in 0.8 M sodium sulphite solution calculated from Eqs. (13) and (14) with literature data (for the experimental conditions see Table 3).

Absorption rate of oxygen N was calculated from relations (9) to (14) for the same conditions under which the over-all absorption rate of oxygen in dispersion Φ had been measured. Concentrations of oxygen ck∗ , c2∗ and cbulk have been calculated from oxygen solubility (Table 1) and pertinent oxygen partial pressures. pO2 = pb − pH2 O (30 ◦ C) = (0.993 − 0.04242) × 105 Pa used for calculation of ck∗ and c2∗ for pure oxygen and for air absorption was evaluated from over-all and oxygen balances in dispersion Q1 Q2 pb = (pb − pH2 O ) +Φ RT RT (16) Q1 Q2 0.21pb = pO2 +Φ RT RT cbulk was calculated from equilibrium partial pressure of oxygen measured by a membrane covered polarographic oxygen probe. The maximum value of the dimensionless oxygen bulk concentration cbulk /c2∗ reached 0.07. Danckwerts’ plot method requires negligible change of interfacial area a in the range of absorption rates used in the

plots for individual operational conditions. The decrease of a in the dispersion due to bubble shrinking relative to the interfacial area a0 at negligible absorption rate can be estimated from the relation given by Linek and Mayrhoferová [21]:

1,0 agitator frequency, RPM =

1130

0,8 860

Y/k, s -2

individual operational conditions (type of solution, agitator frequency, gas flow rate). The over-all oxygen absorption rate was calculated from the decrease of sulphite concentration during the experiment using a standard iodometric titration. The Danckwerts’ coordinates X and Y were calculated from Eq. (3a), from which for n = 2 it follows that 2  ∗ Φ 2 c2 X=N ∗ 3 Y= (15) c2∗ − cbulk (ck )

k = 0.75

0,6

600 0.25 0,4

330

0.04

0

0.0025

0,2

0.0004 0,0

0

5,0x10-7

10-6

X,

1,5x10-6

m2 s -2

Fig. 5. Danckwerts’ plot of the data measured by pure oxygen absorption in 0.8 M sodium sulphite solution with 0.2 wt.% CMC TS.5 in mechanically agitated vessel and bubble column for superficial gas velocity 4 mm/s. (Parameter k is dimensionless scale factor to condense all the plots into one scale.)

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V. Linek et al. / Chemical Engineering and Processing 44 (2005) 353–361

a 1 − Q2 /Q1 = 0.2 a0 1 − (Q2 /Q1 )0.2

(17)

Q1 and Q2 are the volumetric gas flow rates on the inlet and outlet of the dispersion, respectively. The change of a in individual plots calculated from (17) did not exceed 5% Fig. 5 shows Danckwerts’ plot with the data measured by pure oxygen absorption in sulphite solution with 0.2 wt.% CMC TS.5, i.e., just in the situation when the viscosity-enhancing additive significantly reduces the sulphite oxidation kinetics. From the slope and the intercept of individual lines, a and kL a were calculated. The results obtained for all operational conditions are presented in Part II. Probable errors of a and kL a were practically the same and matched ±6%.

6. Conclusion The viscosity affecting additives polymeric acrylate and carboxymethylcellulose significantly but reproducibly decelerate the reaction in the region of cobalt catalyst concentration lower than 5 × 10−5 kmol/m3 . Addition of 3 ppm of Ocenol or of 100 ppm of PEG 1000 into sodium sulphite solution for lowering its surface tension did not change the reaction rate. The Danckwerts’ plot method was successfully applied using sufficiently low cobalt catalyst concentrations to keep negligible change of interfacial area due to changes in absorption rate. Non-zero oxygen concentration in liquid bulk due to deceleration of the chemical oxidation of sulphite in the presence of viscosity enhancing additives was taken into account.

Acknowledgements The authors gratefully acknowledge financial support provided by the Grant Agency of the Czech Republic through the Grant No. 104/98/1126 and by Czech Ministry of Education through the Project No. 223400007.

Appendix A. Nomenclature a a0 B cA cbulk ck∗ c∗ c2∗ D

interfacial area per unit of liquid volume (m−1 ) interfacial area per unit of liquid volume at negligible absorption rate (m−1 ) = kL /(aD) concentration of A (kmol/m3 ) oxygen concentration in liquid bulk (kmol/m3 ) oxygen concentration at the interface in the rate N measurement (kmol/m3 ) oxygen concentration at interface (kmol/m3 ) oxygen concentration at the interface in the over-all absorption rate Φ measurement (kmol/m3 ) oxygen diffusivity (m2 /s)

E FP Ha kn kL n N pb pO2 P Q1 , Q 2 R t T X Y

activation energy (kJ/kmol) oxygen partial pressure correction factor 

2 Dkn (c∗ )n−1 /kL2 Hatta number = n+1 nth-order rate constant (kmol1−n /s m3(1−n) ) physical mass transfer coefficient (m/s) reaction order with respect to oxygen oxygen absorption rate measured in stirred cell (kmol/m2 s) barometric pressure (Pa) partial pressure of oxygen (Pa) total power dissipated per unit of liquid volume (W/m3 ) volumetric gas flow rates on the inlet and outlet of the dispersion (m3 /s) universal gas constant (kJ/kmol K) temperature (◦ C) temperature (K) defined in Eq. (3a) (m2 /s2 ) defined in Eq. (3a) (s−2 )

Greek letter Φ over-all specific oxygen absorption rate measured in gas–liquid dispersion (kmol/m3 s)

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