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An absorption peak in the oxidation of sodium sulphite in aqueous solutions
PergamonPress. Printed in Great Britain
Chemical Engineering Science, 1975, Vol. 30, pp. 155457.
An absorption peak in the oxidation of sodium sulphite in aqueous solutions (Received 30April 1973; accepted 16 July 1974)
While investigating the absorption of oxygen into copper(B) ion-catalysed sodium sulphite solutions in a stirred transfer cell the absorption rate was found to pass through a sharp maximum some time after the start of each experiment (Fig. 1). This finding helps to explain why the copper-catalysed reaction rate can be unreproducible (as has been mentioned in the review of the oxygen-sulphite reaction by Danckwertsll, section 10-q). The results of the present investigation also indicate suitable conditions for determining physical mass transfer coefficients.
concentrations,
Cu”
r
kmol/m3
-
10-3
---
10-4
---
10-6
-x-
0
Stirrer
speeds,
-
7.78
-x-
4.45
The sodium sulphite concentrations used were from 0.05 to 0.5 kmol/m’ and copper(B) ion concentrations were between 10m6 and 1O-3 kmol/m3. Some investigations were also made with cobalt(E) ion catalyst. The stirred transfer cell was similar to that used by Davies et al.[2], except that the liquid volume was 0.250 dm”. The liquid was agitated by contra-rotating flat-blade stirrers; a baffle in the plane of the gas-liquid interface around the stirrer shafts prevented vortex formation. The agitator speeds were low enough for the interface not to be disrupted, and so the absorption rate per unit area could be determined. The gas phase was oxygen, supplied from a cylinder through a heating coil and a water saturator in a thermostat, and its absorption rate in the gas-tight system was determined at frequent intervals by a soap-film meter. The transfer cell and soap-film meter were maintained at 25°C by circulating water from the thermostat through jackets around them. Analar quality sodium sulphite, copper(D) sulphate and cobalt(D) sulphate were used, and the solutions were made with distilled water. With cobalt catalyst the pH was adjusted to 8 by addition of sulphuric acid and sodium hydroxide. The catalyst solution was added immediately before the start of a run. Figure l(a) shows the variation in absorption rates with time for the uptake of oxygen into 0.25 kmol/m’ sodium sulphite solutions using different copper(E) sufphate concentrations, with the same stirrer speeds. With copper(D) sulphate concentrations of lo-’ and lo-’ kmol/m’ there was a sharp rise to a maximum absorption rate about three times the early rate, followed by a decrease to either a lower rate or a second, more gentle, rise and fall in rate. Even when no catalyst was added there was still a significant rise in the absorption rate, although the maximum peak was very much less marked. In Fig. I(b) absorption rate vs time plots are shown for the conditions often used when simulating oxygen uptake into fermentation media, 0.25 kmol/m’ sodium sulphite and IO-’ kmol/m” copper(B) sulphate concentrations, for three stirrer speeds. At each speed the same effect is noticed; however the magnitude of the maximum absorption peak appears to be affected by the stirrer speed. When cobalt(B) ion catalyst was used a rise in the absorption rate after a period of time was still noticed [Fig. l(c)] but the maximum absorption peak was much less pronounced, and the oxygen absorption rate was almost constant after the rise had occurred. To investigate whether the stainless steel of the stirrer unit used had a catalytic effect, similar oxygen absorption determinations were made in a conical flask agitated by a magnetic stirrer with a plastic-coated stirrer and a four-bladed vertical glass baffle suspended just below the liquid surface, to prevent vortexing. Similar peaks in the absorption rates were observed, showing that they were not due to catalysis by the metal. The maximum absorption peaks may be associated with the induction effects known to exist in the system. These have been described by Barron et al. [3,4] and include initial reduction of the copper ion followed by its oxidation when oxygen is dissolved, possible
set-1:
---5.55
I
I
2rr I
0
I
I
I
100
200
300
Time,
min.
Fig. 1. Variation of oxygen absorption rates with time. Sodium sulphite concentrations: (a) and (b) 0.25 kmol/m’, (c) 0.8 kmol/m’. In (a) the stirrer speed is 5.55 se?, in (b) the copper (II) concentration is lo-‘kmohm’, and in (c) the stirrer speed is 7.78 set-‘. The absorption rates were determined at short intervals (1 to 3 min, early in the run) so individual points are not shown on thecurves. 155
Shorter
156
Communications
precipitation of copper oxide and hydroxide, and a chain oxidation reaction of the sulphite. A more quantitative explanation would require knowledge of the kinetics of these processes. Although no kinetic model can be proposed for the induction period, the determination of the rate-controlling process after the maximum absorption peak had passed (both maxima, if there were two) was more successful. In some experiments the stirring speed was changed (after the maximum absorption peaks had occurred), and this was found to produce negligible alteration in the oxygen absorption rate when compared with the effect of similar speed changes on a physical absorption process (dissolving carbon dioxide in water[5]). This suggests chemical reaction as the rate-controlling process; Phillips and Johnson[h] also found little effect of agitator speed on absorption rate in similar studies. The reaction model tested was a generalised bimolecular reaction[l, p. 49; 7, p. 721 I = kB “C”, which gives
[
R = ~B,,“(C*)‘“+”
100 -
IO
(I)
0.5 1
I 0.05
I 0.3
I 0.1
Sulphite
concentration.
-J
kmol/m3
(2)
Here B is effectively constant and equal to Ba, because it is much greater than C. Also C, = 0, because the reaction is rapid enough to remove all oxygen in the bulk of the liquid[7, pages 17-191. In the calculation of R from the measured oxygen absorption rates over short time intervals allowance was made for the vapour pressure of the liquid. Strictly, the measured rate should also be corrected for the desorption of nitrogen[8], but calculations based on the initial solutions being saturated with nitrogen from the air showed that after the maximum peaks the desorption rate would not exceed 3 per cent of the absorption rate. The sulphite concentration in the bulk of the solution at any time was calculated by subtracting from the initial concentration the amount which had reacted with oxygen up to that time, obtained by graphical integration of the plot of the absorption rate against time and the stoichiometry of the reaction. The diffusivity of oxygen in sodium sulphite solutions was estimated from the diffusivity of nitrogen in similar solutions, which was measured in this work. Gubbins et al. [9] and Sada et al. [IO] have for gases in aqueous salt solutions shown that Dso~-/Dw,, depends on the nature of the salt and its concentration, but not on the gas. The diffusivities of nitrogen in water and solutions of sodium sulphite and sodium sulphate were determined with a wetted-sphere column; from these values and the diffusivity of oxygen in water at 25°C of 2.4~ 10~9m2/sec[ll] the estimated diffusivities of oxygen in sodium sulphite solutions at 25°C were 2.33 x 10m9m’/sec in 0.1 kmol/m’, I.90 X 10m9m’/sec in 0.5 kmol/m’, and I.62 X IO-’ m2/sec in 0.8 kmolim’. For oxygen in sodium sulphate solutions at 25°C the values were 2.37~ 10e9 m2/sec in 0.1 kmol/m’, 2.11 X 10m9m*/sec in 0.5 kmolim’, and I.89 X 10e9 m’/sec in 0.8 kmol/m’. For the mixtures of sulphite and sulphate which are formed during a run a linear relationship was assumed between diffusivity and ratio of sulphite to sulphate. Figure 2 is a plot of R/D’ 5 against B, on log-log coordinates, for the same initial sulphite concentration, so that C* is constant. Values for two of the stirring speeds used are plotted, which show the slight effect of speed (the rate of physical absorption at 7.78 set-’ is more than twice that at 4.45 see-‘[5]). From the line of best fit through the points m = I.5 (this agrees with the value found by Barron and O’Hern[3] in a homogeneous reaction system), and [2k(C*)‘“+“/(n + I)]“’ = 2.43 x 10e2 (kmol/m’)“25 set-“‘. In the present work C* was not varied sufficiently to determine n, but Phillips and Johnson[6] found n = 2 from an
Fig. 2. Variation of RID”’ with sulphite concentration for an initial sulphite concentration of 0.5 kmol/m’. Stirring speeds: 0, 4.45 set-‘; l,7.78 see-‘. investigation with different oxygen partial pressures. For this value of n, k = I.6 x IO6m”’ kmol-’ ’ set-‘. When cobalt catalyst was used the absorption rate was independent of both stirring speed and sulphite concentration after the initial rise in rate [Fig. l(c)]. Hence m = 0, as has been found in other investigations with cobalt catalyst[l2-141, but the variation in C* in the present work was not sufficient to determine n. Because the oxygen absorption rates were independent of stirring speed and could be related to reaction kinetic models, both the copper- and cobalt-catalysed reactions were in the ‘fast reaction regime’ under the conditions in the stirred transfer cell. But the physical mass transfer coefficient, kr, is low in transfer cells (in the range 0.4 to 4 x IO-’ m/set) and in situations where k, is higher the absorption process can be in the ‘slow reaction diffusional regime’. An approximate estimate of the value of k, above which this applies may be obtained from the condition[7, p. 161 kL = k=
(3)
(i.e. the rate of physical absorption, with negligible oxygen concentration in the bulk of the liquid, is equal to the rate of chemical absorption). Values of C* were found from the solubilities of oxygen in sodium sulphite solutions estimated by Linek and Mayrhoferova[l4]. For the copper-catalysed reaction, with a copper(H) sulphate concentration of IO-’ kmol/m’, the values of k, are 1.6~ IO-’ m/set for 0.05 kmol/m’ sodium sulphite, 5.4 X lO-4 m/set for 0.25 kmol/m’, and 7.6 x IO-‘m/set for 0.5 kmol/m’. From the reaction rate constant for the copper-catalysed reaction given by de Waal and Okeson[lZ] for Eq. (I) with m = 0 and n = 1, the value of k, would be 3.7 x 10m4m/set at 3O”C, which is in the same range as found here. However the rate constant of 9800 see-’ found by Westerterp et al. [15] predicts k, of 47 x 10e4 m/set, but the validity of this value has been questioned[l2,13]. With a cobalt catalyst concentration of 10-6kmol/m3 the value of k, is 3.6~ IO-‘m/set for 0.8 kmol/m’; extrapolation of the rate constants given by Reith[l3] gives I.2 x 10m4mlsec. In agitated vessels k, values in the range l-6 x 10S4m/set have been found[l6], so in equipment where gas is dispersed into the
ShorterCommunications liquid the absorption process may be in the ‘slow reaction diffusional regime’. Phillips and Johnson[6] and Linek[l7] found this was the case for a vigorously agitated vessel with copper(B) ion catalyst. A similar study was made as part of this work, using a conical filter flask as the absorption vessel, agitated by a magnetic stirrer in such a way that the gas was dispersed through the liquid. Absorption rates were measured in solutions with a copper(H) sulphate concentration IO-”kmol/m3 and sodium sulphite concentrations from 0.05 to 0.25 kmol/m’ at oxygen pressures from 0.16 X IOJ to I.01 x 10JN/m2. At atmospheric pressure the absorption rates were measured by a soap-film meter, while at lower pressures liquid samples were withdrawn from the vessel and the sulphite concentrations determined by analysis[18]. In this equipment maximum absorption peaks were not noticed; they may have occurred too early in the runs to be detected. In contrast to the transfer-cell experiments, the absorption rates were found to be independent of sodium sulphite concentration, and directly proportional to the oxygen pressure (and hence C*). These findings confirm that the rate-controlling process now is in the slow reaction diffusional regime. The condition in this regime for the oxygen concentration in the bulk of the liquid to be negligible compared with C*, and so for the rate of oxygen absorption to be k,aC*, is, from[l, p. 1681, k,aC* = kBO”‘C2.
(4)
For a sodium sulphite concentration of 0.25kmol/m3 and a copper(H) concentration of IO-’ kmol/m’ C is less than 5 per cent of C* for kLa less than 0.49 set-‘; however Eq. (4) is based on the assumption that the rate expression for the heterogeneous reaction applies in the bulk of the liquid and Barron er al. [3,4] have suggested that this could be incorrect. When the rate of oxygen absorption is k,a C* the reaction can be used to determine kra.
CONCLUSIONS
occurrence of maximum absorption peaks in equipment with low mass-transfer coefficients and the erratic absorption rates before the peaks provide some explanation of the unreliability of the copper-catalysed reaction mentioned in the literature. This type of behaviour could occur in any single-pass system with low gas-liquid contact times, so the copper(H) ion-catalysed reaction is unsuitable for the determination of k, or a in such systems. However in highly turbulent gas-liquid systems (k, greater than 3 to 5 x 10e4m/set for sodium sulphite concentrations not greater than 0.25 kmol/m3)the induction period is short and, after it, the copper(B) ion-catalysed reaction is in the ‘slow reaction diffusional regime’, so the rate of oxygen mass transfer can be used to determine kLa, if the values are less than 0.5 set-‘. However, in electrolyte solutions bubble coalescence is reduced and the bubble size is less than in water, so k,a values determined in this way willnot apply for other liquids. The
tPresent address; Hydronyl Ltd., King Street, Fenton, Stokeon-Trent.
157
Department of Chemical Engineering S. H. GREENHALGHt University of Birmingham W. J. McMANAMEY Birmingham B 15 2 TT K. E. PORTER? England NOTATION
interface area per unit volume, m-’ sulphite ion concentration, kmol/m” oxygen concentration in solution, kmol/m3 interface value of C (in equilibrium with gas phase), kmol/m’ diffusivity of oxygen in solution, m*/sec reaction rate constant physical mass transfer coefficient, m/set exponents reaction rate per unit volume, kmol/m’ set rate of chemical absorption per unit area, kmol/m’ set Subscript o concentration in bulk of liquid REFERENCES
[I] Danckwerts P. V., Gas-Liquid Reactions, McGraw-Hill, New York, 1970. [2] Davies J. T., Kilner A. A. and Ratcliff G. A., Chem. Engng Sci. 196419 583. [3] Barron C. H. and O’Hern H. A., Chem. Engng Sci. 196621 397. 141Chen T. I. and Barron C. H., Ind. Engng Chem. Fund. 1972 11 466. 151Woollen J. M., Ph. D. Thesis, University of Birmingham, 1968. 161Phillips D. H. and Johnson M. J., Ind. Engng Chem. 195951 83. [71 Astarita G., Mass Transfer with Chemical Reaction, Elsevier, Amsterdam, 1967. [8] Linek V., Chem. Engng Sci. 197126 491. 191Gubbins K. E., Bhatia K. K. and Walker R. D., A.1.Ch.E. J. 196612 548. [IO] Sada E., Ando N. and Kito S., .I. annI. . . Chem. Biotechnol. 197222 1185. [III Davidson J. F. and Cullen E. J., Trans. Inst. Chem. Engr, 195735 51. 1121De Waal K. J. A. and Okeson J. C., Chem. Engng Sci. 196621 559. r131Reith T., Physical Aspects of Bubble Dispersions in Liquids, Thesis, Delft Technical University; Delftsche Uitgevers Maatschappij N. V., 1968. [I41Linek V. and Mayrhoferova J., Chem. Engng Sci. 197025 787. [I51Westerterp K. R., Van Dierendonck L. L. and De Kraa J. A., Chem. Engng Sci. I%3 I8 157. [16] Calderbank P. H., Biochemical and Biological Engineering Science, (Ed. Blakebrough N.) Vol. 1, Academic Press, London, 1967. [17] Linek V., Chem. Engng Sci. 1%6 21 777. [I81 Elsworth R., Williams V. and Harris-Smith R., .I. appl. Chem. 19577 261.
Chemical Engineering Science, 1975, Vol. 30, pp. 155457.
An absorption peak in the oxidation of sodium sulphite in aqueous solutions (Received 30April 1973; accepted 16 July 1974)
While investigating the absorption of oxygen into copper(B) ion-catalysed sodium sulphite solutions in a stirred transfer cell the absorption rate was found to pass through a sharp maximum some time after the start of each experiment (Fig. 1). This finding helps to explain why the copper-catalysed reaction rate can be unreproducible (as has been mentioned in the review of the oxygen-sulphite reaction by Danckwertsll, section 10-q). The results of the present investigation also indicate suitable conditions for determining physical mass transfer coefficients.
concentrations,
Cu”
r
kmol/m3
-
10-3
---
10-4
---
10-6
-x-
0
Stirrer
speeds,
-
7.78
-x-
4.45
The sodium sulphite concentrations used were from 0.05 to 0.5 kmol/m’ and copper(B) ion concentrations were between 10m6 and 1O-3 kmol/m3. Some investigations were also made with cobalt(E) ion catalyst. The stirred transfer cell was similar to that used by Davies et al.[2], except that the liquid volume was 0.250 dm”. The liquid was agitated by contra-rotating flat-blade stirrers; a baffle in the plane of the gas-liquid interface around the stirrer shafts prevented vortex formation. The agitator speeds were low enough for the interface not to be disrupted, and so the absorption rate per unit area could be determined. The gas phase was oxygen, supplied from a cylinder through a heating coil and a water saturator in a thermostat, and its absorption rate in the gas-tight system was determined at frequent intervals by a soap-film meter. The transfer cell and soap-film meter were maintained at 25°C by circulating water from the thermostat through jackets around them. Analar quality sodium sulphite, copper(D) sulphate and cobalt(D) sulphate were used, and the solutions were made with distilled water. With cobalt catalyst the pH was adjusted to 8 by addition of sulphuric acid and sodium hydroxide. The catalyst solution was added immediately before the start of a run. Figure l(a) shows the variation in absorption rates with time for the uptake of oxygen into 0.25 kmol/m’ sodium sulphite solutions using different copper(E) sufphate concentrations, with the same stirrer speeds. With copper(D) sulphate concentrations of lo-’ and lo-’ kmol/m’ there was a sharp rise to a maximum absorption rate about three times the early rate, followed by a decrease to either a lower rate or a second, more gentle, rise and fall in rate. Even when no catalyst was added there was still a significant rise in the absorption rate, although the maximum peak was very much less marked. In Fig. I(b) absorption rate vs time plots are shown for the conditions often used when simulating oxygen uptake into fermentation media, 0.25 kmol/m’ sodium sulphite and IO-’ kmol/m” copper(B) sulphate concentrations, for three stirrer speeds. At each speed the same effect is noticed; however the magnitude of the maximum absorption peak appears to be affected by the stirrer speed. When cobalt(B) ion catalyst was used a rise in the absorption rate after a period of time was still noticed [Fig. l(c)] but the maximum absorption peak was much less pronounced, and the oxygen absorption rate was almost constant after the rise had occurred. To investigate whether the stainless steel of the stirrer unit used had a catalytic effect, similar oxygen absorption determinations were made in a conical flask agitated by a magnetic stirrer with a plastic-coated stirrer and a four-bladed vertical glass baffle suspended just below the liquid surface, to prevent vortexing. Similar peaks in the absorption rates were observed, showing that they were not due to catalysis by the metal. The maximum absorption peaks may be associated with the induction effects known to exist in the system. These have been described by Barron et al. [3,4] and include initial reduction of the copper ion followed by its oxidation when oxygen is dissolved, possible
set-1:
---5.55
I
I
2rr I
0
I
I
I
100
200
300
Time,
min.
Fig. 1. Variation of oxygen absorption rates with time. Sodium sulphite concentrations: (a) and (b) 0.25 kmol/m’, (c) 0.8 kmol/m’. In (a) the stirrer speed is 5.55 se?, in (b) the copper (II) concentration is lo-‘kmohm’, and in (c) the stirrer speed is 7.78 set-‘. The absorption rates were determined at short intervals (1 to 3 min, early in the run) so individual points are not shown on thecurves. 155
Shorter
156
Communications
precipitation of copper oxide and hydroxide, and a chain oxidation reaction of the sulphite. A more quantitative explanation would require knowledge of the kinetics of these processes. Although no kinetic model can be proposed for the induction period, the determination of the rate-controlling process after the maximum absorption peak had passed (both maxima, if there were two) was more successful. In some experiments the stirring speed was changed (after the maximum absorption peaks had occurred), and this was found to produce negligible alteration in the oxygen absorption rate when compared with the effect of similar speed changes on a physical absorption process (dissolving carbon dioxide in water[5]). This suggests chemical reaction as the rate-controlling process; Phillips and Johnson[h] also found little effect of agitator speed on absorption rate in similar studies. The reaction model tested was a generalised bimolecular reaction[l, p. 49; 7, p. 721 I = kB “C”, which gives
[
R = ~B,,“(C*)‘“+”
100 -
IO
(I)
0.5 1
I 0.05
I 0.3
I 0.1
Sulphite
concentration.
-J
kmol/m3
(2)
Here B is effectively constant and equal to Ba, because it is much greater than C. Also C, = 0, because the reaction is rapid enough to remove all oxygen in the bulk of the liquid[7, pages 17-191. In the calculation of R from the measured oxygen absorption rates over short time intervals allowance was made for the vapour pressure of the liquid. Strictly, the measured rate should also be corrected for the desorption of nitrogen[8], but calculations based on the initial solutions being saturated with nitrogen from the air showed that after the maximum peaks the desorption rate would not exceed 3 per cent of the absorption rate. The sulphite concentration in the bulk of the solution at any time was calculated by subtracting from the initial concentration the amount which had reacted with oxygen up to that time, obtained by graphical integration of the plot of the absorption rate against time and the stoichiometry of the reaction. The diffusivity of oxygen in sodium sulphite solutions was estimated from the diffusivity of nitrogen in similar solutions, which was measured in this work. Gubbins et al. [9] and Sada et al. [IO] have for gases in aqueous salt solutions shown that Dso~-/Dw,, depends on the nature of the salt and its concentration, but not on the gas. The diffusivities of nitrogen in water and solutions of sodium sulphite and sodium sulphate were determined with a wetted-sphere column; from these values and the diffusivity of oxygen in water at 25°C of 2.4~ 10~9m2/sec[ll] the estimated diffusivities of oxygen in sodium sulphite solutions at 25°C were 2.33 x 10m9m’/sec in 0.1 kmol/m’, I.90 X 10m9m’/sec in 0.5 kmol/m’, and I.62 X IO-’ m2/sec in 0.8 kmolim’. For oxygen in sodium sulphate solutions at 25°C the values were 2.37~ 10e9 m2/sec in 0.1 kmol/m’, 2.11 X 10m9m*/sec in 0.5 kmolim’, and I.89 X 10e9 m’/sec in 0.8 kmol/m’. For the mixtures of sulphite and sulphate which are formed during a run a linear relationship was assumed between diffusivity and ratio of sulphite to sulphate. Figure 2 is a plot of R/D’ 5 against B, on log-log coordinates, for the same initial sulphite concentration, so that C* is constant. Values for two of the stirring speeds used are plotted, which show the slight effect of speed (the rate of physical absorption at 7.78 set-’ is more than twice that at 4.45 see-‘[5]). From the line of best fit through the points m = I.5 (this agrees with the value found by Barron and O’Hern[3] in a homogeneous reaction system), and [2k(C*)‘“+“/(n + I)]“’ = 2.43 x 10e2 (kmol/m’)“25 set-“‘. In the present work C* was not varied sufficiently to determine n, but Phillips and Johnson[6] found n = 2 from an
Fig. 2. Variation of RID”’ with sulphite concentration for an initial sulphite concentration of 0.5 kmol/m’. Stirring speeds: 0, 4.45 set-‘; l,7.78 see-‘. investigation with different oxygen partial pressures. For this value of n, k = I.6 x IO6m”’ kmol-’ ’ set-‘. When cobalt catalyst was used the absorption rate was independent of both stirring speed and sulphite concentration after the initial rise in rate [Fig. l(c)]. Hence m = 0, as has been found in other investigations with cobalt catalyst[l2-141, but the variation in C* in the present work was not sufficient to determine n. Because the oxygen absorption rates were independent of stirring speed and could be related to reaction kinetic models, both the copper- and cobalt-catalysed reactions were in the ‘fast reaction regime’ under the conditions in the stirred transfer cell. But the physical mass transfer coefficient, kr, is low in transfer cells (in the range 0.4 to 4 x IO-’ m/set) and in situations where k, is higher the absorption process can be in the ‘slow reaction diffusional regime’. An approximate estimate of the value of k, above which this applies may be obtained from the condition[7, p. 161 kL = k=
(3)
(i.e. the rate of physical absorption, with negligible oxygen concentration in the bulk of the liquid, is equal to the rate of chemical absorption). Values of C* were found from the solubilities of oxygen in sodium sulphite solutions estimated by Linek and Mayrhoferova[l4]. For the copper-catalysed reaction, with a copper(H) sulphate concentration of IO-’ kmol/m’, the values of k, are 1.6~ IO-’ m/set for 0.05 kmol/m’ sodium sulphite, 5.4 X lO-4 m/set for 0.25 kmol/m’, and 7.6 x IO-‘m/set for 0.5 kmol/m’. From the reaction rate constant for the copper-catalysed reaction given by de Waal and Okeson[lZ] for Eq. (I) with m = 0 and n = 1, the value of k, would be 3.7 x 10m4m/set at 3O”C, which is in the same range as found here. However the rate constant of 9800 see-’ found by Westerterp et al. [15] predicts k, of 47 x 10e4 m/set, but the validity of this value has been questioned[l2,13]. With a cobalt catalyst concentration of 10-6kmol/m3 the value of k, is 3.6~ IO-‘m/set for 0.8 kmol/m’; extrapolation of the rate constants given by Reith[l3] gives I.2 x 10m4mlsec. In agitated vessels k, values in the range l-6 x 10S4m/set have been found[l6], so in equipment where gas is dispersed into the
ShorterCommunications liquid the absorption process may be in the ‘slow reaction diffusional regime’. Phillips and Johnson[6] and Linek[l7] found this was the case for a vigorously agitated vessel with copper(B) ion catalyst. A similar study was made as part of this work, using a conical filter flask as the absorption vessel, agitated by a magnetic stirrer in such a way that the gas was dispersed through the liquid. Absorption rates were measured in solutions with a copper(H) sulphate concentration IO-”kmol/m3 and sodium sulphite concentrations from 0.05 to 0.25 kmol/m’ at oxygen pressures from 0.16 X IOJ to I.01 x 10JN/m2. At atmospheric pressure the absorption rates were measured by a soap-film meter, while at lower pressures liquid samples were withdrawn from the vessel and the sulphite concentrations determined by analysis[18]. In this equipment maximum absorption peaks were not noticed; they may have occurred too early in the runs to be detected. In contrast to the transfer-cell experiments, the absorption rates were found to be independent of sodium sulphite concentration, and directly proportional to the oxygen pressure (and hence C*). These findings confirm that the rate-controlling process now is in the slow reaction diffusional regime. The condition in this regime for the oxygen concentration in the bulk of the liquid to be negligible compared with C*, and so for the rate of oxygen absorption to be k,aC*, is, from[l, p. 1681, k,aC* = kBO”‘C2.
(4)
For a sodium sulphite concentration of 0.25kmol/m3 and a copper(H) concentration of IO-’ kmol/m’ C is less than 5 per cent of C* for kLa less than 0.49 set-‘; however Eq. (4) is based on the assumption that the rate expression for the heterogeneous reaction applies in the bulk of the liquid and Barron er al. [3,4] have suggested that this could be incorrect. When the rate of oxygen absorption is k,a C* the reaction can be used to determine kra.
CONCLUSIONS
occurrence of maximum absorption peaks in equipment with low mass-transfer coefficients and the erratic absorption rates before the peaks provide some explanation of the unreliability of the copper-catalysed reaction mentioned in the literature. This type of behaviour could occur in any single-pass system with low gas-liquid contact times, so the copper(H) ion-catalysed reaction is unsuitable for the determination of k, or a in such systems. However in highly turbulent gas-liquid systems (k, greater than 3 to 5 x 10e4m/set for sodium sulphite concentrations not greater than 0.25 kmol/m3)the induction period is short and, after it, the copper(B) ion-catalysed reaction is in the ‘slow reaction diffusional regime’, so the rate of oxygen mass transfer can be used to determine kLa, if the values are less than 0.5 set-‘. However, in electrolyte solutions bubble coalescence is reduced and the bubble size is less than in water, so k,a values determined in this way willnot apply for other liquids. The
tPresent address; Hydronyl Ltd., King Street, Fenton, Stokeon-Trent.
157
Department of Chemical Engineering S. H. GREENHALGHt University of Birmingham W. J. McMANAMEY Birmingham B 15 2 TT K. E. PORTER? England NOTATION
interface area per unit volume, m-’ sulphite ion concentration, kmol/m” oxygen concentration in solution, kmol/m3 interface value of C (in equilibrium with gas phase), kmol/m’ diffusivity of oxygen in solution, m*/sec reaction rate constant physical mass transfer coefficient, m/set exponents reaction rate per unit volume, kmol/m’ set rate of chemical absorption per unit area, kmol/m’ set Subscript o concentration in bulk of liquid REFERENCES
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