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The absorption of CO2 in carbonate—bicarbonate buffer solutions containing hypochlorite catalyst on a sieve plate
Chemical EngineeringScience,
1968, Vol. 23, pp. 1447-14.5 1.
Pergamon Press
Printed in Great Britain.
The absorption of CO, in carbonate-bicarbonate buffer solutions containing hypochlorite catalyst on a sieve plate R. POHORECKI Katedra Inzynierii Chemicznej, Politechnika Warszawska, Warsaw, Poland (First received
1 February
1968; in revisedform
3 May 1968)
Abstract-The rate of absorption of carbon dioxide into potassium carbonate-bicarbonate buffer solutions, containing sodium hypochlorite and potassium chloride, has been experimentally determined for a 30.5 X 30.5 cm square sieve plate. The values of the first-order reaction rate constant have been measured for the system studied by the laminar jet technique. An analysis of these results using the Danckwerts pseudo-first order reaction method gives values of specific interfacial area and surface renewal rate comparable with earlier estimates for a similar system[l]. IN AN
attempt to determine the interfacial area of the froth on a sieve plate by means of the Danckwerts pseudo-first order reaction method, Barrett[l] measured the rate of absorption of CO, into NaOH solutions in a sieve plate apparatus. However, these results could not be represented as straight lines on the Danckwerts plot, giving definite curves (though similar measurements for the spray regime gave straight lines). Barrett gave a tentative explanation of these phenomena, assuming that the interfacial area of the froth was not constant, but changed during a run as a function of the solution composition (carbonation ratio). It has been decided that additional data were necessary and that a different system should be used to extend the measurements down to the region of low k, values (of the order of lo3 set-I). In this region it should be possible to determine more exactly the rate of surface renewal, which could not be determined with sufficient accuracy from the Barrett’s measurements. Moreover, the new system should ensure substantial constancy of the physical properties of solution during a run, thus minimizing the changes of the interfacial area. The potassium carbonate-bicarbonate solution has been chosen with sodium hypochlorite as a catalyst. Hypochlorite catalyses the reaction CO, + H,O + HCO,- + H+.
Hypochlorite has been chosen because of its comparatively high catalytic power, which made it possible to change the first-order reaction rate constant, kl, in the range O-2 X lo3 set-‘. To increase the catalytic rate constant of hypochlorite a comparatively large amount of KC1 was added to the solution[2]. The addition of KC1 helped also to minimize changes of the physical properties of the solution during a run or between different runs. EXPERIMENTAL
METHOD
AND RESULTS
Apparatus
The apparatus used was that built by Barrett and described in his thesis[l]. It consisted of a 30.5 X 30.5 cm (12 X 12 in.) square cross-section Perspex column, containing a single stainless steel sieve plate. The sieve plate was 2.38 mm (3/32 in.) thick and contained 5.56 mm (7/32 in.) holes 1.90 cm (3/4 in.) apart in a triangular pattern. To minimize weeping, a strip 2.54 cm (1 in.) wide was left unperforated round the edges of the plate. The free area of the plate was 5.5 per cent. The experimental technique was developed in collaboration with Barrett (and used by him in his measurements with NaOH [ 11).The apparatus was operated at constant pressure with a batch of solution and a closed gas loop. CO, was supplied at a constant rate to the gas loop and the COZ concentration in the gas phase (air) was measured continuously by means of a
1447
R. POHORECKI
pH-metric method as described below. The instantaneous absorption rate was then calculated from the mass balance by means of a suitable differentiation process. To measure continuou,sly the concentration of CO, in the gas loop, a sample gas stream was bubbled through a dilute sodium bicarbonate solution and the pH of the solution was measured with a suitable electrode system (a screened glass electrode and a calomel reference electrode), to an accuracy of 1Cr3 pH unit. The partial pressure of CO, could then be calculated from the relation log pcoz = - pH + const. the constant being previously determined by The experimental calibration. independent details of the method are given in Reference[l]. No differences in the electrode behaviour due to the presence of chlorine in the system were observed. Since the value of pK for hypochlorous acid is about 7.7 at 25”C, and pH values of the absorbing solution on the plate and of the electrode solution were about 10.4 and 7-O respectively, no significant differences in the electrode calibration should have been expected; this conclusion was proved experimentally. The electrode solution was changed frequently to avoid any possible accumulation of the products of side reactions of chlorine; the electrodes were recalibrated before and after each run.
Measurements Every run made on the sieve plate apparatus furnished data for the whole range of values of the carbonation ratio [HCO,-]/[CO,=] (from 0 to 00). Had all the necessary physicochemical data been available, it would be possible to analyse all the points obtained for each run. Since the data on k, available so far (see below) cover only a limited number of solution compositions, it has been decided to use for calculations a single point taken from each run, namely that corresponding to [CO,=]/[HCO,-] = 2.4. There was only a limited amount of information available concerning the values of the reaction rate constant for the absorption of CO, into potassium carbonate-potassium bicarbonate solutions containing KC1 and with NaOCl as a Additional measurements have catalyst[2]. therefore been made by means of the laminar jet technique. Laminarjet The jet apparatus used was similar to that described by Sharma[3]. The hydrodynamics of the various jets were checked by studying the physical absorption of CO, into water. The composition of the buffer solution used for the laminarjet measurements was as follows: [K&O31 = 0.60 g mole/l; [KHCO,] = O-25 g mole/l; [KC11 = 1.% g mole/l; [NaOCl] = O-0.27 g mole/l; [CO,=]/[HCO,-] = 2.4.
Analysis of the solutions The solutions were analysed as follows: hypochlorites by standard iodometric technique; carbonates and bicarbonates by titration with HCl against thymol blue-cresol red and bromophenol blue respectively; chlorides by Mohr methodt. Technical grade substances and deionized water were used for preparation of the solutions.
tThe last three determinations before hypochlorite was added.
were,
of course,
Most of the measurements were made at 21°C. The physical solubilities of CO, in various solutions were calculated by the method of Van Krevelen and Hoftyzer: log (H/H,)
= - ZZthi,
hi = h, + h_ + h,
using the values of the contributions hi corrected by Barrett[l]. The diffusivities were estimated by means of the relation
made
(0~)~ = const. 1448
The absorption of CO, in buffer solutions
The values of viscosity and density were determined experimentally. The results of the laminar jet measurements are shown in Fig. 1. The value of HdD for the K, ,
8’
210’cK&o;l = 060 CKW33,J=O25
gEQ!Q
u1
= 6.9 & O-2 cm Liquid hold-up = 19.043 cm Froth height = 0.63 * 0.05 Froth voidage Froth temperature = 22.7 + 1~5°C = 1.165-1-185, g/cm3 Liquid density Liquid viscosity = 1.17-l-35, CP = 1 atm. Total pressure Partial pressure of CO, = O-9 X 10e2 - 3.5 X 10m2 atm.
CKCIJ= 196
The unavoidable differences between different runs produced considerable scatter of the results?; to minimize the influence of this scatter several (2-5) runs were carried out for a given catalyst concentration and, after appropriate corrections were introduced, mean values were used for the Danckwerts plot. The plot is shown in Fig. 2; the straight line was
03 CboCIJ
y
Fig. I. The dependence of k, (see-‘) on [ 21°C.
po
buffer solution without catalys t was also determined from the slope of a plot of absorption rate against dVl, and found to be equal 6.80 X lo-* g mo1e/cm2sec1~2atm, as compared to 6.79 X lo-’ calculated from the correlation mentioned above (the reaction rate constant could be neglected in the absence of catalyst, being very much smaller than the surface renewal rate, s = 100 set-l). The energy of activation of the reaction catalysed by hypochlorite was found to be 8,400 cal/mole for the solution investigated, 19 per cent lower than Sharma’s estimate of 10,000 cal/mole for sodium buffers [2 3. Sieve plate All the sieve plate measurements were carried out under the following conditions (changing for different runs in the limits indicated). Composition of solutions: [K,CO,]
= 0*60? 0.01 g mole/l = O-25f 0.005 g mole/l = 192 + O-05 g mole/l WC11 [NaOCl] = O-O.30 g mole/l [CO,=l/[HCO,-] = 2.40 + 0.05 Gas velocity = O-86f 0.06 m/set
[ KHCOJ
(g$o-4.
clii2
9.’
c
I.0
-
OP 0
I
I
,
0.5
I.0
I.5
K x Kr3,
1945
I5700
6’
Fig. 2. The Danckwerts plot.
fitted by the method of least squares, giving the following values of the interfacial area and the surface renewal rate s: a = 2.64 cm-‘,
s = 340 secl.
Since about 10 per cent of the observed absorption rate is attributable to drops on the apparatus walls[ 11, the true interfacial area per unit volume of the froth is about 2.4 cm-‘. tEspecially at low concentrations of catalyst, since the absorption rate was measured as a difference of two comparatively large quantities: [CO, supply rate - (accumulation rate of CO, in the apparatus+loss of CO2 through the atmospheric vent)].
1449
R. POHORECKI
These values agree with those obtained by Barrett for final parts of his runs (fully carbonated caustic solutions). Barrett found: a = 2.3 cm-‘.
s = 100-500 set-‘.
APPENDIX Danckwerts[4] has shown, that the criterion for no depletion of catalyst near the interface is:
Taking k,,,,, = 2 x lo3 se@, and pcoo = 3.5 X 1O-2atm for the sieve plate we obtain for the laminar jet
V(Dkl) k L
for the sieve plate
d(Dk,) kL.
= 4.47 6 33.3 = a 2
= 2.42 G 9.52 = a C*
The temperature rise near the interface, calculated according to Danckwerts[6] using the value of 25,400 J/mole for the heat of absorption of CO, into carbonate -bicarbonate buffers [7] was negligible both in the case of laminar jet and sieve plate (about 6 x 10-20C and 1 x 10-30C respectively). The error introduced by neglecting the gasside mass transfer resistance for the sieve plate measurements was estimated on the basis of the adiabatic humidification experiments. It was found to be less than 1.5 per cent at the most stringent conditions.
c*(:+;)[J(1+$)-1] ~ (1)
1*
K
l+Pg b z
Under the experimental
conditions:
Laminar jet Partial pressure of co, Temperature a = [COa’] b = [HCO,-] kL = IDS
Sieve plate
= 1 atm
= 3.5 X
= = = =
= = = =
21°C 0.60 g mole/l. 0.25 g mole/l. 3.8 X 1O-9 cm/set
lo+
atm
23°C 0.6Og mole/I. 0.25 g mole/l. 6.9 x IO-* cmlsec.
taking D = l-4 X low5 cm2/sec, H = I.8 x 10e5 g mole/cm3atm, KHClo = 2 x IO+ g ion/l, K2 = 4.2 x IO-” g ion/l (the values of K are taken at infinite dilution), and klcmax,= 2 x lo3 set-‘. The left-hand side of the criterion (1) is then O-535 x 1O-3 for the laminar jet and 0*812X 10e5 for the sieve plate, thus satisfying the condition (1). The criterion for irreversibility of the reaction is[5]:
c* % cb
=
K2 K,‘;.
b2
Acknowledgment-Part of this work was carried out during the author’s stay at the Department of Chemical Engineering of the University of Cambridge. The author wishes to express his gratitude to Professor P. V. Danckwerts for his kind help and encouragement, to Dr. P. V. L. Barrett for his assistance, and to The British Council for financial support.
(2)
In the case considered here, taking K, = 4.2 X lo-‘, we have: for the laminar jet c * = 1.8 X 10e2 + cI, = 1’04 x 10m5g mole/l, for the sieve plate c * = 1.62 x 1O-4 s cb = 1.04 x 10m5g mole/l, using the smallest value of pcoz (0.9 X 10T2atm) i.e. at the most stringent conditions. The criterion for no diffusion control is[5]: 1450
NOTATION
a
b
c* Cb
D H h
effective interfacial area per unit volume of froth, cm-’ concentration of carbonate ion, g mole/l. (in the Appendix), concentration of bicarbonate ion, g mole/l. or g mole/cm3 concentration of free carbon dioxide at interface, g mole/l. or g mole/cm3 concentration of free carbon dioxide in bulk of liquid, g mole/l. diffusivity of carbon dioxide in liquid, cm2/sec solubility of carbon dioxide in liquid (H, in water), g mole/cm3 atm contributions of various species in the solubility correlation, l/g ion
The absorption of CO, in buffer solutions I
K,
strength, g ion/l. equilibrium value of
kL liquid-film coefficient in absence of reaction, cmlsec 1 length of the laminar jet, cm pcoz partial pressure of C02, atm R rate of absorption of carbon dioxide per unit inter-facial area, g mole/cm2sec s surface renewal rate, set-‘, V liquid flow rate, cm3/sec p viscosity of solution, CP
ionic
[H+][HCO,-I/
[coz1’ g mol;~hre of [H+][CO =]/ equilibrium 3 [HC4-I, g mole/l. K HClO dissociation constant of HCIO, g mole/l. k, pseudo-first order reaction rate constant, see-r K2
[1] -21 ;3] [4] [S] ;6] [7]
REFERENCES BARRETT P. V. L., Ph.D. Thesis, University of Cambridge 1966. SHARMA M. M. and DANCKWERTS P. V., Chem. Engng Sci. 18 729 1963. SHARMA M. M., Ph.D. Thesis, University of Cambridge 1964. DANCKWERTS P. V., unpublished work. DANCKWERTS P. V. and SHARMA M. M., lnst Chem. Engrs Review Series No 2, Chem. En&YCB 244 1966. DANCKWERTS P. V., Chem. Engng Sci. 22 472 1967. RAMM V. M., Gas Absorption (in Russian). Moscow 1966. Resume-Le taux d’absorbtion de bi-oxyde de carbone dans des solutions tampons de carbonatebicarbonate de potassium, qui contiennent de l’hypochlorite de sodium et du chlorure de potassium, a QC determine de maniere experimentale pour un tamis de 30,5 x 30,5 cm de section. Les valeurs de la constante du taux de reaction d’ordre premier ont dte mesurees pour Ie systeme Ctudit en utilisant la technique du jet lamellaire. L’analyse de ces resultats par la mtthode Danckwerts de la reaction d’ordre pseudo premier donne des valeurs de surface interfaciale specifique et de taux de renouvellement de surface comparables aux previsions anterieures pour un systime comparable [ 11. Zusammenfassung- Die Absorptionsgeschwindigkeit von Kohlendioxyd in Kaliumcarbonat-bicarbonat Pufferliisungen Natriumhypochlorit und Kallumchlorid enthaltenden wurde experimentell fur eine Siebplatte mit einem Querschnitt von 30,5 x 30,5 cm bestimmt. Die Werte der Geschwindigkeitskonstante fur die Reaktion erster Ordnung wurden fur das mitt Laminarstrahltechnik untersuchte System gemessen. Eine Analyse dieser Ergebnisse unter Verwendung der Danckwertsschen Methode der Reaktion pseudo-erster Ordnung ergab Werte fur die spezifische GrenztXche und die Oberthachenemeuerungs geschwindigkeit die mit friiheren Schiitzungen fur ein iihnliches System [ I] durchaus vergleichbar waren.
1451
1968, Vol. 23, pp. 1447-14.5 1.
Pergamon Press
Printed in Great Britain.
The absorption of CO, in carbonate-bicarbonate buffer solutions containing hypochlorite catalyst on a sieve plate R. POHORECKI Katedra Inzynierii Chemicznej, Politechnika Warszawska, Warsaw, Poland (First received
1 February
1968; in revisedform
3 May 1968)
Abstract-The rate of absorption of carbon dioxide into potassium carbonate-bicarbonate buffer solutions, containing sodium hypochlorite and potassium chloride, has been experimentally determined for a 30.5 X 30.5 cm square sieve plate. The values of the first-order reaction rate constant have been measured for the system studied by the laminar jet technique. An analysis of these results using the Danckwerts pseudo-first order reaction method gives values of specific interfacial area and surface renewal rate comparable with earlier estimates for a similar system[l]. IN AN
attempt to determine the interfacial area of the froth on a sieve plate by means of the Danckwerts pseudo-first order reaction method, Barrett[l] measured the rate of absorption of CO, into NaOH solutions in a sieve plate apparatus. However, these results could not be represented as straight lines on the Danckwerts plot, giving definite curves (though similar measurements for the spray regime gave straight lines). Barrett gave a tentative explanation of these phenomena, assuming that the interfacial area of the froth was not constant, but changed during a run as a function of the solution composition (carbonation ratio). It has been decided that additional data were necessary and that a different system should be used to extend the measurements down to the region of low k, values (of the order of lo3 set-I). In this region it should be possible to determine more exactly the rate of surface renewal, which could not be determined with sufficient accuracy from the Barrett’s measurements. Moreover, the new system should ensure substantial constancy of the physical properties of solution during a run, thus minimizing the changes of the interfacial area. The potassium carbonate-bicarbonate solution has been chosen with sodium hypochlorite as a catalyst. Hypochlorite catalyses the reaction CO, + H,O + HCO,- + H+.
Hypochlorite has been chosen because of its comparatively high catalytic power, which made it possible to change the first-order reaction rate constant, kl, in the range O-2 X lo3 set-‘. To increase the catalytic rate constant of hypochlorite a comparatively large amount of KC1 was added to the solution[2]. The addition of KC1 helped also to minimize changes of the physical properties of the solution during a run or between different runs. EXPERIMENTAL
METHOD
AND RESULTS
Apparatus
The apparatus used was that built by Barrett and described in his thesis[l]. It consisted of a 30.5 X 30.5 cm (12 X 12 in.) square cross-section Perspex column, containing a single stainless steel sieve plate. The sieve plate was 2.38 mm (3/32 in.) thick and contained 5.56 mm (7/32 in.) holes 1.90 cm (3/4 in.) apart in a triangular pattern. To minimize weeping, a strip 2.54 cm (1 in.) wide was left unperforated round the edges of the plate. The free area of the plate was 5.5 per cent. The experimental technique was developed in collaboration with Barrett (and used by him in his measurements with NaOH [ 11).The apparatus was operated at constant pressure with a batch of solution and a closed gas loop. CO, was supplied at a constant rate to the gas loop and the COZ concentration in the gas phase (air) was measured continuously by means of a
1447
R. POHORECKI
pH-metric method as described below. The instantaneous absorption rate was then calculated from the mass balance by means of a suitable differentiation process. To measure continuou,sly the concentration of CO, in the gas loop, a sample gas stream was bubbled through a dilute sodium bicarbonate solution and the pH of the solution was measured with a suitable electrode system (a screened glass electrode and a calomel reference electrode), to an accuracy of 1Cr3 pH unit. The partial pressure of CO, could then be calculated from the relation log pcoz = - pH + const. the constant being previously determined by The experimental calibration. independent details of the method are given in Reference[l]. No differences in the electrode behaviour due to the presence of chlorine in the system were observed. Since the value of pK for hypochlorous acid is about 7.7 at 25”C, and pH values of the absorbing solution on the plate and of the electrode solution were about 10.4 and 7-O respectively, no significant differences in the electrode calibration should have been expected; this conclusion was proved experimentally. The electrode solution was changed frequently to avoid any possible accumulation of the products of side reactions of chlorine; the electrodes were recalibrated before and after each run.
Measurements Every run made on the sieve plate apparatus furnished data for the whole range of values of the carbonation ratio [HCO,-]/[CO,=] (from 0 to 00). Had all the necessary physicochemical data been available, it would be possible to analyse all the points obtained for each run. Since the data on k, available so far (see below) cover only a limited number of solution compositions, it has been decided to use for calculations a single point taken from each run, namely that corresponding to [CO,=]/[HCO,-] = 2.4. There was only a limited amount of information available concerning the values of the reaction rate constant for the absorption of CO, into potassium carbonate-potassium bicarbonate solutions containing KC1 and with NaOCl as a Additional measurements have catalyst[2]. therefore been made by means of the laminar jet technique. Laminarjet The jet apparatus used was similar to that described by Sharma[3]. The hydrodynamics of the various jets were checked by studying the physical absorption of CO, into water. The composition of the buffer solution used for the laminarjet measurements was as follows: [K&O31 = 0.60 g mole/l; [KHCO,] = O-25 g mole/l; [KC11 = 1.% g mole/l; [NaOCl] = O-0.27 g mole/l; [CO,=]/[HCO,-] = 2.4.
Analysis of the solutions The solutions were analysed as follows: hypochlorites by standard iodometric technique; carbonates and bicarbonates by titration with HCl against thymol blue-cresol red and bromophenol blue respectively; chlorides by Mohr methodt. Technical grade substances and deionized water were used for preparation of the solutions.
tThe last three determinations before hypochlorite was added.
were,
of course,
Most of the measurements were made at 21°C. The physical solubilities of CO, in various solutions were calculated by the method of Van Krevelen and Hoftyzer: log (H/H,)
= - ZZthi,
hi = h, + h_ + h,
using the values of the contributions hi corrected by Barrett[l]. The diffusivities were estimated by means of the relation
made
(0~)~ = const. 1448
The absorption of CO, in buffer solutions
The values of viscosity and density were determined experimentally. The results of the laminar jet measurements are shown in Fig. 1. The value of HdD for the K, ,
8’
210’cK&o;l = 060 CKW33,J=O25
gEQ!Q
u1
= 6.9 & O-2 cm Liquid hold-up = 19.043 cm Froth height = 0.63 * 0.05 Froth voidage Froth temperature = 22.7 + 1~5°C = 1.165-1-185, g/cm3 Liquid density Liquid viscosity = 1.17-l-35, CP = 1 atm. Total pressure Partial pressure of CO, = O-9 X 10e2 - 3.5 X 10m2 atm.
CKCIJ= 196
The unavoidable differences between different runs produced considerable scatter of the results?; to minimize the influence of this scatter several (2-5) runs were carried out for a given catalyst concentration and, after appropriate corrections were introduced, mean values were used for the Danckwerts plot. The plot is shown in Fig. 2; the straight line was
03 CboCIJ
y
Fig. I. The dependence of k, (see-‘) on [ 21°C.
po
buffer solution without catalys t was also determined from the slope of a plot of absorption rate against dVl, and found to be equal 6.80 X lo-* g mo1e/cm2sec1~2atm, as compared to 6.79 X lo-’ calculated from the correlation mentioned above (the reaction rate constant could be neglected in the absence of catalyst, being very much smaller than the surface renewal rate, s = 100 set-l). The energy of activation of the reaction catalysed by hypochlorite was found to be 8,400 cal/mole for the solution investigated, 19 per cent lower than Sharma’s estimate of 10,000 cal/mole for sodium buffers [2 3. Sieve plate All the sieve plate measurements were carried out under the following conditions (changing for different runs in the limits indicated). Composition of solutions: [K,CO,]
= 0*60? 0.01 g mole/l = O-25f 0.005 g mole/l = 192 + O-05 g mole/l WC11 [NaOCl] = O-O.30 g mole/l [CO,=l/[HCO,-] = 2.40 + 0.05 Gas velocity = O-86f 0.06 m/set
[ KHCOJ
(g$o-4.
clii2
9.’
c
I.0
-
OP 0
I
I
,
0.5
I.0
I.5
K x Kr3,
1945
I5700
6’
Fig. 2. The Danckwerts plot.
fitted by the method of least squares, giving the following values of the interfacial area and the surface renewal rate s: a = 2.64 cm-‘,
s = 340 secl.
Since about 10 per cent of the observed absorption rate is attributable to drops on the apparatus walls[ 11, the true interfacial area per unit volume of the froth is about 2.4 cm-‘. tEspecially at low concentrations of catalyst, since the absorption rate was measured as a difference of two comparatively large quantities: [CO, supply rate - (accumulation rate of CO, in the apparatus+loss of CO2 through the atmospheric vent)].
1449
R. POHORECKI
These values agree with those obtained by Barrett for final parts of his runs (fully carbonated caustic solutions). Barrett found: a = 2.3 cm-‘.
s = 100-500 set-‘.
APPENDIX Danckwerts[4] has shown, that the criterion for no depletion of catalyst near the interface is:
Taking k,,,,, = 2 x lo3 se@, and pcoo = 3.5 X 1O-2atm for the sieve plate we obtain for the laminar jet
V(Dkl) k L
for the sieve plate
d(Dk,) kL.
= 4.47 6 33.3 = a 2
= 2.42 G 9.52 = a C*
The temperature rise near the interface, calculated according to Danckwerts[6] using the value of 25,400 J/mole for the heat of absorption of CO, into carbonate -bicarbonate buffers [7] was negligible both in the case of laminar jet and sieve plate (about 6 x 10-20C and 1 x 10-30C respectively). The error introduced by neglecting the gasside mass transfer resistance for the sieve plate measurements was estimated on the basis of the adiabatic humidification experiments. It was found to be less than 1.5 per cent at the most stringent conditions.
c*(:+;)[J(1+$)-1] ~ (1)
1*
K
l+Pg b z
Under the experimental
conditions:
Laminar jet Partial pressure of co, Temperature a = [COa’] b = [HCO,-] kL = IDS
Sieve plate
= 1 atm
= 3.5 X
= = = =
= = = =
21°C 0.60 g mole/l. 0.25 g mole/l. 3.8 X 1O-9 cm/set
lo+
atm
23°C 0.6Og mole/I. 0.25 g mole/l. 6.9 x IO-* cmlsec.
taking D = l-4 X low5 cm2/sec, H = I.8 x 10e5 g mole/cm3atm, KHClo = 2 x IO+ g ion/l, K2 = 4.2 x IO-” g ion/l (the values of K are taken at infinite dilution), and klcmax,= 2 x lo3 set-‘. The left-hand side of the criterion (1) is then O-535 x 1O-3 for the laminar jet and 0*812X 10e5 for the sieve plate, thus satisfying the condition (1). The criterion for irreversibility of the reaction is[5]:
c* % cb
=
K2 K,‘;.
b2
Acknowledgment-Part of this work was carried out during the author’s stay at the Department of Chemical Engineering of the University of Cambridge. The author wishes to express his gratitude to Professor P. V. Danckwerts for his kind help and encouragement, to Dr. P. V. L. Barrett for his assistance, and to The British Council for financial support.
(2)
In the case considered here, taking K, = 4.2 X lo-‘, we have: for the laminar jet c * = 1.8 X 10e2 + cI, = 1’04 x 10m5g mole/l, for the sieve plate c * = 1.62 x 1O-4 s cb = 1.04 x 10m5g mole/l, using the smallest value of pcoz (0.9 X 10T2atm) i.e. at the most stringent conditions. The criterion for no diffusion control is[5]: 1450
NOTATION
a
b
c* Cb
D H h
effective interfacial area per unit volume of froth, cm-’ concentration of carbonate ion, g mole/l. (in the Appendix), concentration of bicarbonate ion, g mole/l. or g mole/cm3 concentration of free carbon dioxide at interface, g mole/l. or g mole/cm3 concentration of free carbon dioxide in bulk of liquid, g mole/l. diffusivity of carbon dioxide in liquid, cm2/sec solubility of carbon dioxide in liquid (H, in water), g mole/cm3 atm contributions of various species in the solubility correlation, l/g ion
The absorption of CO, in buffer solutions I
K,
strength, g ion/l. equilibrium value of
kL liquid-film coefficient in absence of reaction, cmlsec 1 length of the laminar jet, cm pcoz partial pressure of C02, atm R rate of absorption of carbon dioxide per unit inter-facial area, g mole/cm2sec s surface renewal rate, set-‘, V liquid flow rate, cm3/sec p viscosity of solution, CP
ionic
[H+][HCO,-I/
[coz1’ g mol;~hre of [H+][CO =]/ equilibrium 3 [HC4-I, g mole/l. K HClO dissociation constant of HCIO, g mole/l. k, pseudo-first order reaction rate constant, see-r K2
[1] -21 ;3] [4] [S] ;6] [7]
REFERENCES BARRETT P. V. L., Ph.D. Thesis, University of Cambridge 1966. SHARMA M. M. and DANCKWERTS P. V., Chem. Engng Sci. 18 729 1963. SHARMA M. M., Ph.D. Thesis, University of Cambridge 1964. DANCKWERTS P. V., unpublished work. DANCKWERTS P. V. and SHARMA M. M., lnst Chem. Engrs Review Series No 2, Chem. En&YCB 244 1966. DANCKWERTS P. V., Chem. Engng Sci. 22 472 1967. RAMM V. M., Gas Absorption (in Russian). Moscow 1966. Resume-Le taux d’absorbtion de bi-oxyde de carbone dans des solutions tampons de carbonatebicarbonate de potassium, qui contiennent de l’hypochlorite de sodium et du chlorure de potassium, a QC determine de maniere experimentale pour un tamis de 30,5 x 30,5 cm de section. Les valeurs de la constante du taux de reaction d’ordre premier ont dte mesurees pour Ie systeme Ctudit en utilisant la technique du jet lamellaire. L’analyse de ces resultats par la mtthode Danckwerts de la reaction d’ordre pseudo premier donne des valeurs de surface interfaciale specifique et de taux de renouvellement de surface comparables aux previsions anterieures pour un systime comparable [ 11. Zusammenfassung- Die Absorptionsgeschwindigkeit von Kohlendioxyd in Kaliumcarbonat-bicarbonat Pufferliisungen Natriumhypochlorit und Kallumchlorid enthaltenden wurde experimentell fur eine Siebplatte mit einem Querschnitt von 30,5 x 30,5 cm bestimmt. Die Werte der Geschwindigkeitskonstante fur die Reaktion erster Ordnung wurden fur das mitt Laminarstrahltechnik untersuchte System gemessen. Eine Analyse dieser Ergebnisse unter Verwendung der Danckwertsschen Methode der Reaktion pseudo-erster Ordnung ergab Werte fur die spezifische GrenztXche und die Oberthachenemeuerungs geschwindigkeit die mit friiheren Schiitzungen fur ein iihnliches System [ I] durchaus vergleichbar waren.
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