Attempts to determine the liquid—film coefficient for physical absorption and effective interfacial area in a sieve plate column by the chemical method

Chemical Engineering Science, 1969, Vol. 24, pp. 1139-l 147.

Pergamon Press.

Printed in Great Britain.

Attempts to determine the liquid-film coefficient for physical absorption and effective interf’acial area in a sieve plate column by the chemical method W. PASIUK-BRONIKOWSKA Institute of Physical Chemistry of the Polish Academy of Sciences, ul.Kasprzaka 44/52, Warsaw 42, Poland (First received 20 February 1968; in revisedform 16 January 1969) Abstract-Values of the liquid-side mass transfer coefficient, kL and the interfacial area, a per unit volume of froth on a sieve plate (perforated area 55%) were found using the technique of absorption accompanied by irreversible pseudo-first order reaction. The experiments were carried out with several reacting systems, for which the attained values of kL andn were O-17-0.27 cmlsec and 1*972.28 cm*/cmS respectively. A method has been employed, which enables these values to be determined without the necessity of measuring kinetic constants. The results confirmed that the Danckwerts equation could be used to predict rates of absorption in sieve plate columns. 1. INTRODUCTION

THE TECHNIQUE of gas absorption

accompanied by irreversible pseudo-first order chemical reaction [ 1] has been verified for deterniination of the physical absorption liquid-film coefficient, kL and effective specific interfacial area, a on a sieve plate. The different reacting systems were used: CO,-NaOH with CaCO,-NaOH/Na&O,, (OH),/CaCO, suspension, and O,-N&SO, with CoSO, as a catalyst. Experiments were carried out at ambient temperature and pressure in the apparatus (Fig. 1) with a single sieve plate (12 X 12 in. with 16 in. radii in corners, free area 5.5 per. cent) on which a batch of an absorbing solution was blown through with gas mixture of an inert and reactant. There was no downcomer on the plate. The apparatus was essentially that used by Barrett [2] with a few changes. For the experiments with CO, the atmospheric vent has been closedt for gas to go out from the apparatus and the wet saturator for the gas entering the electrode vessel of the pH measurtTo prevent losses of air (in fact the poorer CO& mixture) at the beginning of every run because of the increase in the total amount of gas in the loop (CO, supplied) and the rise in temperature with the reaction going.

ing device removed& and for those with OS the top of the apparatus has been opened. In all runs liquid hold-up and the superficial gas velocity in the column were maintained constant and equal to 6 1. and about 0*6m/sec respectively. 2. ABSORPTION OF CARBON DIOXIDE IN AQUEOUS CAUSTIC SODA SOLUTIONS

In these experiments the concentration of the absorbing solution was originally l-2 g mole NaOH/l. and O-2-1% CO,-air mixture (air circulated in a closed loop and pure CO, supplied with the constant rate) was blown through the solution until hydroxide ions were spent completely. In such a system the rate of absorption may be assumed with a useful degree of accuracy equal to the rate of CO, supply and given by the equation: RA = Ac+d(kL2 + Dk,c)

(1)

where c is the concentration of hydroxide ions in bulk of the solution, k2 the second order rate constant for the reaction CO, -t OH‘ + HC03-, STo avoid desorption of CO, accumulated in the liquid (filling the saturator) during calibration.

1139

W. PASIUK-BRONIKOWSKA

Fig.

1. Simplified scheme of the experimental sieve plate column.

set-up for

c+ and D the solubility and diffusivity of carbon dioxide in the solution, A, effective interfacial area developed in the absorber. The gas-side mass transfer coefficient has been neglected as not more than a few per cent of k, [2]. As c changes continuously with the absorption going on, c+, D, and k, also change. Physical properties of the particular solution do not vary appreciably with spending hydroxide ions, partly because their lack is compensated by simultaneous enrichment in carbonate ions. Therefore it was reasonable to expect A constant during a batch experiment and so a straight line on the diagram (RA/c+~D)~ vs. k,c. To plot such a diagram from the experimental data c+ and D for the solutions of different hydroxide and carbonate ion concentrations were needed. They were calculated from the known Eqs. (1,2): Dp = const.

at constant temperature; the solution,

p is the viscosity

c+=Hp

= k: I’ + kb’l”,

Z?A = Ac+d(kL*+

of (3)

(4)

Dk,c)-Ac,k,*/~(k,*+

Dk,c). (5)

The inter-facial area, A found directly from the slope of the diagram was within the range (4*20-4*92)104 cm* for all the runs. The specific interfacial area (per unit volume of the froth) and kL found by extrapolation of the straight line to the value:

(2)

where H means Henry’s constant for carbon dioxide in the solution and p-partial pressure of carbon dioxide, and - log,,H/H,

where H, is Henry’s constant for carbon dioxide in water, k:, k:-constant values for the individual electrolytes in the solution (NaOH and NqCO,), and I’, I”-the contributions to the ionic strength due to these electrolytes. To simplify the calculations H and D for pure NaOH solution of the initial concentration and pure N&CO, solution of the final concentration only were found and their average values taken to interpret the results of a run. This implied inaccuracy, but less than 3 per cent in H and 8 per cent in D. The partial pressure of carbon dioxide was measured continuously by the pH method[2,3] and thence its equilibrium value with the frothing solution on the plate estimated (the average value for the gas mixture entering and leaving the froth). The second-order reaction rate constant, k, for the system CO,NaOH/Na&03 has been found from Barrett’s data on the laminar jet [2]. All the results lie on straight line (Fig. 2) with slight tendency to curve for c s kL2/Dk2. In this region the system ceases to obey the condition c0 = 0 (where co is the concentration of CO, in the bulk of liquid) and the following Eq. (4) satisfactorily explains the case:

(ZWc+~D);,_,

= k,*A*lD,

as well as some principal characteristics run are given in Table 1. 3. ABSORPTION OF CARBON DIOXIDE AQUEOUS CAUSTIC SODA SOLUTIONS WITH SUSPENDED LIME

(6)

of the IN

If CO, is absorbed into a suspension of Ca(OH), in NaOH solution the rate-determining reaction is the same as for absorption of CO,

1140

Attempts to determine the liquid-film coefficient

,*,+/+++++

Ml++-

$$++

I.olon/l. l

1.0-150

” l.78- 257 + 202-303 o 250-3.00

7

Fig. 2. Plot of experimental results, according to Danckwerts’ equation. Table 1. Operating conditions and some calculated data for the absorption of CO2 in aq.NaOH solutions

co2

[OH-I,

(g mole/l.)

K%=1,

[co,=1

(g mole/l.)

(g mole/l.)

1.00 1.78 2.02 1.00

0 0 0 0.50

0.50 0.89 1.01 1.00

supply rate (g molelsec) 0.97 x 0.95 x 2.33 x 0.97 x

Temp. (“C)

10-s 10-S lo+ 10-s

21 22 22 22

in NaOH solution of the same concentration, without the suspension[S]. But such a system has the advantage of a buffer solution as the composition of the solution should remain unchanged with CO, absorbed. The condition for it is that the rate of dissolution of Ca(OH), is as great as the rate of absorption of CO,. The overall reaction is: Ca(OH),(solid)

+ CO, + CaCO,(solid).

However some complications might be expected as the rate of dissolution of Ca(OH), depended upon surface (A,) of the solid in contact with liquid: &A, = &Uc,,t.

-c),

(7)

where cSd. and c are saturated and actual concentrations of Ca(OH), solution respectively, and k, is the coefficient of dissolution. With the consumption of Ca(OH), particles in the reaction with CO, the surface A, decreases. Also CaC03 precipitate may deposit on Ca(OH),

H

D

(g mole/cmS atm)

(cm*/sec)

2.73 x 2.00 x 1.86 x 1.84 x

lo+ 10-S 10-S 10-S

1.41 x 1.20 x 1.13 x 1.10 x

kL

10-s 10-S 10-S 10-s

(cm$m3) 2.05 1.97 2.04 2.28

(cm/set) 0.17 0.27 0.27 0.19

particles thus making them inaccesible for the surrounding reagent. The rate of dissolution should also vary with the concentration of NaOH as the solubility of Ca(OH), increases with the decrease of this concentration. Examples of typical runs are shown in Fig. 3 compared with a run without lime. As COz supply rate was kept constant during a run, changes of the partial pressure of CO, (above the reacting mixture) with time resulted from changes in the rate of reaction (see the Eq. (1)). If RA > A sk,c,,t. the product k,c decreases and the carbonate ion concentration c& builds up in bulk of the solution. As long as Ca(OH), particles were present in the reacting mixture the rate of absorption remained constant with the error not more than 20per cent (Fig. 3). It indicated that in the presence of solid Ca(OH), c&,/c was low and did not interfere appreciably. The values of pcoz used for calculations of a and kL were extrapolated to I = 0 (t means time of duration of an experiment). The interfacial area 2.18 cm2/cm3 and k, = 0*19cm/sec have been found (Fig. 4) for the

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W. PASIUK-BRONIKOUSKA

+’

O-6

IO

20

30

40

50

60

70

60

90

Min Fig. 3. Variation of CO, concentration in gas phase measured at 1 min intervals during a run (absorption of COz in aq. NaOH solutions with suspended lime).

K2cx10-&c’ Fig. 4. Plot of experimental results according to transformed Eq. (1) (absorption of CO, in aq.NaOH solutions with suspended lime) .

experiments described in Table 2. As it is seen from the plot here also the straight line tends to curve in the vicinity of zero point.

The experiments with suspension were rather difficult to carry them out as the droplets catcher got stuck with lime. Losses of lime on the

1142

. Attempts to determine the liquid-film coefficient Table 2. Operating conditions and some calculated data for the absorption of CO, in aq.NaOH solutions with suspended lime CO* supply rate (g molelsec)

[OH-I (g mole/l.)

2.31 x 2.36 x 2.34 x 146x 1.50 x 1.52 x 2.36 x 2.36 x

2.00 1.50 1.00 0.635 0.318 0.159 0+x4 oGl2

Temp. (“C)

(g moleEm atm)

24 23 23 20 21 21 21 21

lo+ 1O-5 1O-3 10-a 10-S 10-s lo+ lo+

catcher were estimated experimentally and confirmed by mass balance; they amounted to about 150 g (21%) of Ca(OH), per a run. To check the suggestion[2] that results of such experiments were sensitive to impurities present in chemicals used main impurities were pointed out from the known content of the chemicals. They were Fe (< 0.001 in NaOH and < 0.005% in Na&O,) and SO,*- (< 0.003 in NoOH and < 0.003% in Na&O,). Then 0.844 g of FeSO, (0.35% of NaOH in a batch) was added to the absorbing solution and the experiment carried out in the usual way. The results are compared with those without additional FeSO, in Fig. 5. There is 10 per cent or less scatter between the curves which is little enough

1.83 x 2.19 x 2.57 x 3.16 x 3.42 x 3.59 x 3.68 x 3.74 x

10-S 1O-5 lo+ W5 lO-+ 10-S lo-5 lo-5

D (cm%ec) 1.26 x 1.38 x 1.54 x 1.52 x 1.67 x 1.72 x 1.75 x 1.77 x

lo+ lo-5 10-S 1O-5 lo+ lo+ 10-S 10-S

thought that traces of a lubricant or grease might change the froth. 4. CATALYSED SODIUM

According the reaction

ABSORPTION SULPHITE

OF OXYGEN

IN

SOLUTIONS

to the recent works by Astarita[5]

2so3*- + 0, + 2so4*-, catalysed by Co*+ is of the second order with respect to oxygen and zero order with respect to sulphite ions in a limited range of concentrations. So if the concentrations within this range are applied and the condition that the rate of reaction is not too slow nor instantaneous holds the rate of absorption is given by [4]:

. 0.

4

:

b

I

IO

1

I

I

20

30

40

RA =&([2D/(n+

I

50

RA = Ac+d((2/3)Dk2c+

Min

be neglected. It seems therefore reasonable to expect reproducible results when using chemicals from different batches but within the same grade of purity (to be sure they are doped with the same species of impurities). It is

+A’D*/c+*)

(9)

or if we put (2/3)k,c+ = k RA = Ac+d(A

to

‘DVc+* + kD).

(10)

The integration constant can be calculated as a function of k, and k from Hikita and Asai’s plot [4]_

1143 H

(8)

where A ’ is an integration constant tending to zero for the fast-reaction regime, k, is a kinetic constant for the n-order reaction. For the case when n = 2 Eq. (8) becomes:

Fig. 5. Influence of FeSO, impurity on reproduction of results (absorption of CO2 in aq.NaOH solution with suspended lime).

CESVd.24No.7

l)]k,c+‘“+“+A’D*),

. W. PASIUK-BRONIKOWSKA

The catalysed oxidation of sodium sulphite in water is very sensitive to impurities which may catalyse or inhibit the reaction (7). The rate of the reaction depends also on pH in the solution (8). On the other hand it is a very convenient reaction as the reagents are easily available and it could be useful for quick estimation of the interfacial surface area in industrial absorption equipment. To avoid the uncertainty as to the real k values achieved in the investigated apparatus with sodium sulphite solutions of different pH and CoSO, concentrations the following technique has been worked out. Experiments were carried out in a batch way as for the CO,-caustic soda solutions systems. Every minute or two a sample of the solution on the sieve plate was taken in the amount of about 10 cc, 2 cc of which were treated with the slight excess of a standardized iodine solution and the excess titrated with a thiosulphite solution with starch as an indicator. The other part of the sample (5 cc) was placed in a rotated tube (Fig. 6) and the rate of absorption of oxygen from air in the tube was determined. The rotated tube was previously calibrated; it meant that the interfacial surface area A r.t. developed in the tube while rotated with constant revlmin (100 revlmin was fixed) had been found. For this purpose the sulphite solution from the same batch was used in a wettedwall column and in the rotated tube to make sure that pH and CoSO, concentration were

Fig. 6. Rotated tube.

exactly the same in both cases, and rates of absorption in these two devices measured. The concentration of a catalyst was chosen to achieve the fast reaction regime so that A,t. could be calculated from the following equation:

At. = A,.,.[(RA),t.I(RA),.,.l

(11)

as c+, k, and D were alike for the solution in the wetted wall column and rotated tube (both operated at the room temperature). Then the same procedure as for the wettedwall column cooperating with the rotated tube could be applied to another cooperating pair of devices- the sieve plate column and the rotated tube. The following equation was obtained: (hQ2 = A2A’D2+ (A2/Af,,)(RA);~,.

(12)

If now the experimental results are correlated as (Z&Q2vs. (M):., the higher values of RA and (I?&,, point out the slope from which AZ/At., and hence A can be found (as A’ equals zero). The straight line, however, should curve at the lower values of RA and (I&4),, as A’ increases with k decreasing. As hydrodynamic conditions were kept constant kL was assumed constant for all experiments. We do not observe this curved part of the diagram in Fig. 7, although for

Fig. 7. Plot of experimental results according to Eq. (12) (catalytic absorption of 0, in Na$O, solution).

1144

Attempts to determine the liquid-film coefficient

and the reaction stopped the precipitate dissolved and the previously pink colour was restored. The presence of the precipitate affected the froth. Its height increased with the amount of the precipitate in the solution. It is probable that the precipitate played the role of a surface active agent. The characteristic parameters for a run are shown in Fig. 8 where the temperature of the solution, height of the froth, and concentration of S032- are plotted against time. To find the specific surface area of the froth the parameters measured just after the catalyst was introduced into the liquid on a sieve plate were taken for calculations. Thus the effect of the precipitate as well as the exhaustion of S032was avoided.

RA = O-65 x 1O-3gmolelsec the estimated product A2A’D2 (the maximum attainable value in these experiments) reached the value almost equal to (ZU)2. But this deviation is within the accuracy of the measurements. The specific interfacial area found from the slope in Fig. 7 was 2.26 cm2/cm3. The following remarks on the behaviour of the sodium sulphite solution in the process of oxygen absorption on a sieve plate seem to be worthy of note. The Na$O, concentration was about 100 g/l. as reported by de Waal and Beek[8] to be sure that the reaction is zero order with respect to sulphite ions. But the concentration of CoSO, ranged up to lob2 g mole/ 1. which was about ten times as high as the highest concentration of the catalyst used by de Waal and Beek. Before the experiment pH of the solution was adjusted to 8-4-8.6 and not controlled during the oxidation. It was found that some time after the catalytic reaction started the pink colour of the solution ‘changed into orange, at first rather light and then more intense. This change in colour resulted from the fact that a very fine precipitate appeared, its amount increasing with time of the oxidation. When sulphite ions were used up completely

0

I 100

I L 200

5. DISCUSSION OF RESULTS There is some published information on interfacial area, derived from chemical absorption measurements, developed in plate columns. For the bubble-cap column (3 ft dia., 13 caps) Porter, King and Varshney [9] found l-5 cm2/cm3. This value increased to 2-O cm2/cm3 by inserting a wire screen into the froth. Sharma and Gupta [lo] reported for a 10-l cm dia. column with sieve plates (no downcomer) of 21.0 and 29.6

I

,

,

300

400

500

Time,

1 600

I

I

I

700

600

900

1000

WC

Fig. 8. Results of measurements of N&SO, concentration, temperature of the solution and height of the froth during a run (catalytic absorption of 0, in NqSO, solution).

1145

W. PASIUK-BRONIKOWSKA

per cent free area the values 2-2-5 cm2/cm3. Rodionov and Vinter[l l-131 worked with 5 X 15 cm2 sieve plates of 6 per cent free area and obtained 4.2 cm2/cm3 for 0.6 m/set gas velocity (3-5-6 cm2/cm3 for 0.3-l-9 mlsec respectively). These authors, however, did not correct the reaction rate constant for composition of the solution. With this correction their results should also approach 2.5 cm2/cm3 at the gas velocity equal to that for our experiments. Similar value has been obtained by Barrett [2]. Our experiments have yielded values of the specific interfacial area reasonably comparable with those mentioned above. We cannot, however, say the same for kL values. Sharma and Gupta[lO] found about O-04 cmlsec for plates of 14-5-29-6 per cent free area which was the same as for a bubble-cap column[9]. They observed for the same height of the froth the values of k, higher for plates of lower free area. This is probably because for the same superficial gas velocity in a column the contribution to the turbulence in the froth due to the gas velocity at which perforations are being blown through is higher when free area of a plate is lower. So it is rather not surprising that for the plate of 5.5 per cent free area we have obtained kL about 0.20cmlsec. At the superficial gas velocity O-6 mlsec it corresponded to about 11 mlsec in perforations to compare with about 4 mlsec for the plate of 14.5 per cent free area. Barrett [2] mentioned the fractional rate of surface renewal 100-500 set-l (k, about O@&O-09 cmlsec) in a froth and 3000-6000 see-’ (kL about O-22-0-31 cmlsec) in a spray after the inversion point was reached, whereas kL should be rather lower in the system with suspended drops in which mixing is much less efficient than in the bubbled liquid. 6. CONCLUSIONS

The experimental data confirm that the technique of gas absorption accompanied by a pseudo-first order reaction may be used for estimation of the specific inter-facial surface area for calculations of industrial plate absor-

bers. However, the discrepancy between the values of kL obtained by different authors leaves the problem of determining kL by means of this technique still open to question. For industrial application the method with a rotated tube enables to make quick estimations of the interfacial surface area without the necessity of measuring kinetic constants of the reaction used. A&nowledgments-The major part of this work was performed at the Department of Chemical Engineering of the Cambridge University. W. P. B. thanks Professor P. V. Danckwerts for his initiative suggestions and advise. She is also grateful to the British Council for the award of a scholarship. NOTATION

a

effective interfacial area per unit volume of the froth, cm2/cm3 A total interfacial area between gas and liquid, cm2 solid AS total inter-facial area between suspension and liquid, cm2 A' integration constant, g mo1e2/cm8 of the ionic reactant in c concentration bulk of liquid, g mole/cm3 cwt. solubility of Ca(OH),, g mole/cm3 concentration of the absorbed gas in CO bulk of liquid, g mole/cm3 C solubility of the absorbed gas in the liquid, g mole/cm3 D diffusivity of solute gas in liquid, cm21 set H Henry’s constant for carbon dioxide in the solution, g mole/cm3 atm Henry’s constant for carbon dioxide in HUl water, g mole/cm3 atm z ionic strength of the solution, g ion/ 1. I’, I” contributions to Z due to NaOH and N&CO, respectively kz kinetic constant for second order reaction, cm3/g mole set kinetic constant for n-order reaction coefficient of dissolution, cmlsec constant values for individual electrolytes NaOH and N&CO, respectively liquid-film coefficient in absence of reaction, cmlsec

1146

Attempts to determine the liquid-film coefficient n

p R R,

order of reaction partial pressure of carbon dioxide, atm rate of gas absorption per unit inter-facial area, g mole/cm2 sec. rate of dissolution of a solid per unit interfacial area, g mole/cm2 set

U p

superficial gas velocity, mlsec viscosity of liquid, CP

Subscripts r.t. rotated tube W.C. wetted column

REFERENCES [l] DANCKWERTS P. V. and SHARMA M. M., Chem. Engr 1966 u)2 CE204. [2] BARRET P. V. L., Ph.D. Thesis, University of Cambridge 1966. [3] CAMPBELL W. B. and HOBBS H. A., Chem. Engng 1966 73 136. [4] ASTARITA G., Mass Transfer wifh Chemical Reaction. Elsevier 1967. [5] WEBER H. C. andNILSSON K. T., Znd. Engng Chem. 1926 18 1070. [6] ASTARITA G., Private communication. [7] WESTERTERP K. R., VAN DIERENDONCK L. L. and DE KRAAJ. A., Chem. Engng Sci. 1963 18 157. [8] DE WAAL K. J. A. and BEEK W. J., Chem. Engng Sci. 1967 22 585. [9] PORTER K. E., KING M. B. and VARSHNEY K. C., Trans. Instn them. Engrs 1966 44 T274. [lo] SHARMA M. M. and GUPTA R. K., Trans. Instn them. Engrs 1967 45 T169. [l l] RODIONOV A. I. and VINTER A. A., Izu. oj%sh. ucheb. Zuoed., Khimiya Tekhnol. 1966 9 970. [12] RODIONOV A. I. and VINTER A. A., Zzo. uyssh. ucheb. Zuued., Khimiyu Tekhnol. 1967 10 102. [13] RODIONOV A. I. and VINTER A. A., Teoret. Osnouy Khimiyu Tekhnol. 1967 1481. R&nms&On a trouve les valeurs du coefficient /q de transfert de masse du c&C liquide et de la zone interfaciaie a par unite de volume de mousse sur une plaque perforce (surface perfor6e 5,5%) a partir de la technique d’absorption, accompagnee dune reaction irreversible, de pseudo-premier ordre. Les experiences ont et6 effect&es avec plusieurs systemes de reactions pour lesquelles les valeurs de 0.174.27 cmlsec et 197-2.28 cmZ/cm3 ont et6 atteintes pour kL et a respectivement. On a employe une methode qui permet de determiner ces valeurs sans mesurer les constantes cindtqiues. Les resultats confirmaient que Ton pouvait utiliser Iequation de Danskwerts pour pr6dire les taux d’absorption darts des colonnes B plaques perforees. Zusammenfassung- Die Werte des fliissigkeitsseitigen

Stoffaustauschkoeffizienten kL und der Grenzschichtiche u pro Raumeinheit Schaum auf einem Siebboden (gelochte FPche 5,5%) wurde unter Verwendung der Absorptionstechnik in Verbindung mit einer irreversiblen Reaktion pseudo-erster Ordnung beitimmt. Die-Versuche wurden mit mehreren Reaktionssystemen durchgefdhrt, bei denen die erreichten Werte von k,. und a 0.17-0.27 cm/set bzw. 1.97-2.28 cm2/cms betruaen. Es wurde eine Methode verwendet, die es ermijglicht, diese Werte zu bestimmen, ohne dass ei& Messung der kinetischen Konstanten erforderlich ist. Die Ergebnisse bestitigen, dass die Gleichung von Danckwerts fiir die Voraussage der Absorptionsgeschwindigkeiten in Siebbodenkolonnen angewendet werden kann.

1147