Oxygen transfer in a rotating disk reactor with continuous flow

cw Printed

lzalgbming .s&nce. in Great Britain.

vol.

OXYGEN

40, No.

12, pp.

2281~22a6,

TRANSFER

MYUNG

JIN KIM,

0

ooo94509/%s 198s. Fw@ltmtt

REACTOR

WITH

198s.

IN A ROTATING DISK CONTINUOUS FLOW YOUNG

SUNG

GHIM+

and HO NAM

s3.00+0.00 ptms Ltd.

CHANG+

Department of Chemical Engineering, Korea Advanced Institute of Science and Technology, P.O. Box 131 Dongdaemun, Seoul, Korea

(Received 12 October 1984) Abstract-The

oxygen transfer characterized by the liquid phase mass-transfer coefficient (kL) was investigated in a three-phase rotating disk reactor. Experimentswere carriedout in steady-state liquid Bow conditions because this type of operation is more commonly pm&red, for example, in wastewater treatment system. The oxygen transfer rate was measured by the sodium sulphite method, but the oxidation was carefully controlled so that the mass transfer was not enhanced by the accompanying chemical reaction. A large portion of oxygen transfer occurred by the convective motion on the fm surface of the bulk liquid in the trough, which was more significant when the flow rate was high in the axial direction.

R’lTRODUCTION

A rotating disk reactor consists of a number of disks mounted on a horizontal shaft, which are placed in a liquid-filled trough (Fig. 1). As the disk rotates, not only is the liquid in the trough well agitated, but also it is continuously entrained to form a liquid film on the disk surface Many workers El-51 have recognized that the large interface of the thin liquid film formed on the disk surfaces is responsible for smooth gas transfer. The first systematic approach to oxygen transfer in a rotating disk reactor was carried out by Yamane and Yoshida [l J. They analysed the diffusive transfer of oxygen through a liquid film with assumptions of uniform film thickness on the disk surface and complete mixing of the bulk liquid. Bintanja et al. [2] and Zeevalkink et al. [3] tried to refine the previous work, but the theoretical predictions were higher than the experimental results. They claimed that an effect of local film flow on the disk surface was important and ascribed the discrepancy between theory and experiment to the development of a boundary layer near the submerged disk. But another path for oxygen transfer from air to water in the trough was noticed by Ouano [4].

Although he believed that oxygen was transferred to the water both by the entrained film and by the surface of bulk liquid in the trough, emphasis was placed on the latter, especially at low rotation speeds. A similar idea was presented by Suga and Boongorsrang [S] with a more elaborated mathematical treatment, but largely incomplete mixing due to the boundary layer near the submerged disk accounted greatly for the lesser contribution of the entrained film. Thus the following questions arise: What is the main mechanism of oxygen transfer? Will it depend on the operating conditions? Although the continuous liquid flow is more common in practice, most previous works dealt with batch operations except for one where the experiment was performed at a fixed flow rate [S]. In batch operations the rotating flow due to disk rotation only influences the fluid motion in the reactor, but in continuous operations the bulk stream flow is equally important [s]. These two flows interact with each other in the mixing of bulk liquid. Surely, the gas transfer to the bulk liquid is related to the fluid motion in the trough. Herein, we will examine the effect of bulk flow rate on the mass transfer as well as that of the rotational speed of in continuous flow operations.

THE SODIUM

Fig. 1. Schematic diagram of a rotating disk reactor.

+Present addressz Energy Laboratory. Korea Institute of Energy and Resources, P.O. Box 339 Daejeon, Chungnam, Korea. *To whom correspondence should be addressed.

SULPHITE METHOD

In batch operations k,a values have usually been evaluated by measuring the dissolved oxygen concentration during oxygenation of initially oxygen-free liquid [l-3]. But in a continuous operation it is possible that liquid becomes saturated with dissolved oxygen even before the steady state is reached. For this reason we have adopted the sodium sulphite method. The volumetric liquid phase mass-transfer coefficient k,a was determined by measuring unreacted sulphite ion concentrations. In analysing gas absorption accompanied by chemical reaction, attention must be paid to the fact that the absorption rate can be increased if the reaction is fast enough to compete with diffusion in the critical region 2281

M. J. KIM et al.

2282

near an interface. The modulus M is often used to assess the effect of simultaneous chemical reaction [7]: The amount

M=

1 {

of dissolved

gas which reacts in the

“diffusion

film” near the

interface

I/

due to the enhancement by the chemical reaction. In order to satisfy the condition required for masstransfer-controlled slow reaction in the system with relatively low k, values, the reaction should be maintained at a correspondingly low rate. In this study we used a low concentration (0.05 M) of sodium sulphite solution without any catalyst, Co’+ or Cu’+.

The amount of unreacted

gas transferred

to the

EXPkRIMENTAL

(1)

-

bulk liquid phase

Table 1 summarizes the possible reaction regimes classified by modulus M. If M is larger than 1, the absorption rate at the interface will be influenced by the reaction and enhanced by a factor E compared with the purely physical absorption rate. But as A4 decreases, the effect of the chemical reaction decreases and finally the physical absorption dominates over the reaction rate near the interface. If the reaction is fast enough to maintain the bulk concentration of dissolved gas nearly at zero in spite of the condition of small M, the reaction enters a regime of “masstransfer-controlled slow reaction” [8]. k,a values in the regime of When determining mass-transfer-controlled slow reaction, we can make use of the following advantages: it is not necessary to know the reaction kinetics since gas absorption is not affected by the reaction; it is immaterial whether perfect mixing of the bulk liquid is achieved or not because the bulk-phase oxygen concentration is almost zero; k,a values can be evaluated owing to the continuous removal of gas by the reaction even though the solubility of gas is low. Some workers [9, lo] who examined the sodium sulphite method pointed out that the method was effective in obtaining the physical absorption rate for large k, values in high turbulence system. But they also warned that in the case of small k, values account must be taken of the enhancement of gas absorption by sulphite oxidation. Greenhalgh et al. with a stirred cell [ll], and Linek and Benes with a stirred cell and individual bubbles [12] proposed the minimum k, values above which the absorption rate was not increased by chemical reaction under their own reaction conditions. In the previous works on oxygen transfer in a rotating disk reactor [l-3] k, values are less than the minima specified by Greenhalgh et al. and Linek and Benes. This is the reason why Artavanis and Todd [ 131 could not obtain a true transfer coe5cient with Cu2+ Table 1. Classification of reaction regimes Slow reaction (A4 Q 1)

Reaction control O
control

Fast reaction (Mall

A=0 R = kLaA*

A=0 R = EkLaA*

Mass transfer

Apparatus and chemicals A schematic diagram of the rotating disk reactor system and its geometrical specifications are given in Fig. 1 and Table 2, respectively. Halfcylindrical trough and disks were made of acrylic resin. If the disk surface is smooth, liquid does not spread uniformly on the’surface, especially at low rotational speeds. Thus, the disk surfaces were finely scratched concentrically to enable good wetting of water on the disk surfaces while Yamane and Yoshida [l] used wire-meshed disks. The sodium sulphite solution was prepared by dissolving anhydrous sodium sulphite (Junsei, Japan) in distilled water. Oxygen was transferred from ambient air to 0.05 M sodium sulphite solution at 24°C. The dissolved oxygen concentration was measured with a dissolved oxygen analyser (Model 0260, Beckman). Determination of sulphite concentration The procedure of well-known iodometry is that the sample of sulphite solution is added to an excess of iodine solution and back-titrated with standard sodium thiosulphate solution using starch as an indicator [14]. However, this titration method is somewhat cumbersome and timeconsuming. We measured the optical density of residual iodine solution with a spectrophotometer (Spectronic 88, Bausch & Lomb) after mixing the sample with an excess of iodine solution. MATERIAL

BALANCES

IN THE SYSTEM

Figure 2 shows typical variations of e5uent sulphite concentration with time in a continuous operation. Generally,

four to five times mean holding

time (V/Q)

for the solution to reach a steady state where the concentration variations were negligibly small. Steady-state effluent sulphite concentration is lower at a higher rotational speed, which means that was sufficient

Table 2. Specifications of the rotating disk reactor Length of trough Inner diameter of trough Height of liquid level Liauid volume Number of disks Distance between disks Thickness of disk Diameter of disk Total interfacial area Interfacial area by wetted disk

(cm) (cm) (cm) (-) (cm) (cm) (cm) (cm2)

28.0 21.8 5.4 2000 10 2.35 0.27 14, 18, 20, 21 1458, 3046,3923,4379

( “/,)

59, 80,85,86

(cm?

2283

Oxygen transfer in a rotating disk reactor 0.05

3 \

G E ,o

0.04

sr” 0” 0.03 z s z s

0.02

5 : ”

0.01

0

40

60 Time

120 ( min

1

160

200

Fig. 2. Time courses of sulphite ion concentration in continuous operations for Q = 36 ml/min, D = 20cm and o = 10 (O), 50 (A), and 1OOrpm (0).

more through

oxygen

is

transferred

to

the

bulk

solution

the interface.

The oxygen

transfer to the liquid phase is given by

R = k,a(A*

- A)

(2)

where A and A* denote dissolved oxygen concentrations in the bulk liquid and in equilibrium with oxygen at interface, respectively. Sulphite ion reacts with half a mole of oxygen:

so:-

++02 =

so:-.

where E is the enhancement factor which depends on the reaction kinetics. In practice, when oxygen is transferred from air to a sodium sulphite solution of low concentration (0.005-0.05 M), oxidation is fast enough even without catalysts to maintain the bulk concentration of dissolved oxygen almost at zero. But attention must be paid in choosing the reaction conditions under which the sulphite oxidation will be a mass-transfercontrolled slow reaction to exclude the effect of chemical reaction. If the variation of bulk sulphite concentration (B) is available with time in a regime of mass-transfercontrolled slow reaction, then k,a is determined by eq. (7). Equilibrium concentration A* in the sodium sulphite solution is calculated according to van Krevelen and Hoftijer [7], which is not much different from that in pure water because of the low sulphite concentration. If k, is needed instead of k,a, the volumetric interfacial area can be obtained from the total gas-liquid contact area whose estimation is relatively simple for this rotating disk reactor [3,4].

Continuous

operation

In a continuous expressed as

operation,

material

balances

are

dA --=$(Ai-~)+~-rr(A,~j dt

(3)

In spite of numerous works, the reaction kinetics for sulphite oxidation are not well understood. The reaction is very sensitive to trace impurities of heavy metal ions (Cu2+, Co2+, Fe’+, Ce2+ and Mn2+), and is known to be influenced by many others such as the source of sulphite solution, kind of catalyst, pH, temperature and concentration of reagents [15-l 73.

The dissolved oxygen concentrations of the feed (Ai) and of the bulk liquid (A) are zero in the present work. Rearranging eqs (9) and (10) at steady state gives

Batch operation

For a mass-transfer-controlled

Material balances for dissolved sulphite ion (B) are given by

oxygen

(A) and

g

R=;$(B,-B).

where

Ek,a - 2r(A, B)

r(A, B) represents the volumetric

reaction rate.

eqs (4) and (5) yields

dB --= dt

2R-22

dt ’

If the steady-state condition is applied for the concentration of dissolved oxygen and the reaction is a masstransfer
(7)

2EkLaA*

= Q (Bi - B)/2 VA*.

(12)

Regime

(8)

(13)

If the sulphite oxidation is a mass transfer controlled slow reaction, the difference in sulphite concentration of influent (Bi) and of efRuent (B) does not depend on the effluent concentration, B. But if a fast reaction takes place, the difference depends on the effluent concentration since the enhancement factor E is a function of the reaction kinetics. As far as eq. (12) holds true, mass-transfer coefficient k, can be evaluated only by measuring sulphite concentrations at two points, Bi and B. k, obtained in batch and continuous operations will be a surface-averaged value where the contributions by the wetted disks and the free surface are mixed. RESULTS

In the case of a fast reaction, dB -_= dt

slow reaction,

k,a = Q(Bi - B)/ZYA*.

dc

Combining

(11)

In the case of a fast reaction, eq. (12) will be altered to

dA -=R--_(A,B) dB -= dt

= ; (Bi - B) - 2r(A, B).

of

AND DISCUSSION

moss-transfer-controlled

slow reaction

Figure 3 shows the variations of bulk sulphite concentration with time in batch operations. Since the

M. J. KIM et of.

2284

2 u

Ll E

E \ z s

0

I 40

I 80 Tune

I 120 (mrtl

I 160

I

Source

Cont. of Na,SO, (8 mol/l)

0

0.5

14

Greenhalgh et 01. El l]

0.25

Yoshida et al. El01

0.125

7

This work

0.05

4

30-50

o

I

1

I

0.04

0.08

I 0.12

Concentration of No, SO, (g

I 0.16 moC/

0 1)

Fig. 4. Dependence of the mass-transfer coefficient on sulphite ion concentration of effluent for Q = 84 ml/mitt and w = 25 rpm.

the feed concentration ranges from 0.025 to 0.2 h4 for different disk sizes. k, values were higher than the minimum of 4.0 x lo- ’ m/s not only in this case, but in all cases of continuous operations. Oxygen transfer in batch operations If the entrained film on the disk surface is sufficiently deep for the diffusion of oxygen, the penetration model gives an approximate solution [7]: k,=2

J

2.

(14) E

In a rotating disk reactor, exposure time tE corresponds to the mean residence time of the entrained film in the gas phase. Being different from other systems, e.g. packed beds, the time is rather simply determined by the height of the liquid IeveI and the rotational speed of the disks if the radii of the disks are given [l. 21. The predictions from eq. (14) are compared in Fig. 5 with the experimental results obtained from batch operations of Q = 0. Most previous works [l-3] have indicated that the penetration model was adequately applied to the operations in high speeds of rotation in which more liquid was entrained along the disk surface and where the residence time of the film in the gas phase was shorter. In general, their experimental data were SO-70 o/0of the theoretical values even estimated by the diffusion model with a finite depth of liquid film. of minimum k~ values

kL x 105, minimum (m/s)

Linek and Benes [ 123

n

14cm

Fig. 3. Time courses of sulphite ion concentration in hatch operationsforD=20cmando=5(0),10(x),25(O),50 (A) and 100 rpm (0).

Table 3. Comparison

a

18 cm 0.5-

200

rate of disappearance of sulphite ion does not depend on the sulphite concentration at high rotational speeds of the disks (25-100 rpm), eq. (7) is applicable at these high rotational speeds and the reaction is a masstransfer-controlled slow one. This does not mean that the reaction rate is zero order in sulphite [7]. But when the disks rotate slowly (S-10 r-pm), the rate of disappearance decreases with the sulphite concentration and finally becomes constant. This implies that the reaction rate is comparable to the mass transfer rate, and that the mass transfer modulus M is close to 1 or larger. Consequently, at a low speed of rotation the initial phase of the reaction is fast enough to enhance the oxygen absorption, but as the reaction proceeds, the reaction enters the mass-transfer-controlled regime. As was already mentioned, some workers [lO--121 reported the minimum values of k, together with the concentrations of sulphite ion and catalyst used. The minimum k, values reported by Yoshida et al. [lo] and Linek and Benes [12] were determined by direct comparison with the results from physical absorption, while those reported by Greenhalgh et al. [l 1) were estimated from the model of absorption with chemical reaction. In this work, when the k, value is higher than 4.0 x lo- 5 m/s, i.e. the rotational speed was higher than 25 rpm, the absorption rate was not enhanced. Table 3 shows that the results of the present investigation are consistent with those of Yoshida et al. and Linek and Benes. Furthermore, the minimum k, value can be reduced by decreasing the sodium sulphite concentration. In continuous operations Fig. 4 confirms that the reaction does not enhance the absorption rate when

I-

LJ

cm

D=21

1.5 -

Method Comparison of oxygen absorption intb sodium sulphite and argon into sodium sulphate solution of identical concentration Model of absorption with simultaneous m, n-th order reaction Comparison of oxygen absorption into sodium sulphite and into sodium sulphate of identical solution concentration Dependence of kLa on sodium sulphite concentration

Oxygen transfer in a rotating diik reactor 1.4

1.2

3 5 “$ x &

I

0.6

0.6

0.4 0.2

0

I

I

,

60

40

Rototionol speed (rpm) Fig. 5. Effect of rotational speed on k~ for D = 20 cm and (2 = 0 (O), 36 (A) and 84 ml/min ( Cl ). The dashed line was obtained from eq. (14) according to the penetration model.

But the values in Fig. 5 are higher than those from the penetration model which are the upper limits of the diffusive transfer. This cannot be explained without considering transfer through the surface of bulk liquid in the trough. Table 2 shows that the interfacial area provided by the liquid film on the disks is 85 % and the free surface of bulk liquid makes up the rest. While oxygen transfer through the entrained film is mainly attained by molecular diffusion, it is reasonably surmised that convective transfer dominates near the free surface of bulk liquid. It is somewhat unnatural to compare the results in this work directly with others obtained under different experimental conditions. But Fig. 6 shows that our results lie between those of Bintanja et al. [Z] and Zeevalkink et 41. [33 and those of Ouano [4]. As mentioned earlier, while the former placed emphasis on the diffusive transfer via the entrained liquid flIm on the disk surface, the latter stressed the role of the free surface of bulk liquid in the trough.

I 0

0.6 7

E

“0 -

0.6

x y’

0.4

M

IO

I 20

Rototionol

I

I 30

40

speed (rpml

Fig. 6. Comparison of the results in batch operations (@ , I$ = 0.79) with others. The data were taken from Bintanja et al. (*, q5= 0.92), Zeevalkink et al. (0. C#I= O.W,A, Q = 0.93) and from Ouano (Cl, I$ = 0.78).

2285

Certainly, the cottvective transfer is much faster than the diffusive transfer if they occur simultaneously. If the transfer through the free surface of bulk liquid is essentially a convective motion, it should depend on the characteristics of turbulence near the interface. We do not think that the several minutes of the experiments by Bintanja et al. [2] and Zeevalkink et al. [3] were sufficient for fully developing the fluid motion in the trough, because it usually takes 34 times mean holding time to reach a steady state under continuous liquid flow conditions [6]. There may have been a possibility that some stagnant region existed, particularly near the free surface of bulk liquid. The large values of Ouano [4] would result from using the different experimental apparatus of rotating disk filters, which might cause more vigorous stirring of bulk liquid to form entrapped air bubbles.

Oxygen transfkr in continuous operations Evidence for involving oxygen transfer through the free surface of bulk liquid can be easily found in continuous operations rather than in batch operations. Increase in the bulk liquid flow rate does not have a great influence on the formation of a liquid film on the disk surface, but sufficiently alters the fluid motion in the trough. That is, if the main mechanism of oxygen transfer from the air is via the entrained liquid film, the rate of oxygen transfer will not be greatly changed with the bulk liquid flow rate. But Fig. 5 clearly demonstrates the effect of flow rate on the oxygen transfer. This may be partly caused by the fact that the axial flow in the trough disturbs the boundary layer near the submerged portion of the disk. However, the effect of flow rate is pronounced at low speeds of rotation, where development of the boundary layer is poor and the amount of oxygen transfer through the entrained film is small. A more plausible explanation is that the intensity of turbulence near the free surface of bulk liquid increases with the flow rate. The mixing of bulk liquid in the trough results from the interaction of the axial flow in continuous liquid flow operations and the rotating flow due to the disk rotation [6]. These two flows complement each other to some extent, so the effect of disk rotation is latent at a high flow rate and that of flow rate is small when the disks rotate rapidly (Fig. 7). Nevertheless, sharp variation of k, with the low speeds of rotation in Fig. 5 indicates that the rotation of disks becomes more necessary with increasing flow rate even if its speed is low. Figure 8 shows the changes of k, values with respect to the submergence of disk to the trough: 9

Submerged area of the disk = Submerged area of the trough (a cross-sectional view)_

(15)

If the mixing of bulk liquid is closely related to refreshing the free surf-, sufBcient agitation by the disk will be essential. As the value of C$increases, more liquid in the trough is directly affected by the move-

2286

M. J.

KIM

et

al.

was confirmed by the minimum k, value above which no chemical enhancement occurred. Acknowledgement-The authors are indebted to the Korea Science and Engineering Foundation (KOSEF) for partial support of this research. NOTATION

tE

concentration of dissolved oxygen, g mol/l volumetric interfacial area, cm-’ concentration of sulphite ion, g mol/l diameter of disk, cm molecular diffusivity of dissolved oxygen, m’/s enhancement factor, k, (chemisorption)/k, (physisorption) height of liquid level, cm liquid phase mass-transfer coefficient, m/s modulus defined by eq. (1) volumetric liquid flow rate, l/min volumetric gas absorption rate, g mol/l/min volumetric reaction rate, g mol/l/min time, min mean residence time of entrained film at gas

V

phase, s total volume

A a B D

0

I

I

1

I

60 120 Flow rate (ml /min)

I60

Fig. 7. Effect of flow rate on kL for D = 20 cm and w = 5 (0). 25 (A) and 100 rpm (Cl ).

DA E H kL

Q”

R r t

of liquid in the trough, 1

Greek

letters

w

rotational speed of disk, s- ’ disk submergence to the trough defined by eq.

9

(15) REFERENCES 0

0.2

0.6

0.4

0.6

I

9

Fig. 8. Effect of disk submergence to the trough on kL for Q =84ml/minandw=5(0),25(A)and lOOrpm(0).

of the disk, which consequently facilitates the oxygen transfer. Although Zeevalkink et al. [33 used the immersion depth for measuring the extent of mixing in the trough, we think that 4 is more general as a design factor because it can cover the variations of trough and disk sizes. ment

CONCLUSION

The transfer of oxygen in a rotating disk reactor was analysed in terms of diffusive transfer through the entrained film on the disk surface and convective transfer through the free surface of bulk liquid. Oxygen from the air was transferred to the bulk liquid in the trough via the entrained liquid film to some extent, but the convective transfer became important as the flow rate in the axial direction increased. Physical absorption rates were obtained by a masstransfer-controlled slow oxidation of sulphite, and it

Cl1 Yamane

T. and Yoshida F., J. hem. Engng Jap. 1972 5 381. PI Bintanja H. H. J., van der Erve J. J. V. M. and Boelhouwer C., Water Res. 1975 9 1147. c31 Zeevalkink 1. A., Keiderman P., Visser D. C. and Boelhouwer C.. Water Res. 1979 13 913. Ouano E. A. R., Water Res. 1978 12 59. E] Suga K. and Boongorsrang A., Chem. Engng Sci. 1984 39 767. C61 Kim M. J., Ghim Y. S. and Chang H. N., Chem. Engng Sci. 1984 39 813. c71 Danckwert P. V., Gas-Liquid Reactions. McGraw-Hill,

New York 1975.

Chhabria M. C. and Sharma M. M., Chem. Engng Sci. 1974 29 993. c93 Phillips D. H. and Johnson M. J., Ind. Engng Chem. 1959 51 83. Cl01Yoshida F., Ike& A., Imakawa S. and Miura Y., Ind. Engng Chem. 1960 52 435. El11Greenhalgh S. H., McManamey W. J. and Porter K. E., Chem. Engng Sci. 1975 30 155. Cl21Linek V. and Benes P., Biotechnol. Bioengng 1978 20 697. Artavanis G. and Todd J. R., Biotechnol. Lett. 1980 2 23. [:J Kolthoff I. M., Sandell E. B., Meehan E. J. and Buckenstein S., Quantitative Chemical Analysis, 4th edn, p. 842. Macmillan. London 1969. Yagi S. and Inoue H., Chem. Engng Sci. 1962 17 411. [:z] Westerterp K. R., van Dierendonck L. L. and de Kraa J. A., Chem. Engng Sci. 1963 18 157. Cl71 Linek V. and Mayrhoferova J., Chem. Engng Sci. 1970 25 787. PI