Mass transfer, mixing and heat transfer phenomena in low viscosity bubble column reactors

The Chemical Engineering

Journal, 28 (1984) B21 - B42

B21

Review Paper

Mass Transfer, Mixing and Heat Transfer Phenomena Column Reactors

in Low Viscosity Bubble

J. J. HEIJNEN and K. VAN’T RIET* Research

and Development,

Gist-Brocades

NV, P.O. Box 1, 2600 MA Delft (The Netherlands)

(Received January 5, 1984)

ABSTRACT

Bubble columns are widely used in chemical and biotechnological process industries. The important reasons for this wide usage are the simple construction, without moving parts, and the high energy efficiency for mass transfer. It is not surprising therefore that much research on this subject has been published, yet selecting material of practical use is rather difficult. To overcome this problem, in this review, attempts are made to extract formulae and guidelines as simply as possible on the basis of currently available material. The starting point is the mechanisms occurring in bubble columns, i.e. bubble formation, bubble rise and resulting circulation patterns. Once these phenomena are understood, mixing and heat and mass transfer are much easier to deal with. Bubble formation is largely dependent on the sparger type, which can be divided into three groups: single orifices, porous discs and two-phase injectors. The original bubble diameter together with the superficial velocity and liquid properties determine the bubble diameter, holdup and circulation patterns in the bubble column. Gas holdup, bubble diameter control kLA and circulation patterns determine mixing and heat transfer. Simple relations are derived for model systems. By means of a mechanistic approach, guidelines are given for more complex liquids.

1. INTRODUCTION

Bubble columns are used in a variety of processes as an apparatus to achieve mass *Present address: Department of Process Engineering, Agricultural University, Wageningen, The Netherlands. 0300-9467/84/$3.00

transfer and/or chemical reaction, usually in low viscosity systems. In the last decade, bubble co’lumns have found widespread application in biotechnological processes such as the production of baker’s yeast, wastewater treatment, single-cell protein (SCP) production [ 11, citric acid fermentation etc. Parallel to this development there has been a tendency to modify the bubble column in order to meet specific process requirements. This has led to a variety of bubble-column-like reactors. For example the need for better liquid circulation has stimulated the development of the air-lift reactors with an internal or external liquid circulation loop. The fact that better mass transfer was needed has resulted in the multiple-stage tower reactor where gas is dispersed many times through sieve plates. Literature surveys of reactor types have been reported by Sittig and Heine [2], Blenke [3] and Schiigerl [4]. This review will be mainly based on a description of the simple bubble column with a low viscosity liquid, emphasis being laid on the mechanisms of the processes occurring in a bubble column. These mechanisms include bubble formation at the sparging device, coalescence and redispersion and the resulting flow characteristics. A better understanding of such mechanisms leads to more insight into the resulting mixing, heat and mass transfer.

2. HYDRODYNAMIC

PHENOMENA IN A BUBBLE

COLUMN AND THEIR INTERACTIONS

The most important process in a bubble column is the formation of gas bubbles at the gas sparger. The smaller the bubbles, the larger is the area for mass transfer between the gas and liquid phases. There exists 0 Elsevier Sequoia/Printed in The Netherlands

B22

the bubble column area. This is called the homogeneous flow regime. Gas holdup, also called porosity or void fraction, can generally be defined as

a large variety of sparger designs, such as a simple pipe, a porous diffuser or a complex two-phase device (ejectors-injectors). The more complex spargers were developed in order to generate very small bubbles. The diameter d,,* of the gas bubble at the sparger is not necessarily the same as the bubble diameter d,, in the bulk of the column. The bubbles from the sparger can undergo a coalescence and/or a (re)dispersion process. The coalescence rate is dependent on the liquid surface properties, varying from coalescing (e.g. pure liquids) to non-coalescing (e.g. water-salt systems). The distinction between coalescing and non-coalescing properties is very important, although most fermentation liquids are situated in between. Dispersion of the bubbles is entirely determined by the turbulence processes in the bubble columns. In addition to gas phase dispersion, gas phase separation in the bubble column should be taken into account. Gas phase separation can present problems, particularly in non-coalescing media where minute bubbles have been generated. The bubbles generated at the sparger rise in a so-called bubble swarm. Bubble swarm behaviour in a bubble column is mainly determined by the gas superficial velocity u,. At low u, values there is a fairly homogeneous distribution of rising bubbles through

I

) sparger

VG + vL

e=

In the homogeneous flow regime the gas holdup can be calculated according to

(lb) Ubs

which !.& is the single-bubble rise velocity. ubS is dependent on d,, and E. At high gas superficial velocities a number of very large bubbles exist as a result of coalescence. This results in an increase in bubble rise velocity and has a self-magnifying effect. As the large bubbles occur mainly in the centre region, this leads to large-scale circulation patterns of liquid as well as gas. This is called the heterogeneous flow regime. Transition from homogeneous to heterogeneous flow occurs at about u, = (2 - 4) X 10e2 m s ‘. The exact value is very dependent on liquid properties and column and sparger configurations. Figure 1 gives a schematic representation of the interrelations of liquid and apparatus properties with flow regime and bubble size. Additionally, it shows how these factors influence holdup and liquid in

1

1

type

(14

VG

I

I

1 liquid

column

mixing

flow reglme homogeneous

configuration

heterogeneous

-

L DE

liquid

I superficial , gas

velocity

YI -

bubble

size

at sparger

1 d,,

I

bubble velocity medium properties T

B

coalescence properties

P

_ -

bubble

rise Vb,

heat

transfer

ma*s

transfer

I

I

1

holdup c

sire

in column

d,,

--

k, A

1

separation

Fig. 1. Interrelated

processes in a bubble column.

B23

flow patterns and therefore mass and heat transfer and mixing. In this review the mechanisms shown in Fig. 1 will be dealt with in particular.

3. GAS PHASE DISPERSION

The gas dispersion in a bubble column can be brought about by means of a variety of spargers. A review has been given by Schiigerl [ 51. Here we shall divide the types of sparger into three groups: (1) single orifices and perforated discs, (2) porous discs and (3) two-phase injectors. Depending on the coalescing or non-coalescing properties of the liquid the bubble diameter d,: at the sparger can differ significantly from the ultimate bubble diameter d,, in the column. Therefore bubble formation and bubble diameters at the spargers will be discussed separately from the bubble diameter in the column. To characterize the bubble size distribution we shall use the Sauter mean diameter

This is widely used as the most representative average diameter for mass transfer. From reports by Buchholz et al. [6], Akita and Yoshida [7] and Nakanoh and Yoshida [8] it is obvious that different definitions of mean bubble diameter can lead to very different values. 3.1. Bubble

size dvz at the sparger 3.1 .l. Gas dispersion through an orifice or perforated disc

With this type of sparger, gas is introduced into the column through one or more holes with a diameter larger than about 1 mm. To prevent the back flow of water into the holes the Weber and Froude criteria given by Ruff et al. [9] need to be met. For bubble formation at increasing gas flow rates, three regimes [lo - 121 need to be distinguished: separate bubble formation; chain bubbling; the jet regime or the turbulent regime. For the separate bubble formation regime, dvs* is dependent on the equilibrium between surface tension and buoyancy forces. d,,* can be calculated according to van Krevelen and Hoftijzer [13] as

d VS

This equation is valid for d,,* > d, [14]. In air-water systems this means that d, < 6 X 10V3 m. As the gas flow rate increases, the bubbleseparating frequency increases so that bubbles leave the sparger as a continuous chain. Here the diameter is frequency determined. Wallis [15] has reviewed a large number of data showing that the simple relation of Davidson and Harrison [ 161 is very appropriate: d

* “S

=

1_17~,0*4d,o*~g-o*2

(4)

More sophisticated relations have been reported by Kumar et al. [ 171 and Mersmann [ 181. Akita and Yoshida [7] have given another dimensionless relation leading to comparable values. Equation (4), although simple, is adequate for our purposes, however. When gas flow rates are further increased, bubble formation becomes unstable. Leibson et al. [lo] and Bhavaraju et al. [ll] found a transition to occur for low viscosity systems at 2000 < Re, < 10 000. In such a case the dependence on gas flow rate is only marginal and it can be stated that for the jet regime 4 X 10m3m < d,:

< 6 X lop3 m

In Fig. 2, d,,* values are given for a number of sparger diameters. To obtain really small bubbles it is desirable to operate in the separate bubble regime. However, it can easily be established that only low superficial gas velocities are achieved in this manner. Therefore orifices will nearly always be operating in the jet regime. If bubble diameters less than 4 X lop3 m are desired, a large number of orifices are required, leading automatically to porous discs as discussed in Section 3.1.2. It must be stressed that dvf for bubbles from this type of sparger is not influenced by the coalescing or non-coalescing properties of the medium. This is in contrast with the other types of sparger (porous disc or ejector) as will be shown later. 3.1.2. disc

Gas dispersion

through

a porous

As shown above, an orifice sparger leads, in practice, to bubbles of (4 - 6) X lop3 m

3m) t separate

bubble

chain

bubbling

transition

jet

regime

o”

000

region

d,=6x10-3m

/

3 0

0

O0

0

I

10-l I_

Fig. 2. Bubble

formation

from an orifice

in the air-water

system:

diameter. For mass transfer, smaller bubbles are far more effective. This has led to the development of spargers which can generate extremely small bubbles. One of these is the porous disc. According to Koide et al. [ 191, d,,* in non-coalescing media can be calculated as

In coalescing

-?_ i (JVJ1

media, dvs* measured

w

2.0

o-6

Fig. 3. Bubble

-1

et al.

I

)

[lo].

above the sparger is expressed

at a short

COALESCING

5x10-4

from a porous

as

-% i o, i

(6)

Figure 3 shows these relations. As can be seen, for non-coalescing media dvs* < 10d3 m. For coalescing media the bubbles are larger, ranging from 2 X 10m3 to 4 X 10m3 m. For coalescing systems it is also apparent that the bubbles rapidly become larger at greater air flow rates.

10-s

-

,&O

0.41

5x10-5

10-5

formation

s

d “S* = 1.04 X 10-2(u,d,)0~16d0-0~07

(5)

5x10-4 5x10-5

NON-COALESCING

10-5

1

2

d~ (m)

4,

4.0

0, data of Leibson

distance

0.38

d YS* = 6.1 X 10-3(u,d,)0*1d00.08

vodo(m

i

10-4

plate in the air-water

--,

system.

vOdo(m2s-1)

B25

3.1.3. Gas dispersion injectors

through

ejectors-

Because porous discs are frequently subject to clogging, alternative small bubble spargers have been developed. This has resulted in two-phase ejectors-injectors [ 20 - 221. In this type of sparger, gas and liquid are concurrently pumped through a small nozzle. Because of the extreme energy dissipation in this nozzle, very small bubbles are generated. In non-coalescing ,media, bubbles with d * = (0.5 - 1) X low3 m are produced [20], lziding to d,, = (0.5 - 1) X lop3 m. In coalescing media, however, the bubble diameter d,,* increases rapidly, especially at higher air flow rates, to about 5 X lop3 m, according to Schiigerl [ 201. These results closely resemble the bubble formation at the porous disc sparger. Therefore we may conclude that ejectors-injectors generate bubbles with d * = (0.5 - 1) X low3 m in non-coalescing midia and with d,,* = (4 - 6) X 1O-3 m in coalescing media. In summary, the following conclusions about d,% can be drawn. (a) From Fig. 2 it is evident that, to generate bubbles with d,,* < (4 - 6) X 10e3 m, very small orifice diameters and low orifice gas velocities are required. In practice, however, gas velocities are large in the orifice and orifice diameters are mostly much larger than 10e3 m to avoid clogging. This means that an orifice sparger usually leads to a bubble diameter dVz of (4 - 6) X lop3 m irrespective of medium properties (coalescing or non-coalescing). This is quite important, especially in bioreactors because coalescing or non-coalescing properties of the broth can change dramatically as a result of microbial activity [ 231. (b) The lower d,,* values (less than 10m3m) can only be reached using porous discs or ejectors-injectors and exclusively for a noncoalescing fluid or extremely low superficial gas velocities in a coalescing fluid. Finally it should be emphasized that gas dispersion through an orifice requires not much more energy than that due to the hydrostatic pressure whereas gas dispersion through porous discs or ejectors-injectors are very energy consuming. For example, the liquid pumping through ejectors can consume as much as 50% of the gas compression energy [ 241.

3.2. Bubble sparger

size d,, at a distance

from

the

The bubbles generated at the sparger can either coalesce to larger bubbles or be dispersed to bubbles of smaller diameter. In coalescing media (e.g. pure liquids), d,, can be calculated as indicated by Calderbank [25] and Lee and Meyrick [ 261 as DO.6

d,, = 4.15

(Pi V)o*4po.2

ea.5 + 9 x 1o-4

(7)

On the assumption that P/V = pgv, and E = vs/vbs with vbs = 0.25 m s-l, this leads for an air-water system to a d,, value of about 6 X lop3 m. This is in accordance with the d,, values for the jet regime of Fig. 2. The d,, value of about 6 X lop3 m is rather insensitive to v, variations as the v, influences on E and P/V cancel each other out largely. Experimental confirmation of this for bubble columns has been given by Akita and Yoshida [7], Buchholz et al. [6, 271, Towel1 et al. [ 281 and Koide et al. [ 191. It should be noted that eqn. (7) is derived for stirred vessels in which circulation is very intensive and the chance of collision for each separate bubble present is high. In bubble columns at very low superficial gas velocities, collision chances may be low and this results for porous discs in bubbles smaller than those calculated from eqn. (7). This was clearly shown by Marrucci and Nicodemo [29]. With a porous disc in an air-water system, d,, increases sharply with increasing gas superficial velocity. These measurements, with those from Buchholz et al. [6,27] and Yoshitome [30], indicate that eqn. (7) is applicable for v, > (1 - 2) X lop2 m s-l. In non-coalescing media for cases where d,,* > d,, the ultimate bubble diameter d,, can be calculated according to Lehrer [31] as follows: oO.6

cl,, = 1.93

(P/ v)o.4po*2

(8)

In Fig. 4, d,, is calculated for air-water systems with coalescing or non-coalescing properties for different P/V values. It is assumed that P/V = pgv,, which is a proper estimate for columns of normal height values as calculated by Roels and Heijnen [32]. Briefly, we can conclude as follows: (a) in coalescing systems, if d,,* > 6 X lop3 m turbulent dispersion to d,, = 6 X 10m3m (eqn.

R26

coalescing medium, and thus to the formation of bubbles 6 X low3 m in diameter with concomitant loss of mass transfer capacity. An alternative is mechanical gas phase separation (e.g. centrifugal devices) for which Schiigerl et al. [ 331 reported power consumption to be as high as 1000 - 5000 W m- 3. In contrast, Zlokarnik [ 341 described watersalt media where small bubbles do not cause difficulties in gas phase separation. This shows that very different mechanisms govern the lack of coalescence in water-salt media compared with water-organic media. 0.1

0.2

Fig. 4. Equilibrium bubble diameter bubble column (air-water system).

0.3 -,

r,(ms-‘)

in a turbulent

(7))

occurs and if d,,* < 6 X 10e3 m coalescence to d,, = 6 X 10P3 m occurs; (b) in non-coalescing systems, if d,,* > d,, turbulent dispersion occurs until the bubble from the sparger has reached a diameter d,, (eqn. (8)) and if dvz < d,, the bubble diameter from the sparger will not change, so d,, = d *. It appears that completely non-coalesc;ig media are rarely seen. Buchholz et al. [ 61 worked with a “coalescence-suppressing” medium which still gives a bubble diameter between dvS* and d,, = 6 X 1O-3 m. In practice this might be the case for many fermentation fluids. It can be concluded that the mechanisms leading to the bubble size in bubble columns are rather complex and involve the bubble size at the sparger, the coalescence properties of the medium and the collision frequency. The mechanisms and formulae given here afford insight into the estimation of the bubble size.

4. GAS PHASE

SEPARATION

As shown above, it is quite feasible to generate very small bubbles of (0.5 - 1) X 10e3 m for promoting mass transfer. However, these small bubble diameters occasionally present serious difficulties. Schiigerl et al. [33] showed that in an ethanol SCP fermentation with very small bubble aeration there was little gas phase separation from the broth. The addition of an antifoaming agent led to a change from a non-coalescing to a

5. LIQUID

MIXING

5.1. Description and quantification processes in bubble columns

of mixing

Liquid mixing in a bubble column is due to several processes. The bubbles themselves contribute to mixing because of liquid transport in the bubble wake as well as transport due to velocity differences around the bubble. This mixing process can be regarded as a kind of diffusive mixing to be characterized by an effective dispersion coefficient. Ruckenstein [35] and Weiland [36] showed that this dispersion coefficient is of the order of only 10m3 - lOed m2 s-i. A very different mixing process is accomplished through the action of large circulating flows in the bubble column under heterogeneous flow conditions. These circulations arise from higher gas holdup values in the centre of the column 16,371, leading to an upward velocity at the centre. Although there is an upward velocity along the whole axis, circulations do not cover the column length. The momentum transport between upward and downward liquid currents leads to a break-up of the large circulation patterns (Fig. 5(a)). The resulting small circulations appear to be of the order of the column diameter [38, 391. A simple way of stabilizing circulation flow over the column length is the introduction of a draught tube (Fig. 5(b)). However, unhampered circulation can be expected to improve mixing characteristics (see Section 5.2). From a mathematical approach based on a flow model with circulatory flows of vessel diameter a liquid circulation velocity can be calculated [ 39, 401. Joshi [39] derived the equation

B27

c)

T1‘I

Ll

(a)

1’I

n

bI

(b)

Fig. 5. (a) Flow patterns in a bubble column without a draught tube; (b) flow patterns in a bubble column with a draught tube. 0

VLC= 1.18 {gZ(v,

-

Evbs)}1’3

(9)

which agrees fairly well with data in the literature. However, a major disadvantage of this equation in engineering calculations is the inclusion of the dependent variables E and &. Joshi reported a rather complicated method of obtaining the values of e and vbs. However, from actual e and v, data it can be argued that under heterogeneous flow conditions v, > e& and eqn. (9) reduces to VLC= o.9(g~v,)“3

(10)

where only the independent variables Z and v, are present. Figure 6 gives the data reviewed by Joshi. It can be seen that up to VL ’ = 0.7 m s-l (v, = 0.2 m s-l) the agreement of both equations with experimental data is satisfactory. Equation (10) was found to be adequate in the following ranges: v, = 0 - 0.4 m s-l; Z = 0.1 - 7.5 m. In the above discussion, vLc was assumed to be dependent only on v, and 2. However, Buchholz et al. [6] clearly showed that vLc increases as the distance from the sparger becomes larger. These increases are of the order of 10% - 50% and it is not clear whether they are due to bubble expansion and/or entrance effects. In any case this indicates that velocity prediction with variations of less than 10% is unnecessary because of a “natural” variation of this size. Liquid superficial velocities only influence vLc for vL Z+v,. Under these circumstances the equations given by Joshi [39] can be used. It was further found [37, 411 that the upward liquid velocity profile is more or

I/

0.5

1.5

1.0

c -

“L

predicted

(ms-‘1

Fig. 6. Comparison between liquid velocities calculated from eqn. (9) (x) and from eqn. (10) (0) and measured velocities (data reviewed by Joshi [39]) (-).

less parabolic and that the mean upward velocity is between 0.6 and 0.9 times the centre velocity, 0.8 times being an adequate estimate. Joshi and Sharma [41] determined that both upward and downward currents flow through equal areas. The liquid mixing flow can thus be calculated as @L = 0.302s’sCpoi’sgi’a

(11)

This type of equation is consistent with the relation of Smith et al. [42] for the liquid entrained by open bubble plumes in shallow systems (H/Z Q 1). Z in eqn. (11) is replaced by H + 0.07, the constant factor in eqn. (11) being the only difference for the larger (H 3- 0.07 m) diameter. Smith et al. found a somewhat lower constant of 0.074 as a general correlation constant for all systems investigated. For the smaller systems the H + 0.07 factor leads to absolute $L values which closely approach those calculated from eqn. (11). It thus appears that liquid mixing in -bubble columns is determined by the smallest linear dimension of the column (this is Z if H/T > 1 and H if H/Z < 1). In much of the literature on liquid mixing in bubble columns the mixing data are presented in terms of an effective dispersion coefficient QEL. Joshi [ 391, when reviewing a vast amount of data, found the following correlation :

B28

‘2)aL = 0.372v,c Combined

(12)

with eqn. (10) this leads to

QsL = 0.33(g~4v,)i’3

(13)

This is in excellent agreement with the correlation of Baird and Rice [43], who derived eqn. (13) directly, the only difference being a constant factor of 0.35. When the scatter of the experimental data is considered, this difference is negligible. Another means of describing the mixing process is provided by the Peclet number Pe. For simple tube flow the relation between the Peclet number Pe and the number n of theoretical mixers is Pe V,“H _=2 2iz>$ (14) Joshi [39] calculated

that

H n=0.82

(15)

On the assumption that n S 1, eqns. (12), (14) and (15) lead to (anL = 0.36(g24v,)“3

and it appears that, precisely when a transition to heterogeneous flow occurs, the dispersion coefficient (although small) reaches a maximum value [45, 461 which depends on a number of variables. In this gas flow region (v, < (2 - 4) X lo-* m se’) the dispersion coefficient must be estimated from eqn. (16). Channelling can also occur, particularly at very low air velocities with one sparger and, at all air velocities, with a slight tilting of the column (5”). A review of flow velocities and dispersion data leads to rather consistent relations. However, the scatter of the data is large (10% - 50%) and deviations can occur because of particular geometries and flow phenomena. It follows that, for a specific geometry, fluid behaviour and range of gas velocities, a critical evaluation is necessary to rule out the possibility of significant deviations from the above relations.

(16)

Equation (16) is in surprisingly good agreement with the other correlations. It also shows the simple background of the dispersion data, i.e. a column consists of n ideally mixed compartments, with n given by eqn. (15), coupled with an exchange flow between the compartments. These relationships are sufficient for engineering purposes. The influence of liquid viscosity and surface tension on liquid mixing has not been investigated extensively. Weiland [ 361 and Alexander and Shah [44] found that these variables have little effect on liquid mixing. However, the liquid flows in the bubble columns used were very turbulent, which might be the main cause of their results. At very large viscosities an influence can be expected, although bubble columns are not used under these circumstances because mass transfer rates are low (see later). In the above sections the dispersion coefficient has been regarded as gradually in,creasing with gas velocity. This is true in so far as the flow is heterogeneous in the column. At low velocities the flow is homogeneous

5.2. Methods to improve or decrease liquid mixing in bubble columns Packings in bubble columns can be expected to suppress circulation. Chen [47] indeed reports very low dispersion coefficient values for packed columns. When a draught tube is inserted, with equal riser, and downcomer cross-sectional areas, the liquid velocity may be influenced by column height instead of column diameter, because the liquid circulation extends along the entire column. Figure 7 contains the results obtained by various researchers and shows poor agreement between the results. However, when we calculate the friction losses in the riser and downcomer at the given velocities, it becomes clear that at small column diameters these losses are rather substantial. Reported influences of the geometries of the riser entrance and outlet [3] also indicate the existence of friction losses. Indeed, the column of large diameter [ 481 results in the highest velocity values. If the velocities are only determined by column height and no friction losses are present, it might be possible to use simply eqn. (10). In Fig. 7 these values are given for H = 3 m. The results for the column of large diameter approximate these values. For engineering purposes with a large-scale draught tube apparatus (‘T: > 0.25 m), eqn. (10) is of value if parameter H is substituted for 2. For smaller pipes, friction losses become more

B29

/’

There is a difficulty, however, in that the change from homogeneous to heterogeneous flow depends on geometric parameters (sparger location, uniformity of gas distribution) and the viscosity of the medium. At present there exist only indications of these influences, and design rules do not exist for the u, value for which homogeneous flow changes into heterogeneous flow. From eqn. (17) it appears that for large bubble column diameters QEG increases sharply. If eqn. (17) is used to calculate the Peclet number, it can be shown that in columns of small diameter with a high H/Z ratio (greater than 10) the gas mixing is of the plug flow type, in contrast with columns of large diameter with a low H/Z ratio (less than 3) and large superficial gas velocities where the gas phase is ideally mixed. It is evident that this phenomenon is especially important in scaling-up procedures for bubble column reactors.

I

0.1

a!2

0,3

vs(ms-1)o.4 -

Fig. 7. Influence of downcomer width on mixing velocities in bubble columns with draught tubes: curve 1, calculated from eqn. (10) with c (= H) = 3 m; curve 2, data of Cook and Waters [48] with H = 3.6 m and D = 10 m; curve 3, data of Blenke [3] with H = 3.5 m and D = 0.29 m; curve 4, data of Blenke [3] with H = 3.2 m and D = 0.10 m; curve 5, data of Lin et al. [49] with H = 3 m and D = 0.05 m.

relevant. These can be estimated by the methods given by Weiland [36] and Blenke 131.

6. GAS MIXING

Data on gas mixing have been given by Towell and Ackerman [50], Carleton et al. [51], Field and Davidson [ 521, Mangartz and Pilhofer [ 531 and Fair [54]. In the homogeneous flow regime, where u, < (2 4) X lo-* m s-i for water, the gas is in plug flow [54] with a very small and constant dispersion coefficient of about 10V2 m* s-l [53]. If the heterogeneous flow regime is reached, the gas mixing increases very rapidly as a result of large liquid circulatory flows which drag down some of the rising bubbles. In this regime QEG for the air-water system [50, 531 is correlated by Qx” = 78(u,2)‘*5

(17)

7. MASS TRANSFER

Gas-liquid mass transfer in bubble columns is mainly determined by the diameter of the bubbles in the column. With a gas holdup E the following relation holds for the volumetric mass transfer coefficient k,A : kLA =;k,

“S

(18)

With respect to d,,, it is clear from Section 3 that a division can be made between systems with coarse bubbles (d,, = (4 - 6) X 10m3m) and those with fine bubbles (d,, = (0.5 - 1) X lop3 m). Coarse bubbles occur with orifice spargers, where the liquid may be either coalescing or non-coalescing. Fine bubbles occur in systems with porous plate spargers or ejector-injector spargers and non-coalescing liquids only. However, for porous spargers or ejector-injector spargers in coalescing liquids the situation is not so clearly defined. The fine bubbles which are formed at the sparger coalesce very quickly. Moreover, the bubble diameter at the sparger increases rapidly at higher gas velocities. From eqn. (18) it appears that, in order to calculate kLA, not only the bubble diameter d,, but also the gas holdup E and the mass transfer coefficient kL must be known. Apart

increasing q and decreasing u. For practical purposes, however, it can be assumed that vbs = 0.25 m s-i for 10e3 < d,, < lo--* m while it is only at d,, < 1O-3 m that the bubble rise velocity decreases significantly with decreasing diameter. In Fig. 8 single-bubble rise velocities are given. In a bubble column, bubbles rise in a swarm. This means that, depending on the void fraction, velocities should be lower [15] than the single-bubble rise velocity. Schiigerl et al. [20] have demonstrated that at low superficial gas velocities (less than 4 X lo-* m s-l) for porous and perforated plates the gas rise velocity decreases slightly with increasing gas superficial velocity. In contrast, under heterogeneous flow conditions, substantial liquid circulation occurs. Bubbles tend to be present mainly in the upward flow regions [ 371, thereby increasing the bubble rise velocity, which is the sum of the liquid velocity and ubs. For high superficial gas velocities, Towel1 et al. [28] and Koide et al. [ 591 measured gas rise velocities (relative to the wall) of up to 1.5 m s-l, which clearly indicates the influence of liquid circulation velocities. Koide et al. calculated vbs in a way similar to that given by eqn. (19). They found that, for a large number of their own data and data from the literature, vbs is almost constant for v, < (1 - 3) X lo-* m s-l and increases considerably for v, > (1 - 3) X lo-* m s-l. The overall result is that the gas holdup increases less

from mass transfer aspects, E is also important with respect to the effective utilization of the bubble column volume. 7.1. Gas holdup in bubble columns 7.1 .I. General aspects The gas holdup in bubble columns is closely related to the bubble rise velocity and gas superficial velocity. For low superficial gas velocities (homogeneous flow) the gas holdup can be calculated from

,=vs

(19)

vbs

It appears that it is necessary to know the bubble rise velocity vbs if the gas holdup needs to be calculated. The bubble rise velocity is mainly dependent on bubble diameter. This is shown for water in Fig. 8, which is based on the data in several publications [55, 561. Two main regions can be distinguished. At small diameters (less than 10m3 m) the bubble behaves as a rigid sphere. At larger diameters the bubble surface becomes completely non-rigid and the rise velocity is much less dependent on diameter. The transition is ruled by surface tension and viscosity as well as by any impurities present [55, 5’71. Wallis [ 151 has provided an extensive discussion on the influence of the medium on vbs, based mainly on the relations given by Peebles and Garber [58]. These descriptions are rather complex but it is sufficient to recall that vbs decreases with 1

“bs (ms-1)

s

100 lo-'

Fig. 8. Bubble circulation.

10-3 rise velocity

in a stagnant

lO-2 pool of water:

-,

10-l dvs(m)

with internal

circulation;

-

-

-,

without

internal

B31

than linearly with v, for heterogeneous flow conditions. For the simplified case of distilled water with d,, > 10M3m we can assume that vbs = 0.25 m s-l. For the homogeneous flow regime it is assumed that vLc = 0; hence eqn. (19) can be applied to give US

E=0.25

(20)

For fine bubble systems (d,, < 10V3 m), ubs is smaller than 0.25 m s-l, resulting in higher values than given by eqn. (20); yet linearity with v, is maintained. For the heterogeneous flow regime, eqn. (19) can be modified to include the sum of vbs and the liquid circulation velocity vLc , leading to e = 0.25 + vLc

(21)

vLc can be calculated from eqn. (10). The curves according to eqns. (20) and (21) together with some data on air-water systems as measured and reviewed by Bach and Pilhofer [ 601 and Hikita et al. [61] are presented in Fig. 9. It is clear that for homogeneous flow conditions eqn. (lb) describes the holdup rather accurately. A nearly linear relationship with superficial velocity is present, particularly for non-coalescing media with very small bubbles (Fig. 9, curves 6 and 7). For heterogeneous flow, holdup values are in the region covered by eqns. (20) and (21) (Fig. 9, curves 1 and 2). Also interesting is curve 7 which shows the data reported by Ohki and Inoue [45]. They, as well as Schiigerl et al. [33] and Mersmann [ 181, found a local maximum in the holdup values, which can easily be explained as a transition from homogeneous to heterogeneous flow. The theoretical curves in Fig. 9 (curve 1 for homogeneous flow and curve 2 for the heterogeneous regime) lend support to this interpretation. From Fig. 9 it is clear that the holdup values are mainly determined by gas velocity but a number of other variables such as column diameter, sparger geometry and liquid properties are important. 7.1.2. Influence of column diameter Because the liquid velocity increases for increasing column diameter, an increased column diameter may be expected to reduce

8 (t

0.

0.

0.

0.

0

I

I

0.1

vs(ms-l)

-

O-2

0.3

Fig. 9. Gas holdup in bubble columns (air-water systems): curve 1, E = uJO.25; curve 2, E = u,/{O.25 + o.9(g2us)O~33}, z = 0.2 m; curve 3, data reviewed by Bach and Pilhofer [60 1; curve 4, data reviewed by Hikita et al. [61]; curve 5, E = 0.6uso.‘; curve 6, data (fine bubbles) measured by Schiigerl et al. [20]; curve 7, data (coarse bubbles) measured by Ohki and Inoue [45].

holdup values. The literature in this respect is rather confusing. Some researchers reported no such influence [ 591, but they mostly compared their own results with the data of others. Because holdup is determined by many factors other than diameter, such comparisons are hazardous. Researchers reporting their own experimental data on the influence of diameter are more consistent. Ohki and Inoue [45], Smith et al. [46], Magnussen et al. [62] and Botton et al. [63] have all mentioned a slightly negative influence of column diameter on holdup. Only at 2< 0.1 m does any significant influence seem to occur. However, this is most probably due to wall effects and different flow phenomena such as plug flow. Only Roustan et al. [64] reported no influ-

B32

ence, but they worked at very low gas flow rates and with a variety of H/Z ratios. 7.1.3. Influence of sparger type The influence of the sparger type is rather complex, mainly depending on fluid characteristics. As already stated, the diameter of the bubbles in the column and thus the holdup are determined by the coalescence behaviour of the liquid and the initial bubble size at the sparger. For a non-coalescing system the bubble diameter is determined completely by the sparger. Indeed, Weiland [36] and Schi.igerl et al. [ZO] have reported a significant increase in holdup values in the order perforated plates -+ sintered discs --f two-phase injectors under otherwise similar conditions. The difference may be as high as a factor of 2. For a coalescing system the bubble diameter in the column is determined by the equilibrium value. Therefore no influence of gas distributor can be expected. Weiland [36] and Schiigerl et al. [20] reported no differences for perforated plates, sintered discs and twophase injectors. However, they worked at H> 102. At lower H/2 values a transition region near the sparger where bubbles have not yet reached a final size becomes important, particularly at low gas rates because of a decreased collision frequency. Towel1 et al. [28] and Koide et al. [ 651 reported a limited but positive influence of porous plates or two-phase fluid injectors uersus perforated plates or single orifices. Towel1 et al. even stated that this limited difference is only due to a larger holdup located in the lower area. Another important phenomenon particularly in shorter columns is the influence of maldistribution of air and the influence of the transition region (from the homogeneous to the heterogeneous flow regime). Freedman and Davidson [40] showed at low gas velocities a negative influence on the holdup for very local gas sparging. Ohki and Inoue [ 451 demonstrated that sparger geometry influences the stability of the flow and therefore the gas flow rate at which the transition region with any maximum gas holdup value occurs. This is only of importance at relatively low H/T values and low u, values. 7.1.4. Influence of liquid properties The influence of liquid properties on gas holdup is considerable and is very dependent

on the sparger type. The liquid properties which are most important are the coalescing or non-coalescing properties, surface tension and the viscosity of the medium. Gas properties have been shown to have only a minor effect (20%) on gas holdup [61,66]. 7.1.4.1. Coalescing or non-coalescing properties. The coalescence properties of liquids can be manipulated by the addition of salts and organics. The addition of salts is known to hinder coalescence as shown by Lessard and Zieminski [67] and Marrucci and Nicodemo [29]. For an injector nozzle after salt addition Schiigerl et al. 2201 found an increase in holdup by up to a factor of 3 compared with the corresponding value in water. Injector nozzles are used to produce very small bubbles, which do not coalesce after salt addition, and therefore the holdup is increased significantly. Bach and Pilhofer [60] and Weiland [36] have reported an increase of only 50% in holdup after salt addition. However, they used perforated plates which produce bubbles near the equilibrium bubble size. Also Hikita et al. [61], using a single nozzle as sparger, achieved only a 10% - 20% increase in gas holdup after salt addition to water. An alternative way to change coalescence is the addition of organics to water. Schiigerl et al. [20] showed that, with porous plates or injector nozzles, holdup can increase by a factor of 3 on the addition of 1% alcohol. For a perforated plate (where large bubbles are produced), only a 50% increase in holdup is achieved on the addition of alcohol to water [20, 361. Alternatively, Schi_igerl et al. [33] showed that the addition of an antifoam compound to a non-coalescing medium (with a fine bubble sparger) results in a coalescing medium with a correspondingly low gas holdup. For fermentation liquids in particular, where the micro-organisms can produce or consume foaming compounds, these phenomena can lead to large variations in gas holdup during the fermentation process. 7.1.4.2. Surface tension. The effect of surface tension on gas holdup can be qualitatively described in that a lower surface tension gives a lower bubble rise velocity and therefore a higher holdup. Such a variation in surface tension can be achieved in

B33

several ways: (1) by the addition of surfacetension-lowering compounds to a pure liquid or (2) by changing to a liquid with a lower surface tension. Method (1) is widely used but it generally also introduces different coalescing properties as well as a lower surface tension. Method (2) has shown that surface tension has only a very weak influence on gas holdup [60,61]. 7.1.4.3. Viscosity of the medium. Gas holdup is very dependent on the viscosity of the medium, and the effect is brought about by two mechanisms: a high viscosity leads to large bubbles and therefore to low gas holdup; a high viscosity decreases the bubble rise velocity, which should lead to a higher gas holdup. In general it is found that an increased viscosity decreases the holdup [60, 661, and therefore the first mechanism seems to dominate. Sometimes, however, an increase in gas holdup is found [68,69] by increasing the viscosity (e.g. by the addition of glycerin). Presumably, this effect is due to increased foaming of the water-glycerin mixture. 7.1.5. Conclusions holdup

with respect

to gas

Clearly the gas holdup depends markedly on liquid properties which are largely governed by the sparger type. For the same liquid properties (e.g. salt addition) the holdup increase can be anywhere between 20% and 200%, varying with the sparger type. Consequently there will be no useful general relationships until research has been focused on the influence of liquid properties in relation to sparger geometry. For engineering purposes, predictions can be made for each individual case by careful estimation of the sparger and liquid properties and by selection of literature relevant to those conditions. The starting point of such estimates is the holdup value for coalescing media. This “minimum value” is more or less independent of sparger geometry. Bach and Pilhofer [60] and Hikita et al. [61] have given extensive reviews and these results are presented in Fig. 9. These data and the combined eqns. (20) and (21) do agree, if the existing scatter is taken into account, thus permitting an even simpler expression (also shown in Fig. 9):

E = 0.6uSo*’

(22)

Equation (22) applies to heterogeneous flow conditions in air-water systems. For homogeneous flow conditions in air-water systems

us

(20)

E=0.25

Roustan et al. [64] confirmed this equation. For the various relationships proposed to date, reference should be made to the reviews by Hikita et al. [61] and Kumar et al. [17]. The above discussion was concerned with batch columns without internal fillings and/or air lifts. In throughflow columns the superficial liquid velocity is relatively unimportant under heterogeneous flow conditions as long as it is lower than the gas superficial velocity [ 53,661. At higher liquid circulation velocities and with concurrent flow, the holdup decreases [ 361. This results in much lower holdup values for an air-lift reactor than for a batch bubble column [ 701. The magnitude of the decrease largely depends on the liquid recirculation velocity. As shown in Fig. 7, this velocity cannot be predicted from data reported in the literature. Therefore, at present, holdup prediction in air-lift reactors is not possible using general relationships. This is confirmed by the reports of Weiland [36], Chakravarty et al. [ 711 and Freedman and Davidson [ 401. In contrast, liquid recirculation can be strongly reduced by internal fillings, screens and sieve plates. For such systems Chen [72] has found a holdup increase of up to 100% depending on liquid throughput which is important for these applications because the liquid recirculation velocities are very low. Other examples have been given by Hsu and Dudokovic [ 731 and Cornelius et al. [ 741. 7.2. Mass transfer coefficient

kL

The volumetric mass transfer coefficient kLA is directly dependent on the mass transfer coefficient kL. In physically controlled absorption the mass transfer resistance in the gas film of the gas bubble is negligible because of the large diffusion coefficient. A thorough review of the parameter kL can be found in a paper by Gestrich et al. [ 751. In Fig. 10 a number of experimental results are reviewed. It can be seen that the bubble diameter has a marked influence on the kL

B34

**

.

.-- --___ ecn (231 . .

I

10-j

5x10-3

1 Oe2 --+

d,,(m)

10. Liquid side mass transfer coefficient in the air-water system: n, data of Aiba and Toda [76];A, data of [ 791; 0, data of Aiba Coppock and Meiklejohn [ 77 ] ; 0, data of Pasveer [ 78 1; *, data of Motarjemi and Jameson from the carbon dioxide et al. [80]; V, data of Garner and Porter [81]; V, data of Lindt [82]; *, recalculated data of Calderbank and Moo-Young [ 831.

Fig.

value for an oxygen-water system. For bubbles smaller than about 2 X 10m3 m the kL value decreases with decreasing d,,. This is also the regime where the bubble surface can be either rigid or mobile, depending on the surface-active materials in the liquid. A rigid bubble surface leads to lower k, values. The dependence of h, on surface-active agents is probably the reason for the large variation in the kL values found. Calderbank and Moo-Young [ 831 (using carbon dioxide) found that for a bubble diameter of 0.8 X 10M3 m kL stabilizes at the lower level. For bubbles larger than about 2 X 10P3 m the bubble surfaces are always mobile and surface-active materials have no influence on kL. For this regime kL can be calculated using the Higbie model, i.e. (23) Calderbank and Moo-Young 1831 have reported on the influence of Q, u andQL on kL. In general, kL shows a minor increase with increasing q or decreasing u. Salt addition at a constant bubble diameter has hardly any influence. However, a possible change in bubble diameter d,, due to a change in n, (T or salt concentration affects kL to a much larger extent. Sometimes an increase in kL is found as the dissipated power rises [28, 83, 841. It may be that this is a minor increase in kL in proportion to dissipated power but other variables (e.g. a decrease

in d,,) could also change under these conditions. The most important conclusion for bubble columns is that, for d,, > 2 X lop3 m, k, = (3 - 4) X low4 m s-l while, at lower bubble diameter values, kL values can be significantly lower, varying with bubble rigidity. Atd,,<0.8X10-3m, kL=1X10-4m s-l is probably a constant value in this region. 7.3. Volumetric mass transfer coefficient k,A When the mass transfer data are correlated, the same problems are encountered as for holdup correlations. It has been shown above that liquid properties and sparger type determine d,, and therefore E, and it has been demonstrated that bubble column reactor systems can be divided into coarse bubble reactors (d,, = (4 - 6) X lop3 m) and fine bubble reactors (d,, Q 6 X 10e3 m). Therefore it seems useful to divide the mass transfer literature into two groups: systems with coarse bubbles where d,, = 6 X 10e3 m, i.e. with coalescing medium properties or with coarse bubble spargers; systems with fine bubbles where d,, < 6 X 10e3 m, i.e. with non-coalescing medium properties corn bined with fine bubble spargers. Furthermore, k,A values are temperature dependent. According to Jackson and Shen [85] and Gilbert and Chen [86], kLA increases according to &,A =

kL200CA(j(T-20)“C

with 8 = 1.020 - 1.024

B35 This is an increase of about 2.5% “C-l over the temperature ranges normally used. Therefore the k,A values given below have been recalculated for a temperature of 20 “C. Data for 2< 0.1 m have been omitted, as have data from measurements done with the sulphite method.

of unaerated liquid height in the bubble column, 0.55% O2 (absolute) is removed from the sparged air. Thus, in a bubble column with a liquid height of 15 m (unaerated) the oxygen concentration in the offgas is {21- (15 X 0.55))s = 12.75%. It can be demonstrated that the above simple rule is in good accordance with eqn. (24). Because the saturated dissolved oxygen concentration decreases at about 2% “C-l it can furthermore be shown that the value of 0.55% 0, m-i is almost temperature independent.

7.3.1. Coarse butble systems In Fig. 11, h,20 CA is given for various superficial gas velocities (as found by the various researchers listed in the table in the caption) for coarse bubble systems. The results are scattered but remain within acceptable limits. Although a linear relationship between k,A and U, is possible the results are best correlated by k,*O°CA = 0.32~~~.’

7.3.2. Fhe bubble systems In Fig. 12, kLZooCA is shown as a function of u, (as found by the various researchers listed in the table in the caption) for fine bubble systems. In non-coale:cing media (water-salt) a very high kLZo ‘A value is obtained at low u, values. Compared with coarse bubble systems, kL20 ‘A increases by a factor of 6 at the same u,. Zlokarnik [ 341 found that in non-coalescing media more than 3% O2 m-l can be removed when twophase injectors are used, which is about six times the value listed in Table 1 for coarse bubble systems. In strongly coalescing media (Owaterdetergent or mixed liquor) the kLZo ‘A value of fine bubble spOargersis approximately equal to the kLZo ‘A values of the coarse bubble systems. This is due to the immediate coalescence of the fine bubbles at the sparger to coarse bubbles in the bulk of the bubble column. However, most media will occupy a position intermediate between the two extremes shown in Fig. 12. For these media kLA is high in comparison with coarse bubble systems for low u, values (less than lo-* m s-l) and at higher u, values kLA levels off

(24)

This correlation is valid for 0.08 m < Z < 11.6 m, 0.3 m < H< 21 m and 0 m s-l < u, < 0.3 m s-l. At low u, values the correlation slightly overestimates the measured values. The kLA values given by eqn. (24) approximate the calculated kLA values derived from eqns. (18) and (22) using k 4 X low4 m s-l and d = 6 X 10e3 m. h&iover, the mass transfii in coalescing (water) and non-coalescing (water-salt) media is described by the same relation. This is in good agreement with the finding that the bubble diameter for orifice spargers is not influenced much by media properties. Some researchers have expressed their mass transfer results (coarse bubble systems) by a simple “rule of thumb” (Table 1). They have found that in the situation where the dissolved oxygen concentration is zero the oxygen transfer capacity can be calculated from the simple fact that, for each metre TABLE1 Oxygen

transfer

(presented

Reference

C(m)

Urza and Jackson Schmit

as the percentage

[93]

et al. [94]

’ H(m)

0.08

17

5

Jackson

et al. [ 951

0.08

Jackson

and Shen [ 851

0.08

Leistner

et al. [ 231

1.56

of oxygen

4-8

4-

22

21

in coarse

bubble systems

Gas sparger

Method

T (“‘7

Amount

Orifice

Sulphite

24

0.6

Dynamic

20

0.5

Orifice

Sulphite

24

0.6

Orifice

Sulphite

20

0.55

Orifice

Dynamic

20

0.6

Diffuser

23

- 7.6

per metre)

(water)

(% O2 m-l)

B36 20°C kL

A 0.1

0.

0.01

.

a0 . . X '0 /,

, 0.1

Fig. 11. k,200cA

0.2 -

values for coarse

Reference

bubble

Z (m)

- 0.3

0.3 V,(ms-‘1

systems

(air-water). T W)

Medium

20

Coalescing

CO2 desorption, absorption steady state

14

Water; water-salt

Ring sparger

CO* desorption, steady state

20

Water

H(m)

Gas sparger

Method

2.5

Nozzle, forated

Dynamic

7.2

Nozzle

perplate

(02)

l

Akita and Yoshida [7]

0.08

X

Deckwer etal. [87]

0.2

Miller

[ 881

0.15

Reith

and Beek

0.14 - 0.29

1.6 - 3.7

Nozzle

Sulphite

30

Water-sulphite

0.4

1.8

Nozzle, spider

CO2 desorption, steady state

20

Water

Orifice

Dynamic

(02)

20

Watersulphite

Perforated plate

Dynamic

( 02)

20

Mineral medium

Perforated plate

Sulphite (contr.)

20

Non-coalescing

- 0.68

0.3

- 1.37

1891 0

Towel1

et al.

- 2.7

[281 *

Jackson and Shen [85]

0.08

A

Lin et al. [49 ]

0.08 - 0.15

3.0

Botton

0.1

0.2

- 0.8

1.5

- 2.4

et al.

- 7.6

4

- 21

[goI Hikita et al. Kataoka

[ 911

et a/. [92]

Nakanoh and Yoshida [8]

Nozzle

Dynamic

22

Water

5.5

5.9

Nozzle

CO* desorption

11

Water

14.5

1.9

Orifice

Dynamic

20

Water

0.1

- 0.19

O2

O2

B37 =OC kL

A

(s-l)

WATER-SALT 0.04-

WATER-QETERGENT MIXED

Fig. 12. kZooCA values for fine bubble systems

LIQUOR

(air-water).

T WI

Medium

(0,)

20

Water

Dynamic

( 02)

20

Waterdetergent

plate

Dynamic

(02)

20

Water

plate

Dynamic

(02)

20

Waterdetergent

plate

COz desorption, steady state

14

Water

Ceramic diffuser

Sulphite

20

Watersulphite

Porous plates (5, 50 and 120

Dynamic

(Oz)

20

Coalescing medium

Sulphite, state

steady

25 - 37

Water-sulphite; water-salt

Reference

Z(m)

H(m)

Gas sparger

Method

.

Lister and Boon [96]

1.5

8.5

Dome

diffuser

Dynamic

0

Lister and Boon [96]

1.5

8.5

Dome diffuser

Sztatecsny

0.4

1.46

Sintered

0

etal. n

[97]

(5 pm)

Sztatecsny

0.4

1.46

et al. [97] n

Deckwer

(25 Rm)

et al.

0.2

7.2

1371 X

Sintered (170

Jackson

et al.

0.076

4

- 7.3

1951 0

Sintered

Akita and Yoshida [ 7 ]

0.08

Greenhalgh

0.09

- 0.3

2.5

pm)

pm)

*

etal.

0.5

Porous

[98]

markedly. This influence of the low gas velocity in the air-water system with fine bubble spargers was also shown by Leistner et al. [24] who found that, for u, > 2 X 1O-2 m s-l, 0.6% O2 m-l is transferred and that, for u, < 2 X 10e2 m s-l, this parameter can have a value up to 1% 0, m-l. The reason that the gas velocity has such an effect is the increasing d,, value at higher

disc

u, values (see Fig. 3). Another important parameter in the mass transfer of these “inbetween” media is the reactor height. The coalescence of the bubbles usually proceeds within a distance of 0.5 - 1 m from the sparger. However, the very small bubbles in this part of the column can cause considerable mass transfer. It will be clear that the effect of this zone of small bubbles on the total

B38 6

lob2 Pa s. Itshas also been established that h does not increase further for u, > 10-l m

removal

02

s-1.

9. COMPARISON OF TRANSPORT PHENOMENA FOR LOW VISCOSITY SYSTEMS IN A BUBBLE COLUMN

AND A STIRRED

VESSEL

Before this review on transport phenomena in bubble columns is concluded, it is illustrative to compare this type of reactor with the well-known stirred tank reactor with respect to liquid mixing and mass and heat transfer.

9.1. Liquid mixing Liquid mixing in standard turbine vessels has been reviewed by Mersmann et al. [ 1031. These workers arrived at the following correlation :

QP -.

PT5

as-

0’

1

I

1

2

3

4 COlUmn

5

0 height(m)

= 300

(26)

This correlation can be transformed to yield a relation for the liquid circulation rate &, on the assumptions that the circulation time is one-third of the mixing time and that the turbine vessel has an H/T ratio of unity. The result for stirred vessels is

7 -

Fig. 13. Influence of column height on mass transfer in a fine bubble system with a coalescing medium.

mass transfer in the bubble column decreases rapidly as the column height is increased (Fig. 13).

8. HEAT TRANSFER

Heat transfer from the suspension to the wall or the coil is mainly determined by u,. There is no influence of geometry (transfer to wall or coil). It has been found that the viscosity reduces the heat transfer coefficient considerably. According to Fair et al. [ 1001, Hart [loll and Burke1 [102], the following correlation may be used to calculate the heat transfer coefficient h : 0.35

($L = ()3()27/3

This correlation has proved applicable to 0.1 m < Z < 1 m and low3 Pa s < q < 5 X

(27)

For comparison the liquid mixing in a bubble column is described by eqn. (11) which can be transformed into an equation analogous to eqn. (27) by realizing that in bubble columns the power dissipation is related to the gas superficial velocity (according to ref. 32) by

P 7 = Pgv, P&G

(28)

= (7V4K2

The elimination of @o from eqns. (11) and (28) yields for bubble columns

GL = O.‘J8~7/3

1’3p--1,3

5 i

(25)

“3p-1/3

p i)V

V

(29)

1

It appears that, when equal power dissipation per reactor volume is provided, liquid mixing is the same in both turbine vessels and bubble columns.

Fig. 14. Comparison of h& for stirred tank reactors and bubble columns (air-water system): curve 1, stirred tank, water, us = 0.02 m s-l ; curve 2, stirred tank, water, us = 0.04 m s-’ ; curve 3, bubble column, water; curve 4, stirred tank, water-salt, u, = 0.02 m s-* ; curve 5, stirred tank, water-salt, us = 0.04 m s-l ; curve 6, bubble column, water-salt,

9.2. Mass transfer

Mass transfer in stirred tank reactors has recently been reviewed by van’t Riet [ 1041. The correlations established for kLA in coalescing media are provided in Fig. 14, where gas superficial velocities of 0.02 and 0.04 m s-l in the stirred tank are included. The P, values in Fig. 14 cover the bubble column kLA correlation for coarse bubbles (eqn. (24)) and for fine bubbles (Fig. 12, water-salt curve). The P/V value for coarse bubble systems follows from the u, values according to P/V = pgu, [ 321 and the P,/V value for fine bubble systems is calculated in the same way from u,, with an additional estimated power consumption of 50% of the gas compression energy due to energy losses in the fine bubble spargers [23]. It appears that in coalescing systems (water) the bubble column kLA is about equal to the kLA values of the stirred tank, except at high stirrer power consumptions and low gas superficial velocities. In non-coalescing water-salt systems it is very evident that a stirrer cannot produce fine (less than lop3

m) gas bubbles at a low energy input while fine bubble spargers (porous discs and twophase injectors-ejectors) can do this quite well. Therefore, the kLA values in noncoalescing systems are much higher for bubble columns than for stirred tanks at equal P,/V values. This conclusion is limited to low gas superficial velocities in the bubble column. 9.3. Heat transfer Heat transfer in standard turbine vessels has been reviewed by Henzler [ 1051. On the assumption of a stirrer power number of 5, a ratio of the stirrer diameter to the vessel diameter of l/3 and a ratio of the vessel height to the tank diameter of 1.0, the heat transfer correlation for stirred vessels can be transformed to h = 930(9)o.222(~)“3

(30)

Equation (30) can be compared with the heat transfer correlation of eqn. (25) (which can be transformed to eqn. (31), if it is borne in

B40

mind that for bubble for bubble columns: h

=

columns

P/V = pgu,)

94*(;r.2s( y3

(31)

It is clear that, for equal power input per unit volume, the same heat transfer is obtained in bubble columns and stirred vessels.

10. CONCLUSION

It appears from this review that mixing and mass and heat transfer in a bubble column can be described by simple correlations which are based on a mechanistic understanding of the hydrodynamic processes in this form of reactor. The most important process is bubble formation. In practice the available sparger systems lead to a bubble size of (4 - 6) X lop3 m (coarse bubbles) or to a bubble size of (0.5 - 1) X 10m3 m (fine bubbles). The fine bubble systems are favourable for mass transfer but they are vulnerable to changes in the properties of the medium (non-coalescing to coalescing) and these systems might hamper gas phase separation. Furthermore, there are two flow regimes: the homogeneous flow regime at low superficial gas velocity and the heterogeneous flow regime at higher gas velocities. This has consequences for both the mixing and the mass transfer processes. It is important to note that the change from the homogeneous to the heterogeneous flow regime depends on a multitude of factors which have not been studied closely. Finally, it appears that in low viscous systems, using equal total power input per unit volume, a bubble column provides about equal liquid mixing, mass transfer and heat transfer compared with a stirred tank reactor.

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V

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104 105

APPENDIX

A

& do

d “S d*“S D

g h H kx. k,A

W. D. Einenkel

and M. Kappel,

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A: NOMENCLATURE

specific surface area (m-l) diameter of gas bubble (m) diameter of sparger orifice (m) Sauter mean diameter of a gas bubble in the bubble column (m) Sauter mean diameter of a gas bubble formed at the sparger (m) width of the downcomer in a bubble column reactor with a draught tube (m) gravitational constant (m 9) heat transfer coefficient (W rnp2 “C’) bubble column height (m) liquid film mass transfer coefficient (m s-l) volumetric mass transfer coefficient (s-l)

volumetric mass transfer coefficient at 20 “C (s-l) number of mixed stages (--) power dissipation in the bubble column (W) power dissipation of the gas and stirrer (W) Peclet number Reynolds number for flow through the orifice (-) mixing time of the liquid (s) temperature (“C) rise velocity of a bubble relative to the liquid (m s-l) liquid superficial velocity through the bubble column (m s-l) liquid circulation velocity in the column centre (m s-l) gas velocity in the sparger orifice (m s-l) gas superficial velocity in the bubble column (m s-l) bubble column volume (m3) gas volume in the bubble column (m3) liquid volume in the bubble column (m3)

Greek symbols gas holdup E

7) 5% 8 P AP

(T ew 7 @G

4JL

(-) viscosity of the medium (Pa s) viscosity of water (Pa s) constant (--) density of the liquid (kg mp3) density difference between the gas and the liquid (kg mm3) surface tension of the gas-liquid system (N m--l) surface tension of water (N m-l) surface tension of the liquid (N m-l) gas flow rate through the bubble column (m3 s-l) liquid mixing flow in the bubble column (m3 s-l) 6

Script letters QEG

QEL QL

z

effective gas dispersion coefficient (m2 s-l) effective liquid dispersion coefficient (m2 s-l) molecular diffusion coefficient of the solute in the liquid (m2 s-l) bubble column diameter (m)