c 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim10.1002/14356007.b04 275

Bubble Columns 1

Bubble ColumnsFor other industrial reactors and their applications, see Stirred-Tanc and Loop Reactors,TubularReactors, Fixed-Bed Reactors, Fluidized-Bed Reactors, Three-Phase Trickle-Bed Reactors,Reaction Columns,Thin-Film Reactors,Metallurgical Furnaces, andBiochemical Engineering.Peter Zehner, BASF Aktiengesellschaft, Ludwigshafen, Federal Republic of GermanyMatthias Kraume, BASF Aktiengesellschaft, Ludwigshafen, Federal Republic of Germany

1. Introduction . . . . . . . . . . . . . . . . 22. Bubble Columns and Modications 42.1. Design and Applications . . . . . . . . 42.2. Gas Distribution . . . . . . . . . . . . . 52.3. Flow Regimes . . . . . . . . . . . . . . . 62.4. Fluid Dynamics . . . . . . . . . . . . . . 72.5. Bubble Size . . . . . . . . . . . . . . . . 82.6. Bubble Rise Velocity . . . . . . . . . . 92.7. Dispersion of the Liquid Phase . . . . 92.8. Dispersion of the Gas Phase . . . . . . 102.9. Gas Holdup . . . . . . . . . . . . . . . . 102.10. Specic Interfacial Area . . . . . . . . 122.11. Volumetric Mass-Transfer

Coefcient . . . . . . . . . . . . . . . . . 132.12. Heat Transfer . . . . . . . . . . . . . . . 142.13. Slurry Bubble Columns . . . . . . . . 14

2.14. Airlift Loop Reactors . . . . . . . . . . 163. Downow Bubble Columns . . . . . . 183.1. Design and Applications . . . . . . . . 193.2. Operating Conditions

and Gas Holdup . . . . . . . . . . . . . 203.3. Mass Transfer . . . . . . . . . . . . . . . 214. Jet Loop Reactors . . . . . . . . . . . . 224.1. Design and Applications . . . . . . . . 234.2. Typical Dimensions . . . . . . . . . . . 264.3. Energy Balance . . . . . . . . . . . . . . 274.4. Mixing Behavior and Fluid Dynamics 274.5. Gas Holdup . . . . . . . . . . . . . . . . 284.6. Mass Transfer . . . . . . . . . . . . . . . 304.7. Three-Phase Loop Reactor . . . . . . 315. References . . . . . . . . . . . . . . . . . 31

Symbols (see also Principles of Chemi-cal Reaction Engineering and Model Reac-tors and Their Design Equations)

Variablesa specic interfacial area, m1A interfacial area, m2d diameter, mdh diameter of holes, mdi inner diameter of draft tube, mdn nozzle diameter, mD diffusion or dispersion coefcient, m2/sDG,L diffusion coefcient of dissolved gas in

liquid, m2/seM energy dissipation rate per unit mass,

W/kgen jet power per unit volume, W/m3eV energy dissipation rate per unit volume,

W/m3f fraction of cross-sectional area

f i fraction of cross-sectional area of drafttube

F cross-sectional area, m2Fi cross-sectional area of draft tube, m2FR cross-sectional area of reactor, m2h height, mhR height of gas liquid mixture, mht height of reactor, mJD dispersion owkL liquid-phase mass-transfer coefcient,

m/sP power, Wr radial distance from column axis, mt time, su supercial velocity, m/sv velocity, m/svrG relative velocity of bubble swarm in liq-

uid, m/svrS relative velocity of particle swarm in liq-

uid, m/sV volume, m3V volumetric ow rate, m3/sz axial coordinate, m

2 Bubble Columns

Greek symbols heat-transfer coefcient, WK1m2 volume fractionG gas holdup drag coefcient of circulation ow dynamic viscosity, kgm1 s1 kinematic viscosity, m2/s density, kg/m3 density difference between liquid and

gas, kg/m3S density difference between liquid and

solids, kg/m3 surface tension, N/m mass concentration, kg/m3

Subscriptsa annular spaceb bubblebS Sauter diameterc, circ circulationD downowG gas phaseh holei inside draft tubeL liquidmax maximum valuemin minimum valueM per unit massn nozzlep particler relativeR upow, reaction mixtureslip slipS solidst reactorV per unit volume

1. Introduction

Bubble columns are devices in which gas, inthe form of bubbles, comes in contact with liq-uid. The purpose may be simply to mix the liq-uid phase. Far more often, however, substancesare transferred from one phase to the other, forexample, when gaseous reactants are dissolvedin a liquid or when liquid reaction productsare stripped. Both processes can take place si-multaneously. A chemical or biological reaction

nearly always proceeds in the liquid phase. De-pending on the application, special measures tointensify mass transfer between the two phasesmay be useful, or the residence-time distributionof one or both phases may be modied.

The liquid may also contain inert, cat-alytically active, or reactive particles in sus-pension. Oxidation, hydrogenation, chlorina-tion, phosgenation, alkylation, and other pro-cesses have long been performed in bubble-column reactors in the chemical industry. In1978, more than 107 t/a of chemical productswere made in bubble columns [1]. Since then,marked growth has occurred. Industrial reac-tors for high-tonnage products have capacitiesof 100 300m3. Larger bubble columns, withcapacities up to 3000m3, are employed as fer-menters for protein production from methanol.The largest units (20 000m3) are those forwaste-water treatment.

Scientic interest in bubble columns has in-creased considerably in the past 10 15 years.Up to the mid-1970s, only 10 to 20 publicationsappeared annually; by themid- to late 1980s, thenumber had increased to 80 per year. This ledto the development of many empirical correla-tions and theoretical models enabling the math-ematical simulation of bubble- column reactors.Some academic research groups and commer-cial software developers have offered simulationprograms.

The mixing of a liquid and a gas having onlypartial mutual solubility is one of the unit op-erations in chemical technology. As Figure 1shows, this operation takes one of three prin-cipal forms. The simplest design is the bubblecolumn (Fig. 1A) in which gas is fed into thecolumn at the bottom and rises in the liquid, es-caping from it at the upper surface; the gas isconsumed to a greater or lesser extent (depend-ing on the intensity of mass transfer and chem-ical reaction). When the off-gas contains highconcentrations of valuable reactants, part of itis recycled to the reactor. This recycle design,however, lowers the concentration prole in thebubble column and must be optimized from aneconomic standpoint. In a simple bubble columnthe liquid is led in either cocurrently or counter-currently to the upward gas streamand has a longresidence time. The ow direction of the liquidphase has little effect on the gas-phase residencetime, which is comparatively short. Thus, in the

Bubble Columns 3

Figure 1. Principal methods of gas liquid mixingA) Bubble column; B) Downow bubble column; C) Jet loop reactor

simple column, the ow of gas is always frombottom to top, and the stream can be made up ofboth fresh and recycle gas.

Longer gas-phase residence times can beachieved with the downow bubble columnshown in Figure 1B. The liquid is pumped downthrough the column at a velocity of more than20 cm/s, so that gas let in at the top is entrained inthe ow and can even be held in a suspension-like state until it has reacted completely. Usu-ally, however, unconsumed gas is removed withthe liquid and separated. Special designs per-mit phase separation inside the apparatus. Thedownow bubble column is used mainly whenlarge liquid streams are to be contacted withsmall gas streams and a short liquid residencetime is required. The necessary velocity cannotalways be obtained with the liquid inlet to thereactor. Thus, like the gas in an ordinary bub-ble column, the liquid in the downow bubblecolumn can be recycled. Typical applicationsfor downow bubble columns are the ozonationof drinking water and the treatment of water inswimming pools. A special use of such devices

in the evacuation and compression of gases hasalso been reported [2].

In both types of column energy must be sup-plied continuously to the two-phase system tokeep the liquid and gas mixed. Only in this waycan separation of the phases be counteracted orreversed. In the rst case, the simple bubble col-umn, this energy is supplied by the gas. In thedownow bubble column the energy is suppliedby the downowing liquid.

A different mechanism comes into play inthe jet loop reactor (Fig. 1 C). Here no net owof gas or liquid occurs along the column; in-stead, an internal circulating ow is produced.One way to achieve this is with a propeller, butother approaches exist. In the most commonlyused type of loop reactor, the jet loop reactor,the ow is driven by a high-velocity liquid jet.Asin the downow bubble column, gas is let in atthe top and dispersed by the jet energy. Bubblescan be distributed throughout the reactor volumeonly if the downward liquid ow velocity in theinternal tube is greater than the slip velocity ofthe bubbles. Accordingly, a minimum power in-put is required.

4 Bubble Columns

These three basic methods of dispersing gasin liquid are generally not used in their pureforms. The variety of problems in chemical andbiotechnical processes has led to many differ-ent contacting devices that combine these basictechniques.

Figure 2. Types of bubble-column reactorsA) Simple bubble column; B) Cascade bubble column withsieve trays; C) Packed bubble column; D)Multishaft bubblecolumn; E) Bubble column with static mixers

2. Bubble Columns andModications

2.1. Design and Applications

Bubble columns are very adaptable gas liquidcontacting devices; possible designs are shownin Figure 2. The simplest form of bubble col-umn (Fig. 2A) consists of a vertical tube withno internals. Gas is fed in at the bottom whileliquid is led through the apparatus cocurrentlyor countercurrently. This simple form is seldomused in practice; instead, a number of modi-cations are employed. The back-mixing of gasand liquid phases in the simple bubble column

and the nonuniform distribution of gas bubblesover the cross section can be reduced by the in-stallation of trays (Fig. 2 B), packings (Fig. 2 C),or shafts (Fig. 2D). All these devices can oper-ate either cocurrently or countercurrently. To setup the most homogeneous possible bubble ow,static mixer elements can also be placed in theascending ow section (Fig. 2 E).

Figure 3. Hydroformylation of propenea) Stripping zone; b) Reaction zone

Hydroformylation. The hydroformylationof propene is carried out in simple bubblecolumns. The reaction is homogeneously cat-alyzed by rhodium complexes. Usually thepropene and the CO/H2 gas mixture are let inat the bottom of the reactor. Incompletely re-acted gas, saturated with the reaction product,exits the reactor. The hydroformylation productis separated from the gas streamby condensationand forwarded to downstream processing, whilethe gas is recycled to the reactor. Because theheat of reaction cannot be completely removedby evaporative cooling using the enthalpy of va-porization of the product, the bubble column isalso equipped with an external cooling loop.

One great advantage of the process is that theproduct is recovered from the reaction mixturewithout additional separation operations whichwould damage the expensive catalyst system.The close coupling between the product and therecycle gas necessary to discharge it (i.e., a cer-tain quantity of gas is required for product dis-charge for thermodynamic reasons), however,presents some problems. First, the gas ow ratecauses a high gas holdup, which reduces the re-action volume and thus decreases the productiv-

Bubble Columns 5

Figure 4. Oxidation of montan waxes in cascade bubble columnsa) Cascade bubble-column reactors; b) Separators; c) Final purication of wax oxidate; d) Off-gas treatment

ity of the reactor. Second, large bubbles occur,which limit the delivery of gaseous reactants tothe liquid phase in the reactor. For these reasons,recycle gas is admitted to the bubble column attwo levels (Fig. 3) [3]. About half of the recy-cle gas is fed via the bottom sparger to dispersereactants into the overlying reaction zone. Theremaining recycle gas is let in via the top sparger,which lies slightly below the liquid surface, tofacilitate separation of the reaction product. Fi-nally, theCO/H2 reactant stream is fed at variouslevels to supply CO that has been consumed bythe reaction in the liquid phase.

Oxidation of Montan Waxes. Bubblecolumns are used in a cascade when a narrowresidence-time distribution is required, for ex-ample, to prevent or limit undesired consecutivereactions. Reducing back-mixing (i.e., a narrowresidence-time distribution) is also useful whenreaction-engineering considerations dictate thatthe gas must be fed to various points in the reac-tor or when a liquid reactant must be degradedto the greatest extent possible.

Montan waxes from brown coal must bederesinied, oxidatively bleached, and esteried(optional) [4], [5]. Oxidation of the waxes con-sists of several consecutive reactions; the rstthree steps (oxidation of resins and dark- coloredsubstances, saponication of montan waxes, ox-idation of wax alcohols) are desirable, whereas

the fourth (oxidative degradation of wax acids)is not. The residence-time distribution in the re-actor must be controlled so that the desired re-actions go as far as possible without the unde-sirable reaction occurring to any marked extent.Oxidation is performed in four cascaded bub-ble columns connected in series (Fig. 4). In therst bubble column, the crude wax for bleach-ing is metered in along with half of the requiredamount of chromic acid. Air is supplied to en-hancemixingof the reactants. The spent chromicacid is separated from the wax downstream ofboth the rst and the second bubble columns.Another 25 % of the total acid required is addedto the second and third columns. The reactionpreferably takes place at 100 125 C and 1 5bar, with a residence time of 1 3 h for the en-tire cascade. The enthalpy of reaction is removedby partial evaporation of the water contained inthe chromic acid. After exiting the fourth bub-ble column, the oxidized product, spent acid, andoff-gas are separated in two separators.

2.2. Gas DistributionUsually, the gas is dispersed to create small bub-bles and distribute themuniformly over the crosssection of the equipment to maximize the in-tensity of mass transfer. The formation of nebubbles is especially desirable in coalescence-hindered systems and in the homogeneous ow

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6 Bubble Columns

regime (Section 2.3). In principle, however, sig-nicant mass transfer can be obtained at thegas distributor through a high local energy-dissipation density [6], [7].

In most cases, gas bubbles are generated bypores or holes or in the shear zone of a liquidjet. Figure 5 shows typical forms of staticgas spargers, in which bubble formation occurswithout any additional energy supplied fromoutside. The simplest of these devices, the diptube (Fig. 5A), only gives an acceptably uni-form gas distribution over the cross section atsome distance above the sparger. Perforatedplates (Fig. 5 B) and perforated ring spargers(Fig. 5 C) are more effective. Both of these re-quire a certain minimum gas ow rate to achieveuniform distribution and prevent the liquid fromgetting into the sparger [810]. Very ne bub-bles can be generated by the use of porous plates(Fig. 5D), but their pores are susceptible to foul-ing, and this type of sparger is seldom used infull-scale equipment.

Figure 5. Static gas spargersA)Dip tube; B) Perforated plate; C) Perforated ring sparger;D) Porous plate

Dynamic spargers offer an alternative to thestatic types. They use the power of a liquid

jet to disperse gas in a zone of high energy-dissipation rate [1113]. Figure 6 illustrates sev-eral frequently used dynamic gas spargers. Thesimple two-phase jet nozzle alone (Fig. 6A) orwith momentum-transfer tube (Fig. 6 B) is notable to simultaneously disperse gas and suck inthe gas stream. This can be achieved, however,with the ejector jet nozzle (Fig. 6 C), the ejec-tor (Fig. 6D), and the Venturi tube (Fig. 6 E). Innozzle selection the ratio of the gas liquid vol-umetric ow rates must always be considered.Commonvalues lie between0.5 and2. However,much higher values can be achieved in specialcases with momentum-transfer tubes [12].

2.3. Flow Regimes

The upwardmotion of bubbles gives rise to threedistinct ow regimes. The crucial quantity for aow regime is the supercial gas velocity. Thehomogeneous ow regime is marked by a nar-row bubble-size distribution, and bubbles aredistributed relatively uniformly over the crosssection of the apparatus. This regime extendsto supercial gas velocities of 0.03 0.08m/s,depending on the gas liquid system and gassparger type.

The uniform distribution of gas bubbles van-ishes at higher gas rates, and a highly turbulentow structure appears. In this heterogeneous orchurn-turbulent owregime, large bubbles or ag-glomerates of bubbles form and travel upward athighvelocity (seeSection2.6),mainly in the axisof the column. The circulating ow that resultsmay be so vigorous that bubbles of a size corre-sponding to that in the homogeneous regime areactually transported downward in the zone nearthe column wall (see Section 2.4).

In the small-diameter columns often used aslaboratory equipment, slug ow occurs at highgas ow rates. Large bubbles are stabilized bythe column wall and take on the characteristicslug shape.

The relationship between supercial gas ve-locity and reactor diameter is illustrated by theow map of Figure 7 [14]. The broad transitionregions are due to the effects of the gas distrib-utor, the gas liquid system, and the liquid rate.A knowledge of the ow regime is particularlyimportant because it strongly affects the produc-tivity of bubble- column reactors.

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Bubble Columns 7

Figure 6. Dynamic gas spargers

Figure 7. Flow regimes in bubble columns

2.4. Fluid Dynamics

Rising gas bubbles entrain liquid in their wakes.As a rule, this upward ow of liquid is muchgreater than the net liquid ow rate. Because ofcontinuity, regions therefore exist in which theliquid is predominantly moving downward.

Many theoretical and experimental studieshave described the ow behavior of the liquidphase [15]. The circulation velocity is given asa function of supercial gas velocity, column

diameter, gas holdup, bubble diameter and risevelocity, viscosity of the liquid, and dispersionheight. Published analyses deal with both lami-nar liquid circulation, which is only of theoreti-cal interest [1618], and turbulent ow, to whichthe following discussion is devoted. For exam-ple, Miyauchi and coworkers use a force bal-ance over an annular, axially symmetrical vol-ume element to obtain the velocity prole shownin Figure 8, [19]. Calculation of the velocities,however, requires knowledge of the gas holdupas a function of radial position.

Models of circulation velocity based on en-ergy balances, in contrast, assume a cell struc-ture in the bubble column similar to that showninFigure 9 [20], [21]. In slender bubble columns,both calculations and experimental results showthat the height of the circulation cells hc is equalto the apparatus diameter dt [20], [22]. Joshiand Sharma take into account the energy inputdue to gas compression and energy losses bydissipation in the wakes of the rising bubbles,as well as liquid transport across the liquid sur-face (hydraulic pump), thus obtaining a veloc-ity prole over the cross section.Hills [23] andKojima and coworkers [24] have determined ve-locity proles experimentally in bubble columns

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8 Bubble Columns

having diameters of 0.14 and 5.5m, respectively(Fig. 10). For the mean circulation velocity L, cin bubble columnswith additional liquid rate uL,Joshi and Sharma [20] give the expression

vL,c= 1.43

gdt

(uG GuL1G

GvrG)

(2.1)

where G is the gas holdup (+ for countercur-rent, for cocurrent). Zehner, using a forcebalance, arrives at a similar relation for themeancirculation velocity [21]:

vL,c= 3

12.5L

gdtuG (2.2)

The velocity proles derived from the modelsand, in particular, themean velocities enable cal-culation of the essential uid-dynamic parame-ters in bubble columns [20], [21], [25].

Figure 8. Radial distribution of liquid velocity in a bubblecolumn

2.5. Bubble Size

Analysis of bubble size in bubble columns mustdistinguish between bubble-size distribution justafter bubble formation at the sparger and sizedistribution further away from the distributor.Because of breakup and coalescence of the risingbubbles, the two distributions can differ signif-icantly. Since the efciency of bubble columns

depends chiey on bubbles far from the gas dis-tributor,the following discussion only concernsthese.

Figure 9. Cell structure in bubble columns

Two basic methods photography and probetechniques exist for determining bubble size;however, they do not lead to identical results.Both methods are subject to certain limitationsin view of the marked bubble selection thatmay occur (i.e., not all bubble sizes can be de-tected) [26], [27]. In particular, any measure-ment method only leads to realistic results if theow is homogeneous (i.e., a narrow bubble-sizedistribution is found). As yet, no method canbe recommended for the measurement of largebubbles in the heterogeneous ow regime.

If bubbles are generated in a region of highturbulence (as with dynamic gas spargers), thefollowing formula [28] can be used to describethe Sauter diameter dbS (mean bubble diame-ter, calculated from the volume to surface ratio)[29], [30].

dbS=2

e0.4M

(

L

)0.60.5G

(G

L

)0.25(2.3)

This formula is based on Kolmogorovs theoryof isotropic turbulence.

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Bubble Columns 9

When static gas spargers are used, the bubblediameter is onlyweakly dependent on gas veloc-ity. Descriptive correlations [3134] are applica-ble only to the systems and sparger geometriesfor which they were obtained; a generally validdescription of bubble size does not yet exist. Themaximum bubble diameter db,max can be usedfor purposes of estimation [27], [35]. For low-viscosity liquids, the maximum bubble diameteris given by

db,max= 3

gL(2.4)

where is the surface tension. For thewater airsystem, db,max = 8mm. Larger bubbles havea high probability of being unstable and thusbreaking up. The Sauter diameter for real distri-butions is between 40 and 60 % of the largeststable bubble diameter. This estimate is not,however, applicable to the heterogeneous owregime due to the binodal bubble-size distribu-tion in this regime.

Figure 10. Calculated radial proles of liquid velocity inbubble columns [20]

2.6. Bubble Rise VelocityIn the homogeneous ow regime, bubbles of al-most uniform size and shape rise in the form ofa swarm distributed uniformly over the columncross section. When the regime changes, largerbubbles or agglomerates of bubbles form in ad-dition to the bubbles already present [36], [37].These aggregates rise at a markedly higher ve-locity than the small bubbles. Figure 11 showsmeasured velocities for large and small bubbles[36]. Large bubbles rst appear at a supercialgas velocity of ca. 0.03m/s. The formation oflarge bubbles, however, depends strongly on thetype of sparger used.With sintered plates, for ex-ample, larger bubbles do not appear at gas rateslower than ca. 0.1m/s. As shown in Figure 11,large bubbles have a rise velocity that is four ormore times larger than small ones. Thus, mostof the gas transport in the heterogeneous owregime is accomplished by large bubbles. In thisregime, the quantity of gas transported by smallbubbles remains constant, whereas the quantitytransported by large bubbles increases linearlywith gas velocity. This relationship applies to co-alescing and coalescence-hindered gas liquidsystems.

Figure 11. Velocities of rising bubbles for the systemwater airReactor: dt = 0.44m, ht = 5m; Gas distributor: perforatedplate (dh = 3mm)

2.7. Dispersion of the Liquid Phase

Because of the large-scale circulation ows,back-mixing occurs in both phases. The result-ing dispersion ow JD is usually governed by an

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10 Bubble Columns

equation analogous to Ficks rst law for molec-ular diffusion. For the one-dimensional case ofaxial dispersion,which is generally sufcient fora description, follows

JD= DL dcdz (2.5)

The dispersion coefcient DL is essentially afunction of the supercial gas velocity and thecolumn diameter (e.g., see [38]). Flow direc-tion or liquid velocity does not show any ef-fect, provided the supercial liquid velocity re-mains within the range common in industry(uL< 0.03m/s). The dispersion coefcient canbe estimated fairly accurately on the basis ofuid-dynamic models. For example, Joshi andSharma [20] and Zehner [21] give dispersioncoefcients derived from the mean circulationvelocity. Each of these formulas gives a good de-scription of the experimentally determined dis-persion coefcients known from the literature.By way of example, Figure 12 compares experi-mental results reported by various workers withthe theoretical relation derived by Zehner:

DL=dtvL,c

2=dt

23

12.5L

gdtuG (2.6)

The equation emphasizes that DL strongly de-pends on column diameter.

Figure 12.Liquid-phase dispersion coefcientmeasured byvarious authors [39]

2.8. Dispersion of the Gas Phase

Due to the large-scale circulation ow both theliquid and gas phases are dispersed. Further-more, the formation of large and small bub-bles, coalescence, and breakup result in addi-tional dispersion in the gas phase. Whereas thegas phase in a bubble column with a smallerdiameter ows with virtually no back-mixing,large units behave more like stirred tanks. Thegas-phase dispersion coefcient depends morestrongly on gas velocity and column diameterthan does that of the liquid phase. For this rea-son, the degree of axial gas mixing is especiallyrelevant for scale-up when the gas phase is ex-pected to show strong concentration variations.

Many formulas in the literature describe thedispersion coefcient as a function of differentindependent variables. A particularly suitableformula is [40]:

DG= 5 104(uG

G

)3d1.5t (2.7)

This formula is not, however, dimensionally ho-mogeneous (DG in cm2/s, uG in cm/s, dt in cm),and the gas holdup must be known. By contrast,the equation

GDG=0.2dtuG

L

gdtuG

v3rG(2.8)

derived by Zehner and Schuch is dimension-ally correct [41]. However, more recent mea-surements [42] have shown that this correla-tion must be modied in the heterogeneous owregime (uG 5 cm/s) because the proportional-ity is somewhat different:

GDG (uGdt)1.65

2.9. Gas Holdup

Gas holdup is one of the most important operat-ing parameters because it not only governs phasefraction and gas-phase residence time but is alsocrucial for mass transfer between liquid and gas.Gas holdup depends chiey on gas ow rate, butalso to a great extent on the gas liquid systeminvolved. Accordingly, many correlations that

Bubble Columns 11

have been published only apply to the systemsinvestigated.

Gas holdup is dened as the volume of thegas phase divided by the total volume of the dis-persion:

G=VG

VG+VL(2.9)

The relationship between gas holdup and gas ve-locity is generally described by the proportion-alityGunG

In the homogeneous ow regime, n is close tounity. When large bubbles are present, the expo-nent decreases, i.e., the gas holdup increases lessthan proportionally to the gas ow rate (Fig. 13).The higher the contribution of large bubbles tothe total gas holdup, the smaller is the exponentn. In the fully developed heterogeneous owregime, n nally takes on values between 0.4and 0.7, depending on the gas liquid system.

Figure 13. Gas holdup and fraction of large bubbles (sys-tem:water air; gas distributor: perforated plate dh = 3mm)

The effect of low liquid velocities uL on gascontent is generally negligible. At high owrates the gas holdup decreases in cocurrent sys-tems because gas bubbles pass through the col-umn more quickly. In contrast, the gas holduprises in countercurrent systems; this can lead toextremely high gas holdup, especially in down-ow bubble columns [43].

Above 0.1m, the reactor diameter is of sec-ondary importance for gas holdup, as measure-ments onunits havingdiameters between0.1 and5.50m show [34], [36], [44], [45].

The effects of physical properties on gasholdup are exceedingly complex. Increasing theviscosity of the liquid phase leads to increasedbubble coalescence and thus a decrease in gasholdup. Above ca. 50mPa s, however, the gasholdup remains constant [46]. Although surfacetension is not very important for the gas holdup,a change in coalescence behavior may have last-ing effects. When gas-phase residence times arelong and gas distribution is obtained with per-forated or sintered plates, the presence of saltsor alcohols that counteract coalescence has lit-tle effect [44]. In contrast, gas holdup increasesmarkedly in systems sparged by two-phase noz-zles when coalescence is hindered [47]. Suchbehavior can be attributed to a small-bubble gasholdup higher than that in coalescing systems,whereas the content of large bubbles is identi-cal [36]. Small bubbles formed under high shearstresses in the region near the two-phase nozzlecannot recombine so the gas holdup increasessignicantly with this type of gas distributor.

The relation of Akita and Yoshida [48] issuitable for estimating the gas holdup and isbased on the investigation of numerous systems:

G

(1G)4c1=

(gd2tL

) 18(gd3tL

) 112(

uGgdt

)(2.10)

For pure liquids and nonpolar solutions the con-stant c1 is 0.2, for electrolyte solutions it is0.25. However, reliable results cannot be ex-pected for systems that have not been investi-gated in this study. The effects of reactor pres-sureongas holduphavenot been fully explained.Although some authors nd no effect between1 and 16 bar [49], others nd that gas holdupincreases with pressure in systems with smallsparging holes (dh 1mm) or with sinteredplates [44], [5052]. Transition from the homo-geneous to the heterogeneous regime occurs athigher gas ow rates as pressure increases.

Gas holdup is generally a function of posi-tion in the bubble column. Axial proles of gasholdup show a zone near the gas distributor inwhich the holdup increases to the value that char-acterizes the following equilibrium zone. Thegas holdup at the top of the column, in the zone

12 Bubble Columns

of bubble breakup, is markedly higher than theequilibrium value [45].

Gas holdup also depends on radial position.The prole shows gradients only near the wall inthe homogeneous ow regime [23], [45], [53]. Incontrast, a parabolic radial gas holdup distribu-tion appears in the heterogeneous regime [23],[37], [45], as a consequence of the preferentialrising of large bubbles or agglomerates of bub-bles in the axis of the column. Figure 14 showsradial proles of gas holdup at various gas owrates in the water air system.

Figure 14. Radial proles of local gas holdupdt = 0.45m; ht = 6.2m; h = 3.03m (at measurement point);perforated plate dh = 1mm

2.10. Specic Interfacial Area

The area of the gas liquid interface is one ofthe most important process parameters. Espe-cially at high reaction rates (e.g., when a bubblecolumn is employed as an absorber), the interfa-cial area becomes a crucial factor in equipmentsizing. Like gas holdup, interfacial area dependson the geometry, operating conditions, and gas liquid system. Gas holdup and interfacial areaper unit volume are related as

a=A

VR=6GdbS

(2.11)

where VR is the volume of the reaction mixtureand dbS is the mean bubble diameter (Sauter di-ameter, Section 2.5). As Figure 15 shows, theinterfacial area increases with increasing gasow rate. An exception occurs when a porous-plate sparger is used; like gas holdup, interfacialarea decreases on transition to the heterogeneousow regime and then approaches the same val-ues observed with perforated plates. The growthin interfacial area with increasing gas velocity isalways greater in the homogeneous than in theheterogeneous ow regime. The reason lies inthe formation of large bubbles in the heteroge-neous regime: the interfacial area of large bub-bles per unit volume is markedly lower than thatof smaller ones.

Figure 15. Specic interfacial area as a function of super-cial gas velocitya)dt= 0.102m; b)dt= 0.29m; c)dt= 0.14m; d)dt=0.1m; Porous plate; - Perforated plate

The specic interfacial areas attainable invarious gas liquid reactors can be compared onthe basis of power input P per unit volume [29].Experimental values can be described by the re-lation

a=k(

P

VR

)mnG (2.12)

The exponent m is between 0.4 and 1 [54]. Theplot in Figure 16 enables a direct comparisonto be made between reactors with respect to theenergy required to produce a given interfacialarea.

Bubble Columns 13

Figure 16. Specic interfacial area as a function of specicpower input [55]a) Stirred tank; b) Bubble columnwith porous plate; c) Bub-ble column; d) Bubble column with two-phase jet nozzle( jet loop reactor); e) Packed column; f ) Bubble columnwith injector nozzle

2.11. Volumetric Mass-TransferCoefcient

The mass transfer between the gas and the liq-uid phase in a bubble column can be described inmost cases by the volumetricmass-transfer coef-cient kL a, which is the liquid-phasemasstrans-fer coefcient kL multiplied by the specic in-terfacial area. Gas-phase resistance can usuallybe neglected, so kL a gives an adequate descrip-tion. To determine the mass-transfer rate, how-ever, the driving concentration difference mustbe known which in turn requires a knowledge ofmixing behavior in the gas and the liquid phase.In industrial units (dt> 1m), estimates can bebased on the assumption of complete mixing inboth liquid and gas phases.

Like gas holdup and interfacial area, kL a alsodepends on the gas ow rate, type of sparger,and gas liquid system. The mass-transfer coef-cient and the gas rate are again proportional toone another:

kLaunGwhere n can be between 0.7 and 0.92 [31], [5659]. Mass-transfer coefcients two- to threefoldhigher can be achieved in the homogeneous owregime if a porous plate is used as sparger insteadof a perforated plate (Fig. 17). In the heteroge-neous regime, however, the effect of the spargeris negligible.

Figure 17.Mass-transfer coefcients in bubble columns

According to experimental results, the col-umn diameter above about 15 cm has no ef-fect on mass-transfer coefcient. Some correla-tions nonetheless include reactor diameter [31],[57], [60]. Akita and Joshida [31] state thatthe value of the column diameter used for cal-culation should not be increased beyond 0.6m.Based on this premise, their correlation for kL ais

kLad2t

DG,L=

0.6(

L

DG,L

)0.5 (gd2tL

)0.62 (gd3t2L

)0.311.1G

(2.13)

andhas the best experimental support. Themass-transfer coefcient increases in coalescence-hindered systems [54], [61]. This increase de-pends on the system and the concentrationof coalescence-hindering substance. The maxi-mum gain in mass-transfer coefcient due to thepresence of electrolytes, however, is only 30 %.

14 Bubble Columns

Figure 18. Examples of heat exchanger insertsA) Parallel single tubes; B) Tube bundle in cross ow; C) Longitudinal tube bundle; D) Tube spiral or helix; E) Draft tubewith jacket

2.12. Heat Transfer

Inmany cases, heatmust be removedwhen oper-ating bubble columns. A particularly simple so-lution is to utilize the latent heat of vaporizationof the liquid phase for heat removal, althoughthis is not always feasible. In addition,manypos-sibilities exist for heat transfer through heated orcooled surfaces, as shown in Figure 18. In thisway, up to ca. 30m2/m3 of heat-transfer area canbe installed in a bubble column.

The turbulent ow generated by rising gasbubbles increases heat transfer even at low gasrates (Fig. 19). The increase in heat-transfer co-efcient , with gas throughput is markedlygreater in the homogeneous than in the hetero-geneous regime.

The heat-transfer coefcient does not dependon the column diameter, type of sparger, or coa-lescence behavior of the gas liquid system.

Two distinct concepts are used to describethe heat-transfer coefcient at the wall.WhereasKast [62] and Deckwer [63] consider ra-dial ow and heat transported by it, Joshi andcoworkers [64] and Zehner [21] use circulationvelocities derived by them for physical model-ing.Herewith the following relation for the heat-transfer coefcient can be derived [21]:

= 0.18 (1G)(2LLcpL

v2L,c

l L

)1/2(2.14)

where

l=db

(

6G

)1/3

and L, c is calculated by Equation (2.2). On thewhole, these two approaches correlate well withliterature data. Heat transfer in bubble columnswith heat-exchange internals has not been in-tensively studied [6569]. For tube bundles ar-ranged in an axial direction (Fig. 18C), the heat-transfer coefcient increases with increasingtube pitch and decreases when the free cross-sectional area increases [68], [69]. A similar re-lationship is found for a tube bundle arranged incross ow (Fig. 18B), but here a marked effectof liquid throughput occurs [67].

The installation of tube bundles leads to anoverall change in uid dynamics and thus inmixing behavior. For example, tubes installedin cross ow hinder ow in the longitudinal di-rection and thus reduce dispersion in the liquidphase [70]. In contrast, the arrangement of heat-transfer surfaces in the ow direction leads tomore intense mixing of the liquid phase by in-tensifying circulation [71], [72].

2.13. Slurry Bubble Columns

Solid particles are present in bubble columns ina wide variety of processes; they must be held

Bubble Columns 15

in suspension by the rapid liquid circulation al-ready discussed. The presence of the solid phasein a slurry bubble column means that all pro-cess parameters behavedifferently, and in amorecomplicated way, than in a two-phase bubblecolumn.

Figure 19. Heat-transfer coefcient at reactor walldt = 0.196m; ht = 6.20m; liquid velocity uL = 1.2 cm/s

The minimum gas velocity necessary to holdthe solids in suspension increases as the con-centration and density of the particles increase.The increment depends, however, on the phys-ical properties of the solid and liquid phases.Many empirical equations for the critical gas ve-locity for complete suspension show a markedincrease with increasing single-particle settlingvelocity. Equation (2.15) [73] can be used fordesign purposes:uG,min

vrS

= 0.801(SLL

)0.6 ( SS

)0.146 (gdtvrS

)0.241 + 807

(g4LL3

)0.578 (2.15)where vrS is the relative settling velocity of theparticle swarm in the liquid. At low solids con-

centration (< 10wt %) and low settling veloc-ity of the particles the gas holdup is nearly un-changed [74]. In contrast, the gas holdup de-creases at higher settling velocities with increas-ing solids concentration [7577]. The strengthof this effect differs from one ow regime to an-other. The decrease is particularly marked whenan increase in solids content leads to a changefrom the homogeneous to the heterogeneousregime. On the other hand, in the heterogeneousregime the reduction in gas holdup is only slightwith increasing solids content. Yasunishi andcoworkers [78] verify and recommend the gasholdup relation of Koide and coworkers [79]

G

(1G)4= (2.16)

0.277(uGL

)0.918 ( g4LL

3

)0.2521 + 4.35

(SS

)0.748 ( SLL

)0.881 ( dtuGLL

)0.168for awide range of solids concentrations and liq-uid properties. For coalescence-hindered aque-ous electrolyte solutions a coefcient 0.364mustbe used instead of 0.277 in Equation (2.16).The mixing behavior of the liquid and thegas phase is very similar to that in the two-phase bubble column. The axial solids distri-bution can be described by a one-dimensionalsedimentation dispersion model. The solidsdispersion coefcient is generally lower than thecorresponding liquid dispersion coefcient [80].The difference between the two values increasesrapidly with increasing settling velocity of par-ticles. For small solid particles (vrS< 0.01m/s),the effect of supercial gas velocity on the axialsolids concentration prole is negligible abovethe minimum gas velocity for suspension [81].

The specic interfacial area declines contin-uously with increasing solids content [76], [82].This phenomenon can be explained by the for-mation of larger gas bubbles, due to the pres-ence of solid particles that lead to the observeddecrease in gas holdup. If, however, very neparticles are used in aqueous electrolyte solu-tions (i.e., systems with hindered coalescence),the interfacial areas produced do not differ fromthose in the two-phase system [83].

The effect of solids on the volumetric mass-transfer coefcient depends largely on particleproperties, solids content, and physical proper-ties of the liquid. At low solids concentration (up

16 Bubble Columns

to ca. 3 5wt %), the mass-transfer coefcientmatches that of the two-phase bubble column.A higher solids content, like increasing parti-cle size, leads to a drop in kL a relative to thesolid-free condition [78], [79], [84], [85]. Forvery ne particles (dP< 36m), however, kL aalso decreases with decreasing particle diameter[86]. Overall, the behavior of kL a is governedby the interfacial area per unit volume becausethe change in kL is generally small.

The mass-transfer coefcient between liquidand solid increases roughly as the fourth root ofthe gas ow rate, decreases with increasing liq-uid viscosity and particle diameter, and becomespartly independent of these factors at high gasrates. Two distinct models can be used for themathematical description, but they lead to simi-lar values if the solids are completely suspended.Values reported by various authors are comparedin Figure 20 [87].

Figure 20. Liquid solid mass-transfer coefcient esti-mated with ve different correlations [87]L = 106m2/s; L = 1000 kg/m3 ; DG,L = 109m2/s;-S/L = 1.5; S/L = 0.3

Hydrogenation of Benzene. In the IFP pro-cess, benzene is hydrogenated to cyclohexane ina slurry bubble column [88] (Cyclohexane,Chap. 4.1.). This process was used to produce1.8 106 t of cyclohexane in 23 plants world-wide in 1991.

Figure 21 shows the slurry bubble column (a)in which benzene is hydrogenated on suspendedRaney nickel. The hydrogen-rich gas that is let inat the bottomof themain reactor provides hydro-gen for the reaction and also strips the productcyclohexane out of the reactor. Thus, the pro-cess can be operated without the need for ex-pensive equipment to separate the product from

the catalyst. In the external cooling loop, the highheat of reaction is removed and suspension of thesolid catalyst is assisted by the circulating liq-uid stream. Complete conversion of benzene isaccomplished in a xed-bed reactor (b) installeddownstream on the gas side.

Figure 21. Hydrogenation of benzene to cyclohexanea) Main reactor; b) Secondary reactor; c) Steamdrumht = 10m; dt = 2.5m; T = 195 C; p= 22 bar; Gas ve-locity: 7.5 cm/s; Liquid residence time 3 h

The usual reaction conditions in the bubble-column reactor are 200 C and 22 bar. Typicalgas velocities are ca. 0.08m/s; liquid-phase res-idence time is ca. 3 h.

2.14. Airlift Loop Reactors

In contrast to bubble columns, airlift loop re-actors are characterized by a well-dened liq-uid circulation, which is achieved by dividingthe reactor into sections with and without gassparging. The difference in gas holdup betweenthese two zones drives the liquid circulation. Inprinciple, two types of airlift loops can be identi-ed (Fig. 22). In the rst (airlift reactors with in-ternal loop), either a concentric tube (Fig. 22A,B) or a plane partition (Fig. 22C) divides thecolumn into riser and downcomer sections. Inthe second (airlift reactors with external loop,Fig. 22D), two separate tubes form the upowand downow zones; the tubes are joined by twohorizontal sections at top and bottom.

The dependence of liquid circulation veloc-ity on supercial gas velocity is described by thepurely empirical relation

vL,c=C1uC2G (2.17)

Bubble Columns 17

The value of the constantC1 is determined by re-actor geometry and the physical properties of thesystem; C2 depends on both ow regime and re-actor geometry [8991].A physicalmodel basedon an energy balance [39], [92] leads to the re-lation

vL,c=c 3ghRuG (2.18)

An exponent of 0.33 for gas ow rate is of theorder of usual experimental results.

Figure 22. Types of airlift loop reactorsA) Concentric draft tube with external recycle; B) Concen-tric draft tube with internal recycle; C) Deep shaft reactor(ICI); D) External loop

Airlift reactors with external loop (Fig. 22D)are usually run at much higher gas and liquidow rates than conventional bubble columns.The high circulation velocities signicantlychange the nature of the two-phase ow, namely,the gas holdup declines with increasing circu-lation velocity (see Fig. 23). The highest gasholdup occurs in the bubble column (uL = 0),where the absolute velocity of the rising bubblesis lowest because of the zero liquid velocity. Pa-rameters such as surface tension, coalescence,

and viscosity have much less effect on airliftloop reactors than on bubble columns becausethe interactions between bubbles are far weakeras a result of the high circulation velocity. Forthe same reason, the homogeneous ow regimein airlift loop devices extends to much highergas rates than in bubble columns [91], [93].

Figure 23. Gas holdup in airlift reactors with external loop(system: 0.1mol/L NaCl solution air)dt = 0.1m;ht = 8.5m; Porous plate = 150m

The gas holdups that occur in airlift reactorswith internal loop are only slightly lower thanthose in bubble columns. The decrease in gasholdup in the riser is partly offset by an increasein the downcomer [94], [95].

As in the bubble column, the volumetricmass-transfer coefcient increases with increas-ing gasow rate.Because the liquid-phasemass-transfer coefcients kL are the same in bubblecolumns and airlift reactors [96], [97], the dif-ference in kL a results from differences in inter-facial area. Airlift reactors with external loop al-ways have lower mass-transfer coefcients thanbubble columns because the lower gas holdupimplies a smaller area for mass transfer. ThekL a values for airlift reactors with internal loop,on the other hand, are similar to the values forbubble columns (Fig. 24) because here the gasholdups differ only slightly [93], [98100].

In contrast to bubble columns, the residence-time distribution of airlift reactors is inuencednot just by longitudinal mixing but also by back-mixing due to the circulation ow. Reactors withan external loop exhibit axial dispersion coef-cients whose values are up to 20 % lower than

18 Bubble Columns

those of bubble columns, depending on the cir-culation velocity [93]. The consequences of thisback-mixing for the reactor yield of airlift loops,however, are far less serious because the high liq-uid velocities lead to far larger Bodenstein num-bers (for a denition of the Bodenstein number,see Mathematical Modeling). The axial dis-persion coefcients of airlift reactors with inter-nal loop are much lower. Measurements of axialmixing of the gas and liquid phases show a de-crease in the dispersion coefcients by roughlya factor of three [101].

Figure 24.Comparison ofmass-transfer coefcients for air-lift reactors and bubble columns(system: salt solutions; gas distribution: small bubbles)

As in bubble columns, mixing times decreasewith increasing supercial gas velocity becausethe circulation velocity becomes greater. Sincethe circulation time tc and the mixing time tMare directly proportional [92]tM

tc=

(FD

FR

)0.5(2.19)

(where = 3.5 for internal circulation and 5.2 forexternal circulation), the relationship betweenmixing time and circulation velocity can be ex-pressed as

tMv1L,cThe mixing time is also directly proportional tothe distance traveled. Five to six passes are re-quired for a degree ofmixing of 90%. The liquidcirculation in airlift reactors, with their high cir-culation velocities, leads to higher heat-transfercoefcients than in bubble columns [102]. As inbubble columns, the heat-transfer coefcient inairlift loop reactors increases with gas ow rate.

Biological Wastewater Treatment. Airliftloops are employed to provide well-denedback-mixing of the liquid phase. This is desir-able, for ex-ample, when uniform temperatureand concentration distributions must be main-tained in the reaction medium to equalize feedvariations as quickly as possible or to preventsettling of solids from the mixture.

Airlift reactors are used in biological waste-water treatment [5], [103], [104]. These units areclosed vessels ca. 15 25m tall and 10 45m indiameter; they have small space requirements,very good oxygen utilization, and greatly re-duced off-gas and noise emissions. The contentsof the reactor circulate through one ormore drafttubes (Fig. 25); sparging occurs outside the drafttubes. During operation, the growing microor-ganisms must constantly be provided with suf-cient oxygen and substrate, and adequate mix-ing of the wastewater activated-sludge mix-ture must be insured. If these conditions arenot satised, solids will settle and anaerobic fer-mentation processes may occur. The usual con-ditions are as follows: supercial gas velocity1 3mm/s, gas holdup between 1 and 3 %, androughly 25 circulations of reactor contents perhour. The utilization of atmospheric oxygen ismore than 50%. The wastewater has a residencetime between 6 and 15 h.

3. Downow Bubble Columns

Chapter 2 described ordinary bubble columnsin which gas ows from bottom to top and hasa short residence time (gas sparging method Ain Fig. 1). In downow bubble columns, by con-trast, the gas and liquid phases are transported to-gether from top to bottom (Fig. 1 B). This regimedemands liquid velocities vL greater than the rel-ative velocity vrG between the two phases. De-pending on the liquid velocity chosen, very lowgas velocities can be achieved

vG = vL vrG (3.1)

or long residence times. This is an advantage es-peciallywhen a large-volume liquid streammustcome in contact with a small-volume gas stream.In the extreme case, a virtually suspended state

Bubble Columns 19

Figure 25. Biohoch reactor (Hoechst)a) Settling zone; b) Aeration chamber; c) Draft tube

of the bubbles can be realized, with an arbitrarilylong residence time. Under certain conditions,this permits complete conversion of the gas.Nor-mally, however, part of the gas must be assumedto exit the reactor without reacting, mainly whenthe gas contains components that do not react. Insuch cases, the cocurrent motion of the phasesis a disadvantage because only one theoreticaltransfer unit can be realized.

3.1. Design and Applications

Aswith bubble columns, a variety of designs ex-ist for downow bubble columns. These differmainly in the way the gas is let in, the bubblesare generated, and the unreacted gas is removed.Figure 26 shows some examples.

The simple downow bubble column(Fig. 26A) is particularly suitable for gases thatare soluble in the liquid phase and/or fast re-actions. Unreacted gases cannot be separatedin the column, so an extra separator may berequired. The simple downow bubble columnis often employed at high pressure (> 100 bar).A slender geometry makes it possible to reducethe wall thickness of the cylindrical reactor. Toimprove mass transfer between gas and liquidphases, the vessel can be packed with particles,which also reduce both the required liquid rateand the axial mixing of liquid and gas. Usually,however, packings are used as catalyst supports.The classical application of this type of device isthe hydrogenation of awide range of substances.

Adding a liquid recycle creates diverse pro-cess design options. The back-mixing involved,which is usually undesirable, can often be ac-ceptable. With a liquid recycle the downowbubble column can be operated on small feed-streams. The recycle loop also provides a sim-ple way of adding or removing heat, so that thetemperature prole in the reactor becomes moreuniform.

From the standpoint of process engineering,the downow bubble column with integratedseparator (Fig. 26B) differs little from the sim-ple downow bubble column. The integratedseparator is well suited when larger quantities ofoff-gas must be removed. A typical applicationis in the ozone treatment of water air or oxygenwith a low ozone content is fed to the reactor andthe quantity of exit gas is almost the same as thequantity of inlet gas. The design of the reactorwith integrated separator is simple. The shoul-dered form is not suitable for high pressure.

The downow upowbubble column(Fig. 26C) combines a downow bubble col-umn and an ordinary bubble column. Particu-larly long gas residence times are possible. Theliquid routing shown in Figure 26C gives a fre-quently desirable residence-time distribution:the downow section features mixing similar toa stirred tank by virtue of the pump stream. Thisis advantageous with a high heat of reaction,which can be removed with the pump stream.The bubble column in the outer annular spacemerely carries the outow, and back-mixing inthis zone can be suppressed by internals (pack-

20 Bubble Columns

ing, static mixers, sieve trays). High conversionare achieved in higher-order reactions.

Figure 26. Designs of downow bubble columnsA)With external gas separator; B)With integrated gas sepa-rator; C) Combined downow upowwith bubble columnin annulus; D) Dip-tube gas sparging with internal gas re-cycle

Downow Upow Bubble Column(Fig. 26D). Another design combines downowand ordinary bubble columns. However, the topof the downow section is in the gas space of thereactor. Fresh gas together with recycle gas (thathas escaped from the liquid surface) is drawn inhere and dispersed in the liquid. Pure gases or

gases with low inerts content can be completelyconverted under pressure with this method, alsocalled dip-tube sparging.

The lower part of the downow bubble col-umn serves as the separator. Only small gas bub-bles are carried out of the reactor, which stillhave some reactivity. The pump is therefore pro-tected against excessive contents of gas in theliquid, even in coalescence-hindered systems.

3.2. Operating Conditions and GasHoldup

Gas is fed in at the top of the column and dis-tributed as uniformly as possible over the crosssection. Large gas holdups (G 0.3 0.35)can be obtained even in coalescing systemssuch as water air [105110]. When the sys-tem is coalescence-hindered, for example, if car-boxymethyl cellulose or ethanol has been addedto the water air system, values up to G 0.45can be achieved [108].

The gas holdup can be estimated as

G=uG

vL vrG(3.2)

The relative velocity vrG for coalescing aqueoussystems takes on values in the range 0.2m/svrG 0.3m/s. The liquid velocity vL can becalculated from the liquid rate uL and the gasholdup G:

vL =uL

1G(3.3)

Hence the gas holdup can be expressed as

G=uG

uL1G vrG

(3.4)

If gas and liquid rates are given, Equation (3.4)can be solved for the gas holdup:

G=B

2

+(

2B

)2 uGvrG

+11

where

B=uL+uGvrG

1 (3.5)

Finally, Equation (3.4) can be written so as toyield the liquid rate:

Bubble Columns 21

uL= (1G)(uG

G+vrG

)(3.6)

A ow chart can then be derived for thewater air system (vrG = 0.23m/s). In Figure 27,the gas velocity is plotted versus the supercialliquid velocity, with the gas holdup G as a pa-rameter. For G > 0.35, ow is in the hetero-geneous regime. In this regime a highly turbu-lent two-phase ow develops, resulting in strongmixing of liquid and gas. In the extreme case,gas accumulates at the top and can propagatethroughout the reactor from there.Kulkarni re-ports somewhat different results [111], possiblybecause of less uniform gas feeding.

Figure 27. Flow chart for downow bubble columnsGas velocity is plotted as a function of liquid velocity,with gas holdup as parameter, for the water air system(vrG = 0.23m/s) calculated with Equation (3.6).

For systems with hindered coalescence, de-termination of these values and other processparameters normally requires experimentation[105].

3.3. Mass Transfer

The following statements are applicable only tocoalescing systems. In the homogeneous owregime, all bubbles in the downow bubble col-umn are almost equal in size. Diameters of3mm db 4mm are observed [112]. A slightdecrease in bubble size with increasing liquid

ow rate and rising pressure has been reported[108].

If the gas holdup is known, the specic inter-facial area can be estimated as

a=6GdbS

which gives maximum values up toa = 450 700m1. Figure 28 compares thesevalues to those measured in simple bubblecolumns and packed columns [108] (referrednot to the total volume but to the liquid vol-ume). This gure illustrates the advantages ofdownow bubble columns, which have higheraL values at low gas rates.

A liquid-phase mass-transfer coefcientkL 3.7 104m/s has been calculated byplotting the volumetric mass-transfer coefcientkL a versus the volumetric gas holdup [110] andthe bubble size stated above. Somewhat lowerestimates, up to 3104m/s, have been re-ported in [109], [112]. However, the mass-trans-fer coefcient kL cannot be measured directly,and large uncertainties are to be expected. Thevolumetric mass-transfer coefcients kL a mea-sured in bubble columns at equal gas holdups areroughly the same. Because of the very differentvolumetric gas ow rates in upow and down-ow bubble columns, different gas conversionsare achieved; Figure 29 compares these guresfor sulte oxidation with air [110].

Data on the axial back-mixing of thegas phase have been reported [111]. At gasrates of uG = 0.001 0.01m/s, the dispersioncoefcient takes on constant high values:DG 0.2m2/s (dt = 0.025m, uL = 0.334m/s,G = 0.025 0.09).

Back-mixing of the liquid phase under com-parable conditions is also markedly less than innormal bubble columns [113].

Examples. Steiner and Herbrechtsmeierstudied the oxidation of sulte solutions withair in the downow bubble column, nding atwelvefold higher depletion than with a simplebubble column (Fig. 29) [110].

A process for the absorption of gases con-taining nitrogen oxides has been reported [114].Virtually complete conversion can be obtainedthrough the use of a downow bubble column3m high.

22 Bubble Columns

Figure 28. Comparison of mass-transfer area per unit liquid volume for various sparged devices as a function of gas velocity,with liquid velocity as parameter, according to [108]

Figure 29. Comparison of oxygen depletion in upow and downow bubble columns for sulte oxidation with air [110]T = 22 C; [SO23 ] = 0.4 0.8mol/L; [Co3+] = 7106mol/L; pH= 8.0

The degradation of organic contaminants byozonolysis is a well-known method of watertreatment. For economic and safety reasons, vir-tually complete depletion of the ozone is desir-able, which can be achieved in downow bubblecolumns as reactors [115]. No danger of foulingexists in these devices, and high liquid through-puts can be handled. Figure 30 is a ow sheetof the entire process. Only a single theoreti-cal mass-transfer unit can be realized, but thisdrawback can be overcome by the proposed useof a reactor cascade [115]. The phases are ledthrough the cascade countercurrently.

4. Jet Loop ReactorsJet loop reactors are among the most versatilegas liquid contactors. The momentum of theliquid jet issuing from the nozzle enhances in-ternal circulation and opposes demixing of thephases (distributionmethodC in Fig. 1). The liq-uid jet can be utilized to suck in, compress, anddisperse fresh or recycle gas (Figs. 31, 32, 33,34). The liquid-jet data are important processparameters. The liquid volumetric ow rate, ve-locity, and power can be varied overwide ranges.Finally, the size of the draft tube and the upper

Bubble Columns 23

Figure 30. Plant with downow bubble column for ozone treatment of watera) Downow reactor; b) Pressurizing pump; c) Ozone generator; d) Compressor; e) Deozonizer

ow-reversal zone strongly affect uid dynam-ics and gas separation. Other possible variationsare offered by the nozzle conguration (Figs. 32,33, 34).

The four examples in Figure 31 illustrate op-tions for the direction ow pattern phases. In allcases the gas is incorporated into the liquid viathe nozzle located in the gas space. The liquidjet entrains gas bubbles until the nozzle oriceis closed by the rising liquid surface. The in-corporation of more gas submerges the nozzleand blocks the gas inlet, the surface level thendrops again; this self-regulating mechanism en-ables the gas holdup to be controlled.

A jet loop reactor (also called a gas-circulation reactor) [116] without net gas or liq-uid throughput is shown in Figure 31A. Bothphases are let in at the top and discharged at thetop (the gas phase is consumed to a higher orlower degree). This corresponds to dispersionmethod C of Figure 1.

If the gas is under pressure, it can also be letin at the bottom to intensify circulation. The re-sult is a net gas rate, as in the bubble column(Fig. 31B); here, distribution methods A and Cof Figure 1 are combined.

Figure 31C shows a combination of spargingmethods B and C in Figure 1. The liquid is fedat the top and discharged at the bottom. This jetloop reactor has an additional net ow of liquid,as in a downow bubble column.

A combination of all three distribution meth-ods (bubble column, downow bubble column,and jet loop) is shown in Figure 31D. The pro-cess characteristics of one sparging typewill pre-dominate, depending on the selected gas and liq-uid ow rates. At high gas ow rates, for exam-ple, the liquid surface level rises above thenozzleorice. The liquid jet then no longer entrains gasbubbles, serving only to drive the circulation anddisperse the bubbles. This versatile type of dis-tribution can be further rened through variationof the nozzle position and the use of self-primingejectors (Figs. 32, 33, 34). To evaluate a design,the essential process parameters must be esti-mated, which is not always feasible because ofthemany possible variations. For the basic formsshown in Figure 31, however, some informationcan be derived from a power balance (Section4.2).

4.1. Design and Applications

LoopReactorswithDownowLiquid Jets.Figure 32 illustrates several loop reactors withdownward-pointing nozzles. These reactors areeven suitable for suspension catalysis. If thepump or feedstream is cut off or fails, the noz-zle drains clear, and the danger of the nozzlebeing plugged by the suspended catalyst is thusreduced. Another advantage is the long gas res-

24 Bubble Columns

idence time. From the inlet at the top, the gascirculates through the loop at least once. More-over, the devices are designed so that the gasis internally recycled. This is important for thecomplete conversion of gases containing little orno inerts.

Figure 31. Options for phase routing in the gas-circulation type of jet loop reactorA, C)With surface gas sparging; B, D)With pressure sparg-ing (with gas throughput); C, D) With bottom outlet forliquid, inlet at top (with liquid throughput)

In the gas- circulation reactor of Figure 32A(see also Fig. 31) [116], the gas can also be letin at the bottom of the reactor, independentlyof the nozzle, if the gas is available at reactorpressure. For a given jet power, this design of-

fers much higher gas holdups and better mass-transfer performance (Sections 4.5 and 4.6). Thejet only has to supply the recycle gas. Anothermarked increase (up to a factor of two) in the gasholdup is achieved by installing a momentum-transfer tube in the reactor. This can be sub-merged (Fig. 33B) or can extend above the liq-uid surface (Fig. 33C).

Figure 32. Types of jet loop reactors with downward liquidjetA) Gas-circulation reactor with pressure sparging; B) Gas-circulation reactor without connected gas space; C) Gas-circulation reactor with submerged nozzle; D) Compactreactor with annular space for liquid injection

Bubble Columns 25

To prevent separation of the gas phase, thenozzle can be built directly into the reactor top(Fig. 32B) [117]. Gas bubbles separating in thiszone are immediately entrained by the liquid jetand redispersed into the circulating ow.

Figure 33. Options for spontaneous gas sparging from topSurface sparging in gas-circulation reactor without (A) andwith (B) momentum-transfer tube; dip-tube sparging with-out (C) and with (D) self-priming ejector

The submerged nozzle in Figure 32C can ei-ther accept pressurized gas from outside the sys-tem [118] or suck the gas in. Internal gas recycleis also possible. The suction of the nozzle canbe enhanced by applying a swirl to break up theliquid jet, provided the liquid nozzle orice isset back somewhat to the rim of the nozzle. Theejectors and ejector nozzles discussed in Chap-ter 2 are suitable for deeper submergence (seealso Fig. 34B and C).

In the jet loop reactor proposed by Rabigerand coworkers, the liquid is fed in via an annu-lar nozzle (Fig. 32D) [119], [120]. Gas can bedrawn in via the center tube (ejector fashion) orsupplied under pressure (injector fashion). Forapplication of this reactor type in wastewatertreatment see [121], [122].

Figure 34. Design options for loop reactors with upwardliquid jetA) With expanded head for gas separation; B) With gas re-cycle via a self-priming ejector; C) With gas recycle via anejector jet nozzle and perforated plates; D) With externalrecycle tube

26 Bubble Columns

Submerged nozzles supply the gas in theloop ow. The penetration depth of the jet dif-fers. The reactor is thus easier to start up andthe circulation ow can be build up in a sim-pler way. This is particularly important in batchprocesses. In principle, submerged nozzles rep-resent an intermediate stage between surfacesparging (Fig. 32A and B) and pressurized gassparging through nozzles at the bottom of thereactor (Fig. 34).

In the gas- circulation reactor of Figure 33,gas sparging takes place through the free surface.If a momentum-transfer tube is used (Fig. 33B),gas enters the circulating ow at a greater depth.This arrangement functions even when the liq-uid level drops and the momentum-transfer tubeextends into the gas space (Fig. 33C). In Fig-ure 33D, the tube is led outside the reactor, sothat gas can be delivered directly from outsidewithout any mixing with recycle gas. The lasttwo types of gas sparging (Fig. 33C and D) arealso referred to as dip-tube sparging designs.

Jet Loop Reactors with Upow Liquid Jet(Fig. 34). In the second major variant of the jetloop reactor, the nozzle points upward. This de-sign is closely related to the airlift loop reactor(Section 2.14). The liquid jet mainly producessmaller gas bubbles so that conversion of thegas phase can be improved. On the other hand,the circulation velocity is increased. At least aportion of the gas is thereby driven through thereactor faster than in airlift reactors, with thepossible result of lower conversion; this dangerexists particularly in the reactor of Figure 34A,which uses a jet nozzle. The widened separationzone at the top can reduce gas recirculation orcut it off altogether; the result is improved mix-ing of the liquid phase because the circulationvelocity increases with increasing gas holdupin the downcomer. Gas recycle is recommendedwhenever part of the gas leaves the column un-converted; it can be accomplished without a me-chanical recycle-gas compressor if an ejector oran ejector jet nozzle is employed (Fig. 34B andC). The ejector jet nozzle offers a higher com-pression efciency than the ejector and produceslarger interfacial areas [12]. From the chemi-cal reaction engineering standpoint the combi-nation of a loop reactor with a series of perfo-rated plates is very interesting (Fig. 34C). Thelower part (loop reactor) exhibits the residence-

time distribution of a stirred tank. Back-mixingis suppressed in the second section (perforatedplates). For higher-order reactions, the conver-sion of both liquid and gaseous components canbe increased in this way. With pure gases, re-cycle ensures adequate distribution because thegas ow rate is sufcient for an even gas load ofthe perforated plate.

Figure 34D shows a reactor (analogous to theairlift loop of Fig. 22D) with external recircu-lation. This device has an operational behaviorcomparable to that of reactors with internal cir-culation. Its advantages include better gas sepa-ration and simpler heating or cooling facilities.The accessible heat-transfer area is larger, anda conventional heat exchanger can be integrateddirectly into the loop.

The most important characteristics of jetloop reactors with upward-pointing nozzles canbe summed up as follows:1) They are particularly suitable for higher gas

throughputs or when the gas has a high con-tent of inerts

2) They have larger interfacial areas than bub-ble columns, especially with system withhindered coalescence

3) They offer more intensive back-mixing thanbubble columns

4) They are less suitable for suspension cataly-sis, because the nozzle can become plugged

4.2. Typical Dimensions

In jet loop reactors, height-to-diameter ratiosht/dt of 5 to 20 are common. When severalnozzles are used along with internal tubes, ar-bitrarily small height-to-diameter ratios can beachieved. Values larger than 20 are also seen inhigh-pressure operation and in pilot plant reac-tors.

The optimal diameter di of the internal tubeis dictated by the direction of ow. If ow inthe tube is downward, tubes with a diameter ra-tio di/dt of 0.2 0.5 are suggested [116], [119].The narrower internal tubes have the principaladvantages of higher gas holdup andbettermass-transfer at low energy dissipation rate (up to1 kW/m3). As jet power increases, the widertubes become better in these respects [119],[123].

Bubble Columns 27

For upward ow, Blenke and coworkers de-termined the optimal internal tube diameter asdi/dt = 0.59 [124]; this result applies to single-and two-phase reactors.

A crucial parameter of the jet loop reactoris the nozzle diameter dn. Common values arein the range of dn/dt = 0.02 0.1. For a givenjet power, large nozzles are more efcient thansmaller ones for coalescing systems. In systemswith hindered coalescence, in contrast, this re-lationship can be reversed.

4.3. Energy Balance

In the general case of Figure 31D (combina-tion of bubble column, downow bubble col-umn, and jet loop reactor), a total of ve me-chanical power terms can be identied [125].These can be referred to the reaction volume

VR=

4d2thR (4.1)

Three types of power are delivered to the reac-tor:

1) Jet thrust power ethrust per unit volume:

ethrust=fiLv2nvL,i

hR

(dn

dt

)2(4.2)

where f i is the fraction of cross-sectionalarea of the inner tube and vn is the nozzlevelocity

2) Power input per volume due to liquid oweL (as in a downow bubble column) :

eL= gGuL (4.3)

3) Power input per unit volume due to gas oweG (as in a bubble column; holds approxi-mately only for small pressure changes):

eG g (1G)uG (4.4)

This power is transformed to heat by twomechanisms:

1) Power dissipation per unit volume due to cir-culation ow:

ecirc= fiv3L,i

2hR(4.5)

2) Power dissipation per unit volume due tofriction between phases (slip power):

eslip= gG (1G) vrG (4.6)

A combination of these terms gives the bal-ance equation:

ethrust+eG+eL+eslip+ecirc= 0 (4.7)

In general, the quantities vL, i (i.e., ecirc) and G(i.e., eslip) are unknown, so direct evaluation isimpossible.

4.4. Mixing Behavior and FluidDynamics

The ow processes in jet loop reactors are par-ticularly crucial for the mixing and residence-time distribution of both phases. The investiga-tion of the relationship betweenmixing time andliquid circulation time showed that complete ho-mogenization of the liquid phase requires ca. tenpasses [126].

The residence-time distribution of the liquidin the jet loop reactor has been investigated bothexperimentally and theoretically [127], [128].Values of dispersion coefcients in the liquid arepresented in [118], [128]. The crucial parameterfor mixing is the internal circulation ow gen-erated by the liquid let in through the nozzle.In certain cases, this quantity can be estimatedfrom the energy balance (Eq. 4.7).

The residence-time distribution of the dis-persed gas phase can be found in [129]. Thedispersion coefcients are not substantially dif-ferent from those of the liquid phase.

Fluid Dynamics of Single-Phase Flow. Thesimplest formulation is that of single-phase ow.For eG = 0, eslip = 0, eL = 0, the following holdsfor liquid circulation ow

vL,idt=

2fi

vndn (4.8)

The drag coefcient of circulation ow canbe found in [118], [130132]. Typical valuesfor bottom gas feed are = 4; for top gas feed, 0.25 2.

28 Bubble Columns

Fluid Dynamics of Two-Phase Flow. Intwo-phase ow the momentum balance can besolved for the circulation ow vL, i only if thegas holdup G is known, which is not normallythe case. Only in the gas- circulation reactor(Fig. 32A, B) can the gas holdup be denitelyspecied within a certain range. Under the as-sumption of low gas holdup G, for example,the following implicit relation is reported [123]:

(vndn)2 ={ fi

2v2L,i+

L

ghRG (vrGuL)uG

vL,i

}d2t (4.9)

The resistance coefcients obtained for single-phase ow can be used to a good approximation.Figure 35 shows a logarithmic plot of Equation(4.9) for uL = 0 and uG = 0. The liquid velocitiesin the two-phase regime are always lower thanin single-phase ow. If the velocity goes below aminimum value, the ow becomes unstable andstops, as shown by the nonlinear behavior of thecurves at low velocities. Gas sparging then takesplace only in the upper part of the internal tube.These features are illustrated in Figure 35. Theminimum ow velocities vL, i,min are a factor of3 smaller than the single-phase velocities. Thismeans that all possible velocities in two-phaseow are in the range

13 vL,idt

2fi

vndn 1

The minimum ow velocity can also be ob-tained from Equation (4.9):

vL,i,min=3

/Lfi

ghR [G (vrGuL)uG] (4.10)

At high gas velocitiesuG orwhen the nozzle is atthe bottom of the reactor (Fig. 34A), gas holdupcannot be freely selected. Instead, it adjusts it-self as a function of uid-dynamic conditions.At present, ow velocities cannot be calculatedin advance.

Bohners measurements for the jet loop re-actor are plotted in Figure 36 in the form

vL,cdt=f (vndn,uG)

[133], [134]. Two regions can be identied. Atlow jet velocities vn, the jet loop behaves likean airlift loop reactor (Section 2.14). The liquid

circulation velocity is almost independent of jetvelocity. Only at larger values does vL, c increaselinearly with vn as in single-phase ow [133135]. Investigations on radial velocity prolesin loop reactors are found in [135].

Figure 35. Circulation ow rate in gas-circulation reactoras a function of jet conditions and gas holdup, calculatedwith Equation (4.9)Assumptions: = 2.5; vrG = 0.23m/s; Geometric dimen-sions: dt = 0.3m; dh = 0.015m; ht = 2.0m; f i = 0.25

Figure 36. Measured circulation ow in pressure-spargedjet loop reactor as a function of jet conditions, with gas ve-locity as parameter [133]dt = 0.29m; ht = 2.0m; f i = 0.35

4.5. Gas Holdup

In the gas-circulation reactor (Figs. 31 and 32Aand B), the gas holdup can be set arbitrarily

Bubble Columns 29

within certain limits. For a given jet velocity vn,the maximum values G,max can be calculatedfrom the power input by the liquid jetPn=

L

2v3nFn where Fn=

4d2n (4.11a)

or the jet power per unit volume

en=Pn

VR=L

2 v

3n

hR

(dn

dt

)2(4.11b)

The equations reported by Tebel and Zehnerare presented here in simplied form [123].The maximum specic energy dissipation ratecaused by the slip between the two phases(Eq. 4.6) is given by

eslip,max=4

31.5

2fi

endn

dt(4.12)

which can be solved as follows for themaximumgas holdup:

G,max=2

31.5

2fi2en dndtgvrG

=2

31.5

2fi

2Pn dndtgvrGVR

(4.13)

Equation (4.13) is comparedwithmeasured val-ues in Figure 37. The lowest gas holdups are ob-tained in the coalescing systemwater air. Even

tiny amounts of methanol reduce the tendencyto coalesce. The primary gas bubbles generatedby the jet retain approximately the same sizeover the whole apparatus because they do notcoalesce. This reduces their slip velocity vrG sothat much higher gas holdups and interfacial ar-eas can be obtained.

Figure 37. Comparison of measured and calculated maxi-mum gas holdup as a function of specic jet power in gas-circulation reactorSystem: water air with added methanol; measured valuesafter [123]; calculations with Equation (4.13)dt = 0.14m; ht = 1.32m; di = 0.055m; dn = 4.9mm

More complex relationships apply if pres-surized gas is let in at the bottom of the gas-circulation reactor. The gas holdup then sets it-self, analogously to behavior in a bubble column,an airlift loop reactor (Sections 2.9 and 2.14),

Figure 38. Gas holdup measured in the pressure-sparged jet loop reactor [133] versus jet conditions at various gas velocitiesht = 2m; dt = 0.29m; f i = 0.33

30 Bubble Columns

or the ordinary loop reactor (Fig. 34A). Typicalmeasured values for this type of gas sparging arepresented in Figure 38. As the gas rate increases,gas holdup increases rapidly. The jet velocity, bycontrast, has relatively little effect.

Zehner and Thelen obtained the expres-sion

eslip

2en dndt=f

(eG

2en dndt

)(4.14)

for jet loop reactors with pressurized gas sparg-ing [125]. Figure 39 shows the gas holdup fordifferent reactor types and sparging types, basedon this relation. To within measurement er-ror, the same values are obtained for the gas-circulation reactorwith pressurized gas sparging(Fig. 31B) and for the jet loop reactor (Fig. 34).These values are tted well by the correlation

eslip

2en dndt= 1.5

(eG

2en dndt

)0.8(4.13a)

which can be solved directly for the gas holdup:

G= 1.5

(2Pn dndt

gvrGVR

)0.2 (uG

vrG

)0.8(4.13b)

Figure 39.Relationship between slip power slip, jet powern, and gas compression power G for determination of gasholdupa) Surface sparging in gas-circulation reactor; b) Transitionbetween surface and pressure sparging; c) Pressure spargingin gas-circulation reactor and normal jet loop reactor

4.6. Mass Transfer

Themean bubble diameter in a sparged reactor isalways the result of distribution and coalescence

processes. In the easily coalescing water airsystem, the bubble diameter corresponds essen-tially to the local energy dissipation rate, a quan-tity that is distributed very unevenly over the vol-ume in jet loop reactors. Zones of particularlyhigh energy-dissipation rate include the imme-diate action regionof the liquid jet and, to a lesserdegree, the regions of loop ow reversal. This isthe reasonwhy the smallest bubbles are observednear the jet in the compact reactor (see Fig. 32D)[120].AsFigure 40 shows, bubble size decreasesfrom ca. 3mm to almost 2mm with increasingenergy dissipation ratePn/VR. In the othermuchlarger regions, the bubbles quickly coalesce tobigger (3 4mm) units. Jet loop reactors accord-ingly donot feature smaller air-in-water bubbles,on average, than bubble columns or downowbubble columns operated in the homogeneousow regime. For a given gas holdup, compara-ble mass-transfer should therefore be expected.The relationships among the mean bubble diam-eter (Sauter diameter) dbS, the gas holdup G,the specic interfacial area a, and the volumetricmass-transfer coefcient kL a have been pointedout in Section 3.3. These considerations lead tothe following guideline values for the water airsystem:

Figure 40. Bubble sizes in the compact reactor (system:water air)dt = 0.1m; ht/dt = 5.9; dn = 5mm; di/dt = 0.6

Usual specic energy dissipation rates:Pn/VR 1 10 kW/m3Mean bubble diameter (Sauter diameter):dbS 3.5mmMaximum gas holdup: G 6 30 %

Bubble Columns 31

Special interfacial area: a 100 600m1Volumetric mass-transfer coefcient:kL a 0.04 0.2 s1If liquid mixtures and ionic or detergent so-

lutions exhibit a noncoalescing behavior, muchhigher gas holdups and smaller bubble diameters(signicantly less than 1mm) can be achieved.The volumetric mass-transfer coefcients andspecic interfacial areas behave in a similarway;in systems with hindered coalescence they maybe a factor of 5 to 10 higher than the water airvalues. A compilation of volumetric mass-trans-fer coefcients in various types of sparged ap-paratus can be found in [136].

Figure 41. Effect of solids on gas holdup in the gas-circulation reactorSystem: 1wt % NaCl air glass spheres; dp = 0.075 0.15mm

4.7. Three-Phase Loop Reactor

When solids are suspended in sparged loop re-actors the same engineering considerations arenecessary as in slurry bubble columns (Section2.13). Many workers have studied the effect ofsolid particles onuid dynamics andmass-trans-fer performance [76], [137139].

The uid-dynamic principles of solid liquidsystems are comparable to those of gas liquidsystems (Sections 4.3 and 4.4) [132], [140].These considerations have been extended tothreephase systems so that theoretical modelsare available for complexmultiphase ow [120],[123], [141]. In principle, the solid phase is ac-counted for by a supplemental energy term forthe slip power dissipation of the particle swarm(Section 4.3). How interactions between phasesinuence individual slip velocities is not clear.For example,Kurten and coworkers examined

the maximum possible gas holdup in a gas-circulation reactor with gas sparging at the sur-face [76]. As Figure 41 shows, the solids contentS has a strong effect that cannot be accountedfor merely by the additional slip power dissipa-tion of ne particles. Instead, the slurry must beassumed to yield larger gas bubbles because ofits higher apparent viscosity. The higher slip ve-locity of these larger bubbles might then explainthe marked dependence on solids concentration.

Rabiger [138] and Wachsmann [139] alsostudied the effect of solids. At constant energydissipation rate and constant volumetric gas owrate, the dependences are roughly similar tothose found in [76]. Only for low solids and gasholdups does a slight increase in gas holdup oc-cur relative to two-phase systems.

This has been explained by bubble breakupby large solid particles [142]. The effect shouldnot occur below the critical Weber number

We=SdSv

2b

= 3

However, this statement partially contradictsRabigers results [138]. Technically, these dis-crepancies are insignicant. Up to a solids con-centrationof 10 vol%, nomajor differences existin gas holdup andmass-transfer between normaland three-phase jet loop reactors. Higher volu-metric particle concentrations do not, however,normally occur in jet loop reactors.

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