Design of Gas-Inducing Reactorsdownload.xuebalib.com/7xe7YoC5R4y.pdf · Design of Gas-Inducing Reactors Ashwin W. Patwardhan and Jyeshtharaj B. Joshi* Department of Chemical Technology,

REVIEWS

Design of Gas-Inducing Reactors

Ashwin W. Patwardhan and Jyeshtharaj B. Joshi*

Department of Chemical Technology, University of Mumbai, Matunga, Mumbai 400 019, India

A gas-inducing impeller enables efficient recycling of gas from the headspace into the liquid.Historically, these impellers were used for the first time in froth flotation machines. The variousdesigns of gas-inducing impellers (including those used in froth flotation) could be classifiedinto three categories, depending on the flow pattern coming into and leaving the impeller zone.These are denoted as type 11, type 12, and type 22 systems. The critical impeller speed for theonset of gas induction (NCG) is governed by a balance between the velocity head generated bythe impeller and the hydrostatic head above the impeller. A number of correlations (for types11 and 22) are based on this balance (Bernoulli’s equation). The rate of gas induction (QG) forthe type 11 system can be accurately determined by equating the pressure difference (betweenthe impeller zone and the headspace) generated by the impeller and the pressure drop requiredfor the flow of gas. For type 22 systems, the correlations for QG are mainly empirical in nature.Correlations for the power consumption, fractional gas holdup, mass-transfer coefficient, andso forth are also available in the literature, although these studies on are not comprehensive.A process design algorithm has been presented for the design of gas-inducing impellers. Thealgorithm consists of the determination of the rate-controlling step, selection of geometry andthe operating conditions, and an economic analysis to choose the optimum design. Guidelineshave been given about the desired geometry of gas-inducing impellers for achieving differentdesign objectives such as heat transfer, mass transfer, mixing, solid suspension, froth flotation,and so forth. It has been shown that the use of a gas-inducing impeller in a conventional stirredvessel can lead to a substantial increase in the productivity. It has been shown that the optimumgeometry may not correspond to the maintenance of equal power consumption per unit volume,or equal tip speed on scale-up. Suggestions have been made for future work in this area.

1. Introduction

In chemical process industries, gas-liquid contacting(with or without solids) is one of the most importantoperations. In many of the cases, the per pass conver-sion of gas is fairly low. It is desirable to recycle theunreacted gas back to the reactor because the gas maybe highly toxic or may pose safety problems. Typicalexamples include alkylation, ethoxylation, hydrogena-tion, chlorination, ammonolysis, oxidation, and so forth.A recent report (Roby and Kingsley, 1996) commentsthat several oxidation reactions that currently use aircan be operated more efficiently using pure oxygen.Typical examples of this are production of adipic acid,low-molecular-weight aliphatic acids, production ofterephthalic acid, and so forth. The worldwide produc-tion of these chemicals amounts to several milliontonnes per year. Hence, the benefits of using pureoxygen in these cases are enormous. In such applica-tions, it is undesirable to use an external gas compres-sor. Moreover, an external gas compressor meansaddition in the capital as well as operating expenditure.Dead end systems would be highly advantageous underthese circumstances. In these systems, the unreacted

gas escapes into the reactor headspace and is recycledinternally without the need of an external gas compres-sor. Gas-inducing contactors (GIC), surface aerators(SA), plunging jet reactors (PJR), an ejector jet loopreactor (EJLR), and rotating biological contactors (RBC)are considered as dead end systems.

Historically, one of the earliest reported use of a gas-inducing impeller is in froth flotation. In such cases,the gas-inducing impeller eliminates the need for asparger. Abrasive solids present in the flotation of theore can cause wear of the sparger holes; the ganguematerial present in the ore can form a muddy solidresidue and block the holes of the sparger. This hasadverse effects on the performance of a sparger system.In such cases, gas-inducing impellers are favorable andthey can adequately deliver the quantity of the gasrequired. Harris (1976) has written an excellent reviewof the flotation machines. This unit process has at-tracted much attention over the past several years.Arbiter and Harris (1962), Arbiter and Steininger(1965), Arbiter et al. (1969), Harris (1976), Harris andMensah-Biney (1977), Harris et al. (1983), Harris andKhandrika (1985a,b), Harris (1986), Schubert and co-workers (Schubert and Bischofberger, 1978; Schubert,1985), and Grainger-Allen (1970) have investigated theperformance of various flotation machines. Their stud-ies, mostly semiempirical, try to correlate the hydrody-

* To whom correspondence should be addressed. E-mail:[email protected]. Fax: (091)-022-414 5614. Tel.: (091)-022-4145616.

49Ind. Eng. Chem. Res. 1999, 38, 49-80

10.1021/ie970504e CCC: $18.00 © 1999 American Chemical SocietyPublished on Web 12/03/1998

namic and performance characteristics of the flotationmachines with the geometry of the system, physico-chemical properties, and the operating conditions. Di-mensionless numbers such as Re, Fr, Fl, NP, We, Sh,and so forth are used for this purpose.

The main objective in froth flotation is to selectivelycapture the particles of a certain mineral of the ore onthe surface of the bubbles. Therefore, it is necessary togenerate a large surface area (fine bubbles) and also tocontrol their size distribution for achieving high selec-tivity. During flotation various chemical agents suchas collectors, activators, frothers, and so forth are added.These chemicals help to increase bubble-particle adhe-sion, activate the bubble surface, promote frothingaction by preventing bubble coalescence, and so forth.The gas-inducing impeller has to generate fine bubblesto achieve a high interfacial area. The frothers preventbubble coalescence and maintain small bubble sizethroughout the equipment. The froth containing themineral particles usually overflows into a second vessel,where the froth is collapsed to recover the desiredmineral. It is necessary to keep a relatively stagnantzone near the top of the flotation machine to preventrecirculation of the “loaded” bubbles to reduce thedisengagement of particles from bubbles. Flint (1973)has reported that it is a usual practice to keep aconstant depth of the froth separation zone on the scale-up. In flotation, gas-inducing impellers are primarilyused to eliminate the difficulties associated with the useof spargers. The solid loading in the vessel can be ashigh as 40-60%. To capture the solid particles selec-tively, the impeller has to suspend the solid particlesand bring about gas-solid contact. Considering allthese aspects, the flotation cell should have the followingcharacteristics: (i) the impeller should disperse the gasin the form of fine bubbles; (ii) the impeller shouldgenerate sufficient flow and turbulence to disperse thebubbles radially away from the impeller; (iii) it shouldsuspend at least a part of the solids and to bring aboutbubble-particle contact; (iv) a stagnant zone should bepresent above the gas-inducing impeller, to allow the“loaded” bubbles to rise vertically upward; (v) a frothlayer should be present near the top, which can thenoverflow into a separate vessel; (vi) there should not beintense backmixing in the liquid and recirculation of“loaded” bubbles should be avoided.

The use of gas-inducing impellers for gas-liquidcontacting in the chemical process industry is gainingimportance. In typical hydrogenation/oxidation applica-tions, the heats of reaction are fairly large and theoverall operation may be heat-transfer-controlled. Inreactions where selectivity is of importance (ethoxyla-tion, alkylation) it may be necessary to maintainuniform concentrations in the reactor; in such casesmixing is of prime importance. If the gas phase issparingly soluble, the dissolved concentration of the gasis fairly small, and the overall reaction may becomemass-transfer-controlled. From this discussion, it isclear that the important design parameters in gas-liquid-solid contacting are the fractional gas holdup,mass-transfer coefficient, critical impeller speed for thesolid suspension, heat-transfer coefficient, mixing, andso forth. Over and above these characteristics, powerconsumption is important because it contributes sig-nificantly to the operating costs.

A preliminary literature survey has indicated severalshortfalls of the existing literature. These are the

following: (i) most of the investigations have beencarried out in small-sized vessels (less than 0.5-mdiameter) and over a limited range of operating condi-tions. The data from such experiments cannot be scaledup with confidence. (ii) Most of the investigations havebeen focused on a single design of the gas-inducingimpeller, and a single-design objective like the rate ofgas induction, mass-transfer coefficient, and so forth.(iii) There is no information in the literature on thedesign aspects of reactors employing gas-inducing im-pellers. To overcome some of these drawbacks, it wasthought desirable to thoroughly analyze the reportedliterature. In this review, the reported designs of gas-inducing impellers are first classified. Extensive dis-cussion has been given about the characteristic featuresof various designs reported in the literature. Thehydrodynamic characteristics like the critical impellerspeed for gas induction (NCG), the gas induction rate(QG), and fractional gas holdup (εG), and so forth: andthe performance characteristics such as the mass-transfer coefficients (kLa), solid suspension, and so forthare examined in detail. The purpose of this examinationis to recommend a suitable geometry and identifycorrelations that can be used with a certain degree ofconfidence for scale-up purposes. A process designalgorithm (stepwise procedure) is then presented for thedesign of reactors employing gas-inducing impellers.The algorithm involves the determination of the rate-controlling step, selection of equipment geometry andoperating conditions, and an economic analysis to chosethe optimum design. It is important to mention herethat the above procedure does not rely on common scale-up rules such as geometric similarity, kinematic simi-larity, constant power consumption per unit mass, andso forth. The final selection of the equipment size andthe geometry depends solely on economic considerations(which is the usual objective of process design engi-neers).

2. Classification of Gas-Inducing Impellers

Before starting a discussion on the various designsof gas-inducing impellers and their characteristics, itis useful to compare the characteristics of gas-inducingimpellers with the other commonly used equipment likestirred tank reactors, bubble columns, packed columns,and so forth. Doraiswamy and Sharma (1984) andKastanek et al. (1993) have given a detailed descriptionof the characteristics of some of the equipment listedabove. These are briefly summarized in Table 1A.

Packed columns and trickle-bed reactors give a verylow-pressure drop and they can handle large quantitiesof gas. However, these reactors have poor heat-transfercharacteristics and are also unsuitable as dead endsystems. Also, these pieces of equipment do not provideflexibility with respect to liquid-phase residence timeand are not suitable when the liquid-phase reactionsare slow.

Stirred tank reactors have good heat- and mass-transfer characteristics. The ability to suspend solidparticles is also very good. For these reasons stirredvessels have become very popular in the chemicalindustry. However, they have a low gas-handlingcapacity. For the recycle of unreacted gas an externalrecycle gas compressor has to be employed which maymake the overall operation economically unattractive.

Bubble columns/air lift loop reactors also have goodheat- and mass-transfer characteristics. The gas-

50 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999

handling capacity is high but the gas-phase pressuredrop is high. For achieving solid suspension, an exter-nal loop has to be provided to generate gross liquidcirculation. Again, the recycle of unreacted gas can bemade possible only with an external recycle gas com-pressor. These types of reactors may be economicallyattractive at large capacities.

Gas-inducing contactors have good heat- and mass-transfer characteristics. Solid suspension can also beachieved. However, the major advantage of such asystem is that it can recycle the gas internally. A deadend system can be used most effectively for systemsinvolving pure gases. A dead end system can inducegas from the headspace and thus eliminates the needfor spargers or porous plates.

The gas-inducing impeller plays a key role in the gas-induction process. It induces the gas from the head-space and creates a gas-liquid dispersion. It alsogenerates a liquid flow for the dispersion of the inducedgas. Therefore, Mundale (1993) has classified the gas-inducing impellers, on the basis of the flow pattern inthe impeller zone. The gas enters the impeller zone atone location and leaves at another location. Along withthe gas, the liquid can also enter the impeller zone andleave along with the gas. The nature of the flowentering and leaving the impeller zone is used as thecriterion to classify the impellers: (i) Single-phase flow(gas alone) at the inlet as well as at the outlet of theimpeller zone (type 11 system) (ii) Single-phase flow (gasalone) at the inlet and two-phase flow (gas and liquid)at the outlet of the impeller zone (type 12 system). (iii)Two-phase flow (gas and liquid) at the inlet as well asat the outlet of the impeller zone (type 22 system).

The above three types of gas-inducing impellers aredepicted in Figure 1. Table 1B summarizes the es-sential features of each type of system. In general, type12 and 22 systems involve gas-liquid two-phase flow,and hence these systems are less amenable to theoreti-cal analysis with the present status of knowledge. Type11 systems are relatively easy to analyze on the basisof the fundamental principles, as they involve onlysingle-phase gas flow. It is interesting to note that the

wide variety of gas-inducing impellers as well as flota-tion machines reported in the literature can be com-pletely classified in the above manner.

2.1. Type 11 Systems. The simplest kind of type11 system is a cylindrical, hollow pipe with an orifice(Figure 2A). These are collectively called hollow pipe

Table 1.A. Characteristics of Different Types of Reactors

packed column/trickle-bed reactors stirred-tank reactors

bubble column/air lift loop reactors gas-inducing contactors

gas-phase pressure drop low low moderate low-moderategas handling capacity high low-moderate moderate low-moderategas-phase residence time distribution plug flow back-mixed back-mixed back-mixedliquid-phase residence time low moderate-high moderate-high moderate-highmass-transfer characteristics poor good good goodheat-transfer characteristics poor good good goodsolid/catalyst suspension packings can be made to

act as catalystgood external loop has to be

provided to induce grossliquid circulation

good (solid suspension inPJR needs to beinvestigated)

unreacted gas recycle/pure gas requires external recyclegas compressor

requires external recyclegas compressor

requires external recyclegas compressor

internal; does not requireexternal recycle gascompressor

B. Comparison of Different Types of Systems

type

feature 11 12 22

standpipe not required not required necessarystator not required optional optionalimpeller hood not required optional beneficialhollow impeller necessary necessary not requiredimpeller shroud not required necessary optionalliquid feed to impeller zone irrelevant optional optionalliquid feed to standpipe irrelevant irrelevant optionalexample hollow pipe impeller outoukumpu flotation cell turboaerator

Figure 1. Three types of gas-inducing impeller designs. (1) Hollowshaft; (2) solid shaft; (3) standpipe; (4) stator; (5) stator vanes; (6)impeller.

Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 51

impellers. The hollow pipe is mounted on a hollowshaft. This type of configuration has been studiedextensively [Zlokarnik and Judat (1967), Martin (1972),Topiwala and Hamer (1974), Joshi and Sharma (1977),Joshi (1980), Baczkiewicz and Michalski (1988), Evanset al. (1990, 1991), Rielly et al. (1992), Forrester andRielly (1994), Forrester et al. (1994), Heim et al. (1995)].When this impeller rotates in a vessel, a pressurereduction occurs at the orifice per Bernoulli’s equation.When the reduction in local pressure is sufficient toovercome the hydrostatic head of the liquid, gas induc-tion occurs.

Martin (1972) has measured the values of the pres-sure differential generated for hollow pipe impellers atdifferent locations of the orifice. The orifice angle wasmeasured from the front stagnation point. He hasreported that, for a given impeller speed, the extent ofpressure reduction is maximum for an orifice angle of80°. He has also measured the rate of gas inductionfor different orifice locations. It was observed that therate of gas induction is maximum when the orifice anglewas 105°, when compared on the basis of the pressuredifferential generated. This difference between thelocation of the maximum pressure differential andmaximum rate of gas induction was attributed to thedifference in the pressure profiles in the presence of gasbubbles. He has proposed that the swarm of bubblesrising upward generates an upward current of water,which modifies the pressure field in the vicinity of theorifice.

Another interesting effect is that the rotation of theimpeller causes flow separation at the downstream sideof the cylinder, forming a wake region. This causes theformation of a gas cavity and a reduction in the averagedensity in the immediate vicinity of the impeller. Thisleads to a reduction in the power consumption, andcorrespondingly the local pressure profile gets modified.To prevent a reduction in the pressure differential, theflow separation has to be prevented.

The studies on type 11 impellers can be consideredto have been carried out with the following objectives:(i) Maximizing the pressure differential generated for

a given impeller speed (This was achieved by varyingthe number of pipes and the shape, number, and angleof attack, and so forth.); (ii) locating the orifice in theregion of lowest local pressure so that the driving forcefor the gas induction is maximum (Changing the orificelocation, both on and off the blades, was used to achievethis. Keeping in mind Martin’s (1972) study, it can beclearly seen that the location of the maximum pressuredifferential need not be the location of the highest gas-induction rate.); (iii) minimizing the pressure dropassociated with the gas flow rate, so that the per unitdriving force, larger amount of gas can be induced.(This can be achieved by varying the size and numberof orifices.). A number of efforts have been made toachieve these different objectives and have resulted intovarious designs of hollow pipe impellers.

Zlokarnik and Judat (1967) have investigated hollowpipe and disk stirrers which can be considered as a largenumber of hollow pipes. Martin (1972) created anaerofoil shape by flattening the cylindrical impeller andchanging the angle of attack of the impeller (Figure 2B).This was done to prevent the flow separation behindthe blades. This improvement lead to a 50-100%increase in the gas-induction rate.

Joshi and Sharma have (1977) varied the total orificearea by a factor of 200, by changing the orifice diameteras well as the number of orifices, which gave a similarincrease in the gas-induction rate. Joshi (1980) hasused a hollow cylindrical impeller but with small holesdrilled on the hub of the impeller (Figure 3). When suchimpeller rotates, a stream of liquid enters through theholes on the hub and comes out through the orifice alongwith the gas. Such a liquid stream was visuallyobserved, and it helped in breaking up the gas cavity.The driving force for this liquid stream is the pressure

Figure 2. Hollow pipe gas-inducing impeller (courtesy, Martin,1972): (A) Schematic representation; (B) flattened hollow pipeimpeller at an angle of attack, R.

Figure 3. Modification to the hollow pipe impeller design(courtesy, Joshi, 1980): (1) hollow tube; (2) hollow shaft; (3) hub;(4) 45° cut at the impeller tip; (5) hole through which gas inductionoccurs; (6) hole drilled on hub; (7) seal; (8) gas inlet; (9) manometer;(10) rotameter; (11) plan view of the impeller.


differential between the orifice located on the blade andthe hole drilled on the hub. The orifice on the impellerblade has a velocity equal to the impeller tip velocity.The impeller tip velocity is equal to ωD/2. Since thehub radius is much smaller than the impeller radius,the hole drilled on the hub has only a fraction of the tipvelocity. This results in a substantial pressure differ-ence between the two, resulting in a jet of liquid streamentering from the hub and leaving the tip. This resultedin a 20-30% increase in the gas-induction rate. Bac-zkiewicz and Michalski (1988) have also used hollowpipe impellers. The pipe was designed in such a waythat the downstream side of the pipe was cut awaycompletely. This amounts to having an infinite numberof orifices on the pipe. However, they have not com-pared the performance of their system with otherdesigns of hollow pipe impellers.

Rielly et al. (1992) and Forrester et al. (1994) haveinvestigated hollow, concave-bladed impellers. Thecurvature of the blades in the downstream side wasintended to reduce the flow separation. The blades insuch a type of impellers were mounted on a disk andconnected to a hollow shaft through which the gasinduction occurs. Rigby et al. (1994) located the orificenot on the blade but slightly off it. The distance of theorifice from the blade surface was varied to achieve themaximum gas-induction rate. The increase in the rateof gas induction was found to be 10-15%. Forrester andRielly (1994) used multiple orifices on the blades toimprove the gas-induction characteristics. By increas-ing the number of orifices, they effectively increased thearea through which gas induction begins, withoutincreasing the bubble size. Heim et al. (1995) have usedfour- and six-pipe impellers. As the number of hollow

Table 2. Comparison of Different Types of Impellers Studied and the Range of Investigation

name type operating parameters refs

pipe impeller 11 T ) 28 cm, D ) 25 cm, DP ) 1.25 cm, N ) 3-6 rps,S ) 20 cm, C ) 10 cm, flattened cylindrical0.86 × 1.48 cm, angle of attack ) 0-15°

Martin (1972)

hollow pipe 11 T ) 0.158 m, D ) 0.075 m, C ) 0.059 m, S ) 0.10 m,N ) 12-25 rps, hollow pipe impeller

Topiwala and Hamer (1974)

conical impeller 12 T ) 0.29 m, D ) 0.045-0.075 m, S/D ) 2-4, N )40-100 rps, impeller consists of two cones withbases touching, conical disperser

Koen and Pinguad (1977)

Denver, Wemco cells, turboaerator 22 T ) 0.1-0.3 m square, D ) 0.07-0.115 m,S/T ) 0.3-0.9, water and polyethylene glycol,

Sawant and Joshi (1979)

turbo aerator 22 T ) 40 cm, D ) 8-12 cm, d/D ) 0.5 and 0.67, DS/D )1.4 and 1.25, S ) 0.5-2.0 m, N ) 16-40 rps,stator blade angle 30°

Zundelevich (1979)

pipe, modified pipe 11 T ) 41-100 cm, D ) 20-50 cm, DP ) 2.5-3.2 cm,no. of pipes ) 2-6, W ) 3.2-5 cm, S ) 0.3-0.9 m,N ) 2-12 rps

Joshi and Sharma (1977),Joshi (1980)

Wemco cell type impeller 22 T ) 30 cm, D ) 10 cm, S ) 7-15 cm, N ) 5-30 rps Sawant et al. (1980)Denver cell type impeller 22 T ) 14 × 14 to 38 × 38 cm, D ) 7-20.4 cm,

S/T ) 0.2-1.0, N ) 5-19 rpsSawant et al. (1981)

multiple impeller system 22 T ) 0.19-0.316, D/T ) 0.25 m, propeller near-surfaceand axial turbine near-bottom mounted on differentshafts, N ) 0-15 rps, water, sodium alginate,tween 20 surfactant

Matsumura et al. (1982a-c)

helical screw in draft tube 22 report based on 2.5 L, followed by 150-L and3900-L test reactor

Litz (1985)

PBTD with stator 22 T ) 57 cm, C/T ) 0.33, S/T ) 0.5-1.25D ) 15-25 cm, N ) 3-14 rps

Raidoo et al. (1987)

pipe impeller 11 T ) 44 cm, D ) 15.4-24.2 cm, DP ) 0.6 cm,C ) 6.6 cm, S ) 60 cm, N ) 6.4-23 rps

Baczkiewicz and Michalksi (1988)

pipe impeller 11 T ) 29 cm, D ) 13 and 22.5 cm, orifice locations2.5-5.5 cm from shaft, C ) 0.1 m, S ) 0.05-0.30 m,N ) 0-8 rps

Evans et al. (1990, 1991)

hollow-bladed impeller 11 T ) 30-60 cm, D ) 21.5 cm, orifice locations 7.5 cmfrom shaft axis, paddle, and concave-bladed impeller,S ) 0.05-0.55 m, N ) 1-9 rps

Rielly et al. (1992)

PBTD with stator 22 T ) 57-150 cm, D ) 19-50 cm, W ) 4-10 cm,DS ) 226-270 cm, blade angle 30-90°, no. of blades4-12, S ) 0.2-1.2 m, N ) 2-14 rps

Mundale (1993)

standpipe and rotor 22 T ) 0.77-15.2 cm2 cylindrical, D ) 0.16-0.41 m,with and without vortex enhancer

Brenner et al. (1994)

pipe and turbine impellers 11 and 12 D ) 5-6.5 cm, DS ) 7.4-9.4 cm, V ) 6 l,T ) 0.20 m, N ) 0-25 rps, water,salt solution, and sucrose solution

Aldrich and van Deventer (1994)

hollow-bladed 11 T ) 0.45 m, D ) 0.154 m, C ) 0.225 m, S ) 0.225 m,N ) 4-10 rps, sparging rate ) 0-400 cm3/s,concave-bladed, multiple-orifice impellers

Forrester et al. (1994), Forresterand Rielly (1994)

hollow-bladed impeller 11 T ) 60 cm square, D ) 21.5 cm, C ) 16.8 cm, S ) 8-40 cm,N ) 2-10-rps orifice locations 7.65 cm from shaft axis,two-bladed disc turbine

Rigby et al. (1994)

Denver 22 T ) 0.19-m square, D ) 0.096 m, DS ) 0.127 m,C ) 1.5 cm, 0-100 ppm PGME additive S ) 0.22 m,N ) 10-25 rps

Al Taweel and Cheng (1995)

hollow pipe 11 T ) 0.3 m, D ) 0.1-0.15 m, 4 and 6 hollow-bladed,disk impeller C ) 6.5 cm, S ) 0.9-2.9 m, N ) 6-12 rps

Heim et al. (1995)

shrouded turbine 22 T ) 0.19 m, D ) 0.05, 0.06 m, shroud consists of aslotted draft tube, N ) 0-25 rps, temp ) 8-80 °C water,sucrose solution, isopropanol

Aldrich and van Deventer (1996)

PBTD with stator 22 T ) 0.57-1.5 m, D ) 0.19-0.5 m, C ) 0.09-0.5 m, S )0.1-0.6 m, N ) 2-10 rps, single- and multiple-impellersystem, different designs of bottom impeller

Saravanan and Joshi (1995, 1996),Saravanann et al. (1996, 1997)

PBTD with stator 22 T ) 1.5 m, D ) 0.5 m, C ) 0.8 m, S ) 0-0.4 m, N ) 1-4 rps.multiple-impeller and sparger system, different designsof bottom impeller, VG ) 0-29 mm/s

Patwardhan and Joshi (1997)


pipes increases, their design approaches that of a diskimpeller. They have shown that such a disk impelleris superior to four- or six-pipe impellers. Table 2summarizes the range of different variables covered inthese studies.

2.2. Type 12 Systems. A large number of flotationmachines fall in this category, for example, Aker (Bar-bery (1984), Figure 4A), Outokumpu (Fallenius (1981),Figure 4B), and BCS (Barbery (1984), Figure 4C). Thecharacteristic feature of this type is that the gas isdelivered into the impeller region via a hollow shaftthrough an orifice or an air port and the gas-liquiddispersion leaves the impeller region via a stator, adiffusor, or an impeller shroud. The rotating dispersersystem (Figure 5) reported by Koen and Pingaud (1977)and the double-finger impeller reported by Schubert andBischofberger (1978) also fall in this category. The

AIRE-O2 system developed by the Aeration IndustriesInternational, Inc. (U.S.) (Figure 6) and EOLO2 systemdeveloped by Acqua and Co. (Italy) (Figure 7) alsobelong to this type.

The essential features of a type 12 system include ahollow shaft, an impeller, orifices/air ports, and a stator/diffuser. The impeller rotation causes a reduction inthe local pressure. At sufficiently high impeller speeds,air is drawn in through the hollow shaft and getsintroduced in the impeller zone through orifices or airports located near the impeller on the hollow shaft.Along with the induced air, extra air may be blownthrough the hollow shaft, depending on the requirementof the specific application. The impeller also helps ingenerating liquid-phase flow for the dispersion of in-duced gas. The stator/diffuser helps to generate highshear in the impeller zone to create finer bubbles. Thevariation between the various designs is mainly in thegeometry of these various parts which depend on themanufacturer.

The Aker design consists of an impeller and a diffusersystem. The impeller hub has air ports which inducethe gas into the liquid. The induced gas gets dispersedin the form of bubbles because of the shear causedbetween the impeller and the diffuser blades. Theblades of this type of impeller resemble those of astraight blade turbine. The diffuser system consists ofblades (or vanes) that surround the impeller. Thediffuser blades can be set at an angle to the radiusvector. The impeller rotation causes mainly tangentialflow in the region between the impeller and the diffuser.This flow impinges on the diffuser blades and getsdeflected. The overall flow pattern leaving the impel-ler-diffuser region therefore becomes radial. In thismanner the diffuser guides the flow out of the impellerzone and improves the dispersion characteristics.

The Outokumpu design is similar to the Aker designbut the impeller is hemispherical in shape. The BCSdesign consists of a hollow shaft with an air port. Theimpeller of this design consists of an assembly of rodsheld between two disks. There are two sets of rods, oneset is inclined radially inward and the other set isinclined radially outward. The two sets alternate eachother, causing the flow generated by one to impinge onthe other. This causes a reduction in the bubble sizeand improves the dispersion characteristics.

The rotating disperser system of Koen and Pingaud(1977) consists of a hollow shaft connected to theimpeller. The dispersing device consists of two coaxiallymounted cones. The top and the bottom cones have ahole at the center that allows an ingress of the liquidfrom the top as well as the bottom. The two cones areslightly separated forming a disk-shaped space between

Figure 4. Different designs of type 12 flotation cells (reproducedfrom Barbery, 1984): (A) Aker; (B) Outokumpu; (C) BCS. (1)Hollow pipe; (2) impeller; (3) stator/disperser vanes; (4) orifice forair delivery into impeller zone.

Figure 5. Rotating disperser system (courtesy, Koen and Pin-gaud, 1977).

Figure 6. AIRE-O2 system (courtesy, Aeration Industries In-ternational Inc., U.S.).


them. The impeller itself consists of two cones mountedwith their bases touching. A gas-liquid dispersionflows radially outward from this disk-shaped space intothe bulk of the liquid. They have further claimed thatthis impeller can also be used for liquid-liquid systems.

The AIRE-O2 system consists of a propeller mountedon a hollow shaft. The motor driving the propeller islocated above the surface of the water. The propellerforces the water to flow past the end of the shaft at ahigh velocity. The high local velocity causes a reductionin the local pressure per Bernoulli’s equation, thusdrawing air from the atmosphere through the hollowshaft. The literature reports that the oxygen utilizationefficiency (oxygen uptake for every unit of oxygendelivered into the water) of such a system is about 16-18% as compared to a diffuser aeration efficiency of8-10% and a surface aeration efficiency of 10-12%. Themixing time for a 1-acre pond with a single 2 hp.AIRE-O2 system is reported to be 32 min. Additionalfeatures of the system are lightweightness, the abilityto position the system at any angle to the vertical, theease of installation, and the ability to operate even whenthe temperatures are below freezing. The EOLO2system is similar in construction. The main differenceis that the entire motor can be kept below the surfaceof water up to a depth of 15 m. Like the AIRE-O2system, it is easy to install and lightweight and can berotated to position at any angle with the vertical. Sucha flexibility gives a wide choice of flow patterns. A directcomparison of these commercial designs with thosereported in the literature is not possible, because of thelack of scientific information on the commercial designs.Data on the gas-induction rate (QG), fractional gasholdup, mass-transfer coefficient, mixing time, solidsuspension ability, and so forth as a function of thepower consumption (PG) would have been very usefulin comparing the AIRE-O2 and EOLO2 systems withother systems.

2.3. Type 22 Systems. A large variety of type 22systems exist. These include the flotation cells as wellas rotor-stator systems. Some of the main designs areWemco (Degner and Treweek (1976), Figure 8A), Wedag(Arbiter and Steininger (1965), Figure 8B), Denver(Taggart (1960), Figure 8C), Agitair (Arbiter and Stein-inger (1965), Figure 8D), Booth (Barbery (1984), Figure8E), Sala (Harris (1976), Figure 8F) flotation cells,turboaerator (Zundelevich (1979), Figure 9), pitchedturbine impellers covered with a stator-standpipeassembly (Raidoo et al. (1987), Mundale (1993), Sara-vanan et al. (1994)), and multiple-impeller systems(Saravanan and Joshi, 1995). The characteristic fea-tures of these systems include a (i) rotor/impeller, (ii)

standpipe through which the gas induction takes place,and (iii) stator/diffuser surrounding the impeller.

The basic principle of operation of the stator-stand-pipe system is as follows. The rotation of the impellercauses a vortex formation in the standpipe. As theimpeller speed increases, the vortex depth progressivelyincreases. When the vortex is sufficiently near theimpeller, the impeller blades shear the gas-liquidinterface, entrapping gas bubbles. The entrapped gasbubbles are then carried away by the flow generatedby the impeller. The rotation of the impeller also causesa reduction in the local pressure per Bernoulli’s equa-tion. This would lead to an ingress of the liquid fromthe region outside the stator. The stator consists of animpeller hood, vanes, and an air ring. The vanes, vaneshrouding ring, and the vane air ring are collectivelyreferred to as a diffuser. The impeller hood preventsthe entry of liquid into the impeller zone from above.The air ring prevents the axial downward flow from theimpeller. As a result of the impeller hood and the airring, the liquid flow coming out of the stator is radial.The stator vanes can be set at an angle to the radiusvector. The entire diffuser zone resembles the diffuserof a centrifugal pump. The radial flow of fluid leavingthe impeller enters the diffuser zone. The fluid thenflows through a region formed between two stator vanes.Since the stator vanes are set at an angle, the crosssectional area gradually increases, and as a result, thevelocity gradually decreases. This results in pressurerecovery to some extent, and the fluid leaves the diffuserwith reduced shock as compared to that in the absenceof a diffuser.

Wemco, Denver, Booth, and Wedag flotation machineshave all these characteristic features. All the designshave some additional features, which vary dependingon the manufacturer. These flotation machines havenot been developed in an evolutionary manner, but arerather empirical in nature. The rotor of the Wemcodesign consists of cylindrical rods called posts mountedbetween two disks. The diffuser and the impeller hoodfor this design consists of a conical perforated plate. Thegas-liquid dispersion is forced out through these per-forations. This system was investigated by Sawant etal. (1980).

The impeller of the Denver-type machines is disk-shaped with blades mounted on the edge of the disk.The stator consists of vanes that are fixed to the statorhood. There is no air ring in this type of design.Outside the standpipe, there is a conical section calledthe recirculation well. Liquid can enter through the topof this well. Because of the conical shape, the liquideffectively gets injected into the impeller region. An air

Figure 7. EOLO2 system (courtesy, Acqua and Co., Italy).


belt is a conical attachment at the bottom of thestandpipe. Its function is to direct the induced air ontothe impeller blades and to prevent the direct entry ofgas bubbles through the recirculation well. The Denvercell was investigated by Sawant et al. (1981).

The Agitair impeller consists of a disk on which thecylindrical rods called fingers are mounted. The diskon which the impeller fingers are mounted has anannular space for pulp recycle into the impeller region.This means that both gas and liquid can enter theimpeller region; the gas-liquid dispersion created in theimpeller region is then distributed with the help of adiffuser.

Matsumura et al. (1982a-c) have investigated amultiple-impeller system. In their work, the two impel-lers are driven independently, so that their speeds couldbe adjusted independent of each other. In their systemthe upper impeller is a propeller. This impeller islocated close to the liquid surface and rotates at highspeeds. It generates turbulence at the liquid surfaceand is able to produce a large number of fine bubbles.The second impeller which is an axial flow type islocated near the base of the tank. This impeller createsgross liquid circulation for the uniform dispersion of thebubbles generated. A draft tube is installed on the freeliquid surface to prevent accumulation of the frothwhich reduces the gas-induction capacity. Matsumuraet al. (1982c) have used the rector as a fermenter usingpure oxygen. They have investigated the performanceof the fermenter in terms of the biomass productivity,energy requirement, and oxygen utilization efficiency.

Litz (1984, 1985) has employed a helical screw in adraft tube as a gas-inducing impeller. Figure 10 showsa schematic of their reactor. A baffle arrangementprovided at the top of the draft tube generates a numberof vortices from which gas induction takes place. Whenthe helical screw impeller rotates, an axially downwardliquid flow is generated. Because of this liquid flow, theentrapped gas bubbles are carried downward throughthe draft tube. At the bottom of the draft tube thesebubbles rise vertically, a circulation pattern is estab-lished, and good gas dispersion is achieved in the rector.Litz (1985) has given certain performance characteris-tics of such reactors. The relative power draw (ratio ofpower consumption under gassed and ungassed condi-tions) is almost 1.0 up to a gas holdup of 10%. It wasalso shown that when such a reactor was employed fora oxyhydrolysis reaction, the residence time can be

Figure 8. Different designs of type 22 flotation cells (reproduced from Barbery, 1984): (A) Wemco; (B) Wedag; (C) Denver; (D) Agitair;(E) Booth; (F) Sala: (1) (solid shaft; (2) standpipe; (3) stator/disperser; (4) disperser hood.

Figure 9. Turboaerator designs (courtesy, Zundelevich, 1979):(1) solid shaft; (2) standpipe; (3) stator vanes; (4) impeller; (5) statorhood.


reduced by approximately 40% as compared to that ofconventional stirred tank reactors. As a result, thepower consumption reduces by 25%.

Litz et al. (1990), Kingsley et al. (1994), and Roby andKingsley (1996) have made further modifications to thisreactor. These modifications consist of providing a gas-containment baffle, a sparger, a compound impellerdesign, and so forth. The helical screw inside the drafttube, or a conventional agitator, generates a liquid flownecessary for the dispersion of the sparged gas. Thegas-containment baffle separates the vessel into twozones and it helps to keep the gas bubbles in circulationin the reactor. The gas-containment baffle is particu-larly useful for reactions employing pure oxygen. Ithelps to keep the partial pressure of oxygen in the rectorheadspace below the flammable limit and ensureshazard-free operation.

The Booth design does not have a stator air ring.However, below the gas-inducing impeller, a secondimpeller, typically a propeller, is provided to improvethe gas dispersion. This is one of the earliest reporteduses of a multiple-impeller system. Saravanan andJoshi (1995, 1996) and Saravanan et al. (1996, 1997)have carried out extensive investigations on the multiple-impeller system. Both the impellers were located on thesame shaft, and hence they have to be operated at thesame speed. They have reported that when a single gas-inducing impeller is located close to the top liquidsurface for maintaining a high rate of gas induction, itsuffers from several drawbacks. These include poordispersion of the induced gas, poor solid suspensionability, and so forth. These arise from the fact that theliquid flow and turbulence characteristics are feeble ina major portion below the gas-inducing impeller. Thesedrawbacks were observed to be more serious with anincrease in the scale of operation. These limitations ofthe single-impeller system have overcome by using asecond impeller below the gas-inducing impeller. Thegas-inducing impeller can then be kept close to the topliquid surface (about 100-200 mm below the liquidsurface), irrespective of the scale of operation, to ensurea high gas-induction rate. For other duties like gasdispersion (distribution of the induced gas throughoutthe equipment), solid suspension, heat transfer, mixing,and so forth to be performed, the second impeller wasused. The design of the lower impeller was furtheroptimized for different duties such as gas holdup, solidsuspension ability, and so forth. This activity hasclearly shown that the optimum design of the lowerimpeller changes with the design objective. For ex-ample, to achieve high fractional gas holdup, it wasdesirable to use an upflow impeller at the bottom,

whereas to achieve good solid suspension, a downflowimpeller at the bottom was desirable.

Aldrich and van Deventer (1994) have investigatedthe effect of solid particles on the rate of gas inductionfrom turbine impellers. Brenner et al. (1994) have useda turboaerator along with a standpipe. The character-istic feature of their system is that the standpipe wasfitted with radial fins which enhance the vortices formednear the impeller and as a result increase the gas-induction rate.

Hsu and Chang (1995), Hsu and Huang (1996, 1997),and Hsu et al. (1997) have described a different config-uration. The system consists of an unbaffled tank fittedwith one or two impellers. Since the tank is unbaffled,a vortex is generated in the tank, whose depth progres-sively increases with the impeller speed. At a certainspeed the vortex reaches the impeller and is broken upinto gas bubbles. This reactor can actually be describedas a surface aerator. The gas phase in their investiga-tions was the ozone in a dead end configuration. Inmuch of their work, Hsu and Chang (1995), and Hsuand Huang (1996, 1997) report the ozone utilizationefficiency as a function of various operating parameters.The data on ozone utilization efficiency are not at alluseful for the design of a reactor for any other applica-tion. Only recently (Hsu and Huang (1997)) havecorrelations been provided for power consumption, criti-cal impeller speed for gas induction, and so forth. Nocorrelation has been given for other important param-eters such as the gas-induction rate, gas holdup, mass-transfer coefficient, and so forth. Moreover, their workis carried out on small-sized vessels (0.17-m diameter);hence, their results are not expected to be useful forscale-up.

Patwardhan and Joshi (1997) have employed a gas-inducing impeller in mechanically agitated contactors.They have also presented a rationale for the use of agas-inducing impeller in MAC. Figure 11A shows aschematic of such a reactor. In such pieces of equip-ment, the gas sparged at the bottom gets dispersedthroughout the vessel with the help of impellers. Un-reacted gas escapes into the headspace. The gas-inducing impeller enables the recirculation of the un-reacted gas from the headspace. The role of the gas-inducing impeller in such reactors is, at least, torecirculate the unreacted gas. If the gas-inducingimpeller is able to induce gas at a rate greater than theunreacted gas rate, then a part of the gas-liquidcontacting duty is performed by the gas-inducing impel-ler. If the amount of sparged gas still remains the same,then on a unit reactor volume basis more gas can behandled and higher productivity can be realized. Theproductivity in such reactors depends on the gas-induction rate (QG), the fractional gas holdup (εG), andso forth. Therefore, the design of the gas-inducingimpeller plays an important role on the overall perfor-mance of the reactor. It is also important to note that,in such reactors, the type of sparger, the rate ofsparging, and so forth. affect the performance of thegas-inducing impeller itself. Thus, the overall perfor-mance of such reactors involves an interplay of thesparged gas and the induced gas. An optimum designof such reactors therefore involves striking a finebalance between the rate at which gas can be sparged,the sparger design, the gas-inducing impeller design,the rate of gas induction, and so forth. Patwardhan andJoshi (1997) have investigated the effects of the sparger

Figure 10. Helical screw impeller in a draft tube (courtesy, Robyand Kingsley, 1996).


size, lower impeller design, and the superficial velocityof the sparged gas on the gas-induction rate and thefractional gas holdup. In the absence of a gas-inducingimpeller, the system resembles a conventional mechani-cally agitated contactor (MAC) and gas recycle takesplace by surface aeration alone (Figure 11B).

The Yastral design (Yastral GMBH) can also beconsidered as a stator-rotor system. This design(Figure 12) was shown to be very convenient forhandling solids. The impeller is located in the vessel,and the standpipe is connected to a hose pipe. Whenthe impeller rotates, suction is created which sucks thesolids from a silo or a bag through the standpipe intothe reaction vessel. In fact, all the type 22 designs canbe conveniently used for the suction of solids.

3. Hydrodynamic Characteristics

3.1. Critical Impeller Speed for the Onset of GasInduction. 3.1.1. Type 11 System. The hollow pipeimpeller (type 11 system) induces gas through an orifice.The impeller rotation causes liquid velocity to increase.This causes a reduction in the pressure at the orificeoutlet. At a particular impeller speed, the local pressure(according to Bernoulli’s equation) becomes low enoughto overcome the liquid head over the orifice and gasstarts to induce into the liquid. This is called the criticalimpeller speed for gas induction and is denoted as NCG.Thus, the critical speed is determined by a balance ofpressure and velocity head. Neglecting, the frictional

pressure losses, Bernoulli’s equation can be written as

Here, P is the combined hydrostatic and pressure head.To predict the critical impeller speed, the velocity andthe pressure heads have to be related to the impellerspeed. The velocity head is typically based on theimpeller tip velocity (with or without slip). The rela-tionship of the local pressure head with the impellerspeed depends on many factors such as the impellergeometry, physicochemical properties of the liquid,shape of the blades, and so forth. If the local pressureis related to the impeller speed, then eq 1 can be usedto estimate the critical impeller speed for the onset ofgas induction. This section deals with the predictionof NCG starting from eq 1.

Martin (1972) has used the theory of flow pastimmersed bodies. A cylindrical impeller rotating insidea liquid can be considered as if the impeller is stationaryand the fluid outside is flowing past the cylinder. If thefluid is considered as ideal frictionless, then the pressureoutside the cylinder at any angular position is given by

The fluids used in practical applications are not ideal;hence, the local pressure does not show the idealbehavior indicated by eq 2. Therefore, he measuredreduction in local pressure by means of a manometerand correlated to the dimensionless parameter P′ withthe angular position of the orifice as a parameter, where

This was the first attempt at understanding the gas-induction process, in a fundamental manner, by lookingat the local pressure. However, the relation betweenthe impeller design, the impeller speed, and the localpressure was not established. The above equation wasalso not extended to the estimation of NCG.

Evans et al. (1990, 1991) extended this earlier modelof Martin (1972). The local liquid velocity was related

Figure 11. (A) Schematic representation of GIC equipped with a gas-inducing impeller and a sparger; (B) schematic representation ofMAC without a gas inducing impeller.

Figure 12. TDS-induction mixer (courtesy, Yastral GMBH).

d(FLU2

2 ) + dP ) 0 (1)

hS - hL

(V2/2g)) 1 - 4 sin2 θ (2)

P′ )hS - hL

(V2/2g)(3)


to the impeller speed as

where K is a factor that accounts for the slip betweenthe impeller and the fluid. The pressure coefficient CPrelating the local pressure P(θ) to the headspace pres-sure PO was defined as

The pressure coefficient is a function of the blade shapeand the orifice location. For inviscid flow, the value ofCP(θ) can be calculated from potential flow theory. Forflow around a cylinder in an infinite medium its value,according to the above definition, is

Since the actual geometry (rotating hollow pipe in afinite viscosity fluid) is far from this ideality, it becomesnecessary to experimentally measure the values CP(θ).The absolute pressure P(θ) on the blade surface can thenbe calculated by substituting eq 4 in eq 5. Furtherrearrangement gives

At critical speed, the gas-induction process just beginsand the local pressure equals the headspace pressure;that is, P(θ) ) PO and N ) NCG and the above equationthen gives

The above equation was very successful in predictingthe NCG values for their system.

3.1.2. Type 12 and 22 Systems. White and deVilliers (1977) also started with Bernoulli’s equation forpredicting the critical impeller speed. They calculatedthe velocity head on the basis of impeller tip velocityand the pressure head was taken as the hydrostatichead. The final form of their equation is

Here, C is an empirical constant which is characteristicof the system. The value of the constant was found tobe 0.23. The term on the left-hand side in the aboveequation is the Froude number, and hence the aboveequation can also be written as

Sawant and Joshi (1979) have studied a wide varietyof impellers and physical properties of the system. They

have modified the above equation to take into accountthe effect of the liquid-phase viscosity. Their equationis given below:

The value of the constant was found to vary between0.21 ( 0.04, for a variety of different designs like pipeimpellers (two pipes and four pipes), flattened cylindri-cal impellers, covered turbine impellers, Wemco flota-tion cells, Denver flotation cells, and shrouded turbinewith a stator. The above equation was able to predictthe critical speed for gas induction within 10% of theexperimentally observed values. In this case, theconstant C accounts for the nonidealities of the fluid,impeller slip, and frictional losses. The value of theconstant is in agreement with that of White and deVilliers (1977).

Heim et al. (1995) have also used eq 10 for correlatingtheir data on NCG. Aldrich and van Deventer (1994)have investigated the effect of solid particles on NCG.They have reported that NCG is unaffected by thepresence of solids up to a loading of 15%; beyond thisvalue, the critical speed increases. This increase in NCGwas attributed to the increase in the viscosity of thesolution because of the presence of solid particles.

Saravanan and Joshi (1995) have proposed a modelbased on the phenomena of forced vortex formation inthe standpipe. As the impeller speed increases, theliquid level in the standpipe falls and takes the shapeof a vortex. This is because the liquid present in thestandpipe essentially behaves like a liquid in an un-baffled tank. They have proposed a mechanism of thegas-induction process as follows:

At speeds less than the critical speed, the vortex isformed. The vortex shape is paraboloid in nature(Figure 13A). As the speed increases, the vortex pen-etrates deeper and deeper, and at a critical impellerspeed the vortex reaches the impeller tip (Figure 13B).The greater the impeller submergence, the greater thespeed required for the vortex to reach the impeller tip.The critical speed for gas induction therefore is stronglydependent on the impeller submergence. Once thevortex reaches the impeller tip, bubble entrapmentoccurs, because of the small vortices generated at theinterface. The mechanism is similar to that of surfaceaeration. The entrapped bubbles get conveyed awayform the interface by the liquid flow generated by theimpeller (Figure 13C). The gas-dispersion characteris-tics depend on the liquid flow pattern generated by theimpeller which in turn depends on the geometricalfeatures of the impeller and stator. A mathematicalmodel was proposed by Saravanan and Joshi (1995), forthe estimation of NCG based on the following assump-tions: (i) The gas-induction process occurs at the centerplane of the impeller. The submergence of the impeller(S) and the impeller clearance from the bottom (C1) aremeasured from the impeller center plane. (ii) Negligibleresistance exists in the gas line connected to thestandpipe.

The differential equation representing the tangentialmotion of the liquid is

U ) (1 - K)2πNR (4)

CP(θ) )(PO + FLgS) - P(θ)

12

FLU2(5)

CP(θ) ) 4 sin2(θ) (6)

P(θ) ) (PO - FLgS) - 12

FLCP(θ)[2πNR(1 - K)]2 (7)

NCG ) x gS2CP(θ)[(1 - K)πR]2

(8)

NCG2D2

gS) C (9)

FrCG ) C (10)

NCG2D2

gS(µ/µw)-0.11 ) constant ) C (11)

dP ) FLfm2ω2r dr + FLg dz (12)


with the boundary condition at r ) R, P ) PO, and

The z-direction increases in the vertically downwarddirection and the origin is at the intersection of the axisof the vessel and the static liquid level. Here, fm iscalled the conformity factor, and it represents the slipbetween the impeller and the fluid surrounding it andis analogous to the “K” defined by Evans et al. (1990).Integrating eq 12 to any r and the corresponding P andz, and using this boundary condition, gives a relation-ship between the local pressure as a function of theradial position, and the vertical position z:

The shape of the free surface of the vortex correspondsto a locus of all points with P ) PO; thus, the equationof the vortex surface is

Here V ) ωR is the impeller tip velocity. The maximumdepression occurs at the axis of the vessel correspondingto r ) 0. At a critical speed this maximum depressionequals the submergence of the impeller (i.e., the vortexreaches the impeller center plane). Setting V ) VCG atthis stage

Let (1 + k)fm2 ) φ, where φ is the vortexing constant,

and using VCG ) 2πRNCG, we get

This equation is very similar to that developed byWhite and de Villiers (1977). The above equation canalso be written in terms of the Froude number, in amanner similar to that of eq 10; then the value of theconstant turns out to be equal to 0.24, which is inexcellent agreement with that of Sawant and Joshi(1979) and White and deVilliers (1977). The basicdifference is that the constant φ is characteristic of thesystem, and it represents the ability of the impeller toform a vortex for a given impeller-standpipe-statorgeometry. Using this equation Saravanan and Joshi(1995) were able to predict the values of NCG for theirsingle- as well as multiple-impeller systems within(10%. Considering the complex nature of the two-phase flow and the fundamental nature of the model,the predicted values agree very well with the experi-mental data.

Patwardhan and Joshi (997) have investigated theeffect of sparging on the critical impeller speed for gasinduction. They have concluded that the change in thecritical impeller speed ∆NCG (N in the presence ofsparging - N in the absence of sparging) depends onlyon the superficial gas velocity, the type of sparger, thelower impeller design, and so forth. That is,

They have reported the values R1, R2, R3, and R4 as afunction of the sparger size and the lower impellerdesign. This equation is nothing more than a fit of theexperimental data and should be used with extremecaution when applying to other systems and scales.However, if the critical parameters such as submergenceand superficial gas velocity are similar to what has beenused in their work, then the above equation may beused. The various models correlating the critical speedfor gas induction are given in Table 3.

3.1.3. Recommendations. All the models for NCGstart with Bernoulli’s equation, that is, eq 1. Equation1 itself neglects the pressure loss occurring within thesystem. This also introduces a small amount of uncer-tainty in the analysis. Martin (1972) has really set the

Figure 13. Vortex shapes formed in a stator-rotor system (courtesy, Saravanan and Joshi, 1995): (A) before the onset of gas induction,N < NCG; (B) at the critical speed for gas induction, N ) NCG; (C) at a speed higher than NCG.

z )k(Rfmω)2

2g

P - PO )FLfm

2ω2

2(r2 - R2) + FLg(z -

k(Rfmω)2

2g ) (13)

z )(Vfm)2

2g ((1 + k) - r2

R2) (14)

S )(VCGfm)2

2g(1 + k) (15)

NCG ) 12πRx2gS

φ(16)

(∆NCG)2π2D2φ

2gS) R1(C3/D)R2VG

R3(S/T)R4 (17)


stage for understanding the gas-induction process bymeasuring the local pressure field. Evans et al. (1990,1991) have made a valuable contribution by extendingthe measured pressure field to the estimation of NCG.Although the type 11 impellers have been analyzed froma fundamental point of view, one important aspect hasnot really been dealt with. The measured local pressurefield has not been related to the impeller geometry suchas blade shape, blade width, impeller diameter, clear-ance, and so forth. When it comes to type 12 and type22 impellers, the investigators have been more empiricalthan desired. At impeller speeds N < NCG, the impellerrotates in the liquid-phase alone; thus, it should bepossible to use an approach similar to the type 11system, at least for the estimation of NCG. Theirequations for NCG do include a balance between thepressure head and the velocity head, but no attempt hasbeen made to experimentally measure or predict thepressure field. The approach of Saravanan and Joshi(1995) does start from the fundamental equations ofmotion. Inside the standpipe, their geometry behavesessentially like an unbaffled system; therefore, thevortex shape can be predicted fairly accurately. How-ever, the assumption that the gas-induction processbegins from the impeller centerline is not completelyvalid. The gas-induction process begins when the vortexis fairly close to the impeller but does not have to reachthe impeller centerline. This has been pointed out bythe authors and is reflected by a value of the constantφ < 1. In summary, it can be said that the physics ofthe process of gas induction is fairly well-understood.One area that needs to be worked on is relating theimpeller geometry (e.g., shape, width, diameter, clear-ance, etc.) to the local pressure field generated.

Figure 14 shows a comparison of the various correla-tions proposed for NCG. The values of NCG have beenestimated on a scale of 0.5 m and an impeller diameterequal to one-third the vessel diameter. From the graph,it can be seen that the different impellers such ascylindrical, paddle, aerofoil, and disk show differentvalues of NCG under otherwise identical conditions. Thisis due to a difference in the local pressure field gener-ated. A hollow paddle impeller shows the lowest valueof NCG. As expected, the correlations of White anddeVilliers (1977), Sawant and Joshi (1979), and Sara-vanan and Joshi (1995) show similar values of NCG.Keeping in mind the present status of knowledge, it isdesirable to use the approach of Evans et al. (1990,1991). However, if the impeller shape under investiga-tion is drastically different from what they have used,then a good first approximation of the NCG value can

be obtained by using the correlation of White and deVilliers (1977) and the value of the constant between0.21 and 0.25, or the correlation of Saravanan and Joshi(1995). The latter correlation is useful for scale-upbecause it has been tested over a wide range of equip-ment sizes (0.57-1.5 m).

3.2. Gas-Induction Rate. 3.2.1. Type 11 Sys-tems. A type 11 system involves the flow of gas alonethrough the impeller. The driving force for the gasinduction is the pressure differential between the head-space and the local pressure at the orifice on theimpeller. The flow of gas causes frictional and resistivepressure drop in the hollow pipe, blades, and the orifice.If the pressure differential generated by the impellerfor the gas flow is equated to the total resistive pressuredrop, then the rate of gas induction can be calculated.

Martin (1972) has measured the local pressure aroundthe hollow pipe impeller and has correlated it empiri-cally to the gas-induction rate, using the orifice dis-charge coefficient. The basis for using such an equationis the analogy with the flow in a pipe containing anorifice. The use of this equation implies fully developedturbulent flow conditions in a pipe with a uniform crosssection. These conditions can hardly be expected to befulfilled in a hollow pipe impeller assembly. The equa-tion also neglects the change in the gravity head. Theorifice discharge coefficient characterizes the frictionalpressure drop occurring in the hollow pipe. The second

Table 3. Critical Impeller Speed for Gas Induction

system investigated basis for calculating NCG, model refs

pipe impellers (type 11) Bernoulli’s equation, measured pressure profiles Martin (1972)

shrouded turbine (type 22) NC2D2

gS) K White and deVilliers (1977)

Denver and Wemco Flotation cells NC2D2

gS(µw/µ)0.11 ) K Sawant and Joshi (1979)

hollow-bladed impeller (type 11) Bernoulli’s equation, pressure coefficient, blade slip factor Evans et al. (1990)

hollow pipe Fr* ) N2d2

gSHeim et al. (1995)

PBTD with stator and standpipe (type 22) NCG ) 12πRx2gS

φSaravanan and Joshi (1995)

PBTD-stator, multiple impellers with sparging ∆NCG2π2D2

φ

2gS) R1(C3/D)R2VG

R3(S/T)R4 Patwardhan and Joshi (1997)

Figure 14. Comparison of different impeller designs for NCG. Allthese have been evaluated at a tank diameter of 0.50 m and animpeller diameter D ) T/3: 9, white and deVilliers (1977); (,Evans et al. (1990), cylinder; ), Evans et al. (1990), paddle; ×,Evans et al. (1990), aerofoil; 4, Saravanan and Joshi (1995); 0,Sawant and Joshi (1979); +, Heim et al. (1995), four-pipe impeller;O, Heim et al. (1995), disk impeller.


term is used mainly as a fitting parameter. Since thevalues of CO, AO, K1, and so forth vary with the designof the hollow shaft, orifice, and the blade design, cautionhas to be exercised while using this equation.

where hS is given as

and V is the impeller tip velocity (V ) 2πNR). K1 canbe considered as a flow correction factor which dependson the angular position of the orifice.

Raidoo et al. (1987) have observed that the pressuredriving force in the presence of gas induction was lowerthan the pressure driving force in the absence of gasinduction by a factor as much as 10-20. The velocityhead generated by the impeller depends on the densityin the impeller region. When the gas is induced, theaverage density in the impeller region decreases sub-stantially (Fj ) FLεL + FGεG ≈ FLεL). Therefore, thevelocity head generated by the impeller is substantiallylower in the presence of the induced gas. Therefore, thepressure driving force (headspace pressure - pressurenear the orifice) decreases substantially due to thepresence of gas. The average density in the impellerregion is very important. The average density in theimpeller region depends on the local fractional gasholdup. This in turn depends on the rate at which gasis induced and the rate of gas dispersion. If the latteris high, then the local density will practically be thesame as the liquid density, and therefore the gasinduction may not decrease the pressure driving forcesubstantially. Whereas, if the former is higher, thenthe gas holdup in the impeller region and the reductionin the pressure driving force due to the induced gas willbe substantial.

Baczkiewicz and Michalski (1988) have given anempirical correlation for the maximum value of the ratioQG/VL. This correlation arises from a data fittingexercise; it does not consider the physics of the processoccurring.

Evans et al.(1990) equated the pressure driving forcegenerated by the impeller rotation to the pressure dropsfor the flow of gas in the hollow-bladed impellers (orificeequation) and the hollow shaft and proposed the fol-lowing equation for the gas-induction rate. Since thestarting point is the orifice equation, it has the samelimitations that were given earlier.

Substituting for [PO - P(θ)] from eq 7, we get

The above equation grossly overpredicts the gas-induc-tion rate. At speeds of N > NCG, gas induction occursand the average density in the impeller region decreases

substantially. After the gas induction begins, the localpressure was related to the impeller speed using theaverage density. Equation 7 was thus modified to givethe following equation:

The average density is defined as Fj ) FL(1 - εG);substituting eq 23 in eq 21, the following equation isobtained:

The above equation was fairly successful in predictingthe gas-induction rate for a variety of different operatingconditions, like the gas feed to the central shaft or theriser tube, effect of submersion depth, and so forth.Their prediction for QG versus N was good at highspeeds but relatively poor at low speeds. This basicmodel was progressively modified by the authors takinginto account the various processes occurring, such asthe frictional pressure drop in the hollow pipe, thepressure drop associated with the kinetic energy im-parted to the liquid for the formation of the bubble, thepressure drop required to overcome the surface tensionforces for the formation of bubbles, and so forth.

Evans et al. (1991) and Rielly et al. (1992) proposedthat the net driving force for the gas induction is ∆PT) [PO - P(θ)] which is generated by the impellerrotation and can be expressed by eq 7 above:

whereas the various resistances responsible for thepressure drop as the gas flows from the headspace intothe liquid are (1) ∆PP ) frictional pressure drop alongthe gas pathway ∝ QG; (2) ∆PO ) orifice pressure drop;(3) ∆PKE ) pressure drop associated with the kineticenergy imparted to the liquid, ) (3QG

2FL)/(32π2rb4); (4)

∆Pσ ) pressure drop required to overcome the surfacetension forces at the orifice, 2σ/rb. The rate of gasinduction at steady state can be obtained by equatingthe net driving force to the sum of all the resistances.The balance is given by the following equation:

The expressions for ∆PKE and ∆Pσ assume that a singlespherical bubble is getting formed in a stagnant liquid.At high gas flow rates, the shape of gas bubbles maydeviate from the spherical; likewise, a stream of gasbubbles may also be formed. In that case, the presentexpressions ∆PKE and ∆Pσ may not hold. One of thebasic limitations of this approach is that the pressurecoefficient CP(θ) must be known.

Rigby et al. (1994) have measured the pressureprofiles in the liquid behind the impeller blades. Theyhave found that the pressure driving force reached amaximum slightly off the blade surface in the wakeregion behind the blade. Locating the orifice at such alocation increased the gas induction rates by 5-10% ascompared to the orifice located on the blade surface.Forrester and Rielly (1994) also used the pressure

QG ) COAOK1[2g(-hS)(FL/FG)]1/2 - 0.00085K1 (18)

hS - hL

(V2/2g)) P′ (19)

(QG/VL)max ) (2.36 × 10-4)N1.53(D/T)1.83nP0.26 (20)

QG ) COAOx2[PO - P(θ)]FG

(21)

QG ) COAOxFL

FG[CP(θ)(2πRN(1 - K))2 - 2gS] (22)

P(θ) ) (PO + FLgS) - 12

FLCP(θ)[2πNR(1 - K)]2 (23)

QG )

COAOx(FL(1 - ε)FG

+ ε)CP(θ)[2πRN(1 - K)]2 -2FLgS

FG

(24)

∆PT ) 12

FLCP(θ)[2πRN(1 - K)]2 - FLgS (25)

∆PT ) ∆PP + ∆PO + ∆PKE + ∆Pσ (26)


balance model developed by Evans et al. (1991) andmodified it for the case of multiple orifices located on asingle blade. By using four orifices, the rate of gasinduction was found to increase by a factor of 3 at animpeller speed of 9 rps as compared to just a singleorifice. They were able to predict the gas inductionrates within 20% of the experimental values.

In a recent work Forrester et al. (1998) have proposedfurther improvements on this model. The first modifi-cation enables good predictions at speeds close to NCG.This is done by allowing the bubble size to be equal tothe orifice size at speeds close to NCG. In the earliermodel of Evans et al. (1991), the pressure loss due tokinetic energy imparted to the liquid was calculated onthe basis of the bubble formation in an infinite stagnantliquid. In this work, this pressure loss term wasmodified by applying potential flow solution for anexpanding sphere. These modifications enabled muchbetter predictions of the gas-induction rate as comparedto those of Forrester et al. (1994).

Heim et al. (1995) have investigated four and sixhollow pipe impellers and a hollow disk impeller. Theyhave correlated the gas-induction rate with Reynoldsnumber and Froude number. Their correlation is asfollows:

Since this is a fit of the experimental data, it is essentialto consider the range of Re and Fr covered by theauthors. Table 4A gives a summary of the variousmodels proposed for type 11 systems.

3.2.2. Type 12 and 22 Systems. Type 12 and 22systems involve the two phases gas and liquid. Thehydrodynamics is complicated and is less amenable totheoretical analysis, mainly because the complex two-phase hydrodynamics is poorly understood. For a gas-inducing impeller, the gas induction rate is zero at thecritical impeller speed. As the impeller speed increasesabove NCG, the velocity head generated by the impeller

increases as (N - NCG)2 or (N2 - NCG2). The gas-

induction rate should be proportional to the pressuredifference created (i.e., velocity head generated), andhence several empirical correlations for QG includeterms such as (N - NCG)a or (N2 - NCG

2)b. White andde Villiers (1977), Sawant et al. (1980, 1981), andAldrich and van Deventer (1994, 1996) have used suchterms for correlating their data. Their correlations arelisted in Table 4B.

Zundelevich (1979) attempted to model the gas-induction rate of a turboaerator by drawing an analogyto a liquid jet gas ejector with the following assump-tions: (i) The gas induction was assumed to be occurringbecause of the action of the liquid flow coming out ofthe impeller periphery. (ii) The impeller liquid flownumber (η) was assumed to be constant at all speeds.(iii) The proportion of the induced gas flow rate to theliquid flow rate was assumed to be the same as that fora geometrically similar water jet ejector. (iv) Anempirical equation for the water jet ejector (correlatingthe ratio of the liquid and the gas flow rates to thepressure differential and the mixing chamber pressuredifferential) was assumed to be valid for the gas-inducing impeller.

With these assumptions, he showed a unique rela-tionship to exist between the two dimensionless param-eters, namely, the impeller head coefficient (CH) and thegas Euler number (EuG):

where EuG ) gS/(QG/D2)2 and CH ) gS/(ND)2.Zundelevich (1979) proposed that this relationship

could be used in the scale-up of these impellers. How-ever, Raidoo et al. (1987) tried to correlate their datafor 0.15-, 0.20-, and 0.25-m diameter impellers using theabove correlation. They have observed that such aunique correlation between CH and EuG did not exist.

Table 4.A. Models for the Rate of Gas Induction for the Type 11 System

impeller type basis for the prediction of QG accuracy refs

hollow pipe and flattened pipe impeller empirical, flow correction factor K1 Martin (1972)hollow pipe (Q/VL)max ) 2.36 × 10-4n1.5(d/D)1.8i0.26 Baczkiewicz and Michalski (1988)hollow-bladed impeller blade slip factor K and pressure coefficient CP(θ) 10% Evans et al. (1990)hollow-bladed impeller K, CP(θ), and ∆PT ) ∆PP + ∆PO + ∆PKE + ∆Pσ 20% Evans et al. (1991)two-bladed disc turbine orifice behind

and off the bladesK, CP(θ) and ∆PT ) ∆PP + ∆PO + ∆PKE + ∆Pσ 20% Evans et al. (1994)

hollow-bladed with multiple orifices K, CP(θ) and ∆PT ) ∆PP + ∆PO + ∆PKE + ∆Pσ 20% Forrester et al. (1994)

hollow pipeKG

KG∞) 1 - exp(-CRec1Fr*c2) Heim et al. (1995)

hollow-bladed with multiple orifices similar to Evans et al. (1991), Forrester et al. (1994) Forrester et al. (1998)

B. Models for the Rate of Gas Induction for Type 12 and 22 Systems

impeller type model for the rate of gas induction refs

Wemco machine Qg ∝ D2.4 ln(N) Degner and Treweek (1976)slotted pipe stator, pump rotor NQgxD/S′ ) 0.0231(Fr′ - Fr′c)1.84 White and de Villiers (1977)Wemco machine Qg ) 51.2(Fr - Frc)0.83(D/S)0.5 Sawant et al. (1980)Denver machine Qg ) 0.0021(N2 - Nc

2)0.75D3 Sawant et al. (1981)multiple-impeller system Vi ) 7.15 × 10-6N1.9D3.95T-0.25σ-2.4µ-0.15 Matsumura et al. (1982a)PTD rotor with stator Qg

2 ) 2.68 × 10-4(∆PD2)1.184 Raidoo et al. (1987)

PBTD with stator Qg ) λ*NR2[1 - 2gSφV2] + R*NR3[1 - A(2gS

ΦV2)]3/2Saravanan and Joshi (1995)

PBTD-stator, multiple impellers with sparging 1 -QGS

QG) â1Flâ2(C3/D)â3 Patwardhan and Joshi (1997)

NQG

NQG∞) 1 - exp(-CRec1Frc2) (27)

1 + ηxEuG/CH ) 3xη2EuG/CH - 3η2( EuG

CH + k2

π2)(28)


This could be because of the several overly restrictiveassumptions used in the model like constancy of theimpeller flow number, equivalency of the liquid jetejector, and a gas-inducing impeller, and so forth. Theinduced gas would tend to form cavities behind theimpeller blades, causing a reduction in the impellerpumping capacity. In summary, the assumptions madeare not representative of the reality. The basic equationused in deriving eq 28 is an empirical equation for theliquid jet ejector which in itself does not represent thephysical picture.

The pressure balance approach used for type 11systems was extended by Raidoo et al.(1987) for type22 systems (shrouded disk turbine; shrouded curvedblade turbine; PBTD). Starting from Bernoulli’s equa-tion, they correlated the experimentally measured pres-sure drops to the impeller tip velocity, for different H/Tratios. This equation neglects the frictional pressuredrop occurring:

The constants R and â were experimentally evaluatedfor H/T ratios of 1.0, 0.75, and 0.6. The ∆P predictedfrom eq 29 was correlated to the gas-induction rateempirically by the following equation:

Matsumura et al. (1982a,b) have investigated amultiple-impeller system. The upper impeller wasdesigned for bubble entrapment and the lower impellerwas designed for bubble dispersion. The lower impellerwas always operated at the speed required for thedispersion of the bubbles entrapped by the upperimpeller. They have determined the gas-induction rateby a chemical method. The liquid under investigationwas a sodium sulfite solution containing a cobaltcatalyst. The kinetics of the reaction were established.A mixture of oxygen and nitrogen was taken in theheadspace. As the impeller rotates, gas is induced andthe oxygen reacts with the sodium sulfite. A pressure-controlling device on the reactor supplies oxygen at therate at which it is consumed. Their experimental setupis shown schematically in Figure 15. The rate of gasinduction is found in the following manner. The gasand the liquid phases were assumed to be well-mixed

and the material balance equations were written asfollows:

Oxidation of sodium sulfite in the presence of a cobaltcatalyst is zero-order with respect to sodium sulfite.Using the theory of mass transfer accompanied bychemical reaction (Doraiswamy and Sharma, 1984), therate of oxygen uptake can be written as RAa )xMkLa[A*]. The quantity xM can be defined in thefollowing manner:

Substituting for the orders of the reaction, that is, m) 2 and n ) 1, gives

Further, assuming that the nitrogen gas is in equilib-rium with the gas and the liquid phases and that gi (1- zGO) ) ge(1 - zφo), the following relations wereobtained by them:

where the fraction of the absorbed oxygen is denotedby êO.

Assuming PHS ) Pφ,the following relation was derived:

The molar volumetric absorption rate JO can be obtainedfrom the pressure changes in the gas holder. If theinterfacial area per unit volume is measured, then thevalue of êO can be calculated. Knowing JO and êO, andzGO (which was also measured), the molar flow rate ofthe induced gas (gi) can be calculated. This can thenbe converted to the volumetric flow rate. The gas-induction rate was correlated to the upper impellerspeed, upper impeller diameter, tank diameter, and the

Figure 15. Schematic representation of the experimental setupof Matsumura et al. (1982a).

∆PT + FLgS ) R[FL(πDN)2/2]â (29)

QG2 ) (2.68 × 10-4)(∆PD2)1.184 (30)

material balance for the oxygen in the holding tank

VHddt

(PH/RGTH) ) -G (31)

material balance for oxygen in the headspace

VHSddt

(PHSzGO/RGTHS) ) G - (gizGO - gezφO) (32)

material balance for oxygen in the dispersedgas phase

Vφ

ddt

(PφzφO/RGTφ) ) (gizGO - gezφO) - VLJO (33)

xM )x 2

m+1DOkmn[A*]m-1[BO]n

kL

JO) -VHddt

(PH/RTH) ) (gizgO - gezφO)

) VLax2/3k2,0DO(PφzφOHO)3/2(34)

zφO

zGO) (1 - êO)/(1 - êOzGO) and ge/gi ) 1 - êOzGO

(35)

êO ) (1 - gezφO/gizGO) (36)

JO ) -VH

VL

ddt( PH

RTH)

) 1VL

êOgizGO

(37)


physical properties of the system with an empiricalequation. Since the lower impeller speed was notvaried, the variation of the gas-induction rate with itcannot be determined.

Mundale and Joshi (1995) have investigated a largenumber of designs of rotors for their stator-rotorsystem. These designs were basically of the pitchedblade downflow turbine (PBTD) type. A number ofvariations were investigated (viz. blade angle from 30to 90°, blade angle varying from hub to tip, number ofblades, blade thickness, curvature along the bladewidth, curvature along the blade length, blade width,perforated blades, and so forth). They have recom-mended the use of a 45°, six-bladed PBTD impeller witha blade width of one-third of the impeller diameter. Theyfurther recommend that a close match between thestator and the rotor is essential for good performance.They have observed that the performance of the impelleris drastically affected by any axial or radial obstructionsto the flow coming into the impeller.

Saravanan and Joshi (1995) have extended theirforced vortex formation model to predict the gas-induction rate. They have proposed that the overall gas-induction process occurs in two steps, namely, bubbleentrapment and bubble carriage. They have assumedthat the rate of gas-bubble entrapment is proportionalto the product of the area of intersection of the vortexwith the impeller center plane and the impeller speed.The proportionality constant was denoted as the gas-induction modulus (λ) and it denotes the ability of theimpeller to generate and entrap gas bubbles from thevortex. Physically, it represents the thickness of thegas film imbibed into the liquid for every revolution ofthe impeller. The gas-liquid interfacial area wasassumed to be proportional to the area of intersectionof the vortex with the impeller center plane that is πX2.The radius of intersection X is depicted in Figure 13C.

Rearranging eq 14 in terms of r2/R2 and denoting r ) Xat the impeller center plane,

Substituting for X2 in eq 38 using eq 39 and denotingλ* ) πλ( + kg),

The rate of the bubble carriage was considered to beproportional to the liquid pumping rate, given as

In reality, the steps of bubble entrapment and bubblecarriage occur in series. However, when the seriesmechanism was fitted to the experimental data, poorfit was observed. Hence, they have attempted to fit thedata assuming that these steps occur in parallel. Thisgave a better fit to the experimental data. In reality,these two steps do occur in series. This is one of theobvious limitations of this early work. It is also likelythat the rate-controlling step changes from the center

to the tip of the impeller: entrapment-controlled in thecentral region and carriage-controlled in the tip region.Therefore, the essentially series mechanism may lookparallel. In our laboratory, further work is being doneto throw more light on the rates of these two processes,which may ultimately result in a better model that isconsistent with the reality as well as with the experi-mental data. The final expression of the model is givenbelow:

The values of the constants λ*, R*, and φ wereobtained by regression analysis of a large amount ofexperimental data in 0.57-, 1.0-, and 1.5-m diametervessels. The constants in the above equation character-ize the system in terms of the ability of the impeller togenerate the vortex (φ), the ability of the impeller toconvert the unstable vortex shape into a gas-liquiddispersion (λ*), and the impeller pumping constant (R*).They were able to predict the values of gas-inductionrates to within 15% of the experimentally measuredvalues. In this model, the empiricism is introducedthrough the values of λ* and R*. The key assumptionof QE being proportional to the product of the area ofintersection of the vortex and the impeller speed needsto be investigated further. Similarly, the bubble car-riage rate is taken as a function of the liquid flow alone.

Table 4B gives an overview of the various models usedto predict the gas-induction rate.

3.2.3. Multiple-Impeller Systems. Saravanan andJoshi (1995) have extensively investigated multiple-impeller systems. They have reported that the PBTD-PU and PBTD-PBTU combinations give the highestgas-induction rate for a given power consumption. Thiswas attributed to the flow characteristics of the bottomimpeller. The PU or PBTU impeller at the bottomgenerates an axially upward flow and this causes anincrease in the amount of liquid reaching the gas-inducing impeller. Thus, the capacity of the liquid tocarry away the gas bubbles increases. The rate of gasinduction therefore increases. Whereas a PBTD impel-ler at the bottom withdraws liquid from the upper gas-inducing impeller. The bubble carriage capacity de-creases, and the gas-induction rate also decreases. Theliquid-phase flow pattern and gas-dispersion character-istics with different designs of the lower impeller areshown in Figures 16, parts A-C. It can also be seenthat a lower PBTU impeller also improves the disper-sion of the induced gas (Figure 16B). The values of λ*and R* were reported for single- and multiple-impellersystems with different designs of the lower impeller.They have reported that the λ* values are essentiallyunaffected by the lower impeller design. Its value isaround 130 for the various systems investigated bythem. The value of R* depends strongly on the lowerimpeller design. The value of R* for a single-impellersystem is 92.42. When a PBTU impeller is used at thebottom, this value increases to 212, indicating that thebubble carriage capacity is increased considerably.When the PBTD impeller is used at the bottom, thevalue of R* decreases marginally to 86, indicating adecrease in the bubble carriage capacity and hence areduction in the gas-induction rate. The design of thelower PBTU was optimized by varying the blade angle,blade width, number of blades, diameter, clearance, andso forth.

QG ) λ*NR2(1 - 2gSφV2) + R*NR3(1 - A(2gS

φV2)3/2) (42)

QG ) λNπX2 (38)

X2

R2) (1 + kg)(1 - 2gS

φV2) (39)

QE ) λ*NR2(1 - 2gSφV2) (40)

QC ) R*NR3(1 - A(2gSφV2)3/2) (41)


Patwardhan and Joshi (1997) have investigated themultiple-impeller system of Saravanan and Joshi (1995)in conventional stirred vessels. The effects of spargerdesign, superficial velocity of the sparged gas, the lowerimpeller design, and so forth were investigated and therate of gas induction in the presence of sparging wascorrelated empirically with the following equation:

Since this is a completely empirical equation, care hasto be taken while using this equation for other systemsand scales.

3.2.4. Recommendations. Figure 17 compares therate of the gas induction of various types of impellersreported in the literature. In this figure, the differenttypes of gas-inducing impellers have been evaluated ona common basis, namely a tank size of 0.5 m, D/T ratioequal to 0.33, and impeller submergence equal to 0.1m. From the figure, it can be seen that the gas-induction characteristics of the multiple-impeller systemPBTD-PU are far superior as compared to any otherdesign previously reported. Thus, for gas-inductionpurposes, such multiple-impeller systems are highlyrecommended. In such systems the upper impeller canbe located very close to the free liquid surface (S ) 100-200 mm), to maintain a high rate of gas induction. Thesecond impeller situated well-below the gas-inducingimpeller is responsible for the generation of a favorableflow field in the liquid phase for efficient gas dispersion.

Such a multiple-impeller system therefore ensures botha high gas-induction rate as well as good gas-dispersioncharacteristics. The design of the second impeller canbe optimized to suit any desired design objective likeheat transfer, solid suspension, mixing, gas dispersion,and so forth.

The prediction of the gas-induction rate (QG) is moredifficult than that of the critical impeller speed. In type11 systems the flow through the impeller zone consistsof single gas phase. This can be considered analogousto the flow of gas through a pipe with various resis-tances. The models developed by Evans et al. (1991)and Rielly et al. (1992) take into account the variousresistances for the flow of the gas phase and the drivingforce (pressure drop) generated by the impeller. Theirmodel is thus based on fundamental principles and canbe used for a priori estimation of the gas-induction rate.What remains to be tackled in such an approach isrelating the local pressure coefficient to the impellergeometry and the speed in a fundamental manner. Ifthis is achieved, then the gas-induction rate for a type11 system can be predicted completely from fundamen-tal principles. Such an exercise would also be suitablefor the optimization of the impeller design. When type11 systems are being considered, their approach ishighly recommended for rational design. It would beinteresting to compare the effects of blade shape,number of blades, orifice location on the gas holdup, orthe rate of gas induction on the basis of equal powerconsumption. But such a comparison is not possiblebecause the data on power consumption (power numberand its variation with gas flow rate) are not availablefor type 11 systems. It is desirable to carry outsystematic experimental investigations on the effect oforifice location, size and shape of the pipes, number ofpipes, and so forth on the power consumption in bothgassed and ungassed states, and simultaneously mea-sure the rate of gas induction, fractional gas holdup, andso forth. Such an exercise will serve as a basis for theselection of optimum geometry of type 11 systems.

Type 12 and 22 systems pose more difficulties as theyinvolve the flow of a gas and liquid through the gas-inducing impeller. The flow pattern in the liquid phaseitself can influence the gas-induction rate. Saravananand Joshi (1995) have proposed that the process of gasinduction depends on the bubble entrapment and bubblecarriage rate. However, further work is still needed inelucidating the effect of impeller design and operatingconditions on the flow field generated and in turn therates of bubble entrapment and bubble carriage andtheir interrelation. Until such an understanding canbe developed, their correlation is recommended for scale-

Figure 16. Liquid-phase flow pattern and gas-dispersion characteristics for different designs of the lower impeller: (A) single gas-inducing impeller; (B) PBTU as the lower impeller; (C) PBTD as the lower impeller.

Figure 17. Comparison of gas-induction characteristics of dif-ferent designs of gas-inducing impellers: 4, Saravanan and Joshi(1995); 0, Raidoo et al. (1987); +, Joshi and Sharma (1977); ),Aldrich and van Deventer (1994); O, Sawant et al. (1981); ×,Sawant et al. (1980); b, Heim et al. (1995).

1 -QGS

QG) â1Flâ2(C3/D)â3 (43)


up, mainly because the experiments have been carriedout on fairly large vessels of different sizes (i.e., 0.57,1.0, and 1.5 m) and over a wide range of impellergeometries and operating conditions.

3.3. Power Consumption. 3.3.1. Type 11, 12,and 22 Systems. Power consumption in stirred vesselsand equipment of this kind contributes significantly tothe utility cost. The power drawn by the impeller isconsumed for various purposes, namely the generationof bulk liquid flow, generation of turbulence, dispersionof induced gas, solid suspension, heat transfer, mixing,and so forth. Thus, power consumption has a directinfluence on the performance of the reactor.

Flotation machines were investigated primarily togenerate the data for scale-up. Several workers havetried to correlate the power consumption (in terms ofthe power number, NP)with the dimensionless quanti-ties such as Re, Fr, NQ, and so forth. [Arbiter et al.(1969), Fallenius (1981), and Schubert and Bischof-berger (1978)]. Researchers who were interested incomparing the gas-inducing impellers with conventionalmechanically agitated contactors have empirically cor-related the ratio of power in the gassed state ascompared to the ungassed state, with the gas flow rate,the design details of the impeller, and the operatingvariables [Topiwala and Hamer (1974) and Joshi andSharma (1977)]. In any case much of the literature onthe power consumption of gas-inducing impellers isempirical.

There is an agreement in the literature among variousworkers that the power consumption in the gassed stateis lower than that in the ungassed state. This reductionin power consumption can be explained by the followingtwo reasons. (i) Cavity formation: The induced gasforms cavities behind the impeller blade; this makes theliquid flow around the impeller blades more streamlined, thereby reducing the drag and causing a reductionin the power consumption. Grainger-Allen (1970) givesexcellent photographic evidence of cavity formationbehind the impeller blades. (ii) Gas recirculation:Because of the flow pattern generated by the impeller,a certain amount of gas gets recycled in the vessel. Theaverage density in the impeller vicinity decreases,causing a decrease in the power consumption.

One of the earliest models for the power consumptionwas developed by Arbiter et al. (1969). The followingassumptions were made in their model. (i) The densityof the gas-liquid dispersion was assumed to be aweighted mean of the gas and liquid densities. (ii) Theratio of the liquid flow generated by the impeller to therate of gas induction was related to the gas flow number,through an empirical relationship obtained by experi-ments on a centrifugal pump. This relationship wasassumed to be valid for gas-inducing impellers. On thebasis of these assumptions they derived the followingequation:

The second assumption of the application of the cen-trifugal pump equation to the gas-inducing impeller isnot completely justified. The gas-inducing impellergenerates both gas flow (induction) and a liquid flow.In this sense it is different from a centrifugal pump. Theempirical nature of the correlation is evident from eq44.

Topiwala and Hamer (1974) and Joshi and Sharma(1977) have investigated hollow pipe impellers and havecorrelated the power consumption with the help of anempirical relationship developed by Michel and Miller(1962) and it is given by the following equation:

Joshi and Sharma (1977) have reported the value of theconstant C as 0.364 for the pipe impellers with twopipes. They further report that, at low gas flow ratesthe value of the constant C becomes sensitive to Q andis lower than 0.364. The correlation of Michel andMiller (1962) is fairly popular in the field of stirredvessels. One of the basic differences between a stirredvessel and a gas-inducing impeller is that, in the latterthe induced gas flow rate cannot be varied indepen-dently. The gas-induction rate is intimately lined to theimpeller speed (power consumption), the impeller de-sign, and geometry. The equation is empirical andcaution has to be exercised while using it.

Zundelevich (1979), drawing an analogy between thegas-inducing impeller and a jet loop reactor, derived anexpression for the rate of gas induction in terms of theimpeller head coefficient and the gas Euler number. Hederived a relationship in terms of the gas-induction rateper unit power consumption (QG/PG). Assuming that theimpeller power number is constant and using an aver-age density of the dispersion, the parameter QG/PG wasrelated by

The optimum value of the (QGS/PG) was 1.08 × 10-5

m4/W‚s for the air-water system, and the values of theconstants were NP ) 3.1 and η ) 0.071. The abovecorrelation also suffers from the limitations mentionedin the earlier section.

Matsumura et al. (1982a) have correlated the powerconsumption in their multiple-impeller system with theReynolds number and the Froude number of the upperimpeller. The power consumption was also correlatedin an alternate form using the gas-induction rate. Sincethe correlation is empirical, care has to be taken whileapplying the correlation beyond the ranges investigatedby the authors.

Baczkiewicz and Michalski (1988) have investigatedhollow pipe impellers and have correlated the gassedpower consumption with the following equation:

Saravanan et al. (1996) have made a first attempt atmodeling the power consumption in terms of the dragforce acting on the blade. In the absence of induced gas(N < NCG), they have modeled the power consumptionin the absence of gas induction in the following manner.The flow pattern generated by the single gas-inducingimpeller is seen in Figure 16A. It can be seen that,below the impeller, there is an inflow. This inflow ofliquid could exert a drag force on the gas-inducingimpeller. This drag force was assumed to result in aconstant torque τr. The slip factor which accounts forthe slip of the impeller blade and the liquid wasassumed to be constant over the entire blade length.

PG/PL

1 - PG/PL)

Fa

FL(R(1/NQG)n + â) (44)

PG ) C(PL2ND3/QG

0.56)0.45 (45)

QGSPG

)CH

NPFg(NQG2

η+ NQG) (46)

PG/VL ) 0.62N3.44(Q/VL)-0.31(d/D)4.48nP1.07 (47)


The torque acting on a differential element of theimpeller blade due to the drag force is

Such a drag coefficient based approach to power con-sumption was given by Tatterson (1991). Integratingthe above equation between the limits r ) 0-R and τ )τr-τ,

Since a power, P ) 2πNτ,

The measured power consumption at N < NCG wascorrelated using the above equation. It was observedthat value of τr was zero for single- as well as multiple-impeller systems, and the impeller system could becharacterized in terms of the drag coefficient completely.

The above model was extended to include the presenceof gas. For this purpose the impeller was divided intothree regions. These are the central zone of the liquidrecycle, the middle zone of the vortex where gas induc-tion occurs, and the outer zone outside the vortex whichconveys the gas (refer to Figure 18). They have madethe following additional assumptions: (i) The fluidrecycle and the associated effects on the power con-sumption are assumed to be represented by a constanttorque τrg acting at the eye of the impeller. (ii) For theimpeller zone in the range 0 e r e Y, the drag coefficientis CDG. (iii) For the impeller zone in the range Y e r eR, the drag coefficient is CDO. (iv) The density of thegas-liquid mixture surrounding the impeller is propor-tional to the liquid density and the square of the radialdistance along the impeller blade (i.e., F ) AFL(r/R)2).

Proceeding in a manner similar to that above, theequation for power consumption is

The above model was also applied by them to themultiple-impeller system. The power consumption forthe different impeller combinations could be adequatelycorrelated in terms of the dimensionless drag coef-ficients. This model has a number of simplifyingassumptions such as a constant value of drag coef-ficients in a particular region and parabolic variationof local density with respect to the radial distance.These assumptions are a simplified picture of reality.Nonetheless, the model helps in characterizing theimpeller systems in terms of the drag coefficients. Theexperiments have been carried out over a large rangeof vessel sizes (0.57-1.5 m), operating conditions, andimpeller geometries. The values of the constants forvarious impeller combinations have been reported inTable 5. This correlation is expected to be useful inscale-up. It was observed that the value of τrg is muchsmaller than the values of CDO

/ and CDY/ . They have

shown that the power numbers for the multiple-impellersystems decreased in the following order:

The design of the lower impellers (PBTD and PBTU)were optimized to reduce the power consumption. Itwas found that the blade angle of 30° gave the lowestpower number. The power number increased with theincreasing number of blades and the blade width. Theblade thickness did not have a significant effect on thepower number. The power number was found toincrease with an increase in the interimpeller clearance.The above equation was successfully used in their datafor single- as well as multiple-impeller systems within(10%.

The pertinent literature is reviewed in Table 6. Itshows the type of impeller investigated, geometry of thesystem, physicochemical properties investigated, andthe key findings.

3.3.2. Recommendations. As compared to thecritical speed and gas-induction rate, studies pertainingto power consumption are not extensive. There is verylittle information on the power consumption for variousdesigns of gas-inducing impellers; whatever informationis there is mainly in the form of empirical correlations.The correlations of Michel and Miller (1962), Arbiter etal. (1969), and Baczkiewicz and Michalski (1988) havenot been tested over a wide range and may giveerroneous results if applied beyond their range ofapplicability. Saravanan et al. (1996) have presented

Figure 18. Vortex model for the prediction of power consumption(courtsey, Saravanan et al., 1996). (I) Inner zone of fluid recycle;(II) impeller zone in the range 0 < r < Y; (III) impeller zone inthe range Y < r < R.

dτ ) r dF ) (CDWFL/2)(2πfSN)2r3 dr (48)

τ - τr ) (WFL/8)(2πfSN)2(CDR4) (49)

P ) τr(2πN) + CD/ (FLWN3R4) (50)

Table 5. Values of Dimensionless Drag Coefficients forVarious Multiple-Impeller Systems, Saravanan (1995)

impeller combination τrg (N‚m) CDO/ CDY

/

single PBTD 1.77 22.2 6.7PBTD-PBTD 0.76 47.9 14.1PBTD-PBTU 0.39 43.2 13.2PBTD-SBT 0.79 111.6 27.6PBTD-DT 0.93 146.5 34.9PBTD-PD 0.49 9.1 3.0PBTD-PU 0.15 8.2 2.8

P - τrg(2πN)

FLWN3R4) CDO

/ - CDY/ (1 - 1

φSF)3(51)

PBTD-DT > PBTD-SBT > PBTD-PBTD >PBTD-PBTU > PBTD-PD > PBTD-PU >

single PBTD


a simplified model, and their correlation is recom-mended for scale-up purposes, provided the geometryis not dramatically different.

3.4. Bubble Formation, Gas Holdup, and Inter-facial Area. 3.4.1. Type 11, 12, and 22 Systems. Theprocess of bubble formation, gas holdup, and powerconsumption are intimately related in the case of gas-inducing impellers. Gas induction occurs at N > NCGwith a corresponding power consumption. Bubble for-mation occurs from the induced gas. In the impellerregion these bubbles get sheared, causing bubble break-age, and bubbles coalesce in the region of lower stressin the vessel. An equilibrium between the two processesdetermines the bubble size.

In the conventional mechanically agitated contactors,the fractional gas holdup and the interfacial areadepend on the power consumption per unit volume aswell as the superficial gas velocity. In the case of gas-inducing impellers, it is not possible to vary the twoindependently, as beyond NCG, the power consumptionand superficial gas velocity are intimately relatedthrough the gas-induction process. The power consump-tion determines the rate of gas induction which in turninfluences the gas holdup.

Bubble formation was qualitatively studied by Grain-ger-Allen (1970). He has used photographic techniquesto investigate the cavity formation behind the bladesand bubble generation from these cavities. He hasstudied a variety of slotted, hollow impellers in a smallPerspex vessel. He has reported that the presence ofstator blades did not influence the bubble size, but itmerely increased the number of bubbles generated. Thestator blades also helped to modify the flow pattern.Bubble generation was shown to occur from the cavityformed behind the trailing edge of the impeller via thevortex shedding mechanism. The bubble generationoccurred only at the tail of the cavity. The presence ofa surface-active agent in the liquid phase did not affectthe cavity size but merely decreased the bubble size.

He further proposed that to improve the bubble forma-tion, energy consumption in the cavity should be in-creased. This can be carried out by using two impellersin close vicinity of each other, or by suitably perforatingthe impeller blade to inject the energy into the cavityby a liquid jet.

Hinze (1955) used the theory of bubble breakage dueto isotropic turbulence, and assuming that no bubblecoalescence takes place, the following equation wasderived:

Calderbank and Moo-Young (1961) modified this toaccount for the bubble coalescence by adding a holdupterm.

Both of the above equations show that the mean bubblediameter is inversely proportional to the power con-sumption per unit volume. The interfacial area (a)should therefore be proportional to (PG/V)0.4. The cor-relations of Joshi and Sharma (1977) and Sawant et al.(1981) show that the exponents of (PG/V) are 0.4 and0.5, respectively (Table 7). However, Sawant et al. (1980)have reported an exponent of 0.86.

The effect of ionic salts on the gas holdup andinterfacial area have been investigated by Joshi andSharma (1977), Topiwala and Hamer (1974), and Sawantet al. (1980, 1981). They have observed that theelectrolytic solutions reduce the bubble coalescence rateand therefore reduce the bubble size and increase thegas holdup. However, this effect diminishes beyond aparticular electrolyte concentration.

Table 6. Power Consumption in Gas-Inducing Type Contactors

impeller type geometry key results refs

Fagergren D ) 5-9.4 cm; T ) 11-20 cmPAL/PL - ø1 - PAL/PL

) RNQn Arbiter et al. (1969)

pipe with orifice T ) 15.8 cm; D ) 7.5 cm PG ) C(PL2ND3/QG

0.56)0.45 Topiwala and Hamer (1974)

Outokumpu (scale-up) V ) 3 and 16 m3; D ) 50 and 76 cmPG

PL) (D′

D )7/2) (L′

L )7/2Fallenius (1981)

Denver Fagergren T ) 5.11-7.8 cm correlated Fr, NP, Re, and NQ Harris and Mensah-Biney (1977)

pipe with orifice T ) 41-100 cm; D ) 20-50 cmPG

PL) (1 - 17NQ) Joshi and Sharma (1977)

PG ) C(PL2ND3/QG

0.56)0.45

Cassiterite flotation V ) 6.6 l correlated P/VL as a function of NQ withN as a parameter

Schubert and Bischoffberger (1978)

turboaerator D/T ) 0.2 related PG as a function of NQg, CH, NP Zundelevich (1979)Wemco T ) 30 cm; D ) 5 cm used (PG/VL) to correlate kLa, QG Sawant et al. (1980)Denver T ) 10-38 cm; D ) 7-11.5 cm used (PG/VL) to correlate kLa, QG Sawant et al. (1981)

multiple-impeller system T ) 0.19-0.36; D/T ) 0.25PG

PL) 0.54(N2D

g )-0.34(ND2Fµ )-0.08

Matsumura et al. (1982a)

PBTD T ) 57 cm; D ) 15-25 cm correlated NPG/NP with VG using N asa parameter

Raidoo et al. (1987)

hollow pipe T ) 0.44 m PG/VL ) 0.6n3.4(Q/VL)-0.3(d/D)4.5i1.1 Baczkiewicz and Michalski (1988)PBTD T ) 57-150 cm; D ) 19-50 cm modeled PG based on the forced

vortex modelMundale (1993)

hollow pipe T ) 0.3 m; D ) 0.1-0.15 mEuG

Eu) 1 - exp(A +

a1

xFr*+ a2Re) Heim et al. (1995)

PBTD-PU T ) 57-150 cm; D )19-50 cmP - τrg2πN

FLWN3R4) CDO

/ - CDY/ (1 - 1

φFS) Saravanan et al. (1996)

dB ) J( σ0.6

FL0.2(PG/V)0.4) (52)

dB ) J( σ0.6

FL0.2(PG/V)0.4)εG

R (53)


Matsumura et al. (1982b) have correlated the frac-tional gas holdup and the interfacial area in theirmultiple-impeller system with the gas flow number, theFroude number, and the Reynolds number on the basisof the lower impeller. This is because the lower impelleris designed and operated for the effective dispersion ofthe induced gas. Hence, it is quite reasonable to assumethat the gas dispersion should be dependent on theoperating conditions of the lower impeller.

Heim et al. (1995) have investigated hollow pipeimpellers with four and six pipes and have given thefollowing correlation for the fractional gas holdup:

Recently, Saravanan and Joshi (1996) reported theuse of multiple impellers in GIMAC for improving thegas-dispersion characteristics. They observed that thegas holdup decreased in the following order:

The geometry of the bottom PBTU and PU impeller wasfurther optimized. For this purpose, the blade angle,the number of blades, the blade thickness, and theimpeller diameter was varied over a wide range for aPBTU impeller. The fractional gas holdup for a bladeangle of 30° was higher than that for blade angles of45, 60, or 90°. The pumping effectiveness of the impellerwas found to decrease with an increase in the numberof blades. Thus, increasing the number of blades abovesix reduced the fractional gas holdup. Further, it wasobserved that the impeller with four blades givesinstabilities in the gas-liquid dispersion. Therefore,they recommend six-bladed impellers. The fractionalgas holdup increased with an increasing W/D ratio. Theblade thickness did not have a significant effect on thefractional gas holdup. The fractional gas holdup wasalso found to decrease with an increase in the inter-impeller distance. For a given system geometry, thefractional gas holdup was found to decrease as the solidloading increases. The data on the fractional gas holdupwas correlated according to the work of Smith (1991)on stirred vessels. The primary reason for using Smith’scorrelation was that he was able to correlate the data

on fractional gas holdup for a range of stirred vesselsizes and over a wide range of operating conditions.Therefore, it is expected that his correlation should bemore scalable. His correlation is given by

The above equation correlates the rate of gas supply tothe stirred vessel (Fl ) QG/ND3), the physical propertiesof the system (Re), and the geometry of the system (Fr),with the fractional gas holdup. The flow numberdefined here does require information on the gas-induction rate before the gas hold-up can be computed.The factor is introduced because different impellerswhen operated at the same value of power consumptionper unit mass show different gas-induction rates, andhence different gas holdups. The values of a, b, and cfor different designs of the lower impeller have beenreported in their work. They have reported that thevalue of “a” varies from 0.06 for a single-impeller systemto 1.45 for a PBTD-PBTU combination, whereas thevalues of “b” are 0.31 and 0.05 for a single-impellersystem and a PBTD-PBTU combination, respectivelyand the value of “c” ranges between 0.51 for a single-impeller system to 0.70 for a PBTD-PBTU system.Since their experiments have been performed over awide range of vessel sizes (0.57-1.5 m) and a wide rangeof operating conditions, the correlation is extremelyuseful for scaleup purposes.

An attempt was also made to correlate the holdupdata in terms of power consumption alone. It was foundthat the data did not correlate well. This is becausedifferent impeller configurations give different QG andhence εG at the same value of overall power consumptionper unit mass.

Patwardhan and Joshi (1997) have also investigatedthe fractional gas holdup for GIMAC undergoing simul-taneous gas induction and sparging. Their data onfractional gas holdup was also correlated with the aboveequation. The values of the constants were reported fordifferent designs of the sparger and the lower impeller.However, their experiments were conducted only on1.5-m vessels and the holdup correlation should be usedvery carefully.

3.4.2. Recommendations. A preliminary estimateof the gas holdup can be made by using a relation that

Table 7. Gas Holdup and Interfacial Area in Gas-Inducing Type Contactors


slotted hollow impellers T ) 15 cm; D ) 10 cm investigated the bubble generationby photographic techniques

Grainger-Allen (1970)

pipe with orifice T ) 15.8 cm; D ) 7.5 cm εG ∝ (PG/VL)â(VG)ø Topiwala and Hamer (1974)pipe with orifice T ) 41-100 cm; D ) 20-50 cm εG ) 0.00112(PG/VL)0.5 Joshi and Sharma (1977)

a ) A(PG/VL)0.4VGâ

Wemco T ) 30 cm; D ) 5 cm a ) 79(PG/V)0.86 Sawant et al. (1980)a unaffected by solids (dolomite

20% by wt < 60 µm)Denver T ) 10-38 cm; D ) 7-11.5 cm εG ) 0.0325(PG/VL)0.5 Sawant et al. (1981)

a ) 75(PG/VL)0.5

multiple-impeller system T ) 0.19-0.36 m; D/T ) 0.25 εG ∝ N2D4.1T-2.6σ-2.8µ-0.15 Matsumura et al. (1982b)hollow-bladed concave T ) 45 cm; D ) 15.4 cm bubble size shows a log normal

distribution with σ ) 0.31Forrester et al. (1994)

hollow pipe T ) 0.3 m; D ) 0.1 m εG ) BFrbReb2NQb3(D/S)b4 Heim et al. (1995)

Denver T ) 19 cm; D ) 9.6 cm εG ) 10-7.8N2.7QG0.15 Al Taweel and Cheng (1995)

a ) 0.14N0.77QG0.28

PBTD with stator multipleimpellers

T ) 57-150 cm; D ) 19-50 cm εG ) λ1(D/T)λ2(ReFrFl)λ3 Saravanan and Joshi (1996)

PBTD-stator, multiple impellerswith sparging

T ) 1.5 m; D ) 0.5 m εG ) η1(ReFrFl)η2(C3/D)η3 Patwardhan and Joshi (1997)

εG ) BFrb1Reb2NQGb3(D/S)b4 (54)

PBTD-PU > PBTD-PBTU > PBTD-PD >single PBTD > PBTD-PBTD > PBTD-SBT >

PBTD-DT

εG ) a(D/T)b(ReFrFl)c (55)


correlates the gas holdup empirically to power consump-tion per unit volume. Such a correlation was given byJoshi and Sharma (1977). The correlation proposed bySmith (1991) is also successful in predicting the holdupin conventional stirred vessels over a wide range ofequipment sizes and scale. His correlation was modifiedand used by Saravanan and Joshi (1996). This correla-tion is recommended for the estimation of gas holdupin type 22 systems. Gas holdup in type 11 has only beeninvestigated very briefly. It is highly recommended thatthe gas holdup characteristics of type 11 systems beinvestigated. The effects of impeller geometry (bladeshape, blade angle, number of blades, orifice location,orifice area, etc.) on power consumption and gas holdupshould be evaluated. With the help of these data, theoptimum geometry for type 11 systems can be estab-lished.

4. Performance Characteristics

4.1. Mass-Transfer Coefficient. Many of the gas-liquid reactions involving sparingly soluble gases suchas hydrogen, oxygen, and so forth are limited by thetransfer of the dissolved gas to the bulk liquid. In suchcases, the productivity of the reactor depends on themass-transfer coefficient. For the design of such sys-tems, the knowledge of the mass-transfer coefficient isof prime importance. Experimentally, the mass-transfercoefficient can be determined by physical or chemicalmethods.

(i) Physical Methods: This involves absorption of asparingly soluble gas in the liquid phase under constantvolume conditions. During absorption, the pressure ofthe gas phase decreases, which can be monitored toobtain the volumetric mass-transfer coefficient. Hichriet al. (1992) used this method:

(ii) Chemical Methods: This involves simultaneousabsorption and reaction of a solute gas into the liquidphase. Several systems are reported in the literaturefor the measurement of a and kLa (Doraiswamy andSharma, 1984). The absorption of lean carbon dioxide

in an aqueous solution of sodium carbonate and sodiumbicarbonate can be used to determine the liquid-sidemass-transfer coefficient, kLa. Absorption of oxygenfrom air into an aqueous solution of sodium hydrosulfitecan be used to determine the effective interfacial area,a. In any case, when the gas phase is not pure, theresidence time distribution of the gas phase plays animportant role in the analysis of the data. The valueof kLa can be calculated by assuming a certain residencetime distribution of the gas phase (plug flow or back-mixed). An assumption of a back-mixed gas phase leadsto much higher values of kLa as compared to those fromthe assumption of plug flow. The difference in the twovalues of kLa increases as the gas-phase conversionapproaches unity. In general, the error between the twovalues is small at gas-phase conversions less than 10%.Thus, in such studies, it is usually desirable to limit thegas-phase conversion to below 10%. Table 8 sum-marizes the various efforts made at investigating themass-transfer coefficient (kLa). The correlations areempirical and correlate the kLa value with either powerconsumption per unit mass or the dimensionless num-bers such as Re, Fr, We, and so forth.

From Tables 7 and 8 it is also possible to see thevariation in kL with the power consumption. Joshi andSharma (1977) have found the liquid-side mass-transfercoefficient (kL) to be proportional to the power input (kL∝ (PG/V)0.15); thus kL depends only on the power con-sumption per unit volume. This is because the powerinput per unit volume governs the superficial gasvelocity through the induction process. The energydissipation rate alone governs the turbulence structure,and hence the value of kL depends only on the powerinput per unit volume. It may be noted that the valueof the exponent is small. Sawant et al. (1980, 1981)found kL to be independent of the power consumptionper unit volume.

4.2. Solid Suspension. Solid suspension is of greatpractical importance in froth flotation as well as inmany of the gas-liquid operations. Suspension of theparticles is important to ensure good gas-liquid-solidcontact. Ore enrichment in froth flotation occurs be-cause of efficient gas-liquid-solid contact. In certaingas-liquid reactions the solid particles act as catalysts;therefore, a uniform solid suspension is necessary for

Table 8. kLa in Gas-Inducing Type Contactors


pipe with orifice T ) 15.8 cm; D ) 7.5 cm no clear trend between kLa and dB.kLa increases with PG/V

Topiwala and Hamer (1974)

pipe with orifice T ) 41-100 cm; D ) 20-50 cm kLa ) A(PG/V)0.55VGB Joshi and Sharma (1977)

kL ∝ (PG/V)0.15

Wemco T ) 30 cm; D ) 5 cm kLa ) 0.0159(PG/V)0.86 Sawant et al. (1980)kL independent of (PG/V)kLa increases by 15% due to solids

(dolomite 20% by wt, < 60 µm)Denver T ) 10-38 cm; D ) 7-11.5 cm kLa ) 0.0195(PG/V)0.5 Sawant et al. (1981)

kL independent of (PG/V)

multiple-impeller system T ) 0.19-0.36; D/T ) 0.25 kL ) 18.2( Fµg)

-0.33(FDµ )0.67(N*3D3

µg )-0.23Matsumura et al. (1982b)

hollow pipe T ) 0.44 m kLa ) 0.17n1.7(Q/VL)0.6(d/D)2.2i0.5 Baczkiewicz and Michalski (1988)Rushton-type hollow shaft T ) 7 cm; D ) 3.2 cm Sh ) ARe1.45Sc0.5We0.5 Dietrich et al. (1992)

A ) 3 × 10-4 for H/T ) 1A ) 1.5 × 10-4 for H/T ) 1.4

hollow shaft T ) 5 cm; D ) 2.9 cm Sh ) ARe0.44Sc0.5We 1.27 Hichri et al. (1992)A ) 0.123

hollow pipe T ) 0.3 m; D ) 0.1-0.15 m ShSh∞

) 1 - exp(-KRek1Fr*k2) Heim et al. (1995)

hollow pipe T ) 0.45 m; D ) 0.154 m kLa ) 0.01(PG/VL)0.475VG0.4 Forrester et al. (1998)

ln( PO - Pi

(P - Pi) - k(PO - P)) ) [(k + 1)k ]kLat (56)


making the entire reactor volume effective. Althoughthe solid suspension is of prime importance, this aspecthas received scant attention. Only Saravanan et al.(1997) have investigated the solid suspension in GIMACin detail.

They have reported that a single gas-inducing impel-ler is very poor for the suspension of solid particles. Ifthe gas-inducing impeller is kept close to the liquidsurface, the flow and turbulence near the bottom of thetank becomes feeble, causing very little solid suspension.Even when the gas-inducing impeller was located closeto the bottom, solid suspension was found to be possibleonly when the particle size is less than 100 µm and solidloading less than 1%. The gas-induction rate in thiscase was extremely low. However, a multiple-impellersystem was found to be more effective for a solidsuspension. In this case, the second impeller can belocated well-below the gas-inducing impeller. The flowand the turbulence near the tank bottom can beincreased substantially, resulting in better solid suspen-sion. The critical impeller speed for solid suspension(NCS) was measured for different impeller systems,under a wide range of operating conditions. It wasobserved that NCS increased in the following order:

This was explained on the basis of the axial velocitygenerated by the different bottom impellers. A PBTDimpeller generates an axial flow in the downwarddirection and is therefore most efficient for the processof solid suspension. SBT and DT, however, are radialflow impellers; as a result, only a small portion of theinput energy dissipated is utilized for the solid suspen-sion. PBTU and PU generate an axial flow in theupward direction and therefore even smaller amountof input energy is available for solid suspension. In thiscase also the interimpeller clearance was found to bean important parameter. The critical impeller speed forsolid suspension, NCS, decreases with an increase in theinterimpeller clearance.

On the basis of the above results, the geometry of thebottom PBTD impeller was optimized. They haverecommend a 45°, six-bladed pitched blade downflowturbine with a W/D ratio of 0.3 for efficient solidsuspension. The blade thickness did not have anysignificant effect on NCS. The value of NCS was foundto decrease with an increase in the impeller diameter.It decreases with a decrease in the terminal settlingvelocity of particle and solid loading. NCS decreaseswith a decrease in the impeller clearance from thebottom. NCS also decreases with an increase in theinterimpeller clearance. It is unaffected by the sub-mergence of the upper impeller. They have also pro-posed a model for the solid suspension on the basis ofthe mechanism of the fluidization of solid particles, andthe liquid circulation velocities generated by the impel-ler. They have developed the following correlation:

The constant 0.031 has the following units (m1.072‚rad0.83‚µm-0.17‚s-1). Since the above correlation wasdeveloped for a large range of vessel sizes (0.57-1.5 m)

and under a wide range of operating conditions, it isexpected to be very useful for scale-up purposes. Theabove correlation also compares favorably with theclassical Zwietering correlation for stirred vessels.

5. Process Design of Gas-Inducing Reactors

The objective of a process design engineer can besimply stated as “design a reactor that will give a certainproduction rate”. More specifically, the process designengineer has to determine the set of parameters thatwill ensure the desired production rate (throughput),such that the overall operation becomes economicallyviable and attractive.

The correlations recommended in sections 3 and 4 arebased on the experimental work carried out by Sara-vanan and Joshi (1995, 1996) and Saravanan et al.(1996, 1997). These experiments have been carried outover a wide range of variables such as locations of theimpellers, interimpeller spacing, impeller designs, vesselsizes, power consumption, and so forth. Therefore, thecorrelations developed from these studies would be validon a larger scale even when any similarity (geometric,constant tip speed, constant power consumption per unitvolume, etc.) is not maintained. Since a wide range ofdesign variables has been covered for developing cor-relations, the only uncertainty is concerned with thedifferences associated with the gas-liquid and gas-liquid-solid systems. The extent of uncertainty can beconsiderably reduced by performing a few experimentswith the actual system (gas, liquid, and solid) at thecorresponding temperatures and pressures and then usethe correlations recommended in this monograph. Thesecorrelations are useful in the estimation of designparameters such as the rate of gas induction, fractionalgas hold-up, power consumption, critical impeller speedfor solid suspension, and so forth.

Before applying these correlations, it is important toknow which of the above design parameters is impor-tant. Thus, the first step in the process design activityis the determination of the rate-controlling mechanism.A particular equipment geometry (reactor size) andoperating conditions (power consumption) are chosen.The power consumption level is chosen such that thereactor gives the desired throughput. These steps arerepeated for several different values of the reactor size.This finally yields a set of reactor sizes and the corre-sponding operating conditions at which the reactor isable to give the desired throughput. An economicanalysis is then carried out to determine the optimumreactor geometry and the corresponding operating con-ditions.

5.1. Determination of the Rate-Controlling Step.A typical reaction between a gas and a liquid (catalyzedby solid particles) involves many steps (diffusion throughthe gas film, diffusion through the liquid film, adsorp-tion on the catalyst-active sites, surface reaction, de-sorption of the products, etc.). It is customary to denotethe gas-phase reactant by A, and the liquid-phasereactant as B. These steps involved are shown sche-matically in Figure 19. Any one of the above steps maybe a rate-determining step. In addition, if the reactionis highly endothermic or exothermic (typical of oxidationand hydrogenation reactions), then heat has to besupplied or removed from the reactor. In certain casesit is possible that this rate of heat supply or removalmay control the overall rate of the reaction. In gas-liquid reactions catalyzed by solid particles, it is also

PBTD-PBTD < PBTD-SBT < PBTD-DT <PBTD-PBTU < PBTD-PU

NCS ) 0.031(FS - FL

FL)A-0.83(W/D)-0.314dP

0.17X0.15 ×

(C3/D)-0.446D-2.42(C1/T)0.127T1.35 (57)


possible that the suspension of catalyst particles candetermine the overall rate of reaction. In such casesthe overall reaction is said to be suspension-controlled.As a first step in the process design activity, the rate-controlling step has to be determined. The determina-tion of the rate-controlling step is usually carried outusing model contactors. This procedure is fairly well-established (Doraiswamy and Sharma, 1984). Table 9summarizes the effect of various parameters such as[A*], [AS], [BO], dP, εS, impeller speed, and so forth, onthe overall rate of reaction for different rate-controllingsteps. During the course of the reaction, it may happenthat one or more operating conditions change. Forexample, the reactant concentration, operating temper-ature, pressure, and so forth may change with time(batch reactor) or location within the reactor (packedcolumn). In that case, it is possible that the rate-controlling step itself may change with time or locationin the vessel. In such cases, the rate-controlling stephas to be determined as a function of time/location in

the reactor, and so forth. Once the rate-controlling stepis known, the overall rate of reaction can be written.This overall rate of reaction can then be integrated withrespect to space, or time, to determine the throughputof the reactor.

5.2. Optimization of the Geometry for the De-sired Design Objectives. It is clear from the discus-sion in sections 3 and 4 that the performance of themultiple-impeller system is superior as compared to asingle gas-inducing impeller. This is mainly because,in such a system, the upper gas-inducing impeller canbe kept close to the liquid surface (about 100-200 mmbelow the liquid surface, irrespective of the scale ofoperation) for achieving high rates of gas induction. Forperforming other duties like gas dispersion (distributionof the induced gas throughout the equipment), solidsuspension, heat transfer, mixing, and so forth, thesecond impeller can used. The design of the lowerimpeller can be optimized for different duties such ashigh fractional gas holdup, good solid suspension ability,

Figure 19. (A) Various steps involved in gas-liquid-solid reaction.

Table 9. Effect of Various Parameters on the Overall Rate of Reaction

effect of increase in the variable on the overall rate of reaction

rate-controlling step [A*] [AO] [AS] [BO] [BS] εS dP N

gas-liquid mass transfer ∝[A*] ∝{[A*] - [AO]} [AS] ) [AO] no effect no effect no effect no effect increasessolid-liquid mass transfer [A*] ) [AO] ∝[AO] ∝{[AO] - [AS]} no effect no effect ∝εS ∝{1/dP} increasespore diffusion [A*] ) [AS] [AO] ) [AS] ∝[AS] no effect no effect no effect ∝{1/dP} no effectchemical reaction [A*] ) [AS] [AO] ) [AS] ∝[AS]m [BO] ) [BS] ∝[BS]n ∝εS no effect no effect


and so forth (Saravanan and Joshi, 1995, 1996) andSaravanan et al. (1996, 1997). This activity has clearlyshown that the optimum design of lower impellerchanges with the design objective. For example, toachieve high fractional gas holdup, it is desirable to usean upflow impeller at the bottom, whereas to achievegood solid suspension, a downflow impeller at thebottom is desirable. It is recommended that such amultiple-impeller system be used for commercial scaleequipment. The recommended lower impeller designsfor different design objectives such as gas dispersion,solid suspension, heat transfer, and so forth along withthe reasons are summarized in Table 10.

The procedure for process design will now be il-lustrated with the help of a case study. It is assumedthat the reaction is characteristic of hydrogenation of atypical organic compound. The gas- and liquid-phasereactants are denoted by A and B, respectively. For thepurpose of illustration it will be assumed that theoverall reaction is mass-transfer-controlled. It is desir-able to carry out such a reaction in a gas-inducingcontactor along with a sparger (Patwardhan and Joshi,1997). The lower impeller will be considered as a PBTU(pitched blade upflow turbine) and a large-size ringsparger will be assumed. Let VGi be the superficialvelocity of the sparged gas. A part of this sparged gasreacts in the vessel and the remainder escapes into theheadspace. Simultaneously, the gas is recycled backinto the liquid with the help of a gas-inducing impeller.A part of the entrained/induced gas also reacts, and theremainder escapes into the headspace. If overall mate-rial balance is taken for the entire vessel, then themaximum permissible value of the superficial gasvelocity (VGi) should be such that the rate of gassparging equals the rate of reaction of the gas in thevessel. This ensures that the headspace pressure willneither rise nor fall with time. Alternatively, if theoverall material balance is written for the headspace,then it is clear that the net rate of escape of theunreacted gas into the headspace (QUG) must be equalto the rate of gas induction.

Figure 20A shows the comparison of fractional gasholdup under sparging conditions, with and without theuse of a gas-inducing impeller. In the absence of a gas-inducing impeller such a system behaves like a conven-tional mechanically agitated contactor (MAC). Thecomparison is made in terms of gas holdup as a functionof power consumption per unit volume for differentsuperficial velocities of sparged gas (VGi ) 0, 6, 18, and29 mm/s). From the figure it can be seen that thefractional gas holdup in the presence of a gas-inducingimpeller is substantially higher as compared to that ofa MAC. Similarly VGi ) 0 corresponds to the case ofgas induction alone (no sparging). It can also be seenthat as the rate of sparging increases, the gas holdup

increases. The following stepwise procedure is recom-mended for design:

(a) The stoichiometry of the reaction under consider-ation is known. Further, the solubility of gas and thephysicochemical properties of the gas and the liquidphases were assumed to be available.

Table 10. Recommendations for Different Design Objectives

design objective recommended design of lower impeller reasons

dispersion/mass transfer upflow impeller at the bottom along with alarge ring sparger

Upflow impeller helps in gas dispersion by creating afavorable flow pattern. Sparger introduces additionalgas in the system which increases the throughput.

suspension downflow impeller at the bottom This results in generating large liquid velocities near thevessel bottom. This aids the solid suspension process.Better solid suspension can be achieved at samepower consumption.

heat transfer upflow impeller at the bottom, cooling coils,jacket depending on the need

The upflow impeller at the bottom generates gross (top tobottom) liquid circulation, which helps in keeping thevessel contents well-mixed and ensures good valuesof the heat-transfer coefficient.

Figure 20. Comparison of MAC with and without a gas-inducingimpeller (open symbols, without a gas-inducing impeller; filledsymbols, in the presence of a gas-inducing impeller). For thecalculations the following correlations were used. NCG in theabsence of sparging: NCG ) [1/2πR]x(2gS)/φ. change in NCG dueto sparging: [(∆NCG)2π2D2φ]/[2gS] ) R1(C3/D)R2VG

R3(S/T)R4. gas-induction rate in the absence of sparging: QG ) λ*NR2(1 - [2gS]/[φV2] + R*NR3(1 - A([2gS]/[φV2])3/2). change in the gas-inductionrate due to sparging: 1 - QGS/QG ) â1Flâ2(C3/D)â3. fractional gasholdup: εG ) a(D/T)b(ReFrFl)c. power consumption: PG/PO ) 0.1-([NV1]/QG)1/4([N2D4]/[WVL

2/3g])-1/5, PO ) NPFLN3D5. (A) the rate ofgas induction as a function of the power consumption with thesuperficial gas velocity as a parameter: O, 0 mm/s; ), 6 mm/s; 4,18 mm/s; 0, 29 mm/s. (B) Mass-transfer controlled. (C) Enhance-ment in the rate of mass transfer due to chemical reaction, xM )5. (D) Enhancement in the rate of mass transfer due to chemicalreaction, xM ) 50. For parts B-D of the reaction it wasassumed that the production rate was 50 ton/day of compound Rby the following reaction: 3A(g) + B(l) f R(l). The solubility of A ina liquid was assumed to be equal to [A*] ) 0.1 kmol/m3. It wasassumed that the reaction takes place at 150 °C and at 10 atm ofpressure. The estimation of the performance was carried out withthe correlations given above. In addition, the following correlationswere used. Mean bubble diameter: dB ) 4.15([(PG/VL)0.4FL

0.2]/σ0.6])-1εG

0.5 + 0.09. Interfacial area per unit volume: a ) 6εG/dB.The volumetric mass-transfer coefficient as k1a ) 0.0002a.


(b) The geometry of the system is first chosen (e.g.,the tank diameter, impeller design, D/T ratio, clearance,submergence, sparger size, impeller speed, etc.). Theseare chosen on the basis of the rate-controlling step andrecommendations in Table 10.

(c) A particular superficial gas velocity is chosen VGi.(d) For this value of superficial gas velocity, the gas-

induction rate (QG), fractional gas holdup (εG), andpower consumption (PG) are calculated both in thepresence of a gas-inducing impeller and in the absenceof a gas-inducing impeller. For estimation of thesehydrodynamic characteristics, the recommended cor-relations are used.

(e) On the basis of these hydrodynamic characteristicsthe volumetric mass-transfer coefficient (kLa) is calcu-lated. Alternatively, the value of kLa could also bemeasured in a small-scale experimental reactor (at leastlarger than 0.5 m in diameter) under the actual condi-tions prevailing (temperature, pressure, physicochem-ical properties, etc.)

(f) From the value of kLa the rate at which the spargedand the induced gas react is estimated.

(g) The net rate at which the sparged gas accumulates(QUG) into the headspace is calculated as the differencebetween the rate of sparging and the rate of reaction ofthe sparged gas.

(h) If the QG is lower than QUG, pressure builds up inthe headspace and VGi is unacceptable, or if QG is higherthan QUG, headspace pressure decreases and again VGiis unacceptable. Thus, a new value of VGi is chosen andthe procedure is repeated from step (c) onward until QUG) QG. Thus, this procedure yields a value of acceptableVGi for a given geometry of the system (step b).

(i) The whole procedure is repeated by choosingdifferent operating conditions such as the impeller speedso that different values of VGi - PG are generated.

(j) The entire procedure can be repeated if there isan enhancement in the rate of mass transfer due to achemical reaction. The results of the above procedureare given in Figure 20, parts B-D.

Figure 20B shows that, for a particular value of powerconsumption per unit volume, a higher value of VGi ispermissible when a gas-inducing impeller is used alongwith a sparger. For example, for a power consumptionof 2 kW/m3 the permissible VGi is about 23 mm/s whena gas-inducing impeller is used as compared to about 6mm/s when the gas-inducing impeller is not present. Ahigher permissible VGi in the existing equipment impliesthat higher productivity can be realized when a gas-inducing impeller is used along with a sparger. If theproductivity is to be kept the same, then a higherpermissible VGi implies that a smaller size of the reactorcan be used. If the reaction being carried out involveshighly corrosive chemicals (hydrogenation of chlorocompounds), then an exotic material of construction hasto be used (hastalloy, titanium, tantalum, etc.). Areduction in size of such a reactor implies a considerablesavings in the equipment cost. Alternatively, if thepermissible VGi is to be kept the same (correspondingto the desired rate of production), then a much smallerpower consumption is required when the gas-inducingimpeller is employed. That is, for a VGi of 10 mm/s, 5kW/m3 are required when a gas-inducing impeller is notused as compared to about 0.5 kW/m3 when a gas-inducing impeller is used. A lower power consumptionresults in a significant reduction in operating costs. Thisis particularly important when the cost of electricity is

very high. A comparison of Figure 20, parts B-D,reveal that the difference in VGi, or power consumption,increases as the enhancement factor increases.

From the above discussion it is clear that a given rateof production can be achieved by different combinationsof the reactor size and the level of power consumption.The selection of the optimum reactor size is based onthe annualized cost of the reactor. The annualized costconsists of the cost of capital (depreciation and intereston fixed cost) and the operating cost. The fixed costconsists of mainly the equipment cost, that is, thematerial cost plus fabrication cost; the operating costconsists mainly of electricity (power) cost. For thepurpose of this illustration, five different materials ofconstruction were selected having costs 0.3, 1.0, 3.0,10.0, 30.0 $/kg. This range of cost covers practically allthe materials commonly used in industry, such as mildsteel, stainless steel, glass-lined, hastalloy, titanium-lined vessels, and so forth. Two levels of (depreciation+ interest) have been examined: 20% and 50% per year.Three different values of the cost of electricity have beentaken: 0.035, 0.10, and 0.30 $/kW‚h.

For a particular reactor volume and the operatingpressure, the thickness of the shell and dished endswere calculated. Knowing the density of the material,the weight of the shell was estimated. An extra amount,50%, was added for the nozzles, supports, shaft, impel-lers, agitator drive, and so forth. In addition, thefabrication cost was considered 60% of the material cost.The operating cost was calculated as the product ofpower consumption and the electricity cost. The an-nualized costs is the sum of the cost of capital and theoperating cost. The selection of the optimum reactorsize can be made on the basis of the annualized cost. Itcan be appreciated that the numbers selected, thoughprovisional, do not matter as far as the objective of theexercise is concerned. Because, in reality, any combina-tion of material and fabrication cost and the rate ofdepreciation and interest will most probably fall in therange considered here. For convenience, Figure 21,parts A-D, indicate the total cost of fabricated equip-ment per kilogram per year.

Figure 21A shows the annualized cost with theelectricity cost of 0.035 $/kW‚h and the cost of capitalat 20% per year. Several conclusions can be drawn fromthis figure. For low-cost materials such as mild steel,the annualized cost decreases as the reactor volume isincreased. This is because the fixed cost is low and theoperating cost contributes significantly to the annual-ized cost. Thus, choosing a larger reactor volume andconsequently keeping a lower level of power consump-tion reduces the annualized cost. For medium costmaterials (10 $/kg), there is a certain reactor size atwhich the annualized cost is minimum. If the reactorsize is larger than this value, then the fixed costincreases more than the decrease in power consumption.Whereas if the reactor volume is lower than theoptimum value, then the operating cost increases morethan the decrease in the fixed cost. This optimumreactor size is shifted to lower volumes as the cost ofthe material increases. That is, if the material cost is10 $/kg, then the optimum reactor size is about 4 m3,and if the material cost is 30 $/kg, then the optimumreactor size is about 2 m3. Thus, for any value of thematerial cost and the electricity cost, the annualized costcan be calculated and the optimum size of the reactorcan be found.


A comparison of Figure 21, parts A, B, and C(electricity cost 0.035, 0.10, and 0.30 $/kW‚h), revealsthat the optimum reactor size shifts toward highervolumes. Thus, as the cost of electricity rises, it ispreferable to use large reactors and decrease the powerconsumption to reduce the operating costs. A compari-son of Figures 21, parts A and D, shows that as the costof capital increases (from 20% to 50%), the optimumreactor size shifts to lower values. This shows theadvantage of a smaller reactor size to keep the fixedcost low, even though the power consumption (operatingcosts) increases.

5.3. Design of Impellers for Froth Flotation.5.3.1. Determination of the Rate-Controlling Step.As with the design of gas-liquid-solid reactors, thedesign of flotation cells involves the determination ofthe rate-controlling step. For this purpose, it is neces-sary to carry out laboratory experiments. The kineticsof flotation are usually represented with a power lawmodel (dC/dt ) k1Cn). The laboratory experimentsshould be carried out to determine the values of k1 andn. The schematic diagram of a experimental setup thatcan be conveniently used to carry out these experimentsis shown in Figure 22. These experiments should becarried out on at least a 0.5-m diameter scale so thatthe results can be scaled up with a fair degree ofconfidence. The gas-inducing impeller should be locatedsufficiently away from the layer of settled solids, so thatit does not play any role in the solid suspension process.That is, the gas-inducing impeller alone should beincapable of suspending the solid particles. The exactlocation of the gas-inducing impeller may vary with the

particle size, loading, and so forth and can be deter-mined from some preliminary runs. Since the submer-gence is high, the rate of gas induction is low and anarrangement should be provided to supply additionalgas at a known and controlled flow rate to the gas-inducing impeller. A second impeller should be usednear the settled layer of solids (downflow turbine type).It is desirable to place this impeller on a separate shaft.The advantage of this is that its speed can be controlledindependent of the speed of the gas-inducing impeller.The speed of this lower impeller can be changed to getsolid suspension to any desired extent. This allows acontrol over the gas dispersion and solid suspensionindependent of each other. In principle, the systemdescribed is similar to that used by Matsumura et al.(1982a).

In the first set of experiments, the effect of interfacialarea, bubble size, and bubble-size distribution on theflotation rate can be investigated. For this purpose, theair flow rate, speed of the gas-inducing impeller, andthe geometry of the stator can be varied. In all theseexperiments, it is necessary to change the speed of thelower impeller to keep the extent of solid suspension atthe same level. In each experiment, the rate of flotation,the interfacial area, mean bubble size, and bubble-sizedistribution should be measured. The effect of theseparameters on k1 and n can then be quantified.

In the second set of experiments, the effect of solidsuspension on the flotation rate can be investigated. Toachieve this, the lower impeller speed and diameter canbe varied. It is well-known that as the impeller speedincreases, the solids slowly start getting suspended andthe interface between the suspended solids and the clearliquid moves upward. The impeller speed can beadjusted to get any desired value of LS (Figure 22).When the lower impeller speed is changed, it may inturn affect the dispersion of gas. This effect on gasdispersion can be minimized by adjusting the gas flowrate and the speed of the gas-inducing impeller. Thisset of experiments can establish the relation betweenthe flotation rate (in terms of k1 and n) and the extentof solid suspension (LS).

A third set of experiments needs to be carried out toinvestigate the effects of additives and their concentra-tion on the flotation rate. These three sets of experi-ments help to identify the rate-controlling step. Thiscompletes the first step in the overall process designactivity.

5.3.2. Optimization of the Geometry for theDesired Design Objectives. The next step in theprocess design involves choosing a system geometry andoperating conditions. Since the depth of the frothseparation zone is an important parameter, it is desir-able to keep constant submergence as the scale ofoperation increases (Flint (1973), Harris (1986)). Also,for solid suspension purposes, the impeller clearancefrom the bottom should be kept low. This limits theoverall liquid depth in the flotation cell. This meansthat as the volume increases, the characteristic lengthof the flotation cell increases like the square root of thevolume (LC ∝ VL

0.5). This criterion has been reportedin much of the literature on flotation. For very largecapacities, the characteristic length (LC) may becomevery large. In that case, the whole operation may besplit up into a battery of small cells operated in series/parallel mode.

Figure 21. Effect of material cost on the annualized cost (reactionconditions and correlations used are the same as those in Figure20). (A) Cost of capital ) 20%; electricity cost ) 0.035 $/kW‚h: ),0.144 $/kg‚yr; 4, 0.48 $/kg‚yr; 0, 1.44 $/kg‚yr; O, 4.8 $/kg‚yr; 3,14.4 $/kg‚yr. (B) Cost of capital ) 20%; electricity cost ) 0.10 $/kW‚h: ), 0.144 $/kg‚yr; 4, 0.48 $/kg‚yr; 0, 1.44 $/kg‚yr; O, 4.8 $/kg‚yr; 3, 14.4 $/kg‚yr. (C) Cost of capital ) 20%; electricity cost )0.30 $/kW‚h: ), 0.144 $/kg‚yr; 4, 0.48 $/kg‚yr; 0, 1.44 $/kg‚yr; O,4.8 $/kg‚yr; 3, 14.4 $/kg‚yr. (D) Cost of capital ) 50%; electricitycost ) 0.035 $/kW‚h: ), 0.36 $/kg‚yr; 4, 1.2 $/kg‚yr; 0, 3.6 $/kg‚yr; O, 12.0 $/kg‚yr; 3, 36.0 $/kg‚yr.


If the flotation operation is dominated by the disper-sion of gas bubbles, then a high shear gas-inducingimpeller should be used. This can be a stator-rotorassembly (Denver, Wemco designs, or the design re-ported by Saravanan et al. (1994)) having a smallclearance between them. This will enable the genera-tion of small bubbles of uniform size. If the suspensionof solids and contact between gas and solids is impor-tant, then it is recommended to use a second impellerbelow the gas-inducing impeller which enables efficientsolid suspension.

6. Conclusions

(1) The various designs of gas-inducing impellers andflotation cells reported in the literature have beenclassified into three types, depending on the flowcharacteristics in the impeller zone.

(2) The critical impeller speed for gas induction, NCG,is reached when the velocity head generated by theimpeller is sufficient to overcome the hydrostatic headabove the impeller. Impeller submergence is thereforea major parameter that influences the overall perfor-mance.

(3) In a type 11 system, the gas-induction rate can beestimated by considering the pressure differential gen-erated by the impeller and various resistances to theflow of gas through the impeller. For type 22 systems,Saravanan et al. (1994) and Saravanan and Joshi (1995)have presented a model based on the processes of bubbleentrapment and bubble carriage. The multiple-impellersystem reported by Saravanan and Joshi (1995) givesa much higher gas-induction rate as compared to otherdesigns reported in the literature.

(4) The gas holdup, mass-transfer, mixing, and heat-transfer characteristics of gas-inducing impellers havenot been studied exhaustively. The multiple-impellersystem reported by Saravanan et al. (1996, 1997) isrecommended because it allows flexibility of design ofthe lower impeller for achieving a certain design objec-tive, and at the same time maintains a gas-inductionrate at a high value.

(5) A process design algorithm has been presented forthe design of gas-inducing impellers. Guidelines have

also been given about the selection of geometry fordifferent design objectives such as dispersion, masstransfer, heat transfer, solid suspension, mixing, andso forth. Recommendations have been made regardingthe correlations to be used for the estimation of theperformance of gas-inducing impellers. The processdesign algorithm has been illustrated for a case study.It has been shown that the use of a gas-inducingimpeller in a conventional stirred vessel can lead to asubstantial increase in the productivity. The optimumvessel size may not correspond to maintaining constantpower consumption, equal tip speed, and so forth onscale-up.

7. Suggestions for Future Work

(1) Since the local pressure plays an important role,further work is needed to establish the relation betweenimpeller design and the local pressure. Such an exercisewill help in the rational design and optimization of alltypes of gas-inducing impellers. Likewise, the relation-ship between the local pressure and the rate of gasinduction needs to be established for type 12 and 22systems.

(2) It is highly recommended that the future experi-mental investigations be carried out using larger sizedvessels (T > 0.5 m) and over a larger range of operatingconditions. Systematic investigations have to be carriedout to quantify the effects of impeller design and theoperating conditions on the performance characteristicssuch as mixing, mass transfer, interfacial area, heattransfer, and so forth. The effects of physical propertieson the hydrodynamic characteristics have been inves-tigated only over a limited range by a few workers.Further work is required in this area.

(3) To be able to design these reactors on fundamentalprinciples, the relation between the impeller-vesselgeometry, the flow and pressure field generated, andthe design objective such as homogenization, powerconsumption, gas dispersion, mass-transfer coefficient,solid suspension ability, and so forth has to be estab-lished. Recent developments in experimental tech-niques such as laser Doppler velocimetry (LDV) and

Figure 22. Schematic diagram of the setup in which experiments should be carried out to determine the rate-controlling step.


computational tools such as computational fluid dynam-ics (CFD) should be used to address these issue.

Acknowledgment

The authors would like to acknowledge the experi-mental work carried out by K. Saravanan and V. D.Mundale. This work has established optimum designsof impellers for achieving different design objectives. Onthe basis of this work guidelines have been given forthe selection of impeller geometries.

Nomenclature

A ) constant in eq 41[A*] ) solubility of the gas in a liquid, kmol/m3

[AO] ) concentration of the solute gas in a bulk liquid, kmol/m3

[AS] ) concentration of the solute gas at the solid-liquidinterface, kmol/m3

Ao ) orifice area, m2

a ) gas-liquid interfacial area, m2/m3

aP ) solid-liquid interfacial area, m2/m3

[BO] ) concentration of the reactant in the bulk liquidphase, kmol/m3

[BS] ) concentration of the reactant at the solid-liquidinterface, kmol/m3

CO ) orifice discharge coefficientC1 ) impeller clearance from bottom, mC3 ) interimpeller clearance, mC ) constant in eq 9CD ) drag coefficientCDG ) drag coefficient in the zone 0 < r < YCDO ) drag coefficient in the zone Y < r < RCD* ) scaled drag coefficientCDO* ) scaled drag coefficientCDY* ) scaled drag coefficientCH ) impeller head coefficient in eq 28CP(θ) ) pressure coefficientc, c1, c2 ) constants in eq 27D ) impeller diameter, mDT ) dist turbineDO ) diffusivity of solute gas, m2/sd ) diameter of pipe, mdB ) mean bubble size in gas-liquid dispersion, mdP ) mean particle size, mEJLR ) ejector jet loop reactorEu ) gas-phase Euler numberF ) constant in eq 51, 2gS/φV2

fm ) conformity or slip factorFl ) flow numberFr ) Froude number based on submergence, N2D2/gSFrC ) Froude number at critical speed, NCG2D2/gSG ) molar absorption rate, kmol/sg ) gravitational acceleration, m/s2

ge ) molar flow rate of entrained gas escaping back intoheadspace, kmol/s

gi ) molar flow rate of surface-entrained gas, kmol/sGIC ) gas-inducing contactorH ) total liquid height, mHO ) solubility coefficient of a solute gas, kmol/MPa‚m3

hL ) liquid head outside the orifice, mhS ) liquid head above the orifice in absence of gas flow,

mJO ) specific absorption rate of solute gas, kmol/m3‚sK ) slip between impeller and fluidK1 ) constant in eq 18k ) head reduction coefficient, eq 28k1, k2 ) first- and second-order rate constants, 1/s and m3/

s‚kmol, respectivelyk2,0 ) second-order rate constant, m3/s‚kmol

kg ) constant in eq 39kmn ) rate constant for the reaction, m3(m+n-1)/kmol(m+n-1)‚

skL ) liquid-side mass-transfer coefficient, m/sLC ) characteristic length of the flotation cell, mLS ) characteristic length of the layer of suspended solids,

mm ) order of reaction with respect to the dissolved gas

concentrationMAC ) mechanically agitated contactorn ) order of reaction with respect to the concentration of

the reactant in the liquid phaseN ) impeller rotational speed, rpsNCG ) critical impeller speed for gas induction, rpsNCS ) critical impeller speed for solid Suspension, rpsNP ) power numberNQG ) gas flow number∆NCG ) NCG with sparging - NCG without sparging, rpsnP ) number of pipesP ) pressure, N/m2

P′ ) dimensionless pressurePG ) power drawn by gassed impeller, WPH ) holding tank pressure, N/m2

PHS ) headspace pressure, N/m2

PL ) power drawn by impeller in liquid, WPO ) headspace pressure, N/m2

PS ) stagnation pressure, N/m2

P(θ) ) pressure at any angular location, N/m2

∆PKE ) frictional pressure drop, N/m2

∆PO ) orifice pressure drop, N/m2

∆PP ) pressure drop associated with the kinetic energy ofthe liquid, N/m2

∆PT ) total pressure drop, N/m2

∆Pσ ) pressure drop required to overcome surface tensionforces, N/m2

Pφ ) pressure of the gas in the dispersed phase, N/m2

PBTD ) pitched blade turbine downflowPBTU ) pitched blade turbine upflowPJR ) plunging jet reactorPU ) propeller upflowQC ) rate of gas bubble carriage, m3/sQE ) rate of gas bubble entrapment, m3/sQG ) gas-induction rate in absence of sparging, m3/sQGS ) gas-induction rate in the presence of sparging, m3/sQSA ) rate of surface aeration, m3/sQUG ) rate of accumulation of unreacted gas in headspace,

m3/sR ) impeller radius, mRG ) universal gas constantr ) radial coordinate, mrB ) radius of bubble, mRAa ) volumetric rate of reaction, kmol/m3‚sRe ) Reynolds numberS ) submergence of impeller in clear liquid, mSA ) surface aeratorsSBT ) straight blade turbineSh ) Sherwood numberT ) tank diameter, mTH ) temperature of gas in the holding tank, KTHS ) temperature of gas in the headspace, KTφ ) temperature of gas in the dispersed phase, KU ) liquid velocity, m/sV ) impeller tip velocity, m/sVH ) volume of gas in the holding tank, m3

VHS ) volume of gas in the headspace, m3

VCG ) liquid velocity at NCG, m/sVG ) superficial gas velocity, m/sVGi ) superficial velocity of the sparged gas, m/sVi ) superficial velocity of the induced gas, m/sVL ) volume of liquid in dispersion, m3

Vφ ) volume of gas in the dispersed phase, m3


W ) blade width, mX ) area of intersection of the vortex with the impeller,

m2

Y ) radial distance form the axis, mz ) axial coordinatezGO, zφO ) mole fraction of solute gas in headspace and

dispersed gas phase

Greek Letters

R ) constantsR* ) impeller pumping number, eq 41â1, â2, â3 ) constants in eq 43εG ) fractional gas holdupεS ) fractional solid holdupη ) impeller pumping numberλ* ) gas-induction modulus, eq 40, mµ ) viscosity of liquid, Pa‚sµW ) viscosity of water, Pa‚sêO ) fraction of the absorbed oxygenFG ) gas density, kg/m3

FL ) liquid density, kg/m3

σ ) surface tension, N/mτ ) torque, N‚mφ ) vortexing constantω ) angular velocity, s-1

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Received for review July 14, 1997Revised manuscript received September 15, 1998

Accepted September 16, 1998

IE970504E


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