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upper part of the vessel. In the secondcase of off-bottom suspension, noparticle comes to rest for longer thanone second on the bottom of the ves-sel. This criterion, often used for large-scale, mineral-processing applications,defines the lowest mixing power atwhich the entire surface area of theparticles is exposed to the liquid phasefor chemical reaction or mass transfer.Zwietering [ 5] produced the followingwell-known correlation for minimumshaft speeds, n js , at which off-bottomsuspension occurs:

n s v g

d c D jss l

l p w=

( )

0 1

0 45

0 2 0 13 0 85.

.

. . .

(13)The third case is visually uniformsuspension, which is defined as hav-ing no large clear zones. Settling of coarse particles may still occur for sol-ids with a wide range of particle sizes.

Occasionally, for very demandingduties such as continuous-overflow op-eration, or manufacture of dispersionsas end products, uniform suspensionis required. In this case, particle con-centration and size distribution areuniform throughout the vessel. Thisis very difficult to achieve unless the

particle settling velocity is very low.

Design fundamentalsIn addition to agitator parameters andthe vessel geometry, the properties of both the liquid and the solid particlesinfluence the fluid-particle hydrody-namics and, thus, the suspension. Theimportant physical properties for agi-tator design are: the liquid density, thedensity difference between solids andliquid, the liquid viscosity, the averageparticle size and the volumetric con-centration of the solids.

A single particles free-settling veloc-ity, vs, is calculated by methods givenin the relevant literature. The hinder-ing effect on the settling process dueto the presence of several particles isquantified by the following relation,where the exponent m is a functionof the particle Reynolds number, and

varies between 2.33 and 4.65:

v v csh s vm= ( )1 (14)

where vsh is the hindered settling ve-locity, vs is the free-settling velocityand cv is the volume fraction of solids.

If it is assumed that all solid particles

in the l iquid are distributed uniformly,and all simultaneously begin to settleunder the effect of gravity, they re-lease a settling power, which can bequantified by the relation:

(15) P v c g V settle sh v=

where is the difference in densitybetween solid and liquid. In order tomaintain a defined degree of unifor-mity in the suspension, the agitatormust provide a power input to theliquid that counteracts this settlingpower. The agitator power alwaysamounts to a multiple of the settlingpower.

When one is using the above Equa-tions (14) and (15), the choice of par-ticle size that is used to calculate thefree-settling velocity, vs, is very impor-tant. In powders or slurries, the indi-

vidual particles vary in size and shape.Choosing the largest particle size canresult in a much higher agitator powerthan is required. From experience, re-liable results are obtained with a de-sign particle size that corresponds to a

value where between 80 and 90% pass

through the mesh size.

Scale upScale up of suspension duties can be

very complex. Various scale up criteriahave been proposed based on the typeof suspension needed, as discussedearlier. Specific process or product re-quirements can impose additional cri-teria for consideration. Some commoncomplications include these: Solids with extremely wide particle

size distributions the fine par-ticles affect the suspension of thelarge particles

Very high-solids concentrations particle interactions affect the ap-parent rheology

Presence of small amounts of ex-tremely large particles impos-sible to suspend but must be movedaround on the base of the vessel

The presence of significant quanti-ties of extremely small particles these essentially behave as partof the fluid

To accommodate these considerations,solid-suspension duties are generally

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50 CHEMICAL ENGINEERIN G WWW.CHE.COM APRIL 2006

FIGURE 7. The degree ofsuspensiondesired for agiven applica-tion dependson the objec-tive. Here,three levels ofsuspension areshown, eachrequiring morepower inputthan the onebefore

FIGURE 8. Todescribe thecomplex natureof suspensiontasks, suspen-sion dutiesare classifiedinto four broadgroups


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classified into four broad categories onthe basis of hindered-settling velocity(see Figure 8).

Type I tasks are simple suspend-ing duties that are readily predictedbecause the liquid flows around theparticles in simple, laminar flow. TypeII are demanding suspension taskswhere the fluid flow is more complexbut predictable from empirical corre-lations this category covers the ma-

jority of industrial applications. TypeIII are difficult or "heavy" suspension

tasks, which probably involving largeor heavy particles. In this category,scale-up is usually based on pilot-scale tests. For type IV tasks, uniformsuspension is no longer attainable, asthey require very high liquid velocitiesthat cannot be achieved economically.

In general, for solids suspension, theagitator power requirement is scaledup as a function of tank diameter ac-cording to the following equation:

(16) PV

D X

where X can vary from 0 to -1 depend-ing on the type of suspension duty. Forexample, if particles with a high hin-dered-settling velocity must be kept in

visually uniform suspension (Type IIIin Fig. 8), a criterion close to constantspecific power input P/V must be used( X = 0). For solids with low hindered-settling velocities, a criterion closer toconstant tip speed ( X = -1) can be used(Type I in Fig. 8). These examples il-lustrate how the specific power inputsrequired to achieve suspension can

vary hugely on an industrial scale.

To achieve homogeneous suspensionof true suspensions, high-efficiency,axial-pumping impellers are gener-ally used because of the lower powerinputs required.

Special considerationsSome considerations for specific sus-pension applications are as follows: In many solids-suspension tasks, es-

pecially in the minerals-processingindustries, abrasion can be a signifi-cant issue. In this case, lower veloci-ties may be required to limit abra-sion. An increased impeller size cancompensate for the lower velocities.

During power failures, sediments

can quickly build up in suspensiontanks. Impellers are often designedto withstand attempted restarts,while submerged in a densely settledslurry. In some instances, restart inslurry becomes the key design cri-terion.

Solids suspension and gas dispersioncommonly occur simultaneously inthe chemical- and minerals-process-ing industries. The presence of gasaffects the performance of the impel-ler and the ability of the fluid to sus-pend solids. Likewise, the presence

of solids affects gas dispersion. Bothmust be taken under consideration. Additional factors that can have asevere impact on the agitator designinclude: the shape of the base of the

vessel (dished, conical or flat); the lo-cation of the draw-off point; and theaspect ratio ( H/T ) of the tank. Con-tinuous processes are most sensitiveto such factors.

LIQUID-LIQUIDDISPERSIONSMany industrial processes require thedispersion of one liquid into another,immiscible liquid. Unstable disper-sions are created in processes such assolvent extraction (to provide a largesurface area for mass transfer), and indispersion polymerizations (to createthe required size distribution of poly-mer particles or provide a heat sink).

In the case of solvent extraction,the dispersion must be fine enough toallow rapid mass transfer and keepthe size of the extractor down, while atthe same time, the dispersion shouldbe coarse enough to enable rapid

separation of the phases afterwards.Mixer-settler systems can generallyuse finer dispersions than solvent-ex-traction columns. The former systemsare generally better suited to slowerextractions, and the latter to fast ex-tractions. Typical industrial applica-tions of solvent extraction are refiningof metals from acid leach liquor andpurification of pharmaceutical prod-ucts.

Surfactants are often used to aidformation of the correct dispersionsize and to hinder recoalescence, inboth temporary and stable emulsions.The interaction of the various factorsaffecting dispersion processes is very

complex and nearly always necessi-tates mixing tests. The main factorsaffecting dispersion include these:1. Physical properties of the liquids

(especially interfacial tension)2. Effects due to mutual solubility or

reaction3. The presence of surfactants, and4. The turbulence and shear created

by the agitator.Most liquid-liquid dispersions areformed in the turbulent regime anddroplet sizes of between 5 and 500 mcan be achieved. Typically, for a spe-

cific power input of 1 W/kg, dropletsizes between 100 and 150 m can beexpected.Droplets break when shear stressesinduced in the droplets by turbulencecause sufficient deformation to over-come the stabilizing effect of surfacetension. Minimum droplet size is gov-erned by the size of the micro-vorti-ces, and is generally between 3 and5 times the size of the micro-vortices.When finer dispersions are required,rotor-stator devices that produce azone of very high energy dissipationcan be used. Stabilizers can be addedto ensure that fine droplets producedin this high-energy zone do not re-coalesce in the bulk. For even fineremulsions (from 5 m to 50 nanome-ters), high-pressure homogenizerswith local energy dissipations of over500 W/kg are used.

Scale upDue to the complexity of the interact-ing factors that affect droplet forma-tion, actual performance is usuallymeasured in pilot trials. Because of

CHEMICAL ENGINEERIN G WWW.CHE.COM APRIL 2006 51

FIGURE 9. High viscosities can hin-der heat transfer. Wall scrapers addedto an agitator, such as this optimizedribbon, can help increase heat transfersubstantially


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the sensitivity of surface propertiesto minor levels of contaminants, pilottrials should use actual chemicalsfrom the process plant rather thanlaboratory-quality reagents. Scale

up to production should follow rulesthat are based on the mechanism(bulk or local turbulence) which wasused to achieve the required perfor-mance.

HEAT TRANSFERStirred vessels are rarely used purelyfor heat transfer because equipmentwith much more-efficient heat ex-change is available. Heat transfer is,however, a critical unit operation thatstirred vessels must be capable of per-forming. A typical batch process, forexample, could comprise the heatingof the bulk to reaction temperature,

blending and cooling during the reac-tion to remove the reaction heat, fur-ther heating to evaporate a solvent,and finally cooling down to near ambi-ent temperature before the product is

discharged.Heat transfer performance is gov-erned by: The flowrate and temperature of the

utilities, and heating/cooling me-dium

The heat-transfer coefficients on theproduct side and the utility side

The type and contact area of heatexchange surfaces

Some of these factors may need to bemodified in order to achieve requiredheat fluxes. In many reactors, the ves-sel, itself, provides insufficient surfacearea and it is necessary to install ad-ditional heat-transfer surfaces.

DesignHeat-transfer coefficients in jackets,coils and plate heat exchangers can bepredicted from well established corre-lations [ 2]. Since the range of utility

fluids encountered is quite small andtheir physical and thermodynamicproperties are generally well docu-mented, the accuracy of predicted filmcoefficients is often very good.

On the process side, however, pre-diction of the heat transfer coefficientis based on a general equation of theform: Nu h T

kC P

P W

= = Re Pr ( ) / / .2 3 1 3 0 14 (17)

where the constant C, which dependson the impeller type and size, canbe found in the literature or derivedby measurements. The viscosity

FIGURE 10. Modern-day impeller systems offer a great range of choice to help meet the mixing challenges facing the CPI

References1. Mersmann, K., Chemie Ingenieur Technik ,

Vol. 23, pp. 953-956, 1975.

2. EKATO (Ed), Handbook of Mixing Tech-nology, EKATO Rhr- und Mischtechnik,Schopfheim, Germany, 2000.

3. Kolmogoro v, A. N., Die lokale Struktur derTurbulenz in einer inkompressiblen zhenFlssigkeit bei sehr groen ReynoldsschenZahlen. Goering, H. (Ed) Sammelbandzur statistischen Theorie der Turbulenz,

Akademie-Verlag, Berlin, Germany, 1958.4. Metzner A.B. and Otto R.E., Agitation of non-

Newtonian fluids, AIChE J, Vol . 3, No. 1, pp.3-10, 1957.

5. Zwieter ing T.N., Chemical Engineering Sci- ence , Vol. 8, pp. 244-253, 1958.

6. DeLaplace, G., others, Numerical simulationof flow of Newtonian fluids in an agitated

vessel with a non standard helical ribbon im-peller, Proceedings 10th European MixingConference, Elsevier 2000.

7. Zlokarnik, M., Rhrtechnik: Theorie undPraxis, Springer-Verlag, Berlin, Germany,1999.

8. Autorenkollektiv, Mischen und Rhren,

Grundlagen und moderne Verfahren fr diePraxis, VDI-GVC, 1998

9. Perry, R.H. and Green, D.W., Perrys ChemicalEngineers Handbook, 7th ed., McGraw-Hill,1997.

10. Paul E.L. and others (Eds.). Handbook of In-dustrial Mixing: Science and Practice, JohnWiley Inc, New Jersey, 2004.

11. Kraume, M. and Zehner, P, Experience withexperimental standards for measurement of

various parameters in stirred tanks, TransI-ChemE, Vol. 79, 2001.

12. Mezaki, R., others, Engineering Data onMixing, Elsevier 2000.

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52 CHEMICAL ENGINEERIN G WWW.CHE.COM APRIL 2006


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term represents the effect of viscos-ity changes in the boundary layerat the heat transfer surface. For in-ternal components, such as coils, the

value of C differs from that for the vessel wall. A further complication isthat physical properties of the vesselcontents are often changing during

processing due not only to chang-ing operating conditions, but also tophysical or chemical processes thatare occurring.

The design engineer is often facedwith the problem that the requiredheat flux cannot be achieved withexisting conditions such as heat-ex-change area or utility temperatures.Here are some common reasons andsuggested remedies:

Effect of scale: Heat generated by areaction increases proportionally withthe volume of the mixture ( Q R V ).

For geometrically similar equipment,however, the area for heat exchangeincreases proportionally to the vol-ume raised to the power 2/3 ( A V 2/3 ).

A reaction that was simple to controlthrough wall cooling at the pilot scalemay therefore require additional heat-ing/cooling surfaces in order to increasethe surface area lost on scale-up. Tubebundles or coils mounted in the reac-tor are often used. In cases where veryhigh surface areas are required, verti-cal plate heat exchangers mounted ap-proximately radially in the reactor canprovide as much as 25 m /m .Viscosity: The material property thatcommonly governs heat exchange is

viscosity, . In industrial applications,the viscosity of mixtures can rangewidely, such as from 0.1 to 10 6 mPas.Because the heat transfer coefficientis proportional to -1/3 , the coefficientsfor high-viscosity fluids are muchlower than those for low-viscosity ap-plications. An increase in viscosity canalso mean that a liquid is no longerin the turbulent regime, so tempera-ture differences within the mixture

would increase. These issues are bestaddressed by careful selection of theagitator to ensure good homogeneityacross the range of operating condi-tions. Consideration should be givento close-clearance impellers, such asthe helical ribbon and the optimizedribbon, which increase shear andtherefore heat transfer at the wall. Indifficult cases, the use of wall scrapers(Figure 9) can further increase heattransfer by a factor of up to 10.Wall fouling: Fouling is a risk inmany processes. In cooling crystal-lization, for example, the liquid canbecome supersaturated in the wall-boundary layer. Scrapers may help,

but they are subject to wear in thesolid layer. In this case, it is better tochange the process to use cooling byevaporation. This process may requireoperation under vacuum, which bringsanother consideration flow veloci-ties at the liquid surface must be fastenough to avoid increased local over-concentrations that can lead to crys-tal nucleation. Impellers with goodaxial-pumping efficiency are used tomaintain concentration and tempera-ture homogeneity and ensure uniformcrystal growth.

Pressure vessels: Wall thicknessescan become the limiting factor forheat transfer, especially with stainlesssteel vessels that contain a low-viscos-ity fluid. It is not possible, for exam-

ple, to achieve an overall heat trans-fer coefficient above 300 W/mK if thewall thickness is 50 mm. This overallheat-transfer coefficient cannot beimproved by more intense agitation.Similarly, deposits on the utility sideof the jacket or heat-transfer surfacescan build up and cause poor thermalconductivity. Only a few millimeters of deposit can have a detrimental effecton the heat transfer. Regular cleaningprocedures may be required in thesecases.

Agitator-power input: The powerinput, P , has a relatively small influ-ence on heat transfer. The process-sidecoefficient is proportional to P 0.22 , so

doubling power will increases the filmcoefficient by only 16%. When cool-ing viscous fluids, increasing agitatorpower can actually have a negativeeffect on cooling rate because the agi-tator-power input to the fluid, whichis converted to heat, can be quite sig-nificant.

SUMMARYCareful consideration of operatingconditions and fluid characteristics isneeded to effectively design and scaleup mixing systems. A broad body of in-

formation in this field is available forguidance, and a wide range of modernimpellers (Figure 10) is available tomeet mixing challenges.

Edited by Dorothy Lozowski

AuthorWerner Himmelsbach ismanager of EKATO RMTsR&D Department (Kppele-mattweg 2, 79650 Schopf-heim, Germany; Phone: +497622 29227; Fax: +49 762229454; Email: [email protected]). He has 25 years expe-rience in process design anddevelopment, plant design

and maintenance havingpreviously worked for majorinternational manufacturers of speciality chemi-cals and pharmaceuticals. Himmelsbach holds amasters degree in chemical engineering from theUniversity of Karlsruhe (Germany).

Wolfgang Keller is seniorprocess engineer in EKATORMTs R&D Department(Kppelemattweg 2, 79650Schopfheim, Germany;Phone: +49 7622 29468;Fax: +49 7622 29454; Email:[email protected]). He has over10 years experience as plantengineer and in process de-

velopment, having previouslyworked for an international

manufacturer of speciality polymer films. Kellerholds a masters degree in process engineeringfrom the University of Karlsruhe (Germany).

David A. Houlton is seniorprocess engineer responsiblefor reaction consultancy anddesign in EKATO RMTsR&D Department (Kppele-mattweg 2, 79650 Schopf-heim, Germany; Phone: +497622 29512; Fax: +49 762229454; Email: [email protected]]. He has over 25 yearsexperience in process plantdesign and research, having

previously worked for major international manu-facturers of speciality and bulk chemicals. Houl-ton holds B.Eng. and M.Phil. degrees in chemi-cal engineering from the University of Bradford(U.K.). He is a fellow of the U.K. IChemE and amember of the German VDI.

Mark Lovallo is the Tech-nology Manager for EKATOCorporation (Ramsey, NJ07446; Phone 201-825-4684).He heads the North Ameri-can Technology center for theEKATO Group also in NJ.Mark has previously workedfor Union Carbide as a re-search engineer in the poly-olefins catalyst division. Heholds a Ph.D. in chemical en-

gineering from the University of Massachusetts Amherst.

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