kraume_2001

0263–8762/01/$10.00+0.00# Institution of Chemical Engineers

Trans IChemE, Vol 79, Part A, November 2001

EXPERIENCE WITH EXPERIMENTAL STANDARDSFOR MEASUREMENTS OF VARIOUS PARAMETERS

IN STIRRED TANKS:A Comparative Test

M. KRAUME1 and P. ZEHNER2

1Technische Universitat Berlin, Institut fur Verfahrenstechnik, Berlin, Germany.2BASF AG, Ludwigshafen, Germany.

S tirred tanks are used for several operations in industrial practice. Numerous scienti� cpapers have been presented in literature dealing with experimental results on theseapplications. Comparisons and valuations of these data often fail because geometric

parameters, experimental conditions, and measurement techniques differ notably. Therefore, itcan be observed that correlations derived on the basis of these experiments often show largediscrepancies. In a cooperative test of nine German working groups different experiments werecarried out in stirred tanks under completely standardized conditions. Thereby, commonmeasurement techniques were examined in their reliability.

Keywords: standardization; power input; homogenization; solids suspension; gas dispersion.

INTRODUCTION

In industrial practice, stirred tanks are used for a variety ofoperations such as homogenization of miscible liquids,dispersion of gas, mixing of immiscible liquids, and suspen-sion of solid particles. Over the last decades numerousscienti� c papers dealing with experimental results on theseapplications have been presented. However, comparisonsand valuations of these data often fail because geometricparameters, experimental conditions, and measurement tech-niques differ notably. In addition, use of various tank sizesmake results more dif� cult to compare. Therefore, correla-tions derived on the basis of these experiments often exhibitlarge discrepancies, e.g. for solids suspension1–2. Thisstatement is very important for practical engineering workas those correlations are used for design and scale-up ofstirred tanks.

Members of the German GVC-VDI working group onmixing carried out a standardization of tank and stirrergeometry as well as measurement techniques. On thisbasis, reliable experimental results were achieved and arenow available for comparison. The data can be useful inparticular:

for selection of suitable stirrer systems,for comparison of different systems,for the valuation and optimisation of newly inventedstirrers,as a basis for mathematical modelling and setting up ofscale-up rules,as reliable data for validation of numerical simulations.

The measurements illustrate the reliability of experimentaldata when obtained by different staff in different labora-tories. To build up a broad data basis, standardized experi-ments were carried out by nine members of the Germanworking party on mixing representing chemical industry,mixing companies, and research institutes (see Table 1).

In order to minimize potential errors and deviations,simple experiments as well as common stirrers and tankswere chosen. Still, for parts of the experiments distinctlydifferent results were achieved, the most important of whichare presented and discussed in this paper.

MATERIALS AND METHODS

Standard Stirred Tank and Media

Figure 1 shows the main features of the selected stirredtank. Vessel, baf� es and stirrers were procured or built byeach experimenter individually. To ensure comparability ofresults, main dimensions were provided with tolerances.A compromise was made when selecting the diameter ofD 0.4 m: On the one hand technical relevance of resultsincreases with vessel volume, on the other higher expendi-ture and costs are incurred.

Rushton and pitched blade turbines were selected becausethey are suited for most applications involving liquids oflow viscosities. The aim of this test was not to utilizeoptimized stirrer types and dimensions but stirrers of highestpossible � nishing accuracy given for plain-shaped turbinesrather than propellers for example.

811

All experiments were performed using water, air and glassbeads. The latter (fractions of two different sizes) originatefrom the same production batch.

Measuring Programme and Techniques

Performed measurements included

power input,homogenization,solids suspension andgas dispersion experiments.

No restraints were made for the power input measuringmethod. Instead, existing and largely different devices wereused, such as strain gauges, shaft-mounted torquemeters, oreven turntables.

Two different basic methods were applied for measuringmixing time for homogenization3–4. First, decolourization ofan iodine-starch solution after addition of sodiumthiosulfatewas used. This way the mixing process could be visuallyobserved throughout the whole vessel and zones of insuf� -cient mixing could be identi� ed. Mixing time was determinedwhen the last streaks disappeared.Electrical conductivitywasmeasured by an exactly positioned probe. A certain amountof NaCl-solution was added and the conductivity signalrecorded. From the concentration–time-curve the timerequired for a certain mixing quality (set to 95% for bothmethods) was derived. In order to rule out deviations due tovarying adding locationsboth solutionswere introducedcloseto the axis. For each set of operating parameters four deco-lourization and ten conductivityexperiments were suggestedto enhance accuracy of statistic averages.

Suspension experiments were performed using glassbeads of two different sizes (fraction 1: 0.15–0.25 mm,fraction 2: 0.8–1.2 mm). Both the 1-s- and the 90%suspended slurry height criterion were employed. The 1-s-criterion is met when no particle remains stationary at thebottom of the vessel for more than 1 s5, while the 90%suspended slurry height criterion requires particles to besuspended up to 90% of the liquid level6. Application ofboth criteria is based on visual observation.

In gas dispersion experiments in addition to power input,gas hold-up and volumetric oxygen transfer coef� cient weremeasured. For determination of the hold-up, a U-tube was� tted to the tank. With increasing hold-up, liquid level in thevessel rises and so does the level in the U-tube, where

� uctuations are considerably less frequent than in the vesselitself. Hold-up is then calculated from level variation.

The oxygen transfer coef� cient was determined by meansof the dynamical method7. First, by introducing nitrogen thetank content was stripped of all oxygen. It was then spargedwith air and the increase in oxygen concentration wasmonitored by a probe and recorded. When evaluating datathe decreasing oxygen concentration of air as well as theinertia of the probe had to be taken into account. Onlyconcentrationsbetween 20% and 90% saturationwere consid-ered in order to exclude erroneous start-up and end effects.Operating conditionswere prescribed for experiments,alwaysresulting in turbulent conditions (Reynolds numbers >104).Data was collected and centrally evaluated and plotted.

Table 1. Participants of the cooperative test.

Chemical companiesBayer AG, Wuppertal HenzlerBayer AG, Leverkusen JudatBASF AG, Ludwigshafen Zehner=Haverkemper

Mixing companiesEkato, Schopfheim KrebsStelzer, Warburg Kuckelmann

Research institutesDIL, Quakenbruck KnochTU Berlin, Institut fur Verfahrenstechnik KraumeUniversitat Dortmund, FB Chemietechnik LangerFH Sachsen-Anhalt Liepe=Sperling

Figure 1. Dimensions of standardized stirred tank and stirrers.


812 KRAUME and ZEHNER

RESULTS

All results are presented anonymously.

Power Input

Figure 2 shows the measured torques over stirrer speedfor both stirrer types. As expected, torque increases propor-tional to N2. On comparison of values it becomes apparentthat, especially below 0.1 Nm, widespread scattering andsystematic differences occur. Deviations of that kind arealways to be expected when measured values only amountto 10% or less of the possible maximum of the gauge.

Independent of this effect, above 0.1 Nm systematic errorsarise, too.

These discrepancies become even more obvious whencomparing power numbers Po, which are shown in Figure 3as a function of stirrer speed N. Below approximately100 min 1 practically no agreement was found. As thiswas expected (see above), these values were discarded fortheir lack of accuracy by all experimenters.

It has to be noted that values measured by differentauthors deviate considerably, while variations within onerun of measurements are usually small. These deviations areintolerable for the pitched blade turbine especially. Stirrersfrom labs 1 to 5 were again investigated by experimenter 6using his own tank and measuring device. For stirrer speedsabove 100 min 1 averaged power numbers and their maxi-mum deviations are shown in Figure 4. Values from allexperimenters and from author 6 are given. Obviously, notonly measuring methods alone lead to dissimilarities inresults. Deviations in the results of author 6 have decreasedso for that they can only be explained by slightly differingstirrer dimensions. When gauged by experimenter 6, stirrerdiameters were found to differ from the required 125 mm by

1 mm. Also, the assumed blade thickness of 2 mm wassmaller for author 1 (1.7 mm) and was distinctly exceededby author 5 (3 mm). It is well known8–9 that Po decreaseswith increasing blade thickness and this is in agreement withmeasurements. The blade angle, too, often turned out to besmaller than expected.

To sum up torque measurements, it can be stated thattorques below 0.1 Nm yielded considerable deviations.Systematic errors above 0.1 Nm resulted from differing stirrerdimensions on the one hand, and from differing measuringdevices on the other. Deviations in power numbers were morepronounced for pitched blade turbines than for Rushtonturbines, where they differed by 15% and 10%, respectively.

Homogenization

With regards to mixing times, averaged results (decolour-ization: 4 measurements, conductivity: 10) for both stirrersare plotted as dimensionless products N tMIX, the dimension-

Figure 2. Dependence of torque on stirrer speed.

Figure 3. Dependence of power number on stirrer speed.


COMPARATIVE TEST OF STIRRED TANK MEASUREMENT STANDARDS 813

Figure 4. Averaged power numbers and their maximum deviations.

Figure 5. Mixing time characteristic of Rushton turbine.

Figure 6. Mixing time characteristic of pitched blade turbine.



less mixing time, over stirrer speed in Figures 5 and 6.Surprisingly good agreement of values from differentauthors was found for both methods. Therefore, the resultsshown in Figures 5 and 6 are distinguished only by therespective method.

Although a scattering of 10 to 20% could be observed,both methods resulted in reasonably similar mixing times. Itis assumed that this is due to mixing taking place evenlythroughout the vessel, thus enabling the locally limitedconductivity measurement to correctly represent the homo-genization process in the vessel as a whole.

Different accuracies of results have to be noted for thetwo stirrer types. Scattering of results was wider for thepitched blade turbine. In this case, also a small distinctionbetween the two measuring methods prevailed, the reason ofwhich could not be satisfactorily explained.

The fact that authors strictly kept to the required addinglocation was of major importance to the overall agreement.In one exemplary investigation, the in� uence of a 150mmshift from the axis was observed to cause a 30% increase inmixing times. Inaccurate adjustment of excess concentrationwas identi� ed as another in� uential source of errors. Sincedosage of amounts is never absolutely correct, this excessconcentration is bound to be faulty. The true excess concen-tration, however, can be easily determined by titration andrelated to a degree of mixing of 95%4.

Suspension

The measured stirrer speeds for solids supension exhibit alargely varying degree of agreement. Determining the state ofsuspensionby use of the 1-s-criterionyields similar results forthe pitched blade turbine (compare Figure 7). According toFigure 8, however, judging the point where the 1-s-criterion is

Figure 7. Critical stirrer speed for complete suspension of 1 mm glass beads with the pitched blade turbine.

Figure 8. Critical stirrer speed for complete suspension of 0.2 mm glass beads with the Rushton turbine.



reached becomes dif� cult when small particles are to besuspended by use of a Rushton turbine. The region justbelow the stirrer is visually inaccessible, so a clear decisionwhether these relatively small particles simply perform asliding movement or whether they get lifted upwards within1 s becomes impossible. Obviously individual interpretationsof the 1-s-criterion differ as results from each author areinternally consistent.A uniform judgement seems to be easierfor larger particles since deviations are distinctly reduced.

When employing the 90% suspended slurry height criter-ion, smaller disagreement between measurements was foundfor the pitched blade turbine than for the Rushton turbine.Results differ especially when the 90% suspended slurryheight is reached before the 1-s-criterion which is the casefor small particle concentrations. Under these circum-stances, some particles indeed rise to a height equivalentto 90% of the liquid level while a reasonably large fractionof solids remains at the bottom. Therefore, the critical stirrerspeeds are almost independent of particle concentration,which is especially striking for particle sizes of 1 mm.

Table 2 summarizes discrepancies between all measuredstirrer speeds. As the corresponding power inputs will differeven stronger (increase proportional to N3) this is a quitesobering result. Still, these data make the large disagreementbetween literature correlations and scale-up rules morecomprehensible.

Gas Dispersion

In contrast to single-phase measurements differencesbetween power inputs are more pronounced in the aerated

tank, as shown in Figure 9 for both impellers and a super-� cial gas velocity of 6.3 mm=s. The slope of the data is stillapproximately 2 as in Figure 2 whereas the values of M aresigni� cantly lower. One possible reason for the discrepan-cies observed might be an inaccurate measurement of gas� ow rate as for constant stirrer speed it is practically the onlyquantity on which torque depends.

The selected method for measuring gas hold-up turned outto be insuf� ciently exact. In spite of the U-tubes dampeningeffect, the liquid level � uctuates considerably—if not asmuch as inside the vessel—thus making observer indepen-dent level measurement hardly possible. As a result, signi� -cantly differing gas hold-ups were determined, as shown inFigure 10 for both turbines. Hold-ups of less than 1% shouldbe regarded with particular care. At higher hold-ups dissim-ilarities are reduced but still leave deviations of 20% andmore. Again, systematic errors can be observed. For compar-ison two correlations from literature are shown in Figure 10.Smith11 proposed an equation for the gas hold-up whenRushton turbines are used. In all cases this equation leadsto an over estimation of measured data. The slope of theexperimental curve is fairly close to v0:35

g as reported bySmith. Nearly the same conclusion can be drawn from theexperimental data of the pitched blade turbine whencompared with a correlation proposed by Rewatkar et al.12.

In general, the measuring method is not suited forobtaining highly reproducible results, a fact, however,which is of minor importance in technical applications.On the one hand, calculation of liquid content is affectedonly to a small extent by gas hold-ups below 10%, abovewhich determination seems to become suf� ciently accu-rate. The main aspect of gas=liquid-systems is masstransfer, characterized by the mass transfer coef� cient.

Results from mass transfer measurements are summarizedin Figure 11. In this plot suggested by Henzler10 a dimen-sionless mass transfer coef� cient is shown as a function of adimensionless power input. With the exception of resultsfrom author 4, all data appear to be well bundled, especiallyconsidering that the power input, a parameter stronglysubjected to errors, is used on the abscissa. Plotting the

Table 2. Deviations of critical stirrer speeds for solids suspension.

Rushton turbine Pitched blade turbine

Criterion0.15–0.25

mm0.8–1.2

mm0.15–0.25

mm0.8–1.2

mm

1-s-criterion 40% 10% 5% 10%90% s. slurry height 20% 20% 10% 10%

Figure 9. Dependence of torque on stirrer speed for gassed impellers.



mass transfer coef� cient versus stirrer speed for the respec-tive super� cial gas velocities does not yield any betteragreement. The slope of the curve yields a proportionalityof kLa P=V 0:58 v0:42

g : The exponent of the speci� cpower input is somewhat higher than the most often usedvalue of 0.4 for coalescing systems13.

CONCLUSIONS

On the basis of identical experimental situations:

standardized tank, baf� e, and stirrer geometry,measuring methods,prescribed operating conditions,central evaluation of data,

an impression on the accuracy of measurements was gainedwith the presented cooperative tests. In fact for part of theexperiments results are widely scattered. It can be assumed

that literature data commonly contain similar deviations.Differences mainly arise from the following reasons:

not meeting the standard,inaccuracy of manufacture,inaccuracy of measuring devices,uncertain criteria,inaccurate measuring methods.

This again emphasizes that even experiments carried out byexperienced experimenters are subject to uncertainties andtherefore have to be critically judged, especially in a situa-tion where the actual daily work leaves little room forcareful performance of measurements.

NOMENCLATURE

c solids volume fraction, m3=m3

d particle diameter, mD stirrer diameter, m

Figure 10. Comparison of gas hold-up measurements for both impellers with results from literature.

Figure 11. Dimensionless mass transfer coef� cient as function of dimensionless power input.



g gravitational constant, m=s2

kLa volumetric mass transfer coef� cient, 1=sM torque, NmN stirrer speed, min 1

P power input, WPo power numberRe Reynolds number Re nd2=nT tank diameter, mtMIX mixing time, sV liquid volume, m3

vg super� cial gas velocity, m=seg gas hold-up, m3=m3

n kinematic viscosity, m2=sr liquid density, kg=m3

REFERENCES

1. EKATO Ruhr- und Mischtechnik GmbH, 2000, EKATO Handbook ofmixing technology, Schopfheim.

2. Kraume, M. and Zehner, P., 1988, Suspendieren im Ruhrbehalter—Vergleich unterschiedlicher Berechnungsgleichungen, Chem-Ing-Tech,60(11): 822–829.

3. Hiby, J., 1979, Homogenization, in Fortschritte der VerfahrenstechnikBd. 17, Abt. B., VDI-Verlag, Dusseldorf, pp. 137–155.

4. Henzler, H., 1978, Untersuchungen zum Homogenisieren vonFlussigkeiten oder Gasen, VDI-Forschungsheft 587, Dusseldorf.

5. Zwietering, T. N., 1958, Suspendingof solid particles in liquid agitators,Chem Eng Sci, 8: 244–253.

6. Kraume, M., 1992, Mixing times in stirred suspensions, Chem EngTechnol, 15: 313–318.

7. Zlokarnik, M., 1999, Ruhrtechnik, Springer-Verlag, Berlin Heidelberg.8. Bujalski, W., Nienow, A. W., Chatwin, S. and Cooke, M., 1987, The

dependency on scale of power numbers of Rushton disc turbines, ChemEng Sci, 42(2): 317–326.

9. Rutherford, K., Mahmoudi, S. M. S., Lee, K. C. and Yianneskis, M.,1996, The in� uence of Rushton impeller blade and disc thickness on themixing characteristics of stirred vessels, Trans IChemE, Part A, ChemEng Res Des, 74: 369–378.

10. Henzler, H., 1982, Verfahrenstechnische Auslegungsunterlagen furRuhrbehalter als Fermenter, Chem-Ing-Tech, 54(5): 461–476.

11. Smith, J. M., 1991, Simple Performance Correlations for Agitated Vess-els, from Proc. 7th Europ. Congress on Mixing (eds.) Bruxelmane, M.and Froment, G., Royal Flemish Society of Engineers, Brugge, 18–20Sept., pp. 233–241.

12. Rewatkar, V. B., Deshpande, A. J., Pandit, A. B. and Joshi, J. B., 1993,Gas hold-up behaviour of mechanically agitated gas-liquid reactorsusing pitched blade down� ow turbines, Can J Chem Eng, 71: 226–237.

13. Van’t Riet, K., 1979, Reviewing of measuring methods and results innonviscous gas-liquid mass transfer in stirred vessels, Ind Eng ChemProcess Des Dev, 18(3): 357–364.

ADDRESS

Correspondence concerning this paper should be addressed toDr Matthias Kraume, Technische Universitat Berlin, Institut fur Verfahrens-technik, Straße des 17 juni 135, D-10623, Berlin, Germany.E-mail: [email protected]



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