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Asian J. Exp. Sci., Vol. 23, No. 1, 2009; 157-164

Energy Efficiency and Mixing Time Calculations in MechanicallyAgitated Liquid Liquid Contactors

G.M. Madhu, A.J. Girish, Priya Ravi Ganesh, Sagar S. Agarwal, RohitKacker and Karanth Akshaya S.Department of Chemical Engineering,R.V. College of Engineering,Bangalore-560 059 (Karnataka); India.

Abstract : The present paper involves the comparison of disc turbine, Rushton turbine andpitched blade turbine in terms of mixing time and energy efficiency for the mixing of miscibleliquids with density difference. Comparison is also based on the change in the tracer volumeadded as well as the effect of change of the impeller diameter. The study has been restricted tothe stirrer controlled regime due to lower mixing times as compared to gravity controlled orintermediate regimes. Conductivity meter has been used to ascertain the total mixing time, whichbeing the time required to reach a constant conductivity. Effect of amount of tracer fluid added,density difference with the bulk and also the type and geometry of the impeller on the mixingtime has been investigated. The pitched blade turbine with lesser diameter is recommendedamongst the different impellers studied in the present work.

Key words : Energy, Efficiency, Time Calculations, Mechanically Agitated, Liquid Contactors

IntroductionThe operational success of many industrial

processes depends on effective agitation andmixing of liquid. Fluid mixers cut across almostevery process industry: minerals, pulp, andpaper, waste and water treatment and almostevery individual process sector. The mainpurposes of agitation are:

1. Suspending solid particles,2. Blending miscible liquids,3. Dispersing a gas in liquid in the form

of small bubbles,4. Dispersing a second liquid, immiscible

with the first,a. To form an emulsion orb. Suspension of fine drops and

5. Promoting heat transfer between theliquid and a coil or jacket (McCabeand Harriot, 1993).

Homogenous mixing of two miscibleliquids with difference in various physicalproperties such as density and viscosity is acommon industrial practice. The equipmentused for the physical operation is selected basedon the components to be mixed such thatmixing takes place in the required time withsmallest amount of power consumption.

There are the three classes of mixingnamely macro scale mixing, micro scale mixingand molecular scale mixing. Macro Scalemixing refers to blending the feed so that everygallon in a reactor has the same averagecomposition. Mixing on the macro scale iscontrolled through the use of agitators. MicroScale mixing refers to interdispersing the feedto give uniform composition to the 10-100Micrometer scale. Mixing on the micro scaleis controlled by eddies and is not much affectedby agitation. Molecular scale mixing is completewhen every molecule in the reactor issurrounded by exactly the same molecule at

* Corresponding author : A J Girish, Department of Chemical Engineering, R.V. College of Engineering,Bangalore-560 059 (Karnataka); India; Mobile : 918026799032; E-mail : aj_girish@indiatimes.com

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Madhu G.M. et al. (2009) Asian J. Exp. Sci., 23(1), 157-164

least on a time-averaged basis. This mixing isalmost totally driven by diffusion.

A completely well stirred tank reactorimplies good mixing in all these levels. Manyagitated vessels are well mixed on the macroscale, however, no commercial reactor isperfectly well mixed or thoroughly plug flow.This incomplete mixing may be unimportant ifthe reaction is dominant or all reactions areslow. In many applications, the reaction andmixing times are often similar and must becarefully studied.

Impellers agitators are divided into twoclasses. Those that generate currents parallelwith the axis of the impeller shaft are calledaxial flow impellers; those that generatecurrent in radial or tangential direction arecalled radial flow impellers. The three typesof impeller for low to moderate viscosity liquidsare propellers, turbines, and high efficiencyimpellers. For very viscous fluid the mostwidely used impellers are helical impellers andanchor agitators.

The simple straight-blade turbine pushesthe liquid radially and tangentially with almostno vertical motion at the impeller. The currentsit generates travel outwards to the vessel walland the flow either upward or downward. Suchimpellers are sometimes called paddles. Inprocess vessels they typically turn at 20 to 150rpm. The disk turbine, with multiple straightblades mounted on a horizontal disk, like thestraight-blade impeller, creates zones of highshear rate; it is especially useful for dispersinga gas in a liquid. A pitched-blade turbine is usedwhen good overall circulation is important(Perry and Green, 1999).Flow Patterns

The way a liquid moves in an agitatedvessel depends on many things: the type ofimpeller; the characteristics of the liquidespecially its viscosity; and the and proportions

of the tank, baffles, and impeller. The liquidvelocity at any point in the tank has threecomponents, and the over all flow pattern inthe tank depends on the variations in these threevelocity components from point to point. Thefirst velocity component is radial and acts in adirection perpendicular to the shaft of theimpeller. The second component is longitudinaland acts in a direction parallel with the shaft.The third component is tangential, or rotational,and acts in a direction tangent to a circularpath around the shaft. In the usual case of avertical shaft, the radial and tangentialcomponents are in a horizontal plane, and thelongitudinal component is vertical. The radialand longitudinal components are useful andprovide the flow necessary for the mixingaction. When the shaft is vertical and centrallylocated in the tank, the tangential componentis generally disadvantageous. The tangentialflow follows a circular path around the shaftand creates a vortex in the liquid. The swirlingperpetuates stratification at the various levelswithout providing longitudinal flow betweenlevels. If solid particles are present, circulatorycurrents tend to throw the particles to theoutside by centrifugal force; from there theymove downward and to the centre of the tankat the bottom. Instead of mixing, its reverse-concentration- occurs. Since, in circulatoryflow, the liquid flows with the direction ofmotion of the impeller blades, the relativevelocity between the blades and the liquid isreduced, and the power that can be absorbedby the liquid is limited. In an unbaffled vessel,circulatory flow is induced by all types ofimpellers, whether axial flow or radial flow. Ifthe swirling is strong, the flow pattern in thetank is virtually the same regardless of thedesign of the impeller. At high impeller speedthe vortex may be so deep that it reaches theimpeller, and gas from above the liquid is drawndown into the charge. Generally this isundesirable.

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Energy Efficiency and Mixing Time Calculations in Mechanically Agitated Liquid Liquid Contactors

Baffled TanksFor vigorous agitation of thin suspensions,

the tank is provided with baffles, which areflat vertical strips set radially along the tankwall. Four baffles are almost always adequate.A common baffle width is one-tenth to one-twelfth of the tank diameter (radial dimension).For agitating slurries, the baffles often arelocated one-half of their width from the vesselwall to minimize accumulation of solids on orbehind them.

For Reynolds numbers greater than 2000,baffles are commonly used with turbineimpellers and with on-centerline axial-flowimpellers. The use of baffles results in a largetop-to-bottom circulation without vortexing orseverely unbalanced fluid forces on the impellershaft. In the transition region (Reynoldsnumbers from 10 to 10,000), the width of thebaffle may be reduced, often to one-half ofstandard width. If the circulation pattern issatisfactory when the tank is unbaffled but avortex creates a problem, partial-length bafflesmay be used. These are standard-width andextend downward from the surface into aboutone-third of the liquid volume.

The present work involves the comparisonof different commonly used impellers, namelydisc turbine, pitched blade turbine and Rushtonturbine, and recommending a particular impellerbased on the study for mixing operation ofadding a tracer pulse to the liquid bulk inturbulent conditions.Materials and MethodsMaterials and Reagents

Tachometer was supplied by Dot tech(Digital Photo type Tachometer model - 792)and was used as received. Conductivity meterwas supplied by Systronics and was used afterinitial calibrations as per its user manual.Purified sodium hydroxide pellets wereprocured from Merck Limited and used without

further purification. Impellers were fabricatedby Mechtrix Engineers, Bangalore as per ourdesign specifications. Weights of the salt to betaken were measured using Class I digitalweighing balance by Essae-Teraoka ltd (modelAQ2130/3EO).Experimental Setup

The experiments have been performed ina mechanically agitated open top cylindricalstainless steel baffled vessel with an innerdiameter of 0.197 m and a height of 0.322 m.The vessel is provided with an opening fittedwith a drainage valve at the bottom center toflush out its contents. The entire setup issupported on a stand that also holds theconductivity meter used for the measurementof the bulk solution conductance. The impelleris mounted vertically on a stand with its shaftpositioned at the center of the tank and paddedto minimize oscillations of the shaft tip. Allimpellers were mounted with a clearance of0.031 m from the bottom of the tank.

All aqueous solutions were prepared withdeionized water. The salt solutions wereprepared as molar concentrations bytransferring a known amount of material to avolumetric flask and diluting to the specifiedvolume with deionized water.Procedure

The baffled vessel was cleanedcompletely and fitted with the stirrer havingthe first impeller to be studied. 6 litres of waterwere filled in it to have the liquid holding volumeas per the standard specifications (Perry andGreen, 1999). The electrode of the conductivitymeter was kept in place near one of the bafflesin a fixed position for all readings. Care wastaken that the electrode was never exposed toair to keep it from drying. The agitator wasswitched on and the speed of rotation of theimpeller was found by using the tachometer.The rpm of the agitator was controlled at thedesired rate and maintained during the course

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of the experiment. The measured volume ofthe tracer (NaOH solution that was preparedof calculated concentration) was added alongthe stirrer rod axis as a pulse input and thestopwatch was switched on. The time wasnoted when the conductivity meter readingshowed a constant steady value. This wasrecorded as the mixing time for that reading.The parameters that were varied were theposition of tracer input, tracer concentration,tracer volume, impeller type and impeller speedto perform the analysis for the present study.Range of variables covered is listed below inTable 1.Results and DiscussionsEffect of amount of tracer added

The mixing time is found to be dependenton the amount of tracer fluid added to thesystem, which is in contradiction with relatedavailable literature (Burmester et al., 1991;Bakker adn Akker, 1997 and Rielly and Britter,1985). All the previous literature dealing withthe effect of volume of tracer fluid on mixingtime is restricted to tracer volume of maximumof 1% of the bulk. Such low volume does notretain its identity even after one circulation inthe stirrer-controlled regime due to the impellerturbulence and the buoyancy forces generateddue to the density difference that are easilyovercome. The mixing times are thus found to

be small in these cases.The volumes added in the present study

(2 to 8% of the total bulk volume) are suchthat the tracer pocket has sufficient volume toretain the identity even after 3-4 circulationsand hence if the volume is increased further,larger mixing times are expected. Thus ourstudy reveals the dependency of mixing timeon the amount of tracer added to the system.Similar observations were made on varying thedensity difference between the tracer input andthe bulk liquid (Gogate and Pandit, 1999).

The effects of tracer volume on mixingtimes were studied at different pulse injectionpoints in the tank for two concentrations of thetracer (for consistency check of trend) and theresults are plotted below in Fig. 1 and Fig. 2.

Variable Range of values coveredRushton turbine,pitched blade turbine,disc turbine

Impeller diameter (Pitched blade turbine)

0.055 m and 0.0695 m

Tracer concentration 30 – 120 gm NaOH in 500 ml solutionTracer volume 2 – 8% of bulk volume

Along stirrer rod axis,Along baffle

Impeller type

Position of tracer input

Table 1 : Range of variables covered in the study

02468

101214161820

0 2 4 6 8 10

% Tracer Volume

Mix

ing

Tim

e

Paddle Agitator

Disc Turbine

Pitched Blade Turbine

Fig. 1 : Mixing time versus tracer volume% intank for various impellers at 492 rpm and tracer

concentration of 150g/1500 ml water inputalong the stirrer rod.

Madhu G.M. et al. (2009) Asian J. Exp. Sci., 23(1), 157-164

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Energy Efficiency and Mixing Time Calculations in Mechanically Agitated Liquid Liquid Contactors

The effect of tracer volume on the mixingtime was found by taking two concentrationsof the tracer to check for consistency of resulttrend (150g and 250 g in 1500 ml water). Themixing time was found to increase as moreamount of the tracer pulse was added to thebulk liquid. This is indeed true as more traceris added to the system, it takes a longer time toget completely mixed as it retains its identityafter many more circulations than minutequantities of tracer take. As the tracerconcentration increased, the mixing time wasmore for the same volume of tracer added.

Also, the mixing time was lesser whenthe tracer pulse was input along the stirrer rodaxis. This is because input along the bafflemakes the tracer pocket take a longer time tocome into contact with the circulation patterncreated by the impeller and thus mixing takelonger time as it first travel all the way downto the bottom of the vessel atleast before theturbulence in the bulk causes mixing to occur.The pitched blade turbine gives the least mixingtimes as observed from the graphs above (Fig.1and Fig.2). However, the Rushton turbine givescomparably low mixing times too. Dependingon the process the impeller must be chosen(Van de Vusse, 1955; Rohatgi et al., 1979;Ahmad. et al., 1985).

Effect of Tracer Concentration (densitydifference)

The mixing times are observed to increasewith increasing density difference between thetracer input and the bulk liquid, as shown in fig3, which can be explained along the lines ofreasoning of effect of tracer volume discussedabove. This is in accordance with literaturethat proposes that heavier liquids take longertime to get completely mixed in a given system(Bakker and Akker, 1997)

Among the impellers used, the Rushtonturbine is found to result in the least mixingtimes for varying density differences betweenthe tracer added and bulk. The pitched bladeturbine resulted in around 30% lesser mixingtime than the disc turbine while the Rushtonturbine gave 70% lesser mixing times. Themixing times of the Rushton and the pitchedblade turbine vary only by few seconds asobserved.

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10% Tracer Volume

Mix

ing

Tim

e

Paddle Agitator

Disc Turbine

Pitched Blade Turbine

Fig. 2 : Mixing time versus tracer volume% intank for various impellers at 492 rpm and tracer

concentration of 150g/1500 ml water inputalong the baffle

0

5

10

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2 0.25Density difference

Mix

ing

times

(s)

Disc Turbine

Pitched Blade Turbine

Paddle Agitator

Fig. 3 : Effect of density difference betweentracer pulse and bulk at 492 rpm and tracer

volume of 300 ml.

On observing the results based on onlymixing times the Rushton turbine may bedecided the best option for the system understudy. However the energy efficiency analysisshow it to consume much higher power thanthe pitched blade turbine that is later found tobe the optimal option. This is because thepitched blade turbine assisted in the downwardmotion of the heavier liquid due to gravity and

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thus helped in early breakage of the tracerpocket resulting in comparatively low mixingtimes. From the Table 2 it can be concludedthat the mixing time dependencies varies linearlywith increase in tracer volume and concentrationwhich is referred in Fig. 1, Fig. 2 and Fig. 3.with the R2 values being above 0.95.

Table 2. R2 values for the linearisation ofthe mixing time dependencies on the tracervolume and concentration for the differentimpellers used.Effect of impeller diameter

The effect of change in the impellerdiameter was studied and the results areillustrated below in Fig. 4. It is found that thereis a marginal increase in the mixing times asthe impeller is larger for the range of volume%of the tracer fluid considered.

Thus the pitched blade turbine with thesmaller diameter is found to give lesser mixingtimes when the amount of tracer added to the

bulk is varied for the given range of volume%.The impeller with the larger diameter alsoconsumes more power than the smaller oneand hence it can be concluded that the pitchedblade turbine with the smaller diameter (0.055m) is preferred. From the Table 2 it can beconcluded that the mixing time dependenciesvaries linearly with increase in tracer volumeand concentration which is referred in Fig 1,Fi.2 and fig.3. with the R2 values being above0.95.Energy Efficiency Analysis of DifferentImpellers

Energy efficiency analysis is an importantstep that must be performed before setting theoperating parameters for mixing in a particularsystem.

The total power consumption ischaracterized by the impeller power number,Np, defined as given below

Np = 53dNnConsumptioPowerActualN P ρ

=

…… (1)The impeller power number was found

from literature to be 5 for Rushton turbine, 2.5for disc turbine and 1.86 for a pitched bladeturbine (1).

Depending on the volume of addition ofheavier fluid to the agitated bulk, there wouldbe a change in the center of mass and hence achange in the potential energy of the system.This change is given as (8,9) :

Et = ½*Ψ*(1-Ψ)*V*(∆ρ)*g …… (2)

Madhu G.M. et al. (2009) Asian J. Exp. Sci., 23(1), 157-164

R2 values for R2 values R2 values Fig .1 for Fig. 2 for Fig. 3

Rushton turbine 0.9581 0.9962 0.9653Pitched blade turbine 0.9055 0.9902 0.9602Disc turbine 0.9897 0.9657 0.9318

Impeller type

Table 2 : R2 values for the linearisation of the mixing time dependencies on the tracer volume andconcentration for the different impellers used.

0

2

4

6

8

10

12

14

0 2 4 6 8 10Volume%

Mix

ing

time

(s)

Diameter: 0.0695 m

Diameter: 0.055 m

Fig. 4 : Effect of impeller diameter with varyingvolume% of the tracer of concentration 150g in

1500 ml water added at speed of 495 rpm.

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The value of Ψ is taken as 0.5 (The Etvalue will be maximum for Ψ=0.5 and henceenergy efficiency is defined for this value.Ahmad et al10, have also used similarapproach.) For a particular mixing process,energy efficiency can be defined as the ratioof Et to the actual measured energy required(given by actual power consumption * mixingtime) for the completion of the mixing process.

η=Et/E ……(3)From Table 3 it can be easily seen from

the results that pitched blade turbine is highlyenergy efficient as compared to other impellers.The values of energy efficiency obtained inthe work are quite similar to those obtained inthe work of Ahmad et al. (1985) and Rohatgiet al. (1979) who have also obtained the valuesof energy efficiency in the same range of 0.3to 1.1%. The values of energy efficiency areinversely proportional to the speed of rotationand hence operation at lower speeds would bepreferred but care should be taken that theoperation does not fall into gravity regime orthe intermediate regime due to lower speedsas mixing times increase about 10 folds in theseregimes. Energy efficiency analysis gave theenergy efficiency of the various impellers usedin the following range of values that werefound to be in accordance with the availableliterature.

Energy Efficiency and Mixing Time Calculations in Mechanically Agitated Liquid Liquid Contactors

Impeller type Energy efficiency values

Pitched blade turbine 0.427 %– 1.187%

Rushton turbine 0 .178% – 0.394%Disc turbine 0.373% – 0.893%

Table 3 : Energy efficiency range for differentimpellers studied

ConclusionsMixing time is found to be dependent on

the location of addition of the tracer pulse withabout 30% reduction in the mixing time when

the tracer addition is in the stirrer plane.However, addition of the tracer in the stirrerplane will be associated with additional pumpingcost as extra energy will be required to releasethe fluid against the head of the turbulent bulk.This dependency of mixing time on the locationof tracer addition is expected to be stronger inlarger vessels with higher reduction in mixingtime on addition in the stirrer plane. Selectionof the optimum impeller must be done on thebasis the total energy consumption and itsefficiency rather than on the basis of mixingtimes alone. From the energy efficiencyanalysis done in our experiments, the pitchedblade turbine with lower diameter (0.055 m) isfound to give the maximum energy efficiencyand hence the least operating costs would beinvolved. The speed of rotation must be keptat a minimum with proper care taken to notallow the regime of operation to go out of theboundary of the stirrer-controlled regime(Oldshue, 1966). The mixing time for theaddition of the tracer pulse (NaOH) into theagitated bulk liquid is found to be dependenton the amount of tracer added and the densitydifference between the tracer input and thebulk. This dependence has been found to be afunction of the type of impeller used. Thus forthe flow protocol of our work, the best impellerwas found to be the pitched blade turbine as itgives comparably similar mixing times on thelower range along with providing the maximumenergy efficiency among the impellers studied.Nomenclature

P = Actual power consumptiong = gravitational acceleration.Da = impeller diameterN = impeller rotational speedD = tank diameterì= viscosity of stirred liquidñ= density of stirred mixtureV = Bulk liquid volume in vessel

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Madhu G.M. et al. (2009) Asian J. Exp. Sci., 23(1), 157-164

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