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Canadian Metallurgical QuarterlyThe Canadian Journal of Metallurgy and Materials Science

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Particle concentration distribution measurementsin stirred tanks using a new experimentaltechnique: time and frequency domain analyses

O. G. Olvera, D. Rival & E. Asselin

To cite this article: O. G. Olvera, D. Rival & E. Asselin (2015) Particle concentrationdistribution measurements in stirred tanks using a new experimental technique: timeand frequency domain analyses, Canadian Metallurgical Quarterly, 54:3, 289-296, DOI:10.1179/1879139515Y.0000000012

To link to this article: https://doi.org/10.1179/1879139515Y.0000000012

Published online: 02 Apr 2015.

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Particle concentration distributionmeasurements in stirred tanks using a newexperimental technique: time and frequencydomain analyses

O. G. Olvera*1, D. Rival2 and E. Asselin1

A novel experimental technique has been used to measure particle concentration distributions in

agitated tanks. This approach consisted in using pyrite (FeS2) particles and a Pt electrode connected

to a potentiostat to measure variations in the electrode potential caused by galvanic interactions

between FeS2 particles and the Pt electrode. In order to discern collisions between the particles and

the Pt electrode from randomvariations in electrode potential, a time anda frequency domainmethod

of analysis were used. The latter showed no periodicity in the collision rate indicating that the process

was stochastic. The presented method is convenient because of its simplicity and it can provide

important information regarding the hydrodynamic behaviour of solids in agitated tanks, particularly

when non-intrusive techniques are not an option. Finally, the advantages and drawbacks of the

technique, and its relevance to hydrometallurgical and other chemical processes are discussed.

On a utilise une nouvelle technique experimentale pour mesurer les distributions de concentration

departiculesdans les reservoirs a agitation.Cette approcheconsiste a utiliser desparticulesdepyrite

(FeS2) et une electrodedePt connectee a unpotentiostat afindemesurer lesvariationsdupotentiel de

l’electrode causees par les interactions galvaniques entre les particules de FeS2 et l’electrode de Pt.

Afin de discerner les collisions entre les particules et l’electrode de Pt des variations aleatoires du

potentiel de l’electrode, on a utilise une methode d’analyse du domaine de temps et de frequence.

Cette derniere n’a pas montre de periodicite dans le taux de collision, indiquant que le procede etait

stochastique.Lamethodepresenteeest commodegrace asasimpliciteetpeut fournirde l’information

importante au sujet du comportement hydrodynamique de solides dans les reservoirs a agitation,

particulierement quand les techniques non envahissantes ne sont pas une option. Finalement, on

discutedesavantagesetdes inconvenientsdecette technique,etdesapertinencepour lesprocedes

d’hydrometallurgie et autres procedes chimiques.

Keywords: Particle concentration distribution, Particle collision frequency, Galvanic interaction, Solid–liquid operations

This paper is part of a special issue on hydrometallurgy

IntroductionLiquid–solid operations are common practice in differenthydrometallurgical processes. Particularly, in the case

of leaching operations in stirred tanks, the presence ofsolid particles in the liquid phase significantly affects thehydrodynamics of the system and has to be considered tomake efficient use of the entire volume of the tank.Therefore, knowledge of the distribution of solid particleswithin the tank is necessary to gain a better understandingof particle flow patterns and to help find operatingconditions for which homogenous particle distributionscan be achieved. This information can also provide anestimate of the particle–particle collision rate as well as

1The University of British Columbia, Department of Materials Engineering,309-6350 Stores Road, Vancouver, Canada V6T IZ42Queen’s University, Department of Mechanical and MaterialsEngineering, 130 Stuart St. Kingston, Ontario, Canada K7L 3N6

*Corresponding author, email oscar.olvera@ubc.ca

289

� 2015 Canadian Institute of Mining, Metallurgy and PetroleumPublished by Maney on behalf of the InstituteReceived 02 January 2015; accepted 17 March 2015DOI 10.1179/1879139515Y.0000000012 Canadian Metallurgical Quarterly 2015 VOL 54 NO 3

the contribution of these interactions to the overallleaching rate in systems where galvanic interactionsbetween particles with different rest potentials takeplace. However, the measurement of particle distributionin stirred tanks is not an easy task and remains anopen problem, both from a modelling and from anexperimental point of view.

Experimentally, a number of techniques have beenused to measure solid concentration distributions inliquid–solid systems. Recent work by Tamburini et al.1

presents a brief literature review of particle concen-tration measurement techniques, both intrusive andnon-intrusive. Briefly, the intrusive techniques can becategorised as impedance, acoustic, optical and samplingmethods. For more details regarding their corres-ponding advantages and disadvantages, the reader isreferred to the abovementioned reference as well as tothe work by Goldstein.2

In this work, the authors present a new experimentalapproach to measure particle concentration distributionsin hydrometallurgical leaching tanks. The techniqueconsists ofmeasuring changes in the open circuit potential(OCP) caused by galvanic interactions between FeS2particles and a Pt electrode in aqueous acid solutions.The advantages and limitations of this technique and itsapplicability to other systems are then discussed.

Experimental

Preliminary testsPreliminary measurements were conducted in a 200 mLbeaker. The objective of these tests was primarily toconfirm that the deviations observed in the measuredpotential could be attributed exclusively to the galvanicinteractions between the Pt electrode and the FeS2particles. For these experiments, 150 mL of a 10 g L21

sulphuric acid solution were poured into a beaker andagitated to 400 rev min21 with a magnetic stirrer; thisacid concentration was used to prevent the formation ofan iron hydroxide layer that could affect the galvanicinteractions between the Pt electrode and the pyriteparticles. Although FeS2 can react and dissolve underthese acidic conditions, it can be considered as inert inthe timescale of the experiments.

Electrode potential measurements were conductedusing a PARSTAT 2273 potentiostat from PrincetonApplied Research, Mississauga, ON, Canada. A Pt wirewas used as a working electrode and a saturated calomelelectrode (SCE) as a reference electrode. Only OCPmeasurements were conducted, and therefore, no coun-ter-electrode was required. All experiments were con-ducted at room temperature (20uC). An acquisition timeof 10 ms (sampling frequency of 100 Hz) was used forthese experiments. Either 3 g of sand or of FeS2 were usedfor these experiments (2 wt-% solids). The FeS2 and thesand used in these experiments had particle sizes rangingfrom 100–200 mm and 600–850 mm, respectively. Quan-titative X-ray diffraction analysis of the FeS2 used in thisstudy revealed FeS2 (96 wt-%), sphalerite (2?4 wt-%) andquartz (1?6 wt-%) as the only mineralogical phasespresent in the sample.

Leaching tank testsThese experiments were conducted in an unbaffled 3 Lglass jacketed tank. The internal diameter of the tankwas 12?8 cm and the length 23?8 cm. The tank wascovered using a stainless steel (grade 316) lid and aRushton turbine of the same material was used to stirthe solution in the tank. Figure 1 shows a schematicrepresentation of the system used in this work. The Ptelectrode used for these experiments was 3?5 mm longand had a diameter of 0?5 mm. The Pt electrode wasconnected to a copper wire and embedded into a 2?4 mmouter diameter plastic tube. In all experiments, 1?5 L of a10 g L21 H2SO4 and 70 g L21 Na2SO4 solution was used;sodium sulphate was used to decrease the ohmic dropbetween the working and reference electrodes. A SCEelectrode was used as reference electrode. 15 g of FeS2particles (100–200 mm) were used for the experiments. Forthe OCP measurements, the Pt electrode was introducedand fixed at the desired position inside the tank throughone of the perforations in the lid of the tank. Open circuitpotential measurements were conducted at differentpositions in the axial direction of the tank with the Ptelectrode placed 0?5 cm away from the wall of the tank inall the experiments. Open circuit potential was measuredfor 3 s with a sampling rate of 1 kHz, unless otherwiseindicated.

Results and discussion

Preliminary testsFigure 2 shows the separate effect of sand and FeS2 onthe recorded OCP. The addition of sand to the solution

1 Schematic representation of the leaching tank used in the

experiments. The values of L (0–9 cm) shown in the

scheme indicate the region of study. L59 cm corresponds

to the level of the liquid inside the tank and L50 cm to the

bottom

Olvera et al. Particle concentration distribution measurements

290 Canadian Metallurgical Quarterly 2015 VOL 54 NO 3

first decreased the OCP from 397 to 374 mV but after5 min the value of the OCP went to 395 mV, only 2 mVlower than the OCP recorded at the beginning of thisexperiment. After a steady OCP was reached (variationswere of no more than 0?1 mV min21), no importantdeviations were observed in the OCP transient profilewhen compared with the baseline experiment (Fig. 3).This last statement is based on comparison with thebaseline experiment. Indeed, the standard deviation, s,for the baseline experiment was 0?38 mV and the largestdeviation from the mean OCP was 1?3 mV. In thepresence of sand, the calculated s and largest OCP

deviation from the mean value were 0?77 (an increaseonly by a factor of 2) and 4?1 mV, respectively. On thecontrary, in the presence of pyrite, the value of sincreased to 22?2 mV and deviations from the meanOCP were larger than 40 mV. This represents anincrease by a factor of 58 with respect to the value of sobserved in the baseline experiment, which was causedby the magnitude of the deviations arising from thecollisions of the FeS2 particles with the Pt electrode.Because these deviations were not observed in thepresence of sand, it is possible to conclude that they werethe consequence of electrical and not mechanical inter-actions between the Pt electrode and the particles insolution. This effect was further confirmed by addingFeS2 particles in the presence of sand (Fig. 3) after theOCP in the presence of sand had become steady.

Leaching tank testsAfter having confirmed that the deviations observed inthe OCP when FeS2 particles collided with the Pt elec-trode were of an electrical nature, tests were conductedin the 3 L leaching tank. The experiments were firstconducted in the absence of FeS2 in order to obtain abaseline, which would allow subtracting the contri-bution of deviations inherent to the experiment(i.e. white noise) from the mean OCP. Figure 4 showsthe transient OCP profiles measured in the absence ofFeS2 particles (baseline) and in the presence of FeS2 attwo different heights in the tank.

For the baseline experiment in Fig. 4, a standarddeviation, s, of 0?78 mV was calculated. After FeS2 wasadded to the leaching tank, changes in potential wereobserved. The frequency of these deviations depended

2 Separate effect of sand (3 g) and FeS2 (3 g) particles in

the recorded open circuit potential (OCP) in a 10 g L21

sulphuric acid solution; stirring rate was 400 rev min21

3 Transient open circuit potential (OCP) profiles in the

absence and presence of FeS2 (3 g) and sand (3 g);

stirring rate was 400 rev min21

4 Open circuit potential (OCP) transient profiles at different

heights in the tank; stirring rate was 800 rev min21.

No solids were added in the baseline experiment,

measurements at 0 and 4?5 cm were conducted in the

presence of pyrite

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Canadian Metallurgical Quarterly 2015 VOL 54 NO 3 291

on the relative position of the Pt electrode inside thetank and deviations of up to 26 mV were observed,a much higher value than the standard deviationestimated for the baseline experiment, indicatingthat these measurements were not white noise but aresult of the collision of pyrite particles with theelectrode.

Figure 5 shows the effect of the stirring rate on theOCP transient profiles with the Pt electrode positionedat 4?5 cm from the bottom of the tank. In this case,increasing the stirring rate from 600 to 800 rev min21

resulted in an increase in the number and magnitude ofthe deviations in the OCP.

To estimate the number of collisions occurring atdifferent positions inside the tank, different approacheswere considered. The simplest approach was based onthe mean OCP value, OCPmean, measured at everyposition and the standard deviation calculated for thebaseline experiment in the absence of FeS2. Equation (1)shows the criterion that was used to consider a sampledOCP value as a collision

jOCP2OCPmeanjNss

. 1 ð1Þ

where Ns is the number of standard deviations and s thestandard deviation calculated for the baseline test.

In equation (1),Ns plays a role similar to that of a filter;the higher its value, the more stringent the criterionbecomes and the lower the chance that a ‘white noise’deviation will be considered as a collision. Figure 6 showsthe effect of this parameter on the collision rate axialdistributions.

One interesting observation is that, despite thedecrease in the magnitude of the estimated collision rate,

as Ns was increased the different profiles presented inFig. 6 are qualitatively very similar. If we assume thatthe number of collisions is directly proportional to theconcentration of particles for a given volume element inthe tank, then Fig. 6 shows that there is a largerconcentration of particles at the bottom of the tank(at 0 cm), right below the horizontal plane where theblades of the turbine are located. A second region ofhigh concentration can also be identified between 2 and4 cm, approximately at the same height correspondingto the position of the turbine in the tank. To helpvisualise this situation, Fig. 6 also shows a schematicrepresentation of the tank where the position of theblade and the level of the solution have beenindicated relative to the scale used for the axialdistributions.

To present the results more adequately, an averagecollision frequency was calculated for each profile shownin Fig. 6 so that the axial distributions could benormalised.

Owing to the difference between the densities of thefluid and the particles, and the relatively large size of thesolids (150–200 mm), it can be assumed that the particleswill not be in dynamic equilibrium with the fluid in thevicinity of the Pt electrode.3 Therefore, the collision ofthe solids with the electrode will be unavoidable and theconcentration of the particles will be proportional tothe collision rates. This can be used to calculatedimensionless particle concentration (c/cav) plots such asthose presented in Fig. 7.

In contrast to Fig. 6, the distributions shown in Fig. 7did not change considerably when Ns was increased.As a matter of fact, for Ns values higher than 3, constantdistributions could be observed. These distributions arein close agreement with those calculated by Derksen4 fora tank of similar geometry.

From the results observed in Fig. 7, a value of Ns53?0was selected to calculate the dimensionless concentrationdistributions presented in Fig. 8 where the distributionsobtained at 600 and 800 rev min21 are presented. Bothdistributions were very similar although particles wereless concentrated at the bottom of the tank when thestirring rate was increased to 800 rev min21. Further-more, a larger concentration of particles was observed ina zone between 4 and 6 cm at 800 rev min21.

Finally, from the transient profiles shown in Fig. 4,it was observed that a moving average would probablybe more appropriate than using the mean OCP inequation (1). When a moving average with linearweights, and taken with the 20 previous data points, wasused instead of the value for OCPmean in equation (1),the distributions shown in Fig. 9 were obtained. Thesedistributions were similar to those observed in Fig. 8 inthe sense that zones of high particle concentration wereobserved at the bottom of the tank and in a zone locatedbetween 2 and 6 cm, depending on the stirring rate.However, given the differences observed in thescales of both figures, it is clear that the results shown inFig. 9 yielded more uniform distributions whencompared to those presented in Fig. 8. This difference isa consequence of the transient profiles in the presence

5 Effect of stirring rate on open circuit potential (OCP)

transient profiles in the presence of pyrite. The Pt

electrode was positioned at a height of 4?5 cm

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292 Canadian Metallurgical Quarterly 2015 VOL 54 NO 3

of FeS2 not being flat as in the case of the baselineexperiment.

Although the profiles shown in Figs. 8 and 9 seem torepresent appropriately the solid particle distributionswithin the leaching tank, there are certain assumptionsand limitations related to the use of equation (1), bothusing the mean and the moving average OCP. Thefollowing is a list with the assumptions behind the use ofequation (1):

N Asmentionedbefore,OCPdeviations are assumed tobeproportional to the concentration of particles. Thisassumption is valid because of the large size of the par-ticles used in this work. However, smaller particles(in the range of 10 mm or less) will have a very rapidresponse to variations in the fluid flowandwill probablynot collide with the probe. Under these circumstances,the OCP deviations will not necessarily be directly pro-portional to the concentration of the solid particles.

6 Change in the axial collision rate profiles as a function of Ns (equation (1)) at 600 rev min21 and the relative position of the

turbine blades with respect to the scale of the axial distribution

7 Dimensionless particle concentration axial distributions

for different values of Ns at 600 rev min21

8 Effect of the stirring rate on the dimensionless particle

concentration axial distributions (Ns53)

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Canadian Metallurgical Quarterly 2015 VOL 54 NO 3 293

N Deviations meeting the criterion proposed byequation (1) are caused only by FeS2 collisions withthe Pt electrode. Any other deviation will not meet thecriterion and will not be counted as a collision. Thisassumption seems to be valid for Ns values higherthan 3 (see Fig. 7).

N One OCP deviation is caused by only one FeS2 particlecolliding with the Pt electrode. This is the equivalent ofsaying that two or more particles are not colliding sim-ultaneously with the Pt electrode.

N The experimental data have a normal distribution.

Because of the previous assumptions, the analysispresented in this work possesses certain limitations. Thesimultaneous collisions of two ormore particles with the Ptelectrode will be counted as only one collision. Thesampling rate of the equipmentwill also be a limiting factorand very high frequency collision rates may represent adifficulty, particularly for high solid concentrations andhigh stirring rates. Some of the collisions will also producedeviations that will not cause deviations in the OCPmeeting the criterion presented by equation (1).

As an attempt to address the limitations mentioned inthe previous paragraph, a different approach to analysethe experimental measurements was followed. For thisapproach, the OCP measurements were directly analysedusing a fast Fourier transform (FFT) algorithm to see if afundamental frequency component corresponding to thecollisions of the solid particles with the Pt electrode couldbe found. First, Fig. 10 shows the FFT correspondingto OCP measurements in the absence of solid particlesat different stirring rates with the electrode located at4?5 cm from the bottom of the tank. In the absence ofsolids, and with no agitation, only a weak frequency

component was observed at 1278 Hz, this was also pre-sent when the tank was stirred at 600 and 800 rev min21

but it shifted to 1313 and 1347 Hz, respectively. Whenthe solution was stirred, some frequency componentscould be observed. At 800 rev min21, the highest inten-sity peak corresponded to a frequency of 7?8 Hz, thefollowing two peaks correspond to some of its harmonicslocated at 15?6 and 31?2 Hz. The objective of findingthese frequencies was to avoid a possible confusionwith frequencies arising from the experiments in thepresence of suspended solids.

Figure 11 shows the frequency content of the OCPmeasurements in the presence of suspended FeS2 particlesat two different stirring rates. At 600 rev min21, a fun-damental frequency was observed at 8?7 Hz with itscorresponding harmonics at 17?4, 26?1 and 34. 8 Hz. Thisfrequency was very close to the frequency componentobserved for the 800 rev min21 experiment in the absenceof pyrite (Fig. 10) and it is not probable to assign it to anychanges in the system caused by the presence of pyrite.The same can be said for the 800 rev min21 experiment inFig. 11 where the highest peak was very close to the firstharmonic of the 8?7 Hz component observed at600 rev min21. Although not shown here, more exper-iments were conducted in the presence of different con-centration of solids, stirring rates, electrode position andsampling frequencies. From these experiments, it was notpossible to find any frequency that could be related tothe collision rate of pyrite with the Pt electrode,indicating that the process was entirely stochastic.Therefore, the analysis of this phenomenon on thefrequency domain does not seem to be an adequatealternative, at least under the experimental conditionsused in this work.

Although this method has been developed in thecontext of hydrometallurgical extraction systems, it is byno means limited to this area. Other possible fields ofapplication may include catalytic reactors, gas–solid–liquid systems, cementation tanks and in the electro-deposition of metal powders, to mention a few. Someexamples will be discussed in the paragraphs below.

As previously mentioned, the distribution of solids intanks is of great importance in fluid–solid operations.A measuring system like the one presented in this workwould be useful to determine if complete solids suspen-sion is achieved as well as the required minimum stirringspeed to achieve uniformity when pulp density or stir-ring rates are varied. The method could also be used tocharacterise and analyse the performance of draft-tube-baffle crystallisers or similar equipment.

The Actimag process consists in the fluidised cemen-tation of copper using iron particles subjected to anexternal pulsating magnetic field. The method presentedin this work could be used to monitor the concentrationof iron particles in the fluidised tank and control itsreplenishment rate to maintain high particle collisionrates, and reaction surface area at all times, thus makingthe process more efficient.

Liquid–solid fluidised bed heat exchangers are analternative to fouling control techniques; in these

9 Effect of the stirring rate on the dimensionless particle

concentration axial distributions (Ns53) using moving

averages in equation (1) instead of the mean OCP

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294 Canadian Metallurgical Quarterly 2015 VOL 54 NO 3

10 Frequency content of the open circuit potential (OCP) measurements in the absence of pyrite. Sampling frequency was

3 kHz

11 Frequency content of the open circuit potential (OCP) measurements in the presence of 1 wt-% pyrite. Sampling frequency

was 3 kHz

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Canadian Metallurgical Quarterly 2015 VOL 54 NO 3 295

systems, fouling is prevented by adding solid particlesthat collide with the walls of the fluidised bed and pre-vent the formation of precipitates or deposition ofsolids. In order for this equipment to work adequately, ahigh particle collision rate on the wall is required,making a uniform particle distribution necessary forhigh equipment performance. A method such as thatpresented in this work could be useful to determine theflow conditions under which uniformity will be achieved.

In flotation cells, a method like this could be used tomeasure the concentration of solids in the processstreams and to adjust the recycle flows in the flotationcircuit.

From the previous discussion, it can be seen that themethod presented in this work, after further develop-ment, could be used not only for the analysis of theperformance of an agitated solid–liquid system but alsofor control purposes, further extending its possibleapplications and uses.

ConclusionsIn this work, the authors have presented a new exper-imental technique to measure particle concentrationdistribution in stirred tanks. This technique consists ofmeasuring the deviations in the OCP measured with a Ptelectrode and caused by FeS2 particles collisions. Withthis technique and simple data analyses, it was possibleto obtain particle distributions that were similar to

results estimated in a previous work for a tank with asimilar geometry.4

The technique is simple and yields results in very shorttimes but has to be further developed to increase itsaccuracy and extend its applicability to other systems.Future work will be oriented in this direction aswell as in the development of a more adequate dataanalysis.

Despite being an intrusive technique, the procedurepresented in this work is simple and allows a qualitativeassessment of the distribution of particles withinthe tank in very short times. The results presented in thiswork correspond to one-dimensional axial distributions.Nevertheless, the experimental system can be easilymodified to extend it to the radial and angular coordi-nates so that concentration distributions for the wholesystem can be estimated.

References1. A. Tamburini, A. Cipollina, G. Micale and A. Brucato: ‘Particle

distribution in dilute solid liquid unbaffled tanks via novel laser

sheet and image analysis based technique’, Chem. Eng. Sci., 2013,

87, 341–358.

2. R. J. Goldstein: ‘Fluid mechanics measurements’, 2nd edn; 1996,

Washinton, DC, Taylor and Francis.

3. C. T. Crowe, T. R. Troutt and J. N. Chung: ‘Particle interactions with

vortices’, in ‘Fluid vortices: fluid mechanics and its applications’, (ed.

S. I. Green), 829–861; 1995, Dordrecht, Kluwer Academic Publishers.

4. J. J. Derksen: ‘Numerical simulation of solid suspensions in a

stirred tank’, Am. Inst. Chem. Eng. J., 2003, 49, 2700–2714.

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