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Chemical Engineering and Processing 49 (2010) 1199–1204

Contents lists available at ScienceDirect

Chemical Engineering and Processing:Process Intensification

journa l homepage: www.e lsev ier .com/ locate /cep

ydrodynamic study on radially cross-flow fluidized bed multi-stagedon-exchange column

upesh Verma, Ravi Kumar, Devesh M. Pandey, Nishith Verma ∗

epartment of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

r t i c l e i n f o

rticle history:eceived 29 May 2010ccepted 2 September 2010vailable online 9 September 2010

a b s t r a c t

A hydrodynamic study was carried out on our patented radially cross-flow fluidized bed staged column,with the salt laden water and solid resins flowing counter-currently, to determine the loading/floodingcriterion for a stable operation of the column, and also to ascertain the mal-distribution in flow. Residensetime distribution measurements were taken to address the latter part of the study. The data collected from

eywords:astewater

on-exchangeluidized bedulti-stage column

the hydrodynamic measurements show a wider range of liquid and solid flowrates that can be used for thestable operation of the column, in comparison to that obtained in the conventional multi-staged column.The extent of mal-distribution or channeling is also relatively smaller in the former. The observations areconsistent with the mass-transfer results obtained in our recent study, where the separation of dissolvedsolids using the radially cross-flow ion exchange column was found to be 40% larger than that in the

ydrodynamicsesidence time distribution

conventional column.

. Introduction

Ion-exchangers are commonly used in removing dissolvedolids in wastewater. Softening of water, de-nitrification of potableater rich with nitrate ions, and treating of industrial aqueous

ffluents from fertilizer industries, containing significantly largeuantities of phosphate ions are some of the common examplesf the application of the ion-exchanger resins. The ion-exchangereatment is typically carried out in the packed bed or column ofolid resins, with wastewater flowing upward through the bed. Theesins in the bed may be fixed or fluidized depending on the veloc-ty of the water. Mal-distribution or channeling of the liquid floweading to under-utilization of the ion-exchangers, and pluggingr fouling of the bed leading to periodic disruption are some ofhe drawbacks of the operation. Fluidized bed staged column, withater and solid resins flowing counter-currently, overcome theserawbacks. The operation is continuous and smooth. The ions load-

ng of the resins is also relatively larger [1]. There are several sucholumns in operation [2–5].

The geometrical configuration of a conventional multi-stagedon-exchanger column is similar to that of a sieve-trays distilla-

ion column used for vapor–liquid contacts, with the liquid flowingcross the stage (sieve) to the downcomer to the subsequent stage,nd the vapor flowing upward through the sieve to the pool of theiquid to the next stage in the column. In the ion-exchange staged

∗ Corresponding author. Tel.: +91 512 2596124; fax: +91 512 2590104.E-mail address: nishith@iitk.ac.in (N. Verma).

255-2701/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2010.09.001

© 2010 Elsevier B.V. All rights reserved.

column, if the velocity of the water is set at or larger than mini-mum fluidization velocity, the fluidized solid resin particles flowacross the sieve and pour onto the next stage through the down-spout, whereas the wastewater flows upward through the sieve,then through voids between the fluidized solids, to the next stage.

In our recent study, we described the configuration and opera-tion of our patented radially cross-flow multi-staged column [6,7].The difference between the configuration of this column and thatof the conventional column is the design of the downspouts. In theformer, there are two different types of downspouts mounted alter-nately on the stages, one at the center of the stage and the othernear the circumference of the column. The mass-transfer study con-ducted on the novel column showed 40% larger rate of the solutetransfer from the water to the resins, or alternatively, 40% fewernumber of stages than that in the conventional column [7].

This study pertains to the hydrodynamic study carried out on thenew column. There are two objectives: (1) establish the operatingrange of water and resins flowrates without loading and floodingin the column, and (2) determine the residense time distribution(RTD) of the liquid phase with a view to ascertaining the mal-distribution or channeling in the column, relative to that in theconventional column.

2. Radially cross-flow fluidized bed ion-exchange column

2.1. Geometrical configuration

Fig. 1a is the schematic of the Perspex made column(height = 500 mm and ID = 100 mm) used as a liquid–solid multi-

1200 R. Verma et al. / Chemical Engineering and Processing 49 (2010) 1199–1204

mn (le

su(woie3scl(ectslvc

2

flsdspstotbSt

2c

oTpetss

Fig. 1. (a) Schematic of three-stage radial-flow fluidized bed colu

tage contactor for purification of water by the removal ofndesirable dissolved solutes. The column consists of six stagesstage height = 65 mm) assembled together with flange jointshere each of the stages incorporates a brass made mesh with

penings (0.2–0.7 mm) fitted on a ring (aluminum), where the rings sandwiched between the flange joints on its either side. In thexisting arrangement, the resin bed heights may be varied betweenand 15 mm. The water flows upward from one stage to the next

tage through the mesh, with the aid of a pump. Solid resins areontinuously fed from the top using a conveyer belt at the regu-ated speed. The unique feature of the contactor is the downspoutdowncomer) placed between the stages, wherein downspout isither central downspout located at the center of the stage or cir-umferential downspout located around the periphery of the stagehrough which resin particles move from one stage to the nexttage. The central downspout or the circumferential downspout isocated in the alternate stages. Fig. 1b is the schematic of the con-entional staged column, which is similar in configuration to theonventional column used for vapor and liquid contact.

.2. Operation

In a typical operation, there is a stable range of water and resinowrates over which the fluidized resin particles flow across thetage, radially inward or outward depending on the type of theownspout (central or circumferential), without choking the down-pouts. Water flows upward without flooding the column. The resinarticles initially fill up the bed only to a certain fraction of thetage height. As the flowrate of water is gradually increased pasthe minimum fluidization condition, the bed expands to the heightf the downcomer and the solid resins start pouring from uppero adjacent lower stage. As the solids pour, difference between theed-depths from the center to the periphery of the stage increases.uitable choice of liquid and solid flowrate ensures smooth opera-ion of the column without loading and flooding.

.3. Mechanistic steps and comparison with the conventionalolumn

Fig. 2 describes the flow-path of the solid particles prevalentn a stage in the conventional and new (radial flow) columns.he schematic shown on the left in the figure is the typical flow

attern existing on the stage of the conventional solid–liquid ion-xchanger column having downspout fitted near the periphery ofhe column. In such design, the location of the downspout on thetage is eccentric. As a result, the flow of solid particles across thetage is non-uniform, with certain fraction of the solids transferred

ft) and (b) conventional cross-flow fluidized bed column (right).

to the subsequent (down) stage through the downspout by takingthe shortest route. This path is marked as “a” in the figure. On theother hand, there are certain fractions of the solids which move tothe downspout through the relatively longer path marked as “b” inthe figure. There are regions around the periphery where there arenearly stagnant resins particles. Some of the particles in this regionalso move to the downspouts. This path is marked as “c”. In otherwords, some particles have longer paths than the others, with sig-nificant regions of the solids being stagnant, thus giving rise to theoverall non-uniform RTD.

This shortcoming (channeling or short-circuiting) is overcomein the present (new) design. The configuration of the two typesof downspout between two successive stages in the column, onearound the outer periphery of the stage and the other at thecenter of the stage, results in the identical path-length of each flu-idized solid particle moving across the stage to the successive stagethrough the downspout (circumferential or radial) in the column.The movement of fluidized resin particles in such an arrangement,where resin particles flow in the radial direction from the cir-cumferential downspout into the central downspout is pictoriallydepicted by the schematic drawn on the right hand side in Fig. 2. Thepath is marked as “a”. The reverse path of equal length correspondsto the solids transferred from the central downspout to the circum-ferential downspout. In either case the path length of each solidparticle is identical. The consequence is the improved (uniform)RTD with no mal-distribution of the solids on the stage. The imme-diate advantages of such distribution in the new column over theconventional designed column are realized in terms of (1) smoothfluidization and movement of the particles over the stage, (2) widerange of operation without flooding and loading (1.5 times wider),(3) small pressure-drop (30% smaller), and most importantly, and(4) few number of stages (40% less) due to higher mass transfer ratebetween solid and liquid phases.

The last advantage was experimentally demonstrated in ourprevious study related to mass transfer [5]. We substantiate theremaining advantages of the new column through the hydrody-namic study described in the subsequent section of this paper.

3. Operating range of resin and water flowrates

In a typical counter-current liquid–solid operation, it followsnaturally to determine a priori the operating range between flood-

ing and loading limits. From the first principle, it is obvious that theminimum liquid velocity must exceed Umf, the minimum fluidiza-tion velocity, and the maximum velocity must not exceed Ut, theterminal velocity of the particle to prevent solids entrainment inthe liquid. The two characteristic velocities, dependent on the par-

R. Verma et al. / Chemical Engineering and Processing 49 (2010) 1199–1204 1201

colum

tetd

tflit

Fs

Fig. 2. Solid flow patterns on a stage in (a) conventional

icle size and the physical properties of water and solid (resin), werexperimentally determined in our previous study [5]. The descrip-ion of the method to determine Umf and Ut and the correspondingata may be obtained from the aforementioned study.

In addition to two parameters, U and U , the physical situa-

mf t

ion in the counter-current operation suggests that at a fixed waterowrate, there are two limits of the solid flowrate. If the flowrate

s set between the limits, the solids will be completely fluidized byhe upward flowing water. Below the lower limit, the stage will be

ig. 3. Progressive steps during fluidization. The bottom figures show radial inward or otage.

n (left) and (b) radial-flow fluidized bed column (right).

flooded with water and above the limit the stage and downspoutwill be loaded with the solids. The similar arguments hold good forthe range of water flowrate at the fixed solid flowrate.

Between the two limits, the fluidized particles flow on the stagedue to the steady height gradient caused by the difference between

the heights of the solid-bed, hu and hd, either from centre to periph-ery or vice versa, as water flows upward through voids betweenthe solids. The scenario of progressive steps during fluidization isdepicted in Fig. 3. The stage may be initially filled with the resin

utward flow of resins under steady-state conditions due to height gradient on the

1202 R. Verma et al. / Chemical Engineering an

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the data for the two columns also show approximately 30% smallerpressure-drop in the new column than in the conventional column,the reason again attributed due to the uniform distribution of thefluidized particles in the new column.

ig. 4. Operating range of solid and water flowrates in multi-stage columnID = 100 mm, ε = 0.53, and dp = 0.92 mm).

articles only till ho < hd. As the water flowrate is increased, the bedxpands and is filled with particles till the stage height hd. Under theteady-state conditions, resin particles flow from centre to periph-ry of the column or vice versa due to height-gradient across thetage.

Fig. 4 describes the experimentally obtained solid flowrate as theunction of water flowrate corresponding to two limits of operationflooding and loading) for the radially fluidized column used in thistudy. The data are shown for different stages. Corresponding toach stage, the dark symbols represent the maximum solid flowrateithout loading of the stages with excess solids at a fixed waterowrate for the steady operation of the column. The blank symbolsepresent the minimum solid flowrate without flooding of the stageith water at a fixed flowrate. The vertical distance between two

ymbols defines the operating range of fluidization without loadingnd flooding of the stages and downspouts at given water flowrate.or example, at a water flowrate of 1.5 l/min the operating rangef solid flowrates is observed to be between 6 and 20 g/min corre-ponding to flooding and loading conditions in the column operatedith one stage. Solid flowrate smaller than 6 g/min gradually leads

o the stage flooded with water, whereas that in excess of 20 g/minauses choking of the downspout tube due to excess solid flowrate.herefore, it may be inferred that if the column is operated at aolid flowrate between 6 and 20 g/min, with the water flowrate sett 1.5 liter per min (lpm), operation will be continuous with theteady heights of hu and hd established on the stage, as shown inig. 3.

As also observed from Fig. 4, the minimum water flowrateequired for the operation is relatively larger in the column oper-ted with more number of stages. The resin flowrate is observed toncrease with increasing water flowrate for both operating curves,

ooding and loading. In addition, the minimum and maximum solidowrates are observed to increase with increasing number of stagest fixed water flowrate. In either case the solid flowrates graduallyevel off. From the plot, the capacity of the water pump and the

d Processing 49 (2010) 1199–1204

maximum speed of the conveyor belt may be determined. Thesequantities are 2.5 lpm and 40 g/min, respectively for the case dis-cussed in Fig. 4. From the foregoing arguments, it also follows thatin the column of relatively larger diameter, flowrate of the upwardgoing water must be kept sufficiently high to ensure that thereis no settling of the solids. In other words, it is the ratio of thesolid to liquid phase velocity (and not the individual velocities orflowrates) that sets the criterion for smooth operation of the col-umn. Therefore, the dimensionless group, us/uo, may be construedas an operating parameter for the multi-staged column, where us

and uo are the superficial velocities of the solid and water.Fig. 5 describes the ratio us/uo as a function of the superficial

velocity of water corresponding to the different number of stagesin the column. The minimum and maximum values of the ratios cor-respond to loading and flooding conditions. As observed the ratioassumes a maximum value when the column is operated for oneand two stages. For larger number of stages, both operating curves(loading and flooding) monotonically decrease and have asymp-totical convergence. The column was typically operated with 5–6stages for the maximum efficiency of separation. The safe and con-servative operating limits of the water and solid flowrates may bedefined from the corresponding plots for the 6th stage of 6-stageoperated column and are shown in the inset of Fig. 5. Comparingthe ratios of us/uo obtained in this study for the new column tothose obtained in our previous study on the conventional column,it can be inferred that the operating range in the former is wider(approximately 1.5 times) than that in the conventional column.From the pictorial presentation of the state of fluidization presentedin Fig. 3, it is logical to conclude that the uniform flow paths (radiallyinward or outward) of the fluidized particles permit the relativelywider margin of operation in the new column than in the old col-umn where the flow paths of the resin particles are non-uniform(eccentric). We also point out that we carried out several pressure-drop measurements (not presented here for brevity) under varyingsolid and water flowrates in the new column. The comparison of

Fig. 5. Operating range of us/uo in multi-stage column (ID = 100 mm, ε = 0.53, anddp = 0.92 mm).

ing and Processing 49 (2010) 1199–1204 1203

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0.2

0.4

0.6

0.8

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J(t

)

T/T res

Data Flow rate Disperson

(lpm) No

1.6 0.08

2.0 0.12

2.6 0.16

J(t

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T/T res

3.02.52.01.51.00.50.00.0

0.2

0.4

0.6

0.8

1.0

Data Flow rate Disperson

(g/min) No

24 0.08

30 0.25

35 0.40

3.02.52.01.51.00.50.00.0

0.2

0.4

0.6

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J(t

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T/T res

Data Stage height Disperson

(mm) No

5 0.08

10 0.15

15 0.25

(a)

(b)

(c)

Fig. 6. (a) Effect of solution flowrate on residence time distribution (top) (hd = 5 mm,

R. Verma et al. / Chemical Engineer

. RTD measurements

RTD measurement is a simple technique to ascertain the extentf deviation from ideal flow. By ideal flow we essentially mean twoypes of flow in the present context of contact between two phaseswater and resin particles) in the staged ion-exchanger: ideal tubu-ar plug flow with segregated fluid elements and ideal mixed floweactor with completely mixed elements. Deviation from ideal flowrises from channeling or dead-spots of fluidized solid particles onhe stage as pictorially described in Fig. 2. It is important to pointut that during a typical operation of the column, the extent ofhanneling or possible bypassing of some of the solid regions byhe fluid element within the bed could not be visually detected,lthough the top surface of the bed appeared completely fluidizedith upward flowing water. In this respect, RTD data are useful in

aining insight into the uniformity of flow on the stage.Typical of an RTD study, the test included injection of a tracer

NaOH at a pre-determined concentration level) in water for thetep change in the concentration at the inlet to the column. Theesponse (variation in the conductivity) was measured at the out-et. The spherical glass beads were used for the solid phase sohat the particles were un-reactive to NaOH laden water. Measure-

ents were made for varying water and beads flowrates within thewo operating limits (loading and flooding) and for different stageeights.

There is another important aspect of the RTD study in theresent context of solid–liquid flow. Although it may be useful toetermine individual RTD of solid and liquid phases, it is fair to notehat the existing analytical techniques to measure concentrationsithin solids are prone to severe measurement error and may not

e truly relied upon to construct RTD response curve for the solidhase. A literature review indeed shows that most of the studiesn G–S or L–S systems pertain to injection and measurement ofracer in the gas or liquid phase only [8–10]. Therefore, the resultsresented in the following section on the RTD data for the liquidwater) phase may be considered reasonably accurate enough toualitatively corroborate the mechanistic steps proposed in Sec-ion 2.3 with regard to the types of solid flow patterns existing onhe stage in two columns (new and conventional).

Fig. 6a describes the RTD data obtained for three water flowrates.he remaining operating variables including the solid flowrate andowncomer height were kept constant. The data are presented inhe non-dimensionalized form, with exit concentration and timeon-dimensionalized with respect to the inlet concentration andverage residence time in the column, respectively. The sigmoidalype of output response curves as observed in the figure is typicalf the RTD data, with the tracer concentration at the exit of theolumn increasing slowly during the initial part of the experimentefore later increasing at a rapid rate. Towards the end, the concen-ration asymptotically approaches the level corresponding to thatf the inlet concentration. The effects of water flowrate on RTD areonsistent with the physical situation.

Fig. 6a also describes the corresponding theoretical curves. Theurves were obtained due to the 2D axial dispersion model. Theodel governing equation incorporates the transport of solute

tracer) in water flowing upward through the bed-voids due toonvective and diffusion/dispersion effects:

∂C∂t

+ V · ∇C = D∇2C (1)

Assuming the flow in the z-direction through the packed bed oforosity, ε, on the stage of height h and radius R and allowing for dis-ersion in both axial and radial directions, the solute conservationquation in the water phase can be re-written in the dimensionless

Cinlet = 0.05 M, and Qs = 24 g/min). (b) Effect of solid flowrate on residence timedistribution (middle) (hd = 5 mm, Cinlet = 0.05 M, and Ql = 1.6 lpm). (c) Effect of bedheight on residence time distribution (bottom) (Qs = 24 g/min, Cinlet = 0.05 M, andQl = 1.6 lpm).

1 ing an

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t

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204 R. Verma et al. / Chemical Engineer

orm as

∂C∗∂t∗ + ∂C∗

∂ϕ= 1

Pe,z∂C∗∂ϕ

+ 1Pe,r

(hR

)1�

∂�

(� ∂C∗

∂�

)(2)

here the liquid phase concentration, axial and radial distances,nd time are non-dimensionalized by the inlet solute concentra-ion, stage height, radius of the column, and average residenceime of the solute in the bed, respectively. The two dimension-ess groups, Pe,z and Pe,r, are the peclet numbers and representhe convective effects in the axial (flow) and radial directions, rel-tive to dispersion effects in the respective direction. The inversef Pe may also be recognized as dispersion number and used as andjustable parameter(s) in the present study to explain the data. Inhe extreme situation, very large dispersion number reflects nearlynfinite mixing as in ideal mixed flow reactor and very small num-er reflects zero mixing as in an ideal tubular flow. As explained

ater in the texts, the RTD data collected in this study were foundo be fitted with the model predicted values by allowing only thexial dispersion number (1/Pe,z) to vary with water or solid veloc-ty, whereas the radial dispersion number was set constant. For theatter, the dispersion coefficient was set equal to the diffusivity ofaOH in water at the experimental temperature. It is important tooint out that to the best of our knowledge, no data for the disper-ion or peclet number in the cross-flow fluidized bed is available inhe literature.

The 3D partial differential Eq. (2) was numerically solved bylternate direct implicit (ADI) method with the initial and boundaryonditions [11]:

∗ = 0, C∗ = 0; ϕ = 0, C∗ = 1; ϕ = 1, ∇∗C∗ = 0;

= 0, ∇∗C∗ = 0; � = 1, ∇∗C∗ = 0 (3)

here the step-change in the concentration level has been set forhe inlet to the bed, symmetric boundary condition is applied at theenter of the column, long tube approximation has been made forhe outlet, and the column walls are assumed to be non-reactive.

As observed from Fig. 6a, theoretical curves fit the correspond-ng data reasonably well, with variation in the dispersion coefficientrom 0.08 to 0.16 as water flowrate increases from 1.6 lpm to.6 lpm. While increase in the dispersion number with increas-

ng flowrate is consistent with the physical situation, there is anmportant inference that can be drawn with regard to the extentf uniformity or channeling on the stage. Since J(t) represents theraction of the fluid elements having residence time between 0 and, single value of dispersion number required to fit the data overhe entire range of residence time shows each fluid element hasqual path length. At this juncture, it is only appropriate to recallur previous study on hydrodynamics and refer the correspond-ng RTD data obtained for the conventional column, in which casewo values of dispersion coefficients were required to explain theata at a fixed flowrate [5]. The results have significance as thetage in the conventional column may be assumed to be segregatednto two zones having different path lengths and thus differentverage residence times. The shorter path length marked as “1”n the schematic (left) in Fig. 2 corresponds to the zone without

hanneling and the longer path length “2” corresponds to the zoneith channeling or nearly stagnant zone. No such segregated zonesay be construed in the new column. The consequence is uni-

ormity in the (fluidized) solid particles distribution in the newolumn.

[

[

d Processing 49 (2010) 1199–1204

Fig. 6b describes the RTD data for varying solid flowrates keepingthe remaining variables constant. Similar experimental observa-tions and inferences are made from the RTD data. The dispersionnumber increases from 0.08 to 0.40 with increasing solid flowratesfrom 24 g/min to 35 g/min. In addition, single value of dispersionnumber is required to fit the data over the entire range of thefluid residence time. Re-referring to the corresponding RTD dataand the model curve for the conventional column, as reported inRef. [5], dispersion coefficient was required to be adjusted overtwo ranges of residence times, one for small residence time andthe other for large residence time, as the solid flowrates weregradually increased keeping the liquid flowrate constant. Finally,from the RTD data obtained for varying stage heights, the modeladjusted dispersion number, constant over the entire residencetime, increases from 0.08 to 0.25 with increasing bed height from5 mm to 15 mm, as shown in Fig. 6c. The results suggest increas-ing dispersion in axial direction with increasing bed height, as thefluid element encounters relatively larger amount of solids flowingacross the stage.Conclusions

The hydrodynamic study conducted on the radially cross-flowfluidized bed ion-exchange column shows a wider range of liq-uid and solid flowrates for the operation of the column, withoutloading and flooding, in comparison to that for the conventionalion-exchange column. The path-length of the solids during fluidiza-tion on the stage in the new column is uniform, with no or minimalchanneling or stagnant zone of the solids on the stage. A 2D modeldeveloped to explain the RTD data corroborates the proposedmechanistic features of the flow in the radially cross-flow fluidizedbed column. The model parameter, the axial dispersion number isfound to be constant over the residence time and increases withincreasing water flowrates, solid flowrates and stage height. Thefindings from the hydrodynamic study are consistent with theresult obtained from the previous mass transfer study that largerseparation is achievable in the new ion-exchange column than inthe conventional column.

Acknowledgement

The authors acknowledge the partial financial support fromthe Department of Science and Technology (DST), New Delhi toconduct this study.

References

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idized bed ion exchangers, Chem. Eng. Process. 45 (2006) 31–35.[5] A. Singh, R. Verma, K. Kishore, N. Verma, Multistage fluidized bed column:

hydrodynamic study, Chem. Eng. Process. 47 (2008) 957–970.[6] R. Verma, N. Verma, Liquid–solid radially cross-flow multi-stage fluidized bed

contactor, Indian Patent IPA No. 830/DEL/2007 (2007).[7] R. Verma, G. Srivastava, N. Verma, Novel multi-staged radially cross-flow flu-

idized bed ion-exchange column, Chem. Eng. Process. 48 (2009) 396–407.[8] L. Dinesh, V.P.S.T. Sai, A model for residence time distribution of solids in a

rotary kiln, CJChE 82 (2004) 392–398.[9] M.P. Babu, Y.P. Setty, Residence time distribution of solids in a fluidized bed,

CJChE 81 (2003) 118–123.10] F. Berruti, A.G. Liden, D.S. Scott, Measuring and modeling residence time distri-

bution of lowdensity solids in a fluidized bed reactor of sand particles, Chem.Eng. Sci. 43 (1988) 739–748.

11] J.H. Ferziger, Numerical Methods for Engineering Application, 2nd ed., Wiley,NewYork, 1986.