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Experimental study of the effect of bubbles, drops and particles on the product distribution fora mixing sensitive, parallel-consecutive reaction systemBrilman, D.W.F.; Antink, R.; Swaaij, W.P.M. van; Versteeg, Geert

Published in:Chemical Engineering Science

DOI:10.1016/S0009-2509(98)00298-X

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Chemical Engineering Science 54 (1999) 2325}2337

Experimental study of the e!ect of bubbles, drops and particles on theproduct distribution for a mixing sensitive, parallel-consecutive

reaction system

D.W.F. Brilman*, R. Antink, W.P.M. van Swaaij, G.F. Versteeg

Department of Chemical Engineering, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands

Abstract

For stirred multiphase reactors the e!ect of a dispersed (gas, liquid or solid) phase on the product distribution for a mixing sensitivereaction was tested. Turbulence modi"cation due to the presence of dispersed-phase particles has been reported frequently inliterature, but the extent of the e!ect in a stirred multiphase reactor was not clear. In this work the well-known mixing sensitive diazo-coupling reaction system was selected to investigate the in#uence of the changes in the turbulent kinetic energy spectrum on theproduct distribution. This reaction system was found to be suitable to study the in#uence of a dispersed (gas, liquid or solid) phase.The Engulfment model could describe the single-phase experiments and describes reasonably well the multiphase experiments whenthe e!ective dispersion properties are implemented. For the liquid}liquid dispersions e!ects of de-localization of the reaction zonewere encountered, due to Naphthol extraction by the dispersed phase. The Engulfment model was extended to incorporate masstransfer and the "rst experimental and simulation results are promising. Additional, experimental and theoretical, research studyingthe combined e!ects of the mass transfer rate and the mixing rate for the liquid}liquid dispersions is highly desired. ( 1999 ElsevierScience Ltd. All rights reserved.

Keywords: Mixing; Multiphase; Experimental study; Chemical reaction

1. Introduction

In multiphase reaction systems with multiple, (ir-)re-versible, chemical reactions mass transfer, mixing andchemical reaction rate determine in an open competitionthe conversion rate and also the "nal product distribu-tion. An example of such a complex multiphase reactionsystem is the Koch carbonylation of ole"nic compoundsto produce carboxylic acids (Falbe, 1980). This complexgas}liquid}liquid reaction system is operated on indus-trial scale in a stirred liquid phase, pressurized reactor.Apart from the desired reaction, the acid-catalyzedaddition of carbon monoxide to an ole"n, undesiredole"n polymerization may occur. On analyzing thissituation, the question rose to what extent the mixing inthe continuous liquid phase near the feedpoint of the

*Corresponding author. Tel.: 0031 534894479, fax: 0031 534894774.

ole"nic reactant (and with this, the product distribu-tion) was a!ected by the presence of a dispersed (liquid)phase. A second important issue is the interactionbetween mixing and mass transfer between the continu-ous liquid phase and the dispersed liquid phase inthe zones neighboring the feedpoint. An experimentalstudy investigating the extent of these in#uences,also at higher volume fractions dispersed phase, usinga well-known model reaction system, as the diazo-coup-ling reaction proposed by Bourne et al. (1981), wasconsidered suitable to study these (micro-)mixingphenomena.

For a complex reaction system with fast chemicalreactions in a parallel-consecutive reaction scheme as,e.g.: A # B P P, P # B P X the production ofcomponent X depends on the local concentrationsof B and P in the reaction zone. In case of poor mixingcharacteristics at the molecular scale local concentra-tions of B near its feedpoint in the reactor may di!ersigni"cantly from its (bulk phase) average value, leading

0009-2509/99/$} see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 2 9 8 - X

to an increase of the production of the consecutivereaction product X.

The micromixing process can be studied experi-mentally by using chemical test reactions. The diazo-coupling reaction of Bourne et al. (1981), for which thereaction kinetics are well established (Bourne et al., 1990),is frequently used for this purpose. This reaction systemconsist of a set parallel, consecutive instantaneously fast,irreversible reactions, see Eqs. (1) and (2):

A#B k1,oN oR, A"1-naphthol, (1a)

A#B k1,pN pR, B"diazotized sulfanilic acid, (1b)

oR#Bk2,oNS, oR"mono-azo coupling product

(ortho), (2a)

pR#Bk2,pNS, pR"mono-azo coupling product (para),

S"bis-azo coupling product. (2b)

Usually the reaction system is operated semi-batch wise.Reactant B is added slowly to the reaction mixture,containing an excess of reactant A, where B is rapidlyconverted into the mono azocompounds (oR, pR) and thebis-azocompound S. The product distribution is uniquelycharacterized by the product ratio X

S, representing the

selectivity of component B towards product S, given inEq. (3).

XS"

2[S]

2[S]#[oR]#[pR]. (3)

Mixing may a!ect the product distribution parameterX

S, signi"cantly. In a well mixed reactor (at high energy

dissipation levels) almost exclusively mono-azo couplingproducts will be formed and, consequently, the X

Svalue

will be low.The process of mixing a reactant into a bulk phase can

be considered at di!erent scales, starting with the spa-tially distribution of feed lumps through the bulk phase(macromixing), followed by reduction of the scale of theunmixed lumps by breakage without in#uence on mo-lecular mixing (mesomixing). The smaller #uid elementsare subjected to laminar strain and molecular di!usionbecomes more and more important with decreasing char-acteristic length scale (micromixing). Finally, homogen-eity at the molecular scale is rapidly attained throughmolecular di!usion.

The mixing process can be related to turbulent energyspectrum (the distribution of turbulent energy over the

eddy length scale) of the bulk liquid phase, see, e.g.Baldyga and Pohorecki (1995) for an overview. The vis-cous-convective deformation of #uid lumps, which in-creases the e!ect of concentration variance dissipation bymolecular di!usion, is considered to be the most impor-tant micromixing feature.

The reactant concentration in the reaction zone canbe in#uenced by macroscale, mesoscale and microscalee!ects. To interpret the experimentally determinedproduct distribution in terms of micromixing character-istics, the macroscale and mesoscale mixing e!ects needto be excluded. This can be checked experimentally byvarying the feed time of the ("xed amount of) reactantB containing solution. For a semi-batch reactor a criticalfeed time can be observed, above which the productdistribution is no longer sensitive to the feed time(Bourne and Thoma, 1991). Under these conditions theproduct distribution is determined by the micromixingprocesses of #uid element deformation and moleculardi!usion in the viscous-convective and viscous-di!usivesubranges of the turbulent energy spectrum. Since theseprocesses are governed by the energy dissipation ratesand #uid viscosity, local energy dissipation rates can bedetermined.

2. Theory

2.1. Single-phase-systems

The micromixing process is determined by viscousdeformations of #uid feed lump elements and moleculardi!usion. The rate of viscous deformation of the #uidelements is generally assumed to be proportional to(e/l)1@2, the Kolmogoro! rate of strain in the viscoussubrange. Due to turbulent vorticity the long thin slabsof the deforming #uid lump are twisted and #uid from theenvironment is incorporated. Now thin lamellar struc-tures are formed in which high concentration gradientsare formed by viscous deformation. In these structures,concentration variances are rapidly dissipated by mo-lecular di!usion, thereby losing the lamellar character.For not too high Schmidt numbers (Sc) the di!usionprocess is faster that the rate of incorporation of #uidfrom the environment, called &&Engulfment'', and thisengulfment process is dominating micromixing (Baldygaand Pohorecki, 1995).

The single-phase experiments with the diazo-couplingtest reaction presented in this work are conductedin the regime where the Engulfment model, E-model(Baldyga and Bourne, 1989) can be used to describethe micromixing process. Due to incorporation of#uid from the environment the feed lumps grow at theexpense of the environment and the concentration inthe reaction zone changes due to chemical reactionand mixing with bulk #uid-phase elements of equal

2326 D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337

volume:

dci

dt"E (c

"6-,, i!c

i)!R

i. (4)

The engulfment rate, E, is the main parameter in thismodel and is related to the local energy dissipation rateby

E+0.058AelB

0.5"0.058A

eok B

0.5. (5)

From experimentally determined product distributions(X

Svalues), using the E-model by Baldyga and Bourne

(1989), the local energy dissipation rates in the reac-tion zone can be derived. Since the relative energydissipation in an agitated vessel may vary stronglywith position, it is important to ensure that the reac-tion is completed in a zone of more or less homogeneousenergy dissipation rate. Otherwise, the trajectory ofa feed lump through zones of di!erent energy dissipa-tion levels needs to be considered (Baldyga and Bourne,1988).

2.2. Turbulence modixcation by particles

For multiphase systems, the presence of dispersed-phase particles may in#uence the macroscale continuous-phase hydrodynamics as well as the turbulent energyspectrum, and thus mixing at di!erent scales. Dependingon holdup, particle size and -density the particlesmay interact with the macroscale #uctuations therebyextracting energy from the average #ow and increas-ing high-frequency turbulence by vortex shedding(&turbulence production'). Small, light particles will tendto interact with high-frequency microscale #uctuations.Turbulent kinetic energy is dissipated for the accel-eration of dispersed-phase particles (&turbulencedamping').

Gore and Crowe (1989) and Hetsroni (1989) reviewedthe limited amount of available experimental data onturbulence modi"cation by (dispersed) particles. The re-sults, mainly obtained for gas}solid and a few forgas}liquid systems at low particle loadings, were inter-preted di!erently. Gore and Crowe (1989) proposed thatthe way in which the turbulence level is modi"ed solelydepends on the particle size; &small particles' with respectto the turbulence length scale pick up energy from theturbulent eddies and thus decrease the turbulence level,whereas &large particles' cause signi"cant vortex shed-ding, thereby increasing the turbulence. From their datacorrelation it seems that the turbulence damping e!ect ismarginally, whereas the turbulence increase by largerparticles is more pronounced. Hetsroni (1989) used theparticle Reynolds number to correlate essentially thesame set of data. Particles with small Reynolds numbers((400) were considered to suppress turbulence, whereas

particles under high particle Reynolds number increasedthe turbulence levels.

Modi"cation of the turbulence kinetic energy spec-trum for a continuous liquid phase by solid particleshas been studied experimentally very scarcely. Kadaand Hanratty (1960) studied the e!ect of solid par-ticles on turbulent di!usion of injected KCl pulses forslurry systems falling through a vertical pipe. They foundthat solids did not have a large e!ect on the turbulencelevel, except for solids having an appreciable slip velocity(high density and/or relatively large (for glass spheres'300 lm) and at su$ciently high solids concentrations(2}3 vol% for glass spheres)). At these conditionsthe turbulent eddy di!usivity calculated increased 2.5times.

Schreck and Kleis (1993) presented a comprehensivestudy on the e!ect of solid spherical particles(600}700 lm, plastic (o

p"1049 kg/m3) and glass

(op"2500 kg/m3)) on grid-generated liquid-phase tur-

bulence. In their study a monotonic increase in energydissipation rate with particle concentration wasobserved. The additional energy dissipation rate forthe glass particles was almost two times that of thelight plastic particles. From the literature overviewby Schreck and Kleis (1993) it is clear that the additionof solid particles may indeed modify the turbulencespectrum (and thus a!ect mixing). For gas}solidtwo-phase #ow, experimentally both the e!ects ofincreasing turbulence for large particles (+1 mm) anddecreasing turbulence for small particles (+200 lm)have been reported (Tsuji et al., 1984). For turbu-lent pipe#ow it was found that intermediate sizedparticles (+500 lm) increased turbulence at thepipe center and reduced it along the wall. Both fromthe work of Schreck and Kleis (1993) and of Tsuji et al.(1984) for gas}solid two phase #ow it is clear that theisotropy of the #ow is enhanced due to the presence ofparticles.

Elgobashi (1994) presented a regime map for turbulent#uid}solids #ow to discriminate between regimes inwhich turbulence is enhanced and suppressed, based onthe solids holdup and the ratio of the particle responsetime q

Pand the Kolmogoro! time scale q

K(turbulence

enhancement for qP/q

K'102). Turbulence enhancement

by vortex shedding will occur at high particle Reynoldsnumbers ('400), requiring relatively large particles andhigh density di!erences. Turbulence damping may becaused by energy dissipation through #uid-particle inter-action (energy required for suspending and oscillatingthe particles due to continuous phase turbulence, &twoway coupling'), particle}particle interaction (so-called&four- way coupling') and due to the fact that in densesolutions a signi"cant fraction of the #uid is present aslow turbulent added mass moving with the particles.According to Elgobashi's classi"cation all the resultspresented in this present study were carried out in the

D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337 2327

four-way coupling regime (dispersed phase holdup'0.1 vol%).

Summarizing, it can be concluded that particles mod-ify the turbulence energy spectrum, e.g. by facilitatingenergy transfer from large to smaller eddies and promo-ting isotropy of the turbulence. The e!ect, however, onenergy dissipation rate and mixing on a scale, which isrelevant to a complex chemical reaction, cannot be de-rived from these studies.

In a few studies the aspect of the in#uence of particleson the product distribution for a mixing sensitive (homo-geneous) chemical reaction has been considered. Bennin-gton and Bourne (1990) and Bennington and Thangavel(1993) used the diazo-coupling reaction of Bourne et al.(1981) to study the e!ect of suspended nylon "bers onmacromixing and micromixing in a stirred tank. Theyfound that the "bers, irrespective of changes to macro-scopic #ow patterns, dampen the observed turbulencelevel, which was assumed to be caused by network forma-tion by the "bers.

Villermaux et al. (1994) used a parallel (iodine}iodate)reaction system to study the e!ect of suspended solidsand inert bubbles on micromixing in stirred reactors.Preliminary results showed that the e!ect of solids((40 lm) was considerable. Micromixing seemed to beenhanced signi"cantly as a strong increase of microm-ixedness was observed at only 4 wt% addition of solidparticles. In a consecutive publication by Guichardonet al. (1995) the preliminary results of Villermauxet al. (1994) were considered to be invalid. After checkingthe mass balance more precisely and re-investigationof the reaction kinetics only a minor e!ect of the pres-ence of particles in this latter paper remained.This example illustrates that especially for multiphasesystems the reaction kinetics for the test system as well ase!ects of product adsorption or absorption in the disper-sed phase should be known. Guichardon et al. (1995)stressed the need for a study of more concentrated sus-pensions.

More recently, Barresi (1997) studied the in#uence ofsolid particles on the product distribution obtained fora fast, parallel reaction scheme. Two preliminary con-clusions were presented, the "rst being that the particleshad only an e!ect at relatively high volume fractions('10 vol%) and, secondly, it was found for three experi-ments at constant volumetric holdup that large glassparticles (425}500 lm) exhibited a signi"cant in#uenceon the product distribution, whereas "ne glass particles(100}177 lm) and PET beads (having a equivalent dia-meter of 3 mm) had a minor e!ect and no e!ect on theproduct distribution respectively.

In the present study attention will be focussed at highdispersed phase holdups. Since for a dispersed liquidphase mass transfer may be important, an inert solid andgas phase were also used, to study the e!ect of dispersedholdup and &particle' size. Macroscopically, the e!ects of

a dispersed phase on turbulence may be noticeable via,e.g. the e!ective viscosity and density of the dispersion. Ininterpreting the experimental data the E-model, valid fora single phase situation, is used to see if macroscopicphysical properties for the dispersion are able to describethe observed trends in the product distribution withincreasing holdup.

2.3. Interpretation of experimental results for multiphasesystems using the E-model

Although the E-model is derived for single-phase sys-tems, the model will be used to interpret the experimentaldata for the multiphase systems used. It will be tested ifthe E-model, using the apparent slurry viscosity andslurry density, can be used to describe the obtainedproduct distributions at changing operating conditions,like dispersed phase holdup. The power input via theimpeller and the average energy dissipation rate e(W/kg)are given by

P"Co%&&

N3d545

(W), (6)

e%&&"

P

(o%&&< )

"

CN3d545

<(W/kg dispersion). (7)

For the kinematic viscosity l (m2/s)"k/o, the changein viscosity was taken into account via correlationsfor the relative dynamic viscosity (k

r) of liquid}solid

and liquid}liquid dispersions at di!erent volumetricholdups. For modeling the liquid}solid dispersions thecorrelation of Graham (1981) was used for estimatingkr. For the e!ective viscosity of liquid}liquid disper-

sions the correlation of Vermeulen (Perry, 1988;Eqs. (21)} (32)) was compared with the Graham correla-tion, which may be applicable at low holdups sincethe droplets are small and rigid and will probably behaveas solid spheres. The density o in Eq. (5) was takenequal to the e!ective dispersion density and to the con-tinuous-phase density, leading to two de"nitions ofthe Engulfment parameter E which were used in thesimulations:

E(I)"0.058AeRe!7

l B"0.058AeRCN3d5

45o%&&

<k%&&

B , (8)

E(II)"0.058AeRe!7

l B"0.058AeRCN3d5

45o

<k B , (9)

For the experiments with a dispersed liquid phase theE-model was extended to incorporate mass transfer be-tween the bulk of the continuous liquid phase and thedispersed liquid phase, both considered to be ideallymixed. The set of additional mass transfer model

2328 D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337

equations is

<"6-,

dcc, i

dt"k

LLA

LL Acd, im

i

!cc, iB

(continuous phase) (10)

<d

dcd, i

dt"k

LLA

LLAcc, i!

cd, im

iB (dispersed phase) (11)

In the present contribution, mass transfer was accountedfor discontinuously by calculating the exchange betweenthe two liquid phases after each (of the p) feed lump(s)during t

&%%$/p (s). The overall mass transfer coe$cient

kLL

was estimated conservatively from the partial coe$-cients for mass transfer inside and outside the droplets byassuming stagnant media; thus Sh

*/4*$%"2p2/3 is used

for mass transfer inside the droplets and Sh0654*$%

"2 forthe external partial mass transfer coe$cient, thereby us-ing D"1]10~9 m2/s as typical liquid-phase di!usioncoe$cient. The interfacial area A

LLwas calculated using

ALL"6<

d/d

pand the correlation of Calderbank for the

drop size.The e!ect of mass transfer can be estimated by com-

paring the timescale for mass transfer (kLL

ALL

/<"6-,

) withthe time for complete engulfment of a feedlump. Depend-ing on initial conditions and the distribution coe$cientsfor Naphthol mass transfer from the dispersed phase maybecome the limiting process. In that case the currentmethod of solving the equations must be adapted.

3. Experimental

For the mixing experiments a ba%ed, #at bottom,stirred tank was used as reactor, equipped with a sixblade Rushton-like turbine (see Fig. 1). The feed pointsare indicated in the "gure, as well as all relevant dimen-sions. Feedpoint A is located at the top of the plane ofthe stirrer (radial #ow zone). Feedpoints B, C and D arelocated just above the stirrer, in the suction stream tothe impeller zone. Feedpoint E is located in a streamleaving the stirrer zone where axial #ow dominates. Toavoid backmixing of bulk reaction liquid into the feed-pipe a small diameter of the feedpipe was chosen (innerdiameter: 1 mm). This diameter was shown to be su$-cient small using the criteria presented by Baldyga andPohorecki (1995).

3.1. Development of the test reaction system

In most experiment series the 1-Naphthol reactionsystem represented by Eqs. (1) and (2) is used. For someexperiments the extended reaction system of Bourne et al.(1992), developed for high energy dissipation rates wasused. This system encompasses reactions (1) and (2), as

well as a parallel reaction of 2-Naphthol (AA) with dia-zotized sulfanilic acid.

AA#B k3PQ. (12)

The product distribution is then characterized byX

S{and X

Q, which are de"ned below.

XS{"

2[S]

[oR]#[pR]#2[2]#[Q], (13a)

XQ"

[Q]

[oR]#[pR]#2[2]#[Q]. (13b)

Before using the reaction system of Bourne et al. (1981),the UV-extinction coe$cients as reported by Lenzner(1991) were veri"ed. Therefore, the reaction product pRwas synthesized, identi"ed by NMR and puri"ed byseveral washing and recrystallisation steps. The UV-ex-tinction coe$cients as reported by Lenzner (1991) werecon"rmed for pR. From other syntheses the products oR,S and Q were obtained at purity levels of 90}95% byelement analysis, but it turned out to be di$cult toimprove on the purity. The UV-extinction coe$cientswere, however, conform the purity level and the extinc-tion coe$cients reported by Lenzner (1991), thus justify-ing the use of the extinction coe$cients reported byLenzner (1991).

Naphthols (1- and 2-) and sulfanilic acid of 99#%purity were purchased from Acros Organics, as well asthe Sodium Carbonate and Sodium Bicarbonate for thebu!er solution (pH "9.9). The reactant B (diazotizedsulfanilic acid) was obtained almost quantitatively, ac-cording to a test based on the Sandmeyer reaction. Theoccurrence of degradation of reaction products, diluted50] for UV analysis, was found to be negligible. Stabil-ity was also tested for 1- and 2-Naphthol solutions andfor a solution of freshly synthesized diazotized sulfanilicacid. 2-Naphthol solutions (1% degradation in 20 h) wasfound to be much more stabile than the 1-Naphtholsolutions (5% in 6 h) and the 1- #2-Naphthol mixtures.Sparging nitrogen through the naphthol solution im-proves the stability. 1-Naphthol was dissolved for eachexperiment in a series separately just before the experi-mental usage. By storing the diazotized sulfanilicacid solutions in an ice-bath the degradation of dia-zotized sulfanilic acid during one experiment series(ca. 5 h) could be reduced to ca. 1%.

3.2. Analysis

Multicomponent regression (over the range of400}600 nm) was used to obtain the individual compon-ent concentrations from the recorded UV spectrum (HP8452A spectro photometer). The regression coe$cientswere usually better than 0.9995. Tests with small shifts in

D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337 2329

the UV spectrum showed that the oR/pR distribution isrelatively sensitive to this, however, the segregation indexX

Sremains almost una!ected. The presence of small

amounts of dissolved octanol and heptane in the analysissamples (reactor samples, diluted 50] with bu!er solu-tion) did not a!ect the UV-analysis. For single-phaseexperiments no e!ect was found in experiments in whichthe Naphthol/bu!er solution was saturated with heptaneor octanol.

3.3. Accuracy

Reproducibility of the XSvalue for experiments within

a series (measured at sequentially) at the same feedpointwas tested for the 1-Naphthol and 1-#2-Naphtholsystem. Standard deviation values for a series of experi-ments under identical conditions revealed thatX

S+0.092$0.002, X

Q+0.284$0.005, *X

S{+0.050

$0.001, mainly due to uncertainties in the analysis part.Therefore, for each experiment three reactor sampleswere taken, diluted with bu!er solution and analyzed.The reproducibility between series of experiments wassomewhat less ($0.005), due to possible variations in thesynthesis of the reactants, small temperature di!erencesor a slightly di!erent feedpoint position. Mass balances(for B) were checked and were found to be accurate($98% was recovered in the products) for the experi-ments in aqueous bu!er solutions.

3.4. Experimental conditions

Typical reaction conditions are listed in Table I. Forthe suspension experiments with varying holdups, thevolume of the Naphthol solution was always kept con-stant. The suspensions of glass beads were prepared byadding the appropriate amount of solids to the Naphtholsolutions. In order to keep the total molar ratio of A andB constant, the amount of B-solution fed to the reactorhad to be adapted. For the glass beads sieved fractionswere used with a rather narrow size distribution, asdetermined with a Microtrax X100 Particle Analyzer.Adsorption of reactants and products on the glass beadswas found to be negligible and, therefore, did not

Table 1Typical reaction conditions

Temperature 298 (K)pH 9.9 dimensionlessVolume Naphthol solution 500}1000 (ml)Injected volume B-solution 10 (ml)Feed rate reactant B 30 (ml/h)Concentration C

B,040 60 (mol/m3)

Concentration CA,0

1.04 1.32 (mol/m3)Stirrer speed 100}1200 (rpm)

in#uence the observed product distribution. This waschecked by &extracting' typical, well-known, reactionmixtures with the glass beads concerned and analyzingagain the reaction mixture. The distribution coe$cientswere roughly estimated to be in the order of magnitude of1}5]10v8 mol/m2 glass beads and S appears to be slight-ly preferentially absorbed. For a typical experiment theX

Svalues will be underestimated by some 0.0001 unit

due to adsorption. Therefore, no disturbing e!ect on theresults is to be expected owing to adsorption phenomenaon the solid particles.

The liquids selected for the dispersion study were oc-tanol and heptane, because of their di!erence in naphtholsolubility. Distribution coe$cients for the individualcomponents were obtained from extraction experiments,but the accuracy of the separate coe$cients for both o-Rand p-R respectively was relatively low. Therefore, themono-azo compounds were regarded as one componentin the analysis of these experiments.

4. Results

4.1. Critical feed rate

First, the critical feed times for the operation condi-tions of Table 1 were identi"ed. The critical feed time,above which the product distribution for the givenamount of reactant does not depend longer on the injec-tion time, is within the range 200}500 s for all conditionsconsidered. A feed time of 1200 s (corresponding witha feed rate of 30 ml/h) was chosen safely above the criticalfeed times determined.

4.2. Single-phase experiments

Before the start of the multiphase experiments severalseries of single-phase experiments were performed. TheEngulfment model by Baldyga and Bourne (1989) wasused to recalculate local energy dissipation rates fromexperimentally determined X

Sand X

Qvalues at di!erent

stirrer speeds, it was found that for N'500 rpm therelative energy dissipation rate, i.e. the ratio betweenthe calculated and the average energy dissipation rate(e!7"CN3d5

45/<

L) remains essentially constant, indicating

that the reaction is localized in a zone of more or lesshomogeneous energy dissipation. Indications of the thusderived relative energy dissipation rates are presented inFig. 1.

4.3. Two-phase experiments: E+ect of a dispersed gasphase

The e!ect of the presence of gas bubbles on the prod-uct distribution in a sparged stirred tank, operatingin the impeller-#ow dominated regime, is not clear

2330 D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337

Fig. 1. Experimental setup.

beforehand. Fort et al. (1994) found a suppression of theenergy dissipation rate in the impeller discharge #ow andan increase in the remaining part of the agitated vessel.This would imply a position-dependent e!ect of spargingon the X

Svalue obtained. Gas sparging experiments were

performed for two di!erent feedpoints, using Nitrogenand SF

6as dispersed phase, see Fig. 2.

The e!ect of sparging or gas entrainment, thus thepresence of gas bubbles, on the product distribution forthe mixing sensitive test reaction seems to be limited fromthe results of this work. The minor e!ects found are,however, in accordance with the results of Fort et al.(1994); the X

Svalue for feedpoint C slightly decreases

(thus suggesting a slightly increased local energy dissipa-tion rate), whereas the X

Svalue for one of the series at

a super"cial gas velocity of 2.8]10~2 m/s for feedpointA just above the stirrer increased from 0.061 to 0.063 (ca.3% increase), corresponding to a decrease of approxim-ately 1.7 W/kg (ca. 7%) in the apparent local powerinput, as was recalculated using the E-model. This latterresult is in line with the expected reduced power input byagitation due to the decreased density of the dispersion.The decrease in the apparent local power input corres-ponds with the gas holdup, which was also estimated tobe 7%, using the correlation of Takenaka and Takahashi(1992).

4.4. Two-phase experiments: E+ect of a dispersed solidphase

In Fig. 3 the results are presented of experiments withdi!erent holdups of solid particles at constant total vol-ume for two di!erent particle sizes. By using e!ectiveproperties for viscosity and density for the slurries in theE-model it was investigated if the measured variation inproduct distribution at increasing holdup can be de-scribed (see Fig. 3). The series with the 290 lm particlesat 500 rpm (and 500 ml total volume) seems to di!ersigni"cantly from the other series, since no e!ect onX

Swas found. This may be explained by insu$cient

suspension of these solid particles at these conditions.Since the feedpoint is located above the stirrer probablythe local solids holdup was insu$cient to produceany e!ect. It appears that a reasonable prediction ofthe experimental trend for the other three series isobtained by just implementing the e!ective viscosity,thus using E"E(II) (Eq. 9). This result was con"rmedfor duplicate series using the 1-Naphthol #2-Naphtholsystem.

Experimental series like those presented in Fig. 3are measured using a freshly prepared stock of dia-zotized sulfanilic acid per series and the experi-ments within a series are performed in random order of

D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337 2331

Fig. 2. E!ect of gas bubbles d gas phase"N2, N"700 rpm, <

L"700 mL, e

G"1}7 vol%, K gas phase"SF

6, N "900 rpm, <

L"700 mL,

eG"1}3 vol%, L gas phase"N

2, N"900 rpm, <

L"700 mL, e

G"1}3 vol%, } } } } } X

Svalues homogeneous liquid phase.

Fig. 3. Glass beads holdup variation for feedpoint C, 1-Naphthol system, cA,o

"1.04 mol/m3, cB,o

"40 mol/m3. Solid and dashed line are E-modelsimulation results using Eqs. (9) and (8), respectively.

holdup, starting and ending with a blank run (zeroholdup), in order to exclude time-dependent trends.Mass balances were found to be satis"ed within 0}4%deviation of the theoretical maximum amount of Binjected. For a single data series (not shown in the

"gures) with 3 mm particles the XS-value was found

to decrease (from XS"0.07 at zero holdup to 0.06 at

5 wt% holdup and 990 rpm, CA,o

"1.32 mol/m3,C

B,o"60 mol/m3, <

A,o"500 ml, <

B,o"10 ml at feed-

point E).

2332 D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337

Fig. 4. Solids particle size variation at constant holdup, <L"500 ml, c

A,o"1.04 mol/m3, c

B,o"40 mol/m3.

The average particle size has been varied at constantholdup. Results for the 1-Naphthol system are presentedin Fig. 4. With the 1-#2-Naphthol system similar re-sults were found (not shown). The trend observed, repre-sented by the dashed line, is approximately within theexperimental accuracy, however, the presented trendcould be recognized clearly for all individual series. Theexperiments were, as stressed before, conducted random-ly with respect to particle size. For very small particlesthe dispersion behaves as a pseudo-#uid with the appro-priate e!ective (density and viscosity) properties. Energyis probably mainly dissipated by particle}particle inter-action. This will decrease due to a strong reduction in thenumber of (&near'-) collisions with increasing particle size,at constant holdup. In the classi"cation by Elgobashi(1994) for the two-way coupling regime the regimetransition between &particles enhancing energy dissipa-tion' and &particles enhancing energy production' is ap-proximately given by q

P/q

k+102. For the glass beads

used under the experimental conditions applied, thetransition is located at approximately 150 lm. This is inagreement with the experimentally determined decreasein the X

Svalue going from particles of 50 to 150 lm, as

shown in Fig. 4. However, the volume fractions used inthis study are such that all experiments are conducted inthe &four way coupling' -regime, according to Elgobashi(1994).

The increase at higher particle sizes may be causedowing to the fact that the particles are being less able tofollow #uid motion (an increase in particle response time)and more energy is required to (re-) suspend the particles

(see, e.g., Zwietering (1958)) and more energy is dissipatedin particle}particle collisions and particle}wall collisions.Another explanation may be an increase in the amount ofstagnant liquid moving with the particles.

A similar result for the turbulence intensity at di!erentparticle diameters has been presented in an overview byZakharov et al. (1993) for gas}solid two phase #ow at lowconcentrations ((1 vol% solids). In their study frictiondrag due to the #ow of a dispersion was studied atconstant dispersed phase holdup for di!erent particlesize. It was found that "rst the drag was reduced withincreasing particle diameter and, with a further increasein diameter the drag started increasing again. The par-ticle regime for which friction reduction may occur wasestimated in their study using the Owen theory, assumingthat (quote:) &friction reduction is possible in a #ow ladenwith particles having a relaxation time which is higherthan the characteristic time of the energy-containing vor-tices, but which does not exceed the characteristic time ofthe maximum possible vortices'. Applying these criteriato the conditions of current investigation, glass particlesof 150}1000 lm may &decrease the friction', implying thatfor these particles the turbulence intensity will be in-creased or less reduced.

The results of this study are in accordance with thosepresented by Guichardon et al. (1995), who found a negli-gible in#uence of solid particles (o"2500 kg/m3 ,dp"27, 201, 1250 lm) on the micromixing index for

their (iodide-iodate) test reaction in the range 1}6 wt%.The scatter of the experimental data of Barresi (1997)in combination with the limited e!ect of solids makes

D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337 2333

Fig. 5. Experiments with heptane as dispersed phase at di!erent volume fractions.Series I: Feedpoint A, C

A,o"1.04 mol/m3, C

B,o"40 mol/m3, 700 ml, 1000 rpm.

Series II: Feedpoint E. CA,o

"1.32 mol/m3, CB,o

"60 mol/m3, 500 ml, 500 rpm. Simulation input: k(I)Nrelative viscosity according to Graham(1981), k(II)Nrelative viscosity according to Vermeulen (Perry, 1988, Eqs. (21)}(32), changing e

Ralong trajectory of reaction zone according to Yu

(1993).

Table 2Distribution coe$cients for reactants and products

Heptane Octanol(m"c

$*41.1)!4%/c

"6&&%3) m dimensionless m dimensionless

1-Naphthol 0.9 2.102

oR 0.12 1.1pR 0.0010 0.06R(oR#pR) 0.020 0.2S 0.19 0.09

comparison with the results of the present study di$cult,though the results are not necessarily con#icting. Scout-ing experiments in this study with 5 wt% solids of di!er-ent density (not shown in "gures), comparing glass beadswith polystyrene, polypropylene and polymethyl methac-rylate beads of the same size at 5 wt% holdup, showed nosigni"cant in#uence of particle density and within theexperimental error, which was larger due to productadsorption on the plastic beads.

4.5. Two-phase experiments: E+ect of a dispersed liquidphase

A dispersed liquid phase may in#uence the obtainedproduct distribution in di!erent ways. Besides possiblee!ects on the state of local mixing, which can be signi"-

cant as was shown in experiments with the solid particles,mass transfer can be important and macroscopic hydro-dynamics may change. In this work the results of scout-ing experiments with two di!erent liquid phases arereported. As dispersed phase a solvent-grade heptanecontaining heptane isomers (82%), octane (15%) andtoluene (3%)), analytical grade (99#% purity) heptaneand octanol (99#% purity) were used. For these sol-vents the (approximate) distribution coe$cients for thereactants and products were determined by extractionexperiments, see Table 2. Heptane was selected for its lowa$nity for 1-Naphthol (thus essentially excluding masstransfer e!ects), whereas octanol was chosen as a solventshowing a high Naphthol a$nity.

In Fig. 5 two sets of experiments for di!erent holdupsof heptane are presented. Optically, the dispersed phasewas distributed homogeneously throughout the disper-sion volume for stirrer speeds exceeding 450 rpm. Fromsimulations for the series at feedpoint A, it seems thattaking the e!ective viscosity (for solid spheres!) accordingto Graham's relation (1981) yields better results for theseconditions than the correlation by Vermeulen (Perry,1988) for liquid}liquid dispersions in ba%ed agitatedtanks. Conclusions with respect to the e!ective viscosityfor liquid}liquid dispersions at higher holdups can, how-ever, not be drawn from these results, considering theassumptions by using the E-model extended with masstransfer. This is especially true for the octanol data series,where de-localization of the reaction zone dominates.

2334 D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337

Fig. 6. Experiments with octanol and heptane as dispersed phase at increasing holdup and CA,o

"1.32 mol/m3, CB,o

"60 mol/m3, 500 ml,N"500 rpm and simulation results assuming m

A"100, e

R"1 and using the viscosity correlation according to Graham (1981) and E"E(II), see

Eq. (9), for the E model.

For the experiment series at feedpoint E the simulationresults started deviating from the experimental data athigher holdups. This is most likely caused by a de-localized reaction zone. Due to the distribution ofNaphthol over both liquid phases the number of engulf-ments required for complete reaction of a feedlumpslightly increases, causing the reaction to take place inzones of di!erent energy dissipation. This e!ect is moreimportant for feedpoint E in the radial #ow leaving theimpeller zone than for feedpoint A in the suction streamto the impeller zone.

This e!ect is even more pronounced in case octanol isused. Fig. 6 shows two octanol data series for di!erentfeedpoints. Since Naphthol is extracted to a large extentby the octanol, the number of engulfments required forcomplete reaction of a feedlump is such that the averageenergy dissipation rate, as experienced by the reactionzone, is essentially the average energy dissipation rate forthe complete tank, e

!7. Assuming this, the E-model ex-

tended with mass transfer was used to see if the experi-mental results could be described. Although the set ofexperimental data is limited, the results seem promising.Using the e!ective dispersion viscosity in the Engulfmentmodel seems to yield reasonable description of X

Svalues

at increasing holdup, both for the viscosity correlation'sof Graham (1981) and Vermeulen (Perry, 1988). It shouldbe noted that in the experiments described the masstransfer rate is relatively unimportant (as the &equilibriummodel', i.e. the model without mass transfer limitationsby using an extremely high mass transfer coe$cientkLL

in the model and presented by the dotted line in

Fig. 6, gives almost identical results as the model includ-ing mass transfer), due to the low feed rate of reactant B.More (and dedicated) experiments are required to inves-tigate (or validate) the mass transfer description.

5. Discussion and conclusions

In this study for a limited set of experimental condi-tions the e!ect of the presence of bubbles, drops and solidparticles on the product distribution for the (micro-)mix-ing sensitive diazo-coupling reaction (Bourne et al., 1981)is investigated. The diazo-coupling reaction system canbe used conveniently for this purpose. Adsorption onglass beads is found to be negligible and the dispersedphases used do not seem to a!ect the intrinsic reactionkinetics and product analysis. The single-phase ex-periments could be satisfactory described using theEngulfment model, and this model was tested on itsapplicability in the multiphase systems. In the presence ofgas, liquid and solid particles in the continuous liquidphase, the product distribution could reasonably well bedescribed by the Engulfment model, if e!ective dispersionslurry properties are implemented. Modi"cation of localliquid-phase turbulence, or the kinetic energy spectrum,at a scale relevant for the test reaction, is then accountedfor.

For the liquid}liquid dispersions the viscosity correla-tion seems less established. From the limited set ofexperiments, it appears that application of the vis-cosity correlation of Graham (1981) for liquid}solid

D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337 2335

applications yields acceptable results for heptane-bu!erdispersions at the conditions considered in this work (a.o.heptane holdup )40 vol%). Additional experimentalwork is, however, recommended.

In the work presented, the mass transfer rate wasrelatively unimportant for the liquid}liquid dispersionsand only preliminary experimental results and a simplemass transfer model have been presented. Further re-search of the combined e!ects of the mass transfer rateand mixing rate is desired for the development of multi-phase reactor models.

Acknowledgements

The authors wish to thank B. Knaken for constructingthe experimental setup and A.K. Jellema and W. Hes-selink for their valuable contribution to the experimentalwork. The Shell Research and Technology Centre, Am-sterdam (The Netherlands) is acknowledged for the"nancial support.

Notation

ALL

interfacial area, m2

c concentration, mol/m3

C con"guration-dependent power constant, di-mensionless

D di!usion coe$cient, m2/sdp

particle diameter, md45

stirrer diameter, mE engulfment rate, 1/ski

partial mass transfer coe$cient, m/skLL

overall liquid}liquid mass transfer coe$cient,m/s

mi

distribution coe$cient (cd,i

/cc,I

)%26*-*"3*6.

, di-mensionless

N stirrer speed, 1/minR

isource term for chemical reaction, mole i/m3 s

Sh Sherwood number ("kidp/D), dimensionless

Sc Schmidt number ("l/D), dimensionlesst time, st&%%$

feed time of a "xed amount of reactant solu-tion, s

< volume, m3

XS

product distribution parameter (de"ned inEq. (3)), dimensionless

Greekletters

e!7

average energy dissipation rate W/kgeR

relative energy dissipation rate ("e/e!7) di-

mensionlessjK

Kolmogoro! length scale ("(l3/e)1@4 mk dynamic viscosity, kg/m s

l kinematic viscosity, m2/so density, kg/m3

p number of feed lumps in E model, dimension-less

qK

Kolmogoro! time-scale ("(l/e)1@2) sqP

particle response time ("opd2p/(18o

cl)) s

Superscripts and subscripts

A 1-NaphtholAA 2-NaphtholB diazotized sulfanilic acidc continuous liquid phased dispersed phasee! e!ective dispersion propertyinside inside0 initial valueoutside outsidep particler e!ective

References

Baldyga, J., & Bourne, J.R. (1988). Calculation of micromixing ininhomogeneous stirred tank reactors. Chem. Engng Res. Dev., 66,33}38

Baldyga, J., & Bourne, J.R. (1989). Simpli"cation of micromixing calcu-lations: 1. Derivation and application of new model. Chem. EngngJ., 42, 83}92

Baldyga, J., & Pohorecki, R. (1995). Turbulent micromixing in chemicalreactors } a review. Chem. Engng J., 58, 183}195.

Barresi, A.A. (1997). Experimental investigation of interaction betweenturbulent liquid #ow and solid particles and its e!ects on fastreactions. Chem. Engng Sci., 52, 807}814.

Bennington, C.P.J., & Bourne, J.R. (1990). E!ect of suspended "bers onmacro-mixing and micro-mixing in a stirred tank reactor. Chem.Engng Commun., 92, 183}197.

Bennington, C.P.J., & Thangavel, V.K. (1993). The use of a mixing-sensitive chemical reaction for the study of pulp "ber suspensionmixing, Can. J. Chem. Engng, 71, 667}675.

Bourne, J.R., Kozicki, F., & Rys, P. (1981). Mixing and fast chemicalreaction-I: Test reactions to determine segregation. Chem. EngngSci., 36, 1643}1648.

Bourne, J.R., Kut, O.M., Lenzner, J., & Maire, H. (1990). Kinetics of thediazo coupling between 1-Naphthol and diazotized sulfanilic acid.Ind. Engng Chem. Res., 29, 1761}1765.

Bourne, J.R., & Thoma, S.A. (1991). Some factors determining thecritical feed time of a semi-batch reactor. ¹rans. I. Chem. E., 69, PartA, 321}323.

Bourne, J.R., Kut, O.M., & Lenzner, J. (1992). An improved reactionsystem to investigate micromixing in high-intensity mixers, Ind.Engng Chem. Res., 31, 949}958

Calderbank, P.H. (1967). Gas absorption from bubbles. Chem. Engng,45 (10), 209}233

Elgobashi,, S. (1994). On predicting particle-laden turbulent #ows. Appl.Sci. Res., 52, 309}329.

Falbe, J. (1980). New synthesis with carbon monoxide (Ch. V.) In H.Bahrmann (Ed.). Koch reactions, Berlin: Springer.

Fort, I., Machon8 , V., & Kadlec, P. (1994). Distribution of energydissipation rate in an agitated gas}liquid system. Chem. Engng¹echnol., 16, 389}394.

2336 D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337

Gore, R.A., & Crowe, C.T. (1989). E!ect of particle size on modulatingturbulent intensity. Int. J. Multiphase Flow, 15, 279}285.

Graham, A.L. (1981). On the viscosity of suspensions of solid spheres.Appl. Sci. Res., 37, 275}286.

Guichardon, P., Falk, L., Fournier, M.C., & Villermaux, J. (1995). Studyof micromixing in a liquid}solid suspension in a stirred reactor.A.I.Ch.E. Symp. Ser. 305, 91, 123}130.

Hetsroni, G. (1989). Particle-turbulence interaction. Int. J. MultiphaseFlow, 15, 735}746.

Kada, H., & Hanratty, T.J. (1960). E!ects of solids on turbulence ina #uid. A.I.Ch.E. J., 6, 624}630.

Lenzner, J. (1991). Der Einsatz Rascher Kompetitiver Reaktionen zur;nter-suchung von Mischeinrichtungen. Ph.D. thesis No. 9469, ETH ZuK rich.

Perry, R.H., & Green, D.W. (1988). Chemical engineers handbook. NewYork: McGraw-Hill.

Schreck, S., & Kleis, S.J. (1993). Modi"cation of grid-generated turbu-lence by solid particles. J. Fluid Mech., 249, 665}688.

Takenaka, K., & Takahashi, K. (1992). Local gas holdup and gasrecirculation rate in aerated vessel equipped with a Rushton turbineimpeller. J. Chem. Engng Japan, 29, 799}804.

Tsuji, Y., Morikawa, Y., & Shiomi, H.H. (1984). LDV measurements ofan air-solid two-phase #ow in a vertical pipe. J. Fluid Mech., 139,417}434.

Villermaux, J., Falk, L., & Fournier, M.C. (1994). Potential use of a newparallel reaction system to characterize micromixing in stirred reac-tors. A.I.Ch.E. Symp. Ser. 292, 90, 50}54.

Yu, S. (1993). Micromixing and parallel reactions, Ph.D. thesis No.10160, ETH ZuK rich.

Zwietering, Th. N. (1958). Suspending of solid particles in liquid byagitators, Chem. Engng Sci., 8, 244}253.

D.W.F. Brilman et al. /Chemical Engineering Science 54 (1999) 2325}2337 2337