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Computers and Chemical Engineering 34 (2010) 421–429

Contents lists available at ScienceDirect

Computers and Chemical Engineering

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

FD analysis of mixing in thermal polymerization of styrene

aresh Patel, Farhad Ein-Mozaffari, Ramdhane Dhib ∗

epartment of Chemical Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario, Canada M5B 2K3

r t i c l e i n f o

rticle history:eceived 17 March 2009eceived in revised form 27 October 2009ccepted 5 November 2009

a b s t r a c t

Thermal polymerization of styrene in a lab-scale CSTR equipped with a pitched blade turbine impellerwas simulated using a computational fluid dynamics (CFD) software package. The rotation of the reac-tor impeller was modeled using the multiple reference frames (MRF) technique. The path lines of the

vailable online 11 November 2009

eywords:omputational fluid dynamicshermal polymerizationolystyrene

particles, released at the reactor inlet, were also generated to analyze the reaction progress throughoutthe reactor vessel. The effects of the impeller speed, the input–output stream locations and the residencetime were investigated. The simulation showed the formation of a well-mixed region around the impellerand stagnant or slow moving fluids elsewhere in the reactor due to high viscosity of the polymer mass.The monomer conversion computed using the CFD model was in good agreement with that obtainedfrom the CSTR model at low residence time. The input–output locations have a significant impact on the

the

ixing monomer conversion and

. Introduction

Mixing of fluids is a basic operation frequently performed intirred tanks, liquid–liquid contactors, particle and droplet suspen-ions, and polymerization reactors. It can improve the chemicaleaction, as it can strongly affect the reaction rates and final productuality. A number of authors have studied the mixing in polymer-

zation and concluded that the mixing quality in a reactor has aignificant impact on the polymerization rate and the final poly-er properties (Harada, Tanaka, Eguchi, & Nagata, 1968; Heidarian,ayef, & Wan, 2004; Kemmere, Meuldljk, Drinkenburg, & German,001; Tosun, 1992). In comparison with solution, suspension ormulsion polymerizations, bulk polymerization process is moreifficult to mix due to the high viscosity of the bulk mass (Moritz,989). Insufficient mixing in bulk polymerization leads to the for-ation of various concentration pockets which in turn influence

he polymer properties like particle size distribution, number andeight averaged molecular weights (Tosun, 1992). The presence

f hot spots accelerates locally the reaction and may end up inharcoal formation, which eventually results in low-grade polymerroduct. Undoubtedly, mixing plays an important role in removinghe excess heat of polymerization and hence affects the conversionn polymerization. Besides, a good understanding of the flow behav-

or in stirred tank reactors is essential for a better equipment designnd process scale-up. Several studies attempted to model the phe-omena of mixing in polymerization reactors (Kim & Laurence,998; Prochukhan, Minsker, Karpasas, Bakhitova, & Yenikolopyan,

∗ Corresponding author. Tel.: +1 416 979 5000x6343; fax: +1 416 979 5083.E-mail address: rdhib@ryerson.ca (R. Dhib).

098-1354/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2009.11.009

system homogeneity in the CSTR.© 2009 Elsevier Ltd. All rights reserved.

1988; Villa, Dihora, & Ray, 1998). But, these studies assumed homo-geneous system which may not always hold in practical applicationsince the fluid viscosity within the reactor increases significantlyduring a polymerization. Another problem arises on the modelingof stirred tank reactors is the difficulty of combining polymerizationkinetics with mixing phenomena. Alternatively, the developmentof computational fluid dynamics (CFD) has opened a new avenueto visualize the mixing phenomena without the need to conductreal-time experiments (Paul, Atiemo-Obeng, & Kresta, 2004). But,it has not been exploited well enough in analyzing polymerizationprocesses. In fact, another benefit of the CFD is that it can provideinformation on turbulent zones so that one can introduce reac-tants into regions with intense turbulence in order to improve thereaction yield. Yet, experimental approach to study the flow behav-ior in polymer reactors remains valuable, but the uneven natureof reactive fluids can make quantitative measurements and flowvisualization time consuming. In addition, experimental means canneither cover all relevant parameters involved in the mixing pro-cess, nor achieve the desired degree of spatial resolution within thestirred tank vessel (Cole, 1975; Harada et al., 1968; Heidarian et al.,2004; Hui, 1967; Kemmere et al., 2001). For these reasons, recentdevelopment in computer capability has made CFD an attractivetool to visualize, optimize and design polymerization processes.

So far few researchers have employed CFD to study polymer-ization systems (Read, Zhang, & Ray, 1997). Zhang and Ray (1997)showed that the mixing affects monomer conversion, initiator con-

sumption, and the molecular weight distributions. On investigatingimperfect mixing in LDPE autoclave, Wells and Ray (2001) com-bined CFD and compartment model in which they assumed noback mixing; as a result, CFD simulation convergence was obtainedmuch faster. Kolhapure and Fox (1999) utilized CFD to simulate

422 H. Patel et al. / Computers and Chemical Engineering 34 (2010) 421–429

Nomenclature

A pre-exponential (m3/kmol s)Dm diffusivity of species j in the mixture (m2/s)E activation energy (J/mol)�F external forces (N)G gravitational acceleration (m/s2)J diffusive flux (g/m2 s)K rate constant or consistency indexM monomerMe homogenous monomer concentration (kmol/m3)Mf monomer feed concentration (kmol/m3)Mw molecular weight (g/mol)P pressure (Pa)Q volumetric flow rate (m3/s)R reaction rateR• radicalRg universal gas constant (J/mol K)S source term in respective equation (kg/m3 s)T temperature (K)Tw wall temperature (K)V volume of a reactor (m3)wj mass fraction of species j in the mixtureY mass fraction

Greek symbols� density of the mixture (kg/m3)�� velocity vector (m/s)��� stress tensor (Pa)�̇ shear rate (1/s)� dynamic viscosity (Pa s)�0 zero shear viscosity (Pa s)� the vector differential operator

Subscripts0 zero shear rateJ species indexm monomerp propagationP polymerr number of monomer unitss number of monomer units

eipocamwficlS(itwian

Table 1Reactor specifications.

Parameter Value Parameter Value

Tank diameter 14 cm Impeller diameter 8.4 cmLiquid level 26 cm Impeller elevation 8.0 cmOutlet diameter 1.5 cm Impeller type 45◦ pitched bladeNo. of blades 4 Inlet pipe elevation 20 cm (Fig. 1)

study. The impeller speed was varied from 100 rpm to 1000 rpm.For isothermal flow conditions, the inlet temperature and the walltemperature were kept constant at 140 ◦C.

tc termination by combinationth thermal initiation

thylene polymerization in a tubular reactor and showed thatmperfect mixing reduced ethylene conversion but increased theolydispersity index. However, their modeling approach consistedf arbitrarily defined mixing parameters, which limited the appli-ation of the model. Zhou, Marshall, & Oshinowo (2001) used CFDpproach to simulate LDPE tubular and autoclave reactor. Theodel allowed predicting initiator consumption and moleculareight distribution of the polymer. For computational simpli-cation, they assumed 5 monomer units in a polymer radicalhain, which is not a reasonable assumption since radical chainength usually varies from 100 to 100,000 monomer units. Further,oliman, Aljarboa, & Alahmad (1994) and Meszena and Johnson2001) used CFD to simulate polystyrene and living polymerizationn tubular reactor, respectively. Due to the plug flow characteris-

ics of the tubular models, the convergence of the CFD simulationas easily achieved. Tsai and Fox (1996) simulated LDPE polymer-

zation under turbulent flow regime in a 2D tubular reactor. Bezzond Macchietto (2004) developed a hybrid multizonal/CFD tech-ique which, was utilized to identify the mixing pattern through

Inlet diameter 1 cm Outlet pipe elevation 3 cm (Fig. 1) and20 cm (Fig. 2)

a simulated tracing experiment for a simple non-reactive mixingsystem. However, no solid work has been done so far using the CFDapproach to relate the mixing quality to polymerization rate or finalpolymer properties in a CSTR.

Despite the importance of the CSTR in polymerization sys-tems, the CFD approach has not been fully exploited to assessthe non-homogeneity impact in stirred polymerization reactors.This study investigates the effect of the key mixing parameters onstyrene conversion in a CSTR polymerization reactor using the CFDapproach. The objective of the present study is to find efficientways to improve homogeneity in the CSTR for a better polymerquality.

2. Reactor geometry

This study simulates thermal polymerization of styrene in a lab-scale CSTR. The reactor geometry was generated using MixSim 2.1(Fluent Inc.), which is a CFD tool for the simulation of agitated mix-ing vessels. The MixSim 2.1 uses another software package calledGAMBIT (Fluent Inc.) in the background, in order to build and meshthe geometry models required for the CFD. The reactor specifica-tions used for the model simulations are tabulated in Table 1. Tworeactor configurations, with different input–output locations, wereconsidered. The discretized domains of these two configurationsare shown in Figs. 1 and 2, which contain 372,571 and 371,784 cells,respectively. Tetrahedral cells were used to generate unstructuredcells in the simulation of the reactors.

In both configurations, fresh styrene is fed to the reactor. Underthermal effect, styrene reacts and produces polymer. The polymerand the unreacted monomer leave the reactor through an outletpipe. The residence time was varied from 48 min to 144 min in this

Fig. 1. Reactor grid for the side inlet (near liquid level) and outlet.

H. Patel et al. / Computers and Chemica

3

wto

3

t

(

w

∇w

�

af

w

�JDr

TV

Fig. 2. Reactor grid for the bottom inlet.

. CFD model

CFD model development for thermal styrene polymerizationas achieved in three steps namely: formulation of transport equa-

ions, formulation of reactive source term and physical propertiesf reactive mass.

.1. Transport equations

The governing transport equations of continuity, mass, momen-um and species in steady-state form are given below:

Continuity:

∇ · � ��) = 0 (1)

here � is the density and �� is the velocity vector.Momentum balance:

· (� �� ��) = −∇P + (∇ · ���) + �g + �F (2)

here ��� is the stress tensor expressed as:

�� = �[(

(∇ ��) + (∇ ��)T)− 23

∇ · ��]

(3)

nd P, g and �F are the pressure, gravitational force and externalorce, respectively.

Species balance:

∂

∂t

(�wj

)+ ∇ · (� ��wj) = −∇ · Jj + Sj (4)

here the diffusive flux Jj of species j in the mixture is given below:

j = −�Dj∇wj (5)

j is the diffusivity of species j in the mixture and Sj is a sourceelated to the jth species.

able 2alues of kinetic parameters and physical properties.

Parameter Values Parameter

Ath 2.190 × 105 m3/kmol s Eth

Ap 2.170 × 107 m3/kmol s Ep

Atc 8.200 × 109 m3/kmol s Etc

l Engineering 34 (2010) 421–429 423

3.2. Reactive source term

Styrene polymerization is a sequence of chain reactions. Previ-ous researchers have extensively studied thermal polymerizationof styrene (Dhib, Goa, & Penlidis, 2000; Hiatt & Bartlett, 1959; Hui &Hamielec, 1972; Mayo, 1968). Hui and Hamielec (1972) determinedexperimentally that this reaction obeys a third order initiation rate.Thermal polymerization of styrene can be achieved in three con-secutive steps:

Thermal initiation:

3MKth−→2R

•1

Propagation:

R•r + M

Kp−→R•r+1 r ≥ 1

Termination:

R•r + R

•s

Ktc−→Pr+s r, s ≥ 1

where M, R• and P refer to styrene, live polymer radical and deadpolymer, respectively; the respective subscripts r and s refer to thepolymer chain length. Kth, Kp and Ktc refer to rate constants for ther-mal, propagation and termination reaction, respectively. Assuminga steady-state hypothesis and equating the rate of thermal initia-tion to that of termination, the total live radical concentration canbe written as:

[R•] =√

2Kth[M]3

Ktc(6)

The polymerization rate RP in terms of the monomer concentra-tion is given by:

RP = −Kp[M][R•] = −Kp[M]

√2Kth[M]3

Ktc(7)

The monomer concentration in the mixture is related to themonomer density � by [M] = M−1

wm�wm where wm is monomermass fraction.

Hence the polymerization rate is expressed as:

RP = −K ′pw2.5

m (8)

where

K ′p = −Kp

([�

Mwm

]2.5√

2Kth

Ktc

)(9)

Eq. (8) expresses the polymer production rate or the monomerconsumption rate per unit volume. For the purpose of implement-ing the polymerization kinetics into the species transport equation,a source term (monomer consumption rate) in kg/m3 s is requiredand it is defined as:

Sj = RP × Mwm (10)

where Mwm is the monomer molecular weight. The reaction rateconstants in the polymerization are given in Table 2 (Gao & Penlidis,1996; Villalobos, Hamielec, & Wood, 1993).

Values Source

2.74400 × 104 cal/mol Villalobos et al. (1993)7.75923 × 103 cal/mol Gao and Penlidis (1996)3.47129 × 103 cal/mol Gao and Penlidis (1996)

4 emica

3

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�

wma

l w3P +

witc

�

es

m

wtwcowD

4

iltdtiicltFeteigtiattimzt

the expense of high computational time. Hence, it was necessary toselect a grid that gives an optimum compromise between the twoconflicting effects. Ein-Mozaffari and Upreti (2009) tested the gridindependency for the velocity field in a mixing tank under laminar

24 H. Patel et al. / Computers and Ch

.3. Estimation of the mixture viscosity

Polymerization takes place in a highly viscosity medium. Theiscosity can significantly affect the flow behavior in a poly-erization reactor (Moritz, 1989). Therefore, it is necessary to

ncorporate the reaction mass viscosity when modeling a polymer-zation reactor. Thus, the shear dependent viscosity of the mixture

as calculated from:

= �0(1 + �0�̇1.2/35000

)0.6(11)

here �̇ is the shear rate. The zero shear viscosity of the reactionass was estimated using the empirical correlation reported in Kim

nd Nauman (1992):

n(�0) = −11.091 + 1109T

+ M0.1413wp

[12.032wP − 19.501w2

P + 2.92

here Mwp is the average molecular weight of the polymer, wPs the polymer mass fraction in the mixture and T is the reactionemperature. The density of the mixture was calculated from theorrelation reported by Soliman et al. (1994):

= (1174.7 − 0.918T) (1 − wP) + (1250.0 − 0.605T) wP (13)

The monomer diffusivity was taken as 2.0 × 10−9 m2/s (Solimant al., 1994). The mass of the polymer sample is calculated from aimple mass balance as follows:

p = mo − mm (14)

here mo is the initial mass of the monomer and mm is the mass ofhe unreacted monomer in the mixture. To compute the viscosity,e took a polymer sample of known molecular weight. Since the

omputation of Mwp was not considered in the CFD model becausef large CPU time, a distribution of the polymer molecular weightas directly read as digitalized data from the Mwp plot provided inhib et al. (2000). The Mwp data was used to compute the viscosity.

. Computational procedure of the reactor model solution

The MixSim 2.1 tool is a part of the CFD simulation package andt is used to analyze the flow in agitated mixing vessels, but it isimited to non-reactive flow. The MixSim 2.1 was used to generatehe CSTR geometry and mesh only, and the rest of the model wasefined using the commercial CFD package (Fluent 6.3). However,he Fluent does not have the option to incorporate the polymer-zation kinetics and therefore a user-defined function (UDF) codedn C language was added to handle the reaction kinetics. The UDFode was written for the source terms previously defined andinked to the species transport model coded in Fluent. The sourceerm was linearized with respect to the monomer mass fraction.urther, the impeller motion was modeled using the multiple ref-rence frames (MRF) technique (Luo, Gosman, & Issa, 1994). Forhe rotating reference frame (RRF), the frame revolutions were setqual to the impeller revolutions. For the region adjacent to thempeller, a rotating frame region was defined and it is shown inreen color in Figs. 1 and 2, whereas a stationary frame includinghe tank walls was used for regions away from the impeller and its shown in black color. As a result, the impeller became station-ry with respect to the MRF. This particular approach can facilitatehe incorporation of the impeller motion even when the geome-

ry of the system considered is complex. At the feed stream, thenlet boundary conditions were such that the inlet velocity, styrene

ass fraction and temperature were supplied. At the reactor outlet,ero normal gradients for all variables were employed. Therefore,here was no diffusive flow normal to the boundary. On the liquid

l Engineering 34 (2010) 421–429

(−1327wP + 1359w2

P + 3597w3P

)T

](12)

level, the symmetry boundary condition was used hence zero nor-mal gradients and no-penetration conditions were assumed for allvariables. On the impeller surface and tank walls, wall boundarycondition was used for all the transport equations. Zero diffu-sive gradients were considered for the species transport equationson rigid surfaces, and hence no-slip and no-penetration condi-tions were imposed on the momentum transport equations on theimpeller and tank walls. The flow is laminar regime with a Reynoldsnumber of approximately 20 for the highest impeller speed andlowest viscosity. Second-order upwind discretization scheme wasused to calculate the face fluxes in the momentums and speciestransport equations. PRESTO scheme was used for the pressure dis-cretization and the velocity-pressure coupling was solved usingSIMPLE algorithm. Integrating the governing transport equations

over small control volumes resulted in an algebraic linear sys-tem, which was solved with the Gauss–Seidel iterative methodand the Algebraic Multi-Grid method (AMG). The reactor modelis comprised of a continuity equation, three momentum equations,a pressure correction and two species transport equations. In addi-tion, the model has property update equations for density andviscosity. Convergence was not easily achievable for the highly cou-pled nature of the transport equations of the polymerization systemand hence a special solution approach was undertaken. First, themomentum and continuity equations were solved without styrenereaction in the flow domain. After getting partially converged solu-tion for the flow, species transport equations were solved withoutthe source term. Once the non-reactive flow field solution has con-verged for all the transport equations, the species source termswere introduced. The under-relaxation factor for the species trans-port equation was increased gradually as the iteration progressed.Convergence was checked using residual and surface integral mon-itors. A coarse grid cannot properly resolve the gradients of the flowfield variables (velocities, species mass fractions and pressure) andmay eventually result in misleading results. Obviously, the accuracyof the solution improves with an increase in grid resolution but at

Fig. 3. Contour for styrene mass fraction at 100 rpm impeller speed and 144 minresidence time.

emical Engineering 34 (2010) 421–429 425

rfCtcianrs3up2Cts5

5

1pcittwmmemtR

5

1sak

ciftettitfltimermlsrCb

algorithm convergence was straightforward. The velocity magni-tude contour for the non-reactive flow is shown in Fig. 7 for aresidence time of 144 min and impeller speed of 1000 rpm. It iseasy to visualize the convective flow throughout the reactor due

H. Patel et al. / Computers and Ch

egime. They found that the grid independency results obtainedor the velocity field can be used for the scalar species transport. InFD analysis, it is a common practice to check the dependency ofhe solution on the grid resolution. Thus, two mesh sizes (372,571ells and 762,435 cells) were compared using the calculated veloc-ty magnitude measured in the regions of high velocity gradientsround the impeller blades. It turned out that this increase in theumber of cells changed the velocity magnitude by 0.78% only inegions of high velocity gradients. Therefore, the lower grid cellize was employed in this study. Most simulations required about00,000 iterations for convergence. Computations were carried outsing Super Computing facilities of HPCVL (High Performance Com-uting Virtual Laboratory). Each simulation was run in parallel with4–35 dual cores SUN Ultra-Spark IV, 1.8 GHz Sun Micro-SystemsPUs. The grid was partitioned into 24–35 parts and one CPU washen assigned to each partition. The convergence for each steady-tate simulation of the polymerization reactor was achieved after–6 days.

. Results and discussion

Thermal polymerization of styrene in a CSTR was simulated at40 ◦C to explore the effect of mixing on polymerization. Althougholymerization reactions are exothermic, isothermal operation isonsidered in this study. Several simulations were conducted tonvestigate the impact of the impeller speed, the effect of residenceime and input–output stream locations on styrene conversion andhe mixture homogeneity. The conversions predicted using CFDere compared with those obtain from CSTR model and experi-ental data. The information acquired through CFD modeling isore comprehensive than that obtained from RTD. In fact, CFD

nables us to compute velocity domain, viscosity variations, andonomer and polymer concentrations throughout the reactor. For

he residence time analysis, the CFD approach is different than theTD method.

.1. Effect of the impeller speed

Three simulations were conducted at N = 100 rpm, 500 rpm and000 rpm for the inlet–outlet locations shown in Fig. 1. Freshtyrene is fed into the reactor through the inlet pipe; the polymernd unreacted styrene leave the reactor. The residence time wasept constant at 144 min in each run.

Unlike in a perfectly mixed CSTR, the monomer and polymeroncentration are not uniform throughout the reactor even at highmpeller speed. Fig. 3 shows the filled contour of styrene massraction for an impeller speed of 100 rpm, on a plane aligned tohe impeller rotation axis. Fresh styrene (shown in dark red color)ntered the reactor at a zone far from the impeller and was pushedoward the top of the reactor by the upward axial-flow generated byhe pitched blade turbine along the reactor wall. The fluid velocityn this region was low and hence there was not enough momentumo quickly entrain the newly entered styrene stream into the bulkuid. Therefore, a styrene-rich region formed at the top of the reac-or whereas the region in the vicinity of the impeller remained richn polymer. Two separate regions are clearly visible in Fig. 3: a well-

ixed region around the impeller and a relatively unmixed regionlsewhere in the reactor. Path lines of the particles released at theeactor inlet were generated using the CFD model to simulate theixing patterns in the bulk flow and are shown in Fig. 4. These path

ines, colored in accordance with the styrene mass fraction, repre-ent the reaction progress as styrene molecules travel through theeactor. They were generated for a virtual distance of 100 m. TheFD capability allows generating path lines for a longer distance,ut the path lines may not be discernible. The path line behavior

Fig. 4. Path lines of the particles released at the inlet (colored by styrene massfraction).

shown in Fig. 4 can be explained more appropriately by analyzingthe flow induced by the impeller. First, fresh styrene was pushedto the top of the reactor by the upward axial-flow generated bythe pitched blade turbine along the reactor wall and then the bulkflow reversed direction along the impeller shaft due to the pump-ing action of the impeller. Styrene polymerizes as it flows down.The contours of styrene mass fraction are shown in Figs. 5 and 6for a higher impeller speed of 500 rpm and 1000 rpm respectively.In contrast with contours in Fig. 3, an increase in momentumexpanded the perfectly mixed region around the impeller.

5.2. Non-reactive flow and reactive flow

The non-reactive mass (pure styrene) has low viscosity and the

Fig. 5. Styrene mass fraction contour at 500 rpm impeller speed and 144 min resi-dence time.

426 H. Patel et al. / Computers and Chemical Engineering 34 (2010) 421–429

Fi

tta1tiatctrds

5

krsla

Fi

rather explained upon examining the propagation rate. For a given

ig. 6. Styrene mass fraction contour at 1000 rpm impeller speed and 144 min res-dence time.

o the low viscosity of the reaction mass. However, the viscosity ofhe fluid increases rapidly during a polymerization. For instance,t 35% monomer conversion, reaction mass viscosity increased to.9 kg/m s, which is approximately 10,000 times higher. Referringo the viscosity contours in Fig. 8, the sudden rise in the viscositymposed high gradient on the momentum imparted by the impellernd hampered the algorithm convergence. In fact, velocity magni-ude contours in Fig. 9 show that the convective flow remainedonfined to the impeller region. Obviously, high momentum ofhe reaction medium resulted in the formation of a well-mixedegion (cavern) around the impeller and the quality of good mixingegraded in regions away from the impeller even at high impellerpeed (N = 1000 rpm).

.3. Conversion analysis and validation

First, the effect of impeller speed on conversion is explored whileeeping the residence time 144 min. Alternatively, the effect of the

esidence time on conversion is also addressed at a fixed impellerpeed of 500 rpm. Further, the impact of the input–output streamocations on conversion is investigated. The CFD and CSTR modelsre compared for their ability to predict conversion. The assump-

ig. 7. Contour of velocity magnitudes (m/s) for the non-reactive mass at 1000 rpmmpeller speed and 144 min residence time.

Fig. 8. Contour of viscosity (kg/m s) of the reactive mass at 1000 rpm impeller speed144 min residence time.

tions made in CSTR model formulations are also debated to showthe advantages of using CFD model over CSTR model.

5.3.1. Variable impeller speedFor the input–output arrangement of Fig. 1, styrene conversion

versus impeller speed is plotted in Fig. 10. The CFD results showthat the conversion decreased with an increase in impeller speed.One possible explanation is that at higher impeller speed, morefluid is pushed from the styrene-rich region to the vicinity of thereactor exit. Hence, unreacted styrene may easily escape in theoutflow stream. In fact, this short-circuiting of unreacted styrenereduces the conversion at higher impeller speed. But the short-circuiting effect can be avoided upon relocating the input–outputstream locations as in Fig. 2. This arrangement is a theoreticalattempt to visualize how the impeller thrust may move the liq-uid upwards when the monomer enters the bottom of the tank.Besides, the decrease of conversion at higher impeller speed is

fixed temperature, the reaction rate constants remain invariant andthe propagation rate depends on monomer concentration only asshown in Eqs. (6) and (7).

Fig. 9. Contour of velocity magnitudes (m/s) for the reactive mass at 1000 rpmimpeller speed and 144 min residence time.

H. Patel et al. / Computers and Chemical Engineering 34 (2010) 421–429 427

Fd

adpo

tm

0

waamssivttosnppaearTCa

5

eFtpbshrCw

another level of mixing (Fig. 13), the impeller pumping force seemsto overcome the outlet suction force. Thus, a better homogene-ity resulted. It is important to underline that for the inlet–outletlocation configuration of Fig. 2, the CFD simulation predicted noconversion dependence on impeller speed (Fig. 14). It is likely that

ig. 10. Conversion versus Impeller speed for the residence time of 144 min Batchata source: Dhib et al. (2000).

With a higher impeller speed, the styrene-rich region shrinksnd therefore, the average propagation rate in the reactor slowsown. This effect can be named a monomer dilution effect on theropagation rate. Erdogan, Alpbaz, & Karagoz (2002) made similarbservations.

The conversion predicted with the CFD model is compared tohat computed with the CSTR model. Thus, the steady-state CSTR

odel form is given below:

= −Kp[Me][R•] + Q

V(Mf − Me) (15)

here Q is the volumetric flow for a reactor volume V, Mf and Me

re the concentrations of styrene in the feed and bulk. Convention-lly, the reaction source term is calculated assuming a perfectlyixed CSTR and consequently the monomer concentration is con-

idered homogenous. However, in the CFD model approach of thistudy, the reaction source term was numerically computed for eachndividual cell and hence the monomer concentration in the cellsaried from pure styrene concentration to the final product concen-ration. In fact Fig. 10 shows that as the impeller speed increases,he CFD prediction gets close to the idealized CSTR prediction. Inther words, the CSTR model considers a completely homogenousystem whereas the CFD model takes into account the presence ofon-homogeneity. Therefore, one may argue that the CFD modelredictions can be more realistic. However, no real data on styreneolymerization with different rpm is available and hence a fullssessment of the CFD prediction capabilities is not possible. Nev-rtheless, data for batch ampoule (no stirring) taken from Dhib etl. (2000) are reported in Fig. 10. Obviously, conversion in a batcheactor is higher than that in a CSTR for the same residence time.his study concludes that styrene conversion predicted with theFD model lies between the homogeneous CSTR model predictionsnd the batch conversion data.

.3.2. Variable residence timeFour CFD simulation runs were conducted to investigate the

ffect of the reactor residence time on conversion at N = 500 rpm.ig. 11 shows plots of monomer conversion versus the residenceime with batch data and compares the CFD model and CSTR modelredictions. At low residence time, both predictions are fairly close,ut they drift away at higher residence time. At first, the conver-

ion and the viscosity are low and the reaction medium is almostomogeneous; thus the CSTR assumption holds. However, at highesidence time, the reacting medium becomes more viscous and theSTR predictions are expected to drift away from the CFD model,hich takes into account the viscosity variation. The CFD conver-

Fig. 11. Conversion versus residence time for the impeller speed of 500 rpm Batchdata source: Dhib et al. (2000).

sion profile lies above the CSTR prediction, but it remains below thebatch reactor data trend.

5.4. Effect of input/output location

On analyzing continuous mixing processes, Saeed and Ein-Mozaffari (2008) showed that the input–output stream locationshave a significant effect on flow non-ideality (e.g. channeling anddead volume). For instance, channeling can take place when theinlet and the outlet positions are close to each other. Setting theoutput in front of the impeller pumping direction can also lead tochanneling. However, placing the input stream against the impellerpumping direction improves the mixing quality. Figs. 12 and 13show the contours of styrene mass fraction at an impeller speed of100 rpm and 500 rpm respectively for the input–output location ofFig. 2. As soon as the styrene inlet stream reached the impellerrotating at 100 rpm, it was dispersed into the bulk fluid. Slightnon-homogeneity is detected even at low impeller speed. In fact,a layer of rich styrene stretching towards the outlet, which is visi-ble in Fig. 12, was the result of an outlet suction force. However, at

Fig. 12. Contour of styrene mass fraction at 100 rpm impeller speed and 144 minresidence time.

428 H. Patel et al. / Computers and Chemica

Fig. 13. Contour of styrene mass fraction for500 rpm and 144 min residence time.

F

ttMsdowtcettoltcf

6

tn

ig. 14. Conversion versus Impeller speed for the residence time of 144 min.

he independence of the conversion in this configuration supportshe assumption of no short-circuiting previously depicted for Fig. 1.

oreover, the system reached homogeneity even at lower impellerpeed. Consequently, CFD capabilities can be exploited further toetermine the most suitable location of input–output stream andther design parameters of a reactor. Besides, polymer productsith homogenous properties are highly desirable. A major limita-

ion of the CFD modeling of a polymerization system is the elevatedomputational time. Due to the highly coupled nature of transportquations in a polymerization reaction, it becomes very challengingo solve these equations and it demands the simplification of reac-ion mechanism as well the dependency of the transport propertiesn the variables. CFD model can be used to augment design corre-ation and experimental data. It also provides comprehensive datahat are not easily obtained from experimental tests. CFD modelan reduce scale-up problems, because the models are based onundamental physics and are scale independent.

. Conclusion

This study incorporates the polymerization rate, variations ofhe reacting system viscosity and density along with the conti-uity equation, momentum equation, species transport equations

l Engineering 34 (2010) 421–429

and impeller rotation with true geometry in a 3D model. Theimpeller rotation with a true geometry was incorporated into theCSTR model under laminar regime. Computational fluid dynamics(CFD) technique was employed to investigate the effect of mix-ing on thermal polymerization of styrene in a lab-scale CSTR. Itallowed flow visualization inside the polymerization reactor. Thepath lines of the particles, released at the inlet, were generatedfor a better understanding of the flow behavior. Various contoursof the styrene mass fraction, medium viscosity, and velocity mag-nitudes were generated to show the effect of mixing. However,computational difficulties arose and hindered rapid convergencefor the flow field variables in this type of reactor due to the com-plex back mixing involved in the CSTR. The CFD analysis revealedthe presence of non-uniform mixing regions within the reactor.More homogeneous mixture is detected near the impeller and lesshomogeneously mixed region is observed in the regions with highreaction mass viscosity. Besides, the CFD results demonstrated thata high degree of homogeneity could be achieved even at a lowimpeller speed when the styrene feed is placed at the reactor bot-tom and near the impeller.

Further, the results show that CFD can be exploited to deter-mine the suitable operating conditions and design parameters for atypical polymerization reaction taking place in a CSTR in a shortertime and with less expense, a task otherwise difficult in experi-mental techniques. The study demonstrated that that the extent ofshort-circuiting and monomer dilution has a significant effect onthe monomer conversion in a CSTR. It also showed that the mix-ing quality can alter the extent of short-circuiting and monomerdilution within the reactor.

Acknowledgements

The authors would like to thank the Natural Sciences and Engi-neering Research Council of Canada (NSERC) and High PerformanceComputing Virtual Library (HPCVL) Canada for providing the finan-cial support for this research.

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