Chemical Engineering Journal 207–208 (2012) 414–420

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Chemical Engineering Journal

journal homepage: www.elsevier .com/locate /ce j

Styrene–butadiene rubber (SBR) production by emulsion polymerization:Dynamic modeling and intensification of the process

Alexandr Zubov a, Jiri Pokorny b, Juraj Kosek a,⇑a Department of Chemical Engineering, Institute of Chemical Technology Prague, Technicka 5, 166 28 Prague, Czech Republicb Synthos S.A., O. Wichterleho 810, 278 01 Kralupy nad Vltavou, Czech Republic

h i g h l i g h t s

" Dynamic model of SBR production by cold emulsion copolymerization was developed." Model was validated by stationary and transient plant data." Mooney viscosity and styrene content are predicted in good agreement with process data." Application of the model for the optimization of SBR production is demonstrated.

a r t i c l e i n f o

Article history:Available online 20 July 2012

Keywords:Styrene–butadiene rubberDynamic modelingEmulsion copolymerizationMooney viscosity

1385-8947/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.cej.2012.06.144

⇑ Corresponding author. Tel.: +420 220 44 3296; faE-mail address: Juraj.Kosek@vscht.cz (J. Kosek).

a b s t r a c t

This paper presents the deterministic model of styrene–butadiene cold emulsion copolymerization in thecascade of up to twelve reactors and its validation by the real industrial production of SBR. Model allowsthe dynamic prediction of basic latex properties (number and weight-average molecular weights, conver-sion of monomers) as well as the key qualitative SBR characteristics (Mooney viscosity and copolymercomposition) along the polymerization line in a good agreement with process data. The developed soft-ware is based on population balances of polymer chains using polymer moments and was successfullyvalidated by plant data of two types: (i) stationary profiles of important quantities along the reactor train,and (ii) dynamic transitions between two SBR grades with different content of bound styrene. We dem-onstrate how the developed model can be utilized in the optimization of SBR production, e.g., for the min-imization of the amount of off-spec products and for the prediction of polymerization line behaviorduring abrupt changes in the technological recipe.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

Styrene–butadiene rubber (SBR) is a synthetic elastomer withwide range of industrial applications. Due to its excellent abrasionresistance and stability it is extensively used as a component of cartires. SBR production by cold emulsion copolymerization is usuallycarried out at temperature around 5 �C in the cascade of six to fif-teen continuous well-agitated reactors.

Since the days of pioneering works of Harkins [1] and Smith andEwart [2], many advances were made in the understanding ofkinetics of emulsion polymerization, mainly in the area of interfa-cial processes like radical entry and exit into and out of the poly-mer particles [3,4]. However, some important aspects of theprocess, like polymer particles nucleation and coagulation, stilllack proper description and explanation [5]. The influence of

ll rights reserved.

x: +420 220 44 4320.

emulsifiers on the quality of produced polymer, the presence ofcomonomer as well as the branching of polymer chains make theproblem even more complex. Therefore, most papers dealing withmodeling of emulsion polymerization focus on the production ofpolystyrene latex, while literature on the modeling of industrialstyrene–butadiene copolymerization is rather scarce.

Different approaches are possible for treating the simulation ofemulsion copolymerization of styrene and butadiene. The generalframework for the modeling of emulsion copolymerization reac-tors as well as the synoptical overview of existing studies on thistopic was provided by Saldivar et al. [6]. Kanetakis et al. [7] usedthe residence time distribution (RTD) for modeling the polymerparticle size distribution for the SBR production in the cascade ofsix to nine continuous stirred tank reactors. Model parameterswere estimated by fitting model predictions to plant data, whichincluded conversion, particle size distribution, modifier consump-tion, copolymer composition and number and weight averagemolecular weights of the copolymer for each reactor at steady-state.

Nomenclature

B butadieneb number of branching pointsCk

ij concentration of monomer i in phase j of the kth reactor(mol dm�3)

cI concentration of initiator (mol dm�3)CTA chain-transfer agent/mercaptanfi fraction of radicals ending with monomer unit iI initiatork rate constant (s�1)Ki overall mass transport coefficient of monomer i (s�1)M monomer phaseMi molecular weight of monomer i (kg mol�1)Mn number-average molecular weight of polymer

(kg mol�1)Mw weight-average molecular weight of polymer (kg mol�1)�n time-averaged number of radicals per one polymer par-

ticleni number of units of monomer i incorporated into poly-

mer chainNA Avogadro numberNP number of polymer particles in the reactor_nk

i;M!P mass transfer of monomer i from droplets into latexparticles in the kth reactor (mol s�1)

P polymer phaseRk

iP rate of formation of monomer i per unit volume of poly-mer phase in the kth reactor (mol m�3 s�1)

S styrenet time (s)_Vk volumetric flowrate of emulsion from the kth reactor

(m3 s�1)Vk volume of emulsion in the kth reactor (m3)Vk

j volume of phase j in the kth reactor (m3)W aqueous phase/waterwk

j weight fraction of phase j in the emulsion of the kthreactor

wkij weight fraction of monomer i in phase j of the kth reac-

torU switch functiongMooney Mooney viscosity (a.u.)k polymer moment of living and dead chains (mol m�3)l polymer moment of living chains (mol m�3)qi density of pure monomer i (kg m�3)qPol density of pure polymer (kg m�3)qk

j density of phase j in the kth reactor (kg m�3)Wi partition coefficient of monomer i

A. Zubov et al. / Chemical Engineering Journal 207–208 (2012) 414–420 415

In recent years, method of artificial neural networks (ANNs) wasapplied to this topic [8,9]. In the article by Delfa et al. [9], inputcharacteristics involved concentrations of the initiator, activatorand chain-transfer agent, while the output properties describingthe produced polymer were latex solid content, polydispersityand Mooney viscosity of the produced SBR. Sayer et al. [10] pre-sented the interesting combination of the first-principle basedmodel with the method of ANNs while focusing on the dynamicsof thermosyphons refrigerating the reactor train. This model wasvalidated by industrial data and designed for the on-line imple-mentation in the control of the 15 reactors train for the SBR pro-duction. Another example of the model utilization in the on-linecontrol is the work by Souza et al. [11], who employed the rationalmodel of the emulsion copolymerization of carboxylated styrene–butadiene rubber (XSBR) in a nonlinear model-based predictivecontrol (NLMPC) of the semi-batch process. In this case the copoly-mer composition, conversion and average molecular weights of theproduct were chosen as the controlled variables.

With respect to contemporary computational facilities, buildingthe model upon the population balance equations (PBEs) appearsto be suitable choice [12,13], even for treating the particle size dis-tribution [14]. In our work we have chosen this approach – rationalmodel based on deterministic equations, where the reaction mech-anism of styrene–butadiene copolymerization was processed bythe population balance of the moments of chain-length andchain-branching distributions (i.e., method of polymer moments).

The goal of this paper is to demonstrate how the industrial pro-duction of SBR can be simulated on the basis of various measuredprocess data and how the resulting model can help both with theinvestigation and with the intensification of the real process withrespect to the quality of the product. First we describe our ap-proach to the modeling of styrene–butadiene emulsion copolymer-ization. Most of the model assumptions that we employed in ourwork (e.g., separation of the emulsion into aqueous, monomerand polymer phase, stage II of the Smith–Ewart theory as a domi-nant mode of polymerization) are common in the emulsion(co)polymerization models. However, our treatment of the poly-merization initiation stage deserves a special note. Instead ofincluding the detailed kinetic scheme of initiation and balancing

all components of the initiator system, we represent the initiatorsystem by only one species whose concentration affects thetime-averaged number of radicals per one polymer particle �n.Therefore, we do not consider parameter �n to be constant, butrather an empirical function depending on the concentration ofone of the initiator system components, which appears to be themost suitable solution with respect to the limited amount of exper-imental data and model robustness.

Results of simulations are compared to two types of plant data:(i) stationary profiles of conversion, chain-transfer agent concen-tration, number and weight-average molecular weights of pro-duced copolymer along the reactor train, and (ii) dynamicevolution of latex Mooney viscosity and styrene content duringthe transitions between SBR grades with different content of boundstyrene. Finally, we illustrate how the developed model can be uti-lized for the improvement of the considered SBR grade transitions,i.e., for the design of technological recipe steps allowing Mooneyviscosity to be kept in a narrow interval during the transition.

2. Mathematical model

2.1. General assumptions

During the development of the mathematical model of SBR pro-duction we made several simplifying assumptions:

� The presence of the following species is assumed: initiator (I),styrene (S), butadiene (B), water (W), mercaptan, i.e., chain-transfer agent (CTA), growing and dead polymer chains charac-terized by polymer moments.� Initiator and mercaptan are trace components, therefore they

are not included in the overall mass balance of each reactor.� Each reactor in the train is considered to be isothermal contin-

uous ideally stirred tank reactor with constant volume. The vol-ume of all reactors is equal.� Reaction mixture consists of three phases: monomer droplets

(M), polymer particles (P) and water (W). Volume additivityassumption holds in each phase.

416 A. Zubov et al. / Chemical Engineering Journal 207–208 (2012) 414–420

� The solubility of monomers in the aqueous phase is negligible.� Monomer partitioning between monomer droplets and polymer

phase can be described by linear equilibria.� The polymerization proceeds in the Stages II and III of the clas-

sical Smith–Ewart theory.� The polymerization takes place only in polymer particles except

the initiation, which proceeds in the aqueous phase.� Growing copolymer chains are terminated only by: (i) transfer

to mercaptan, (ii) transfer to monomer, (iii) transfer to polymer(butadiene unit), and (iv) reaction with terminal or internaldouble bond (butadiene unit).

Most of the above mentioned assumptions are adequate andrather standard for dynamic models of emulsion polymerization.

2.2. Reaction mechanism

The assumed reaction scheme of styrene–butadiene copolymer-ization is presented in Table 1 except the initiation stage, which istreated in a different way from other reaction steps and will be dis-cussed later after the introduction of polymer moments.

The symbols used in Table 1 should be explained: S, B and CTArepresent the styrene, butadiene and chain-transfer agent mole-cules, respectively. Symbol Pj

nS ;nB ;bstands for the growing copoly-

mer chain with nS units of styrene and nB units of butadieneincorporated, b branching points and ending monomer unit j. ThusPS

1;0;0 can be explained as a growing chain one monomer unit longwith styrene as an ending unit. Symbol DmS ;mB ;c denotes the deadcopolymer mS + mB units long with c branching points. It is evidentfrom the kinetic scheme that last four reactions correspond to thechain branching.

In order to perform population balances of all polymer chainspresent in the reactor, two types of moments of chain-length dis-tribution are introduced into the model. In this text they will be re-ferred to as simply ‘‘polymer moments’’. The first of them, lj

kS ;kB ;l, is

a moment of the kSth and kBth order with respect to the number ofmonomer units of styrene and butadiene, respectively, lth order

Table 1The considered kinetic mechanism of copolymerization of styrene and butadiene.

PropagationPS

nS ;nB ;b þ S ��!kpSSPS

nSþ1;nB ;b

PSnS ;nB ;b þ B ��!kpSB

PBnS ;nBþ1;b

PBnS ;nB ;b þ S ��!kpBS

PnSþ1;nB ;b

PBnS ;nB ;b þ B ��!kpBB

PBnS ;nBþ1;b

Chain transfer tomonomer

PSnS ;nB ;b þ S ��!ktrmSS DnS ;nB ;b þ PS

1;0;0

PSnS ;nB ;b þ B ��!ktrmSB DnS ;nB ;b þ PB

0;1;0

PBnS ;nB ;b þ S ��!ktrmBS DnS ;nB ;b þ PS

1;0;0

PBnS ;nB ;b þ B ��!ktrmBB DnS ;nB ;b þ PB

0;1;0

Chain transfer tomercaptan

PSnS ;nB ;b þ CTA ��!ktrCTAS DnS ;nB ;b þ CTA�

PBnS ;nB ;b þ CTA ��!ktrCTAB DnS ;nB ;b þ CTA�

Reinitiation CTA� þ S ���!quicklyPS

1;0;0ðwith probability f sÞ

CTA� þ B ���!quicklyPB

0;1;0ðwith probability f B; fS þ fB ¼ 1Þ

Chain transfer topolymer

PSnS ;nB ;b þ DmS ;mB ;c ����!mB ;ktrPS DnS ;nB ;b þ PB

mS ;mB ;cþ1

PBnS ;nB ;b þ DmS ;mB ;c ����!mB ;ktrPB DnS ;nB ;b þ PB

mS ;mB ;cþ1

Polymerization ofterminal or internaldouble bond

PSnS ;nB ;b þ DmS ;mB ;c ����!mB ;kpSTS

PBnSþmS ;nBþmB ;bþcþ1

PBnS ;nB ;b þ DmS ;mB ;c ����!mB ;kpStB

PBnSþmS ;nBþmB ;bþcþ1

with respect to the number of branching groups in the growingpolymer chains and it also contains the index of ending monomergroup j = S, B

ljkS ;kB ;l

¼X1nS¼1

X1nB¼1

X1b¼1

nkSS nkB

B bl½PjnS;nB;b

�; ð1Þ

where symbol ½PjnS;nB;b

� represents the molar concentration of grow-ing (living) polymer chains consisting of nS units of styrene, nB unitsof butadiene, having b branching points and ending with monomerunit j. The second type is the polymer moment of all (growing anddead) polymer chains

kkS ;kB ;l ¼X1nS¼1

X1nB¼1

X1b¼1

nkSS nkB

B bl DnS;nB;b

h iþXj¼S;B

PjnS;nB;b

h i !: ð2Þ

For the processing of the reaction scheme and prediction of thechain branching we need polymer moments up to the second order.

Let us now discuss the initiation stage of polymerization. Initi-ator system in real SBR production is based on redox system con-sisting of three species:

(i) ROOH = peroxide (initiator),(ii) ferrum complex (activator),

(iii) SFS = sodium formaldehydesulfoxylate (reducing agent).

Mechanism of polymerization initiation can be described, forexample, by three reactions listed in Table 2.

Regarding the mathematical treatment of initiation, one wouldexpect incorporating of elementary reaction steps of the redox ini-tiation system (cf. Table 2) into the kinetic scheme and conse-quently balancing all the components of the initiation system.The following methodology of modeling of polymerization initia-tion is rather empirical and thus less rigorous, however, from allthe approaches that we have tested it represents the most robustway with respect to the model sensitivity to changes in the compo-sition of the initiator system.

The usual assumption of the constant time-averaged number ofradicals per one polymer particle (�n ¼ const:) was abandoned andthis quantity was changed to the function �n dependent on the con-centration of one component of the initiator system cI, so the initi-ator system is now represented by only one species. The shape ofthe function �n was semi-empirically chosen so that the predictedchanges in the conversion of monomers during the shift in the con-centration of the initiator agree with the process data. The compar-ison of predicted and measured conversion versus initiatorconcentration is presented in Table 3.

The function �n finally has the following form for all the reactorsin the cascade:

�n ¼ a � ðcIÞb: ð3Þ

With respect to the initiator concentration default for most of theproduced SBR grades, the �n calculated according to Eq. (3) is equalto approx. 0.51, however, due to changes in the initiator systemcomposition during the transitions between different SBR grades,values of �n can belong to a wider interval. During our simulationsthe value of �n moved from 0.46 to 0.62. The variable �n is

Table 2Simplified mechanism of redox initiation in the emulsion polymerization. Allreactions take place in the aqueous phase.

Formation of peroxide radical ROOHþ Fe2þ !k1 RO� þ Fe3þ þ OH�

Reduction of ferric ions Fe3þ þ SFS!k2 Fe2þ

Activation of monomer M by radical RO� þM!k3 ðP1Þwater

Table 3Comparison of the total conversion measured during SBR production and theconversion predicted by the model. These data were used for finding constants a andb in Eq. (3).

Initiator concentration(a.u.)

Measured conversion(%)

Predicted conversion(%)

0.075 60.6 59.50.080 61.9 61.40.090 63.6 64.2

A. Zubov et al. / Chemical Engineering Journal 207–208 (2012) 414–420 417

subsequently used for the calculation of the equilibrium concentra-tion of radicals per the unit volume of polymer phase leq

0 ; i.e., thesteady value of l0 moments that should be reached after the changein the concentration of initiator cI

leq0 ¼

�n � NP

NA � VP; ð4Þ

where NP stands for the number of polymer particles in the reactor,NA is the Avogadro number and VP represents the volume of poly-mer phase. The rate of change of lS

0 moments by the mechanismof initiation is calculated in the following way

dlS0

dt¼ k � fS leq

0 � lS0 þ lB

0

� �� �; ð5Þ

where k represents the formal rate constant and fS is the fraction ofradicals ending with styrene unit defined by

fS ¼lS

0

lS0 þ lB

0

: ð6Þ

The rate of change of lB0 moments is calculated analogously to Eq.

(5).

2.3. Model equations

Model equations describing the production of SBR in one reac-tor of the train are represented by:

� non-stationary mass balances of present phases (aqueous,monomer and polymer),� non-stationary mass balances of involved low molecular

species:o balance of styrene, butadiene and mercaptan both in mono-

mer droplets and in polymer particles,o balance of initiator in the aqueous phase,

� non-stationary population balances of polymer moments l andk,� overall mass balance of the reactor,� evaluation of the density of monomer and polymer phase

(assuming constant density of water), evaluation of the densityof the reaction mixture,� summation relations.

As already mentioned, the volume of the kth reactor in the traincan be formally divided into three phases denoted by appropriatesubscript:

VkM þ Vk

W þ VkP ¼ Vk: ð7Þ

The computation of densities is based on the simplifying assump-tion of volume additivity in each phase

1qk

M

¼ wkSM

qSþwk

BM

qB; ð8Þ

1qk

P

¼ wkSP

qSþwk

BP

qBþ 1�wk

SP �wkBP

qPol; ð9Þ

qk ¼ VkM

Vkqk

M þVk

W

Vkqk

W þVk

P

Vkqk

P; ð10Þ

where qk;qkW ;qk

M and qkP are densities of the reaction mixture,

water, monomer droplets and polymer phase in the kth reactor,respectively. Water density qk

W is constant. Symbols qS, qB and qPol

represent densities of pure styrene, butadiene, and polymer, resp.Weight fractions of styrene and butadiene in monomer dropletsare wk

SM ;wkBM (their summation gives unity) and weight fractions

of styrene and butadiene in polymer particles are wkSP and wk

BP .The structure of the balance equations can be demonstrated on

the case of monomer phase. Balance equations must be able to re-flect the transition between the Stages II and III of the emulsionpolymerization

d VkMqk

M

� �dt

¼ _Vk�1qk�1wk�1M � _Vkqkwk

M

�UðVkMÞ _nk

S;M!PMS þ _nkB;M!PMB

� �; ð11Þ

where wkM stands for the weight fraction of monomer droplets in the

kth reactor. The mass transfer of monomer i from droplets into latexparticles (mol s�1) _nk

i;M!P is defined as

_nki;M!P ¼ Kiðc�;kiP � ck

iPÞ; i ¼ S;B; ð12Þ

with Ki being the overall mass transfer coefficient and ckiP the actual

concentration of monomer i in the polymer phase. The equilibriumconcentrations between monomer droplets and polymer particlesare calculated from the concentrations of styrene and butadienein monomer droplets ck

SM and ckBM using linear partition coefficients

wS, wM

c�;kiP ¼ wickiM; i ¼ S;B: ð13Þ

In Eq. (11) the mass transfer of monomers from the droplets to thepolymer particles is (owing to appropriate units) multiplied bymonomer molecular weights MS, MB. The function U dependingon the volume of monomer droplets Vk

M is a small but sharp switchbased on hyperbolic tangens, so that U = 1.0 when the polymeriza-tion is in the second stage (Vk

M > 0; monomers are diffusing fromdroplets to particles) and U = 0.0 when the process is in the thirdstage and the monomer droplets are depleted (Vk

M ! 0), thus themass transfer to polymer is halted. The function U allows a smoothtransition from Stage II to Stage III of emulsion polymerization, i.e.,a convenient modification of Eq. (11) during the simulation withoutthe necessity to restart the integration and re-initialize statevariables.

In the balance of monomers sorbed in polymer particles, thereaction terms should be also included, therefore we write

dðckiPVk

PMiÞdt

¼ _Vk�1qk�1ðwk�1P wk�1

iP Þ � _VkqkðwkPwk

iPÞ

þUðVkMÞ _nk

i;M!PMi þ RkiPVk

PMi; ð14Þ

where RkiP stands for the reaction rate of formation of monomer i per

unit volume of polymer phase. On the other hand, reaction termdoes not appear in the balance of initiator, since in our model theinitiator concentration only affects the value of function �n, cf. Eq. (3)

dðckIW Vk

W MIÞdt

¼ _Vk�1qk�1ðwk�1W wk�1

IW Þ � _VkqkðwkW wk

IWÞ: ð15Þ

Several other ways of modeling the initiator system including thedetailed kinetic scheme and balance of all components of the initi-ator system were tested. However, due to the limited experimentaldata the implemented simplification (dependence �nðcIÞ) was foundto be the most robust solution.

Table 4Selected model parameters and their values.

Parameter Symbol Value

Active volume of one reactor Vk 10.9 m3

Typical emulsion flowrate _Vk 17.0 m3 h�1

Number of polymer particles in thereactor

NP 1023

Rate constant of propagation kpSS 5.05 � 10�3 m3 mol�1 s�1

Rate constant of chain transfer tomonomer

ktrmSS 1.38 � 10�6 m3 mol�1 s�1

Rate constant of chain transfer tomercaptan

ktrCTAS 4.93 � 10�4 m3 mol�1 s�1

Rate constant of chain transfer topolymer

ktrPS 2.20 � 10�7 m3 mol�1 s�1

Rate constant of polymerization ofdouble bond

kpStS 2.20 � 10�7 m3 mol�1 s�1

index of reactor1 2 3 4 5 6 7 8 9 10 11

conv

ersi

on o

f m

onom

ers

(%)

0

20

40

60

80simulation resultsplant data

Fig. 1. Profile of measured and predicted conversion of monomers along thecascade of 11 reactors for the SBR production.

400Mn (simulation)

418 A. Zubov et al. / Chemical Engineering Journal 207–208 (2012) 414–420

Balance of both monomers in droplets, balance of mercaptan(chain-transfer agent) in monomer and polymer phase, as well asbalances of polymer moments are arranged analogously withabove Eqs. (11), (14), and (15).

Polymer moments are finally used for the evaluation of severalcharacteristics of SBR copolymer architecture, like number andweight-average molecular weight Mn, Mw, or copolymer composi-tion distribution. Besides the content of bound styrene, the mostimportant characteristics of SBR is the so-called Mooney viscosity,which is correlated to the polymer molecular weight distributionutilizing plant data according to the following relation [15]

gMooney ¼ AffiffiffiffiffiffiffiffiffiffiffiffiffiffiMnMw

pþ B: ð16Þ

Model equations, forming a system of differential–algebraic equa-tions (DAEs), were solved simultaneously for all reactors of the cas-cade using the public domain package DASPK [16]. The values ofselected model parameters are listed in Table 4. The number ofpolymer particles in the reactor NP was evaluated from the mea-surements of latex particle size distribution conducted at SynthosKralupy company using Zeta-Sizer. Rate constants of elementarypolymerization steps were found by the minimization of the objec-tive function F expressing the difference between experimental andpredicted values of the monomers conversion X and of the numberand weight-average molecular weight of SBR along the reactor trainMn and Mw, respectively

F ¼ ðXexp : � XmodelÞ2 þ ðMn;exp : �Mn;modelÞ2 þ ðMw;exp :

�Mw;modelÞ2: ð17Þ

For the minimization of the objective function we employed theNelder-Mead (i.e., ‘‘downhill simplex’’ or ‘‘amoeba’’) algorithm [17].

index of reactor1 2 3 4 5 6 7 8 9 10 11

Mn,

Mw

/ 10

3 g m

ol-1

0

100

200

300

Mw (simulation)

Mn (experiment)

Mw (experiment)

Fig. 2. Comparison of predicted and measured number and weight-averagemolecular weights (Mn and Mw) of produced copolymer along the reactor train inthe steady-state.

3. Results and discussion

The developed model was validated using two types of dataprovided by Synthos company. The first type included profiles ofseveral variables measured from samples taken along the reactortrain when the polymerization line was in steady-state regime.Among these variables were conversion of monomers, numberand weight-average molecular weight of produced copolymer(from GPC measurements), Mooney viscosity and concentrationof residual mercaptan.

The second type of data were the detailed records of dynamictransitions between different SBR grades. During these transitions,the time evolution of both process inputs and outputs was re-corded. Inputs were represented by the feed composition, whilethe output variables consisted of conversion, copolymer composi-tion and Mooney viscosity of the produced latex.

3.1. Stationary profiles of variables along the reactor train

Mathematical model predicts the linear growth of monomersconversion along the reactor train, which is consistent with realplant data (cf. Fig. 1). The profile of average molecular weightsMn and Mw along the cascade (simulated and process data) is pre-sented in Fig. 2. The number-average molecular weight Mn appearsto grow linearly along the cascade, whereas the weight-averagemolecular weight Mw has the more progressive character due tothe increased effect of chain-branching in the second half of thereactor train.

An important validation for our model is the mercaptan profile,which is also in a good agreement with experimental data (Fig. 3).

3.2. Dynamic transitions between different SBR grades

The important property of the developed model – the ability topredict dynamic evolution of latex properties along the polymeri-zation reactor train – will be demonstrated on two cases of thecrossover between grades of styrene–butadiene rubber with differ-ent copolymer composition. Both cases begin with the stationaryproduction of SBR with approx. 23% of the bound styrene, thenthe recipe is changed so that the copolymer with 40% of styreneis produced for about 30 h, and finally the process is directed back

time (hours)0 10 20 30 40 50 60 70 80 90

Moo

ney

visc

osity

(a.

u.)

0

40

80

120

160

cont

ent o

f bo

und

styr

ene

(%)

0

20

40

60

80

100

time (hours)0 10 20 30 40 50 60

Moo

ney

visc

osity

(a.

u.)

0

40

80

120

160

cont

ent o

f bo

und

styr

ene

(%)

0

20

40

60

80

100

(a)

(b)index of reactor

1 2 3 4 5 6 7 8 9 10 11

dim

ensi

onle

ss c

once

ntra

tion

of m

erca

ptan

0.0

0.2

0.4

0.6

0.8

simulation resultsplant data

Fig. 3. Predicted and experimental residual concentration of chain transfer agentalong the SBR polymerization line.

A. Zubov et al. / Chemical Engineering Journal 207–208 (2012) 414–420 419

to the production of latex with lower amount of styrene incorpo-rated into copolymer.

Fig. 4a and b depicts the measured and the calculated evolutionof styrene content and Mooney viscosity of produced SBR for thetwo above mentioned transitions. In both cases the agreement be-tween the predicted and the measured styrene content is excellent,however, it is less favorable for Mooney viscosity, probably due tolower quality of correlation (16) for latex with a high content ofstyrene (cf. Fig. 5). Nevertheless, despite this discrepancy thedeveloped software can be effectively used for the design of opti-mal transition trajectory, which is going to be demonstrated inthe following section.

Fig. 4. Comparison between predicted and measured latex characteristics duringtwo cases of transitions between SBR grades with different content of boundstyrene. Rectangles – experimental values of styrene content; circles – experimen-tal values of Mooney viscosity; dashed line – predicted styrene content; solid line –predicted Mooney viscosity.

(MnMw)0.5 / 105 g mol-1

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Moo

ney

visc

osity

(a.

u.)

0

50

100

150

200Experimental dataLinear regression

Fig. 5. Dependency of SBR latex Mooney viscosity on the geometric mean ofnumber and weight-average molecular weights Mn, Mw. Comparison of experimen-tal data with regression line.

3.3. Application of model for optimization of SBR production

Mathematical model of SBR production allows optimization anddeeper understanding of the industrial process with the followingobjectives:

� minimization of the off-spec product during transitionsbetween different SBR grades,� study of production line behavior with respect to varying qual-

ity of incoming monomers and suggestion of control actions,� investigation of possible technological improvements of the SBR

production:o side inlets of mercaptan for more effective control of the

latex Mooney viscosity,o side inlets of monomers for increasing the production

capacity,� determination of reasons for undesirable quality of produced

latex.

Regarding the transition between two different SBR grades de-picted in Fig. 4a, it is important from the manufacturer’s point ofview to keep the variance of Mooney viscosity in the narrow inter-val while the varying styrene content defines the actually producedlatex grade. We employed the developed model and proposed theoptimal strategy for the above mentioned transition with respectto keeping the Mooney viscosity in a narrow interval. The require-ments on the quality of the produced SBR are very severe – for agiven SBR grade the Mooney viscosity is allowed to vary withinthe limit of only 10 units to be on-spec. Simulation results pre-sented in Fig. 6a indicates that it is possible to carry out the tran-sition between SBR grades with different styrene content and tokeep the latex viscosity in a narrow interval at the same time.

Although the original recipe cannot be published due to confiden-tiality, optimized version of recipe consisting of several stepchanges in the concentration of butadiene and mercaptan in thefeed is shown in Fig. 6b. We can reveal that the optimized reciperequires a smaller number of control actions than the originalone. During the original transition the concentration of initiatorwas altered slightly (probably to correct the value of conversion

time (hours)0 10 20 30 40 50 60 70 80 90

Moo

ney

visc

osity

(a.

u.)

100

110

120

130

140

150

160

real transitionoptimized transition

time (hours)0 20 40 60 80

frac

tion

of b

utad

iene

in m

onom

er p

hase

(%

)

0

20

40

60

80

conc

entr

atio

n of

mer

capt

an (

a.u.

)

0.00

0.05

0.10

0.15

0.20

0.25

butadiene concentrationmercaptan concentration

(a)

(b)

Fig. 6. (a) Dynamic evolution of latex Mooney viscosity during the transitionbetween two SBR grades with different content of bound styrene. Plant data(circles) previously presented in Fig. 4a are compared with Mooney viscositycalculated using the recipe optimized for the lowest possible viscosity variance(solid line). (b) Proposed sequence of changes in the feed composition resulting inthe optimized transition (a).

420 A. Zubov et al. / Chemical Engineering Journal 207–208 (2012) 414–420

in the course of the transition). On the other hand, the model pre-dicts that it is possible to optimize the recipe using changes only inthe concentration of mercaptan and in the composition of incom-ing monomer phase and to keep the latex Mooney viscosity inthe desired interval at the same time. The value interval in whichbutadiene and mercaptan concentrations were varied are similarfor both the original and the optimized transitions, however, theirtime schedule is different.

4. Conclusions

We developed the dynamic model of SBR production in the cas-cade of up to twelve reactors by the technique of cold emulsionpolymerization based on the population balance of polymer mo-ments and assumptions usual for most emulsion polymerizationmodels. Our model however differs from the classical approachto the modeling of initiation stage of polymerization, since we con-sider the time-averaged number of radicals per polymer particle �n

to be a function depending on the concentration of only one com-ponent of the initiator system.

Model provides good agreement with both stationary and tran-sient plant data. It allows the prediction of latex composition andMooney viscosity, which serve as the most important characteris-tics of the produced SBR. Simulation software is accompanied by auser friendly input/output interface and can be effectively used byour industrial partner for further investigation and optimization ofthe SBR production process, e.g., for the minimization of the off-spec product during transitions between different SBR grades, orfor the study of prospective technological improvements (side in-lets of monomers or mercaptan into the polymerization line).Moreover, the model is intended to be extended so that moreimportant topics related to the industrial process can be investi-gated (e.g., the influence of type of the emulsifier and of the qualityof incoming recycled monomers on the copolymerization kinetics).

Acknowledgement

Project MPO FT-TA4/081 and financial support from the specificuniversity research (MSMT No. 21/2011) are acknowledged.

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