Thermodynamic Modeling and Simulation of Styrene-Butadiene Rubbers (SBR)Solvent Equilibrium Staged Processes

Gabriel Ovejero,* M. Dolores Romero, Eduardo Dıez, Ismael Dıaz, and Ponciano Perez

Grupo de Catalisis y Procesos de Separacion (CyPS), Departamento de Ingenierıa Quımica, Facultad de C.Quımicas, UniVersidad Complutense de Madrid, AVda. Complutense s/n, 28040, Madrid, Spain

The main purpose of this paper is to describe the necessary steps to model the equilibrium based operationsin styrene-butadiene rubbers (SBRs) processing. First of all, we include a brief introduction to polymer-solventthermodynamics, so later on, we can discuss about the experimental techniques reported in literature for thiskind of system, emphasizing those we have used in our work (intrinsic viscosity and inverse gaschromatography). General comments about the thermodynamic models used and experimental data treatmentare also included. But, the development of an accurate simulation model which can predict the final purity ofthe polymer involves other thermodynamic studies, in order to determine the relative affinities of severaladditives with both polymer and solvent. Thus, the behavior of several polar modifiers, which are commonlyemployed in the synthesis process, is also reported. Experimental equilibrium data, evaluation of predictivemethods, and simulation results are also reported for these additives, showing that the selection of a suitablethermodynamic model is essential for the reliability of the simulations performed.

1. Introduction

The generic term “polymer” includes a great variety of bothnatural, such as starch and some proteins, and syntheticmaterials, such as polyamides. They can be divided in two maingroups depending on their mechanical behavior: plastic materialsand rubbers or elastomers.1

Styrene-butadiene rubber (SBR) is the most importantsynthetic rubber. Due to its low manufacturing cost and its goodproperties, it is a good replacement for natural rubber. Thismaterial is a copolymer of both butadiene and styrene with astyrene weight fraction equal or less than 0.2-0.3.

There are two types of SBRs. The first, or random one, isobtained by polymerization of the two monomers withoutcontrolling their relative position in the final product. Thesecond, SBS (styrene-butadiene-styrene), one is constitutedby a block of styrene molecules, followed by a block ofbutadiene molecules, and a last block of, again, styrenemolecules. From SBS rubbers, SEBS rubbers (styrene-ethylene-butadiene-styrene) can be obtained by partial hydrogenationof the double bonds of butadiene fraction.

These last compounds are mainly applied to manufactureadhesives and sealants, as plastic modifiers, or in the compound-ing of other products.2 In addition, other specific applicationshave been described for these polymers, as in the case of thepharmaceutical field3 or for asphalts modifications.4

As in a typical chemical process, the main steps of a rubbersynthesis process are the raw materials fitting out, the reactionstep, and the product separation. The first step is performedmainly by means of distillation or adsorption processes. Thesecond one can be done either by an emulsion process (inaqueous media) or by an anionic polymerization process (in anorganic solvent media). At last, the product separation isdeveloped, either by devolatilization or direct evaporation orby steam stripping.

Although the raw materials fitting out and the reaction stepshave widely been studied both by experimental measurements

and by simulation, there is not so much work concerning theproduct separation step.

In a steam stripping process, polymer and solvent areseparated by contact with a steam stream which vaporizes thesolvent, while the condensed water remains with the polymer.Later on, both water and polymer can be easily separated in afilter, because they are absolutely immiscible, and the solventalong with the steam are separated by a flash distillation.

Although the first stripping processes were carried out in asingle stage,5-8 nowadays, these processes are carried out intwo following stages, so the fresh steam can be fed to the secondstage and the vapor recovered from this stage can be used as astripping agent in the first stage.

In a devolatilization process, the solvent is directly evaporatedwithout employing any stripping agent. It has the advantage,when compared with a steam stripping process, that it is notnecessary to add any equipment to recover the separated solvent.But it has the inconvenience that, due to the fact that theviscosity of the polymer crumbs increases a lot while the solventevaporates, the separation of the last portions of solvent is verydifficult (and involves a high energy consumption).

Due to the fact that both devolatilization and steam strippingare thermodynamically controlled processes, it is very importantto study the thermodynamic behavior of all the componentsinvolved: polymer, organic solvent, and water.

Solvent-water mixtures are constituted by components whosemolecular sizes are close to each other. Therefore, they can bestudied by means of classical thermodynamics, using eitherequations of state (EOS) models, such as Peng-Robinson9 orRedlich-Kwong-Soave,10 or activity coefficient models, suchas NRTL11 or UNIQUAC.12

But, the mixtures involving polymers can not be studieddirectly by means of classical thermodynamics because thereis a great difference between the molecular size of the polymerand the molecular size of the other component. For this reason,a binary polymer-solvent mixture does not strongly behave asa conventional solution, and it is necessary to use specificthermodynamic models.

Several authors have proposed different models to character-ize polymer-solvent mixtures. One of the most important,

* To whom correspondence should be addressed. Tel.: +34-91-394-4111. Fax: +34-91-394-4114. E-mail address: govejero@quim.ucm.es.

Ind. Eng. Chem. Res. 2009, 48, 7713–7723 7713

10.1021/ie9006497 CCC: $40.75 2009 American Chemical SocietyPublished on Web 07/02/2009

which has been mainly used in the results presented in thissection, is the Flory-Huggins theory. In this theory, proposedby Flory13,14 and Huggins,15 the activity of the solvent in asolvent (1)-polymer (2) mixture is calculated as the sum oftwo contributions, a configurational one and an energetic one,according to eq 1.1.

In this equation, p is the vapor pressure of the polymer solution,and P1° is the vapor pressure of the pure solvent

The first two terms in the right side of the former equationbelong to the entropic configurational contribution. It takes intoaccount the differences in size and shape of the molecules, whichdetermine the different configurations that a molecule of polymercan adopt in the solution. This contribution is calculated as afunction of the polymer volumetric fraction (φ2) and the molarvolume of the polymer divided by the molar volume of thesolvent (r).

The last term of the equation is the energetic contribution. Itis defined as a function of a nondimensional parameter calledthe polymer-solvent interaction parameter or Flory-Hugginsparameter (). This parameter, eq 1.2, has two contributions:an entropic one (s), eq 1.3, whose value ranges between 0.2and 0.5, being 0.34 the most common value,16 and an enthalpicone, eq 1.4, which can be calculated from the Hildebrand andScott theory17,18 as a function of the difference between thesolubility parameters of polymer (δ2) and solvent (δ1) and themolar volume of the solvent (Vm,1)

The application of this model is a very easy way of obtainingexperimental equilibrium data in polymer-solvent solutions,although it has a few limitations. For example, although thepolymer-solvent interaction parameter was originally definedas independent of the polymer volumetric fraction, this couldnot be completely true. In the literature, both increasing19 anddecreasing20 values of with polymer composition have beenreported. Besides, in solutions with very low polymer content,the theory could also fail in the calculation of the entropy andvolume of mixing.

Other thermodynamic models that can also be used toreproduce the thermodynamic behavior of a polymer-solventsystem are the theories of Prigogine-Flory-Patterson,21-23

Sanchez and Lacombe24-26 LF (lattice fluid), or SAFT (statisti-cal associated fluid theory), proposed by Wertheim.27,28 Inaddition, predictive activity coefficient models such as UNIFAC-FV29 or equations of state based models such as High-Danner30

or the perturbed-hard-sphere-chain EoS31 have been developed,showing a great potential in phase-equilibria prediction involvingpolymer solutions.

The aim of this paper is to describe a procedure to simulatethe polymer-solvent steam stripping separation step in a SEBSrubber production plant. Due to the importance of developinga thermodynamic study for this kind of simulation, in thebeginning, the more important experimental methods to getequilibrium data in both polymer-solvent and conventional

mixtures are described, indicating the results obtained with thetwo techniques employed in this work (inverse gas chromatog-raphy and intrinsic viscosity). Later on, the paper includes adescription of the simulation model of the separation stepconsidered. At last, the influence of the different thermodynamicstudies over the simulation results is also discussed, in termsof the distribution of different additives in the outlet streams ofthe model.

2. Experimental Measurements of Polymer-SolventEquilibria

Thermodynamics of polymer-solvent pairs is important notonly from a scientific point of view but also in many interestingindustrial processes. Examples of its applicability are thepreparation of asymmetric membranes,32 the microlithography,employed in chips fabrication,33 or the study of the oralabsorption of drugs.34

Modeling polymer-solvent equilibrium requires using non-conventionaltechniques.Typicalisothermalorisobaricvapor-liquidequilibrium (VLE) measurements can not be carried out directly,due to the specific properties of polymer solutions (high boilingpoint, viscosity,...). For this reason, it is difficult to characterizepolymer-solvent interactions. But, these drawbacks have beenovercome by applying novel experimental methods for thedetermination of both polymer-solvent interaction parametersand polymer solubility parameters.

There are a wide variety of methods described in literaturefor this purpose (Table 1), depending on the polymer composi-tion in the mixture and the kind of polymer (glassy, amorphous,thermostable,...). Between them, intrinsic viscosity (IV) andinverse gas chromatography (IGC) are two of the most widelyused due to their reliability and ease of startup.

In a rubber obtaining process, there are several steps in whichthe composition of the polymer solution is changing. Once therubber is synthesized, the polymer mass fraction in the reactoris below 0.3. Later on in the process, solvent and additives areremoved from polymer, a steam stripping mechanism being oneof the mostly used. This step is designed to purify the finalproduct, so the final polymer mass fraction can be greater than0.99.

As it has been previously reported,40 polymer-solventsinteraction parameters depend upon composition; in addition,the change in the behavior of the solvent is more importantwhen its concentration is going to zero. Therefore, to simulatea polymer-solvent steam stripping step, a thermodynamic studyof polymer solutions over a wide range of compositions isneeded. There is not any experimental method covering theoverall range so it is necessary to start up with two differentmethods.

2.1. SEBS Rubber. All the experimental measurements inthis work were carried out with a SEBS (poly(styrene-b-butene/

ln a1 ) lnp

P1° ) ln(1 - φ2) + (1 - 1

r )φ2 + φ22

(1.1)

) S + H (1.2)

S ) 0.34 (1.3)

H )Vm,1

RT(δ1 - δ2)

2 (1.4)

Table 1. Comparison of Experimental Techniques forPolymer-Solvent Equilibrium

high polymercomposition techniques

intermediate-low polymercomposition techniques

inverse gas intrinsic viscosity38

chromatography35 light scattering38

polymer swelling36 ultracentrifuge39

polymer sorption37 turbidimetry39

microanalytical39

ultraviolet and infrared spectrometry39

size exclusion chromatography38

osmotic pressure38

matrix-assisted laser desorption ionization38

7714 Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009

ethylene-b-styrene) triblock copolymer) synthesized and sup-plied by Alfonso Cortina Technology Center of REPSOL-YPF,with a styrene content of 32% by weight, a density of 960 kg/m3, and an average molecular weight of 86238 g/mol. Thisrubber is obtained by hydrogenation of poly(styrene-b-butadiene-b-styrene) triblock copolymers.

2.2. Intrinsic Viscosity Measurements. The background ofthe technique is the change in the viscosity by consecutiveadditions of polymer over the solvent. The more the viscosityincreases, the more compatible polymer and solvent are.

Intrinsic viscosity [η] is the viscosity of an infinitely dilutedpolymer solution. It can be calculated with the experimentallydetermined values of the relative (ηr) and specific (ηsp) polymerviscosities, according to the Huggins (2.1) and Kraemer (2.2)equations.

where c is the concentration of polymer solution, KH is theHuggins coefficient, a constant for a series of polymers ofdifferent molecular weights in a given solvent and temperature,and KK is the Kramer coefficient, where theoretically KH - KK

) 0.5.So the intrinsic viscosity can be determined, as usual, as the

common intercept of the Kraemer and Huggins relationships,using ηr and ηsp previously determined.

For the intrinsic viscosity measurements,41 all polymer-solventmore concentrated solutions were prepared by adding 200-300mg polymer over aprox 60 g of pure solvent and shaking untilpolymer dissolution. The rest of the solutions were preparedfrom the former ones by dilution, by adding pure solvent.

Viscosity data were carried out in a JP-Selecta Ubbelohde0b type of capillary viscosimeter. Once prepared each solutionwas transferred into viscosimeter and immersed in a water bath,thermostatted at 20 °C ( 0.01. The solutions were allowed toequilibrate at this temperature before starting the measurement.The accuracy of the measurements was 10-2 s. From the flowtimes, relative and specific viscosities were determined.

From our previous results,41 it can be concluded that,according this technique, cyclohexane shows the highestcompatibility with an SEBS rubber (highest intrinsic viscosityvalue) and n-hexane shows the lowest (lowest intrinsic viscosityvalue). Besides, the lower the polymer-solvent interactionparameter, the more compatible the polymer and the solvent.This happens when enthalpic term of this parameter, proportionalto (δs - δp)2, is the lowest. So the solubility parameter of thepolymer should be close to the solubility parameter of thesolvent. According to literature,42 this occurs when intrinsicviscosity is the highest; for this reason, the maximum of theplot intrinsic viscosity vs solubility parameter of the solventcorresponds to the polymer solubility parameter. The resultobtained in our previous work41 is δ2 ) 17.1 MPa0.5.

Then, by using eqs 1.2-1.4, the Flory-Huggins interactionparameter of each polymer-solvent pair, in the range ofintermediate-low polymer compositions, can be obtained. Thecalculation only requires the knowledge of the solubilityparameter of each pure solvent, which can be easily obtainedfrom vaporization enthalpy values.

2.3. Inverse Gas Chromatography (ICG) Measurements.By IGC measurements, the stationary phase of a chromato-graphic column is characterized. Using a polymer as stationary

phase, measurements of the differential affinity of solvents canbe performed and polymer-solvent interaction parameters canbe fitted.

The background is that, once the polymer is immobilized intoa packed column, small amounts of different solvents, alongwith air (inert component), are injected and carried through thecolumn by the carrier gas of a typical gas chromatograph. Thedifference between the retention times of the air and the solventcan be related with the compatibility between the polymer andthe solvent. The higher the time the solvent is in the column,the higher the affinity of the solvent and the polymer. Theconcept is

According to the IGC technique,43 the relation between theinfinite dilution activity coefficient of the solvent and theretention volume is given by eq 2.5, where T is the temperaturein kelvin, R is the ideal gas constant, M1 is the solvent molecularweight, and f 1° is the standard fugacity of the solvent. Usually,this last value is calculated by using a virial EOS truncated afterthe second term, as shown in eq 2.6.

For the inverse gas chromatography measurements, ChromosorbW/AW-DMCS 80-100 mesh was used as support. The station-ary was prepared by dissolving a weighted sample of thepolymer in cyclohexane and depositing the solution on aweighted amount of support. The mixture was allowed to dryunder vacuum by slow evaporation in a rotavapor, being stirredto ensure a homogeneous mixture; the evaporation time was8 h. The final amount of polymer deposited in the support was11.9% w/w, which was determined with thermogravimetricanalysis on a Seiko EXSTAR 6000 TG/DTA 6200.

Afterward, the coated support was packed into a 1/4 in.nominal diameter and 1.9 m length column, which was installedin a VARIAN 3800 gas chromatograph, equipped with a thermalconductivity detector and an electronic flow controller.

All the measurements were carried out with a helium flowof 30 mL/min, as a carrier gas, and in a temperature rangebetween 20 and 150 °C. The amount of solvent inyected was0.2 µL along with 0.8 µL of air, as an inert component.

From the values of infinite dilution activity coefficient, theFlory-Huggins interaction parameter can be calculated by usingeq 2.7,44 where r is the ratio between molar volume of thepolymer divided by the molar volume of the solvent and F1

and F2 are solvent and polymer densities, respectively.

The Flory-Huggins theory, modified by Blanks and Prausnitz,16

allows establishing a relation between Flory-Huggins parameter() and the solubility parameters of polymer (δ2) and solvent(δ1), where S is the entropic contribution to , eq 2.10.

ηsp

c) [η] + KH[η]2c (2.1)

ln(ηr)

c) [η] + KK[η]2c (2.2)

num molec mobile phasenum molec mobile + num molec stationary

)

time molec mobile phasetime molec mobile + time molec stationary

(2.3)

ln(Ω1∞) ) ln( RT

Vg·M1f1°) (2.5)

ln(Ω1∞) ) ln( RT

VgM1p1°) -(B11 - Vm,1)p1°

RT(2.6)

) ln Ω1∞ - (1 - 1

r ) + lnF1

F2(2.7)

Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009 7715

Rearranging terms, eq 2.11 is obtained. Thus, the polymersolubility parameter can be obtained in the range of infinitedilution of solvents.

In our previous work45 appear the values of Flory-Hugginsinteraction parameters of SEBS-solvent mixtures, calculatedwith eq 2.7. According this technique, the value of the solubilityparameter of polymer obtained is δ2 ) 15.7 MPa0.5.

2.4. Comparison between IV and IGC Experiments. Asit can be seen, data of polymer solubility parameters are differentdepending on the technique used (17.1 MPa0.5 IV, 15.6 MPa0.5

IGC). From the literature for polydienes,40 similar results havebeen found (Table 2).

It could be thought that there is an influence of thetemperature, but they were calculated taking into account valuesof the thermal expansion coefficient and this influence does notjustify the results obtained. In addition, Yilmaz and Cankurta-ran46 found a similar effect comparing both IV and IGCtechniques, so it can be seen that there is a concentrationdependence of the interaction parameters in polymer-solventsystems; therefore, it is necessary to obtain data for them in awide range of polymer compositions.

3. Polymer-Solvent Separation Step Simulation

3.1. Introduction to Process Simulation. The importanceof the simulation tools in the chemical industry has grown verymuch in the last two decades. With these kind of tools,preliminary tests can be carried out in order to determine thepurity of the final product of a process or the behavior of anew compound introduced in this process (for example, whenone additive is being replaced by another one). The availabilityof commercial software, such as Aspen Plus or Hysys Pro, hasmade it easier to obtain such models.

3.2. Polymer-Solvent Separation by Means of a SteamStripping Process. In several patents,5,6 many methods ofdeveloping a steam stripping process in one or more stages andwith or without steam recirculation have been described,although in the scientific literature there are few referencesconcerning this topic.

As a first approach, each steam stripping stage can beconsidered as a flash stage in which polymer, solvent, and waterare separated in three streams: one vapor stream which containssteam, water, and solvent; one organic liquid stream whichcontains the polymer and the solvent nonflashed; and oneaqueous stream which contains the condensed water. In a secondapproach, a more complex model should involve two stages,each one assimilated to a flash stage, and maybe it could beadequate to study the possibility of mass transfer limitations.

In the experimental sections, cyclohexane, methylcyclo-hexane, and cyclopentane were selected as the most compat-ible solvents for an SEBS rubber. In this chapter, to comparethe behavior of these three solvents in a steam strippingprocess, Aspen Plus was used to simulate one separation stagebetween polymer and solvent by means of a steam strippingprocess.

3.3. Thermodynamic Study to Simulate a SteamStripping Process. To accurately simulate the process, anexhaustive thermodynamic study with the three components

involved in the system, solvent (1), polymer (2), and water (3)is required. For this reason, NRTL interaction parameters ofall binary mixtures have been obtained.

The NRTL activity coefficient model11 can describe bothvapor-liquid (VLE) and liquid-liquid (LLE) equilibrium ofstrongly nonideal solutions, such as polymer-solvent solutions.For binary mixtures, this model has three binary interactionparameters: τ12, τ21, and R12. The first two are normally fitted andhave a temperature dependence according to eq 3.1. The third one(R12, nonrandomness parameter) usually ranges between 0.2 and0.47; but, 0.3 is an acceptable value for nonpolar mixtures, and0.2 is an acceptable value for polar systems.11

Concerning solvent (1)-polymer (2) mixtures (cyclohexane-SEBS,methylcyclohexane-SEBS, and cyclopentane-SEBS), fromthe values of polymer solvent interaction parameter at 293.15 K(0.455 for the SEBS-cyclohexane couple, 0.459 for theSEBS-methylcyclohexane couple, and 0.460 for theSEBS-cyclopentane couple) experimentally determined in ourprevious works,41,45 P-xy data (pressure, liquid phase massfraction, vapor phase mass fraction) have been obtained, accordingthe procedure showed in Figure 1 and based on Flory-Hugginstheory.

In a first step, fixing different values of SEBS volume fractionand using SEBS density (960 kg/m3, data supplied by theREPSOL-YPF Company) and solvent density (data takendirectly from the bottle), the liquid mass fraction of bothcompounds can be obtained. On a second step, the pressure ofpolymer solution for different polymer fractions can be obtainedfrom the pure solvent vapor pressure values, polymer solventinteraction parameter, and polymer volume fraction, applyingthe Flory-Huggins equation, eq 1.1.

In this way, P-xy data can be obtained from polymer solventinteraction parameter at a given temperature (293.15 K). Theprocedure is valid for mixtures which are completely miscible,asithappensinthecaseofSEBS-cyclohexane,SEBS-cyclopentane,and SEBS-methylcyclohexane, but not for mixtures partiallymiscible, as it could happen with other organic solvents.

Table 3 shows the P-xy data obtained, following theprocedure previously described, for all binary mixtures, using

) S +Vm,1

RT(δ1 - δ2)

2 (2.10)

(δ12

2- RT

2V1) ) δ2

∞δ1 - (δ2∞2

2+

SRT

2V1) (2.11)

Table 2. Comparison between the Values of the Polymer SolubilityParameter by Means of IGC and IV Techniques40

δ2 (IGC) MPa0.5 δ2 (IV) MPa0.5

polystyrene 17.8 15.6polybutadiene 17.2 16.2

Figure 1. Procedure to obtain P-xy data from polymer solvent interactionparameters.

τij ) aij +bij

T(3.1)

7716 Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009

the values obtained for polymer-solvent interaction parameters.Because the polymer content in the vapor phase has beenconsidered to be equal to zero, this variable does not appear inthe table. At 293.15 K, the vapor pressure of cyclohexane,methylcyclohexane, and cyclopentane are 10.4, 4.8, and 34.5kPa, respectively.47 As it can be seen in Table 3, Flory-Hugginstheory predicts that the decrease of the solvent vapor pressuredue to polymer is important only at elevated polymer composi-tions (polymer volume fraction higher than 0.6).

With Table 3 values and considering the polymer vaporfraction equal to zero, nonlinear fittings to the NRTL modelwere done. For this purpose, Aspen Plus commercial softwarewas employed. In the three cases studied, good fits (a residualroot-mean-square error of 7.7% in the case of cyclohexane, 8.7%in the case of cyclopentane, and 8.7% in the case of methyl-cyclohexane) were obtained, both in the low polymer concentra-tion zone as well as in rich polymer concentration one, indicatingthat the procedure employed is valid. In all the cases, a12, a21,b12, and b21 parameters of NRTL equation were adjusted, whilekeeping R12 parameter constant and equal to 0.3. With them,activity coefficient (γ) can be obtained, in order to predict thevapor-liquid equilibrium.

Figure 2 shows the results in terms of x1-P (SEBS massfraction versus pressure) curves at constant temperature. As itcan be seen, due to the fact that cyclopentane has the highervapor pressure at 293.15 K, the decreasing pressure is moreimportant in the mixture of SEBS with this solvent than in thecases of the mixtures with the other two ones.

For solvent (1)-water (3) systems, NRTL binary interactionparameters obtained from the LLE-Aspen Plus database48 wereused. This database has been demonstrated to be appropriatefor predicting both liquid-liquid and liquid-vapor equilibriumfor water-hydrocarbon mixtures when comparing prediction

with experimental solubility data obtained from the literature.49,50

Table 4 shows the NRTL binary interaction parameters of thisdatabase, being, R12 a parameter equal to 0.2. With theseparameters, the predicted solubility of water in cyclohexane at298.15 K is 1.127 × 10-8 w/w, the literature value being equalto 1.001 × 10-8 w/w.49 The predicted inverse solubility(cyclohexane in water) result is 5.44 × 10-8 w/w, which showsa very small deviation in comparison with literature (5.5 × 10-8

w/w).50

Finally, a polymer-water mixture was studied consideringthat they are both completely immiscible with each other andobtaining NRTL parameters accordingly. This is a goodapproach because the polymer can be considered as an aliphaticchain of infinite length and it is demonstrated experimentally49,50

that an increasing chain length gives a decreasing watersolubility due to the decreasing polarity.

3.4. Simulation Results. This process can be assimilated toan adiabatic liquid-liquid-vapor equilibrium flash stage,without considering mass transfer phenomena. For this purpose,a FLASH3 model was employed; this model represents a singleliquid-liquid-vapor equilibrium stage, so the three outletstreams are in equilibrium.

The flow diagram is shown in Figure 3. In this process, amixture of SEBS and solvent (cyclohexane, cyclopentane, ormethylcyclohexane) is fed to the FLASH3 block (SEBS + solstream), along with steam (steam stream). The block has threeoutlet streams: vapour, which contains steam, along with theevaporated solvent, polymer, which contains the organic phase(SEBS with solvent left), and aqueous, which contains mainlythe liquid water.

To compare the behavior of the solvents, three simulationswere done with Aspen Plus. The conditions specified for theFLASH3 model were 160 kPa of pressure and a duty equal tozero (adiabatic equipment).

In such processes, the temperature is controlled by varyingthe amount of steam introduced in the stripping stage.5,51 Tosimulate this situation, a design specification was included inthe FLASH3 block which calculates the necessary amount ofsteam to reach a temperature specification of 368.15 K in theblock. Typical conditions of the stripping process are 160 kPapressure and 368.15 K temperature.5 A greater separation couldbe achieved by decreasing the pressure, but in this case, theamount of necessary steam would be much greater.

Table 3. P-x Obtained from the Polymer Solvent InteractionParameter

SEBS-methylcyclohexane SEBS-cyclohexane SEBS-cyclopentane

φ2 P (kPa) x2 φ2 P (kPa) x2 φ2 P (kPa) x2

0 4.8 0 0 10.4 0 0 34.5 00.20 4.8 0.236 0.20 10.3 0.234 0.20 34.4 0.2420.40 4.6 0.451 0.40 10 0.449 0.40 33.3 0.4590.60 4.1 0.649 0.60 8.9 0.647 0.60 29.7 0.6570.80 2.9 0.832 0.80 6.2 0.830 0.80 20.6 0.8360.90 1.7 0.917 0.90 3.7 0.917 0.90 12.3 0.9200.99 0.2 0.992 0.99 0.4 0.992 0.99 1.5 0.992

Figure 2. Experimental (dot) and regressed data for SEBS-solvent mixturesat 293.15 K.

Table 4. NRTL Binary Interaction Parameters for Water-SolventMixtures

parameterwater-

cyclopentanewater-

cyclohexanewater-

methylcyclohexane

aij 7.4 13.1 9.8aji -9.7 -10.5 -9.5bij 282.1 -1067.0 340.6bji 4571.6 4954.9 4601.1cij 0.2 0.2 0.2

Figure 3. Flow diagram of a single stripping stage.

Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009 7717

In all simulations, the conditions of the SEBS + sol streamwere kept constant at 298.15 K, 200 kPa, 15% mass of SEBS,and 3 kg/s mass flow. The conditions of the other inlet stream(steam) were in all cases saturated vapor at 1000 kPa pressure.

The temperatures and pressures of all streams are summarizedin Table 5. Table 6 shows the overall flow rate, water, andsolvent flow rates and solvent (w1), polymer (w2), and water(w3) mass fractions in all the streams of Figure 3.

Comparing the composition of the polymeric phase (polymerstream) in the three simulations, it can be seen that, when usingcyclohexane and methylcyclohexane, the mass fraction ofsolvent in this phase (0.0503 for cyclohexane and 0.130 formethylcyclohexane) is higher than when using cyclopentane(3.11 × 10-5); this is due to the highest volatility of cyclopen-tane compared with the other two solvents.

The difference between cyclohexane and methylcyclohexanecan be explained according the same vapor pressure phenomena(cyclohexane has slightly high volatility). This reasoning is validbecause the Flory-Huggins parameter of SEBS with the threesolvents is quite similar, so when obtaining equilibrium P-xydata from the Flory-Huggins parameter and from pure vaporpressure, the main different between one data set and the othersis due to vapor pressure.

From these studies, it can be seen that, with cyclopentane assolvent, the purity of the final product is really high but involvesa large amount of steam consumption to reach the temperaturespecification. With methylcyclohexane as solvent, the amountof steam is smaller, but the purity of the final product is verylow. With cyclohexane as solvent, the steam consumption isjust 9% higher than in the case of methylcyclohexane, but thepurity of the final product is 95%, which is an adequate value,and really higher when comparing with the final purity usingmethylcyclohexane as solvent.

In this section, a first step to develop a more complexsimulation model has been described. With this model, it ispossible to estimate the amount of each compound that remainsin the polymer phase, in order to assess the quality productspecifications.

3.5. Influence of Additives in the Separation Process. Aspreviously said, styrene-butadiene rubbers (SBR) are mainlyproduced by a block polymerization process of monomers,catalyzed with alkyl lithium compounds in the presence of anorganic solvent (i.e., cyclohexane). In a strongly nonpolar media,the organometallic catalyst molecules tend to form oligomersby association with other ones. Therefore, a polar modifier isadded to the polymerization reactor in order to stabilize the alkyllithium compounds, improving the efficiency of the catalyst.Polar modifiers can also change other polymer properties astheir microstructure and glass transition temperature.52 Gener-ally, these process additives have a hydrocarbon chain and apolar domain, which perform chelant activity with the catalyst.A wide variety of compounds have been tried as polar modifiers,being ethers and amines the most widely studied.53-55

This point is focused in the behavior of these compounds ina SEBS rubber-solvent separation step by means of a steamstripping process. For several additives, some experimentalequilibrium data of their binary mixtures with cyclohexane(solvent), polymer, and water have been obtained; later on, thesedata have been fitted to the NRTL11 equation, and the binaryparameters obtained have been used in a simulation model. Foranother group of additives, the Aspen Plus database48 includesthe values of the NRTL interaction parameters of the binarymixtures of these additives with both water and cyclohexane,so it is not necessary to obtain experimental data.

The NRTL binary interaction parameters either experimen-tally determined or taken from the Aspen Plus database wereintroduced in a steam striping simulation model developed withAspen Plus. For this purpose, a two-stage model was employed,according the diagram which appears in Figure 4. In this model,a stream from the polymerization reactor, consisting of polymerand solvent goes to the steam stripping process. Later on, thecondensed bottom water is separated from the final polymer bysedimentation, whereas top steam carrying the solvent iscondensed and two liquid phases (aqueous and organic) areseparated by decantation.

The objective is to determine the distribution of eachcompound in the different outlet streams of the process.

The additives from whom experimental vapor-liquid orliquid-liquid equilibrium data were obtained are ethyl tetrahy-drofurfurylether(ETE),triethyleneglycoldimethylether(TEGDME),

Table 5. Temperature and Pressure of All Streams, in a SingleStage Process

stream SEBS + sol steam vapor polymer aqueous

pressure (kPa) 100 1000 160 160 160temperature (°C) 298.15 453.1 368.15 368.15 368.15Table 6. Simulation Results with All Solvents

Cyclohexane

steam vapor polymer aqueous

flow rate (kg/h) 4011 11283 1711 1817CHex flow (kg/h) 0.0 9089 91 0.029water flow (kg/h) 4011 2194 1817w1 0 0.806 0.053 1.58 × 10-5

w2 0 0 0.95 6.33 × 10-8

w3 1 0.194 1.16 × 10-4 1

Methylcyclohexane

steam vapor polymer aqueous

flow rate (kg/h) 3669 10781 1862 1826MChex flow (kg/h) 0 8938 242 0.037water flow (kg/h) 3669 1841 1826w1 0 0.829 0.130 2.04 × 10-5

w2 0 0 0.870 8.89 × 10-8

w3 1 0.171 1.74 × 10-4 1

Cyclopentane

steam vapor polymer aqueous

flow rate (kg/h) 4682 11845 1620 2016CPent flow (kg/h) 0 9180 0.050 0.102water flow (kg/h) 4682 2665 2016w1 0 0.775 3.11 × 10-5 5.04 × 10-5

w2 0 0 0.99997 9.98 × 10-8

w3 1 0.225 2.82 × 10-6 0.99995

Figure 4. Two-stage steam stripping process scheme.

7718 Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009

N-N-N’-N’-tetramethylethylene diamine (TMEDA), tetrahydro-furfurylamine (THFAM), and 4-ethylmorpholine (4EMORF).The additives whose binary interaction parameters were takenfrom the Aspen Plus database are 1,4-dioxane (DIOX), ethyl-eneglycol dimethylether (EGDME), and tetrahydrofuran (THF).The source of the binary interaction parameters of the NRTLmodel for each binary mixture is shown in Table 7.

The vapor-liquid experiments were performed using theisobaric ebullometric technique in the range of low additivecompositions (the typical compositions used in the industrialprocess are below 1000 ppm). The apparatus has been previouslyused for similar purposes.56 In this equpment, entirely made ofglass, both the liquid and vapor phases are continuouslyrecirculated, in order to provide mixing of the phases and toensure that equilibrium is established. The vapor condenser is

connected to a constant-pressure system controlled by a Car-tesian manostat, so the pressure could be kept constant at 101.32kPa, with an accuracy of (0.1 kPa. The equilibrium tempera-tures were measured with a certified thermocouple type J withan accuracy of (0.1 °C. Both samples were analyzed with aPerkin-Elmer A/S gas chromatograph with a flame ionizationdetector. In this apparatus 4EMORF-cyclohexane, 4EMORF-water, THFAM-cyclohexane, THFAM-water, TEGDME-cyclohexane, TEGDME-water, TMEDA-cyclohexane, andTMEDA-water equilibria were measured. For the mixture ofthe heaviest additive studied (TEGDME, the one with the lowestcomposition in the vapor phase) with cyclohexane, the uncer-tainties (in terms of standard deviation/average of the molefraction) of the VLE data were 7.8% for the vapor phasecomposition and 3.8% for the liquid phase composition.

Table 7. Source of the NRTL Binary Interaction Parameters of Each Mixturea

THF DIOX EGDME TMEDA 4EMOR ETE THFAM TEGDME

Chex lit lit lit exp exp n/a exp expwater lit lit lit exp exp exp exp exp

a All of these were also estimated using the UNIFAC method (exp parameters obtained from experimental fitting, lit Aspen Plus database).

Figure 5. y-x equilibrium curves predicted with the binary parameters obtained from the Aspen Plus database and those predicted with the UNIFAC methodat 101.32 kPa. (a) THF-water. (b) THF-cyclohexane. (c) EGDME-water. (d) EGDME-cyclohexane. (e) DIOX-water. (f) DIOX-cyclohexane.

Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009 7719

Figure 6. VLE and LLE experimental and predicted data of heavy polar modifiers, at 101.32 kPa. (a) TMEDA-water. (b) TMEDA-cyclohexane. (c)4EMORF-water. (d) 4EMORF-cyclohexane. (e) ETE-water. (f) THFAM-water. (g) THFAM-cyclohexane. (h) TEGDME-water. (i)TEGDME-cyclohexane.

7720 Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009

In order to model the VLE, a valid vapor pressure equationis needed. Parameters for Antoine expression of water, cyclo-hexane, ETE, TEGDME, TMEDA, THF, DIOX, and EGDMEare available in commercial databases (in this work the AspenPlus database48 was used). However, THFAM and 4EMORFvapor pressure experiments were performed. To vary thepressure of the system, the experiments were carried out in theebullometer previously described, by setting a vacuum pumpand a vacuum controller. The pure substances were introducedinto the ebullometer and then vacuum was set. The temperatureof both vapor and liquid was measured after 30 min.

For liquid-liquid experiments, the ebullometric technique isnot adequate because it can be only used in homogeneoussystems. If two liquid phases are present, then a simple stirredtank in a thermostatically controlled bath is needed. Thus,ETE-water LLE measurements were performed. Consecutiveadditions of small quantities of ETE over a great amount ofwater were added until two phases were observed. Later on, asample of the aqueous phase was taken and analyzed by totalorganic carbon (TOC) measurements (Shimazdu VCSH).

Figure 5 shows the y-x equilibrium curve predicted with thebinary parameters taken from the Aspen Plus database, alongwith the equilibrium curve predicted by UNIFAC groupcontribution method.57 It can be observed that the higher theboiling point of the additive, the worse the UNIFAC predictions.

Figure 6 shows the y-x equilibrium curve predicted with thebinary parameters obtained by fitting experimental data to NRTLmodel, along with the equilibrium curve predicted by theUNIFAC group contribution method.57 It can observed thatadditive-water mixtures are even worse predicted thanadditive-cyclohexane ones. Therefore, it is necessary to obtainexperimental data of VLE or LLE to get a reliable thermody-namic model, when working with heavy polar modifiers.

The NRTL binary interaction parameters of polymer-additivemixtures were obtained following the same procedure describedin section 3.3 with the polymer-solvent interaction parameterdetermined by means of eq 1.2, with the values of the solubility

parameter of both polymer (experimentally determined) andsolvent (taken from literature).

Concerning simulation results, Table 8 quantifies the distribu-tion of the heavy polar modifiers, from whom experimental datahave been obtained, in the different streams of the process, asa function of the NRTL parameters employed (experimentalfitting or UNIFAC predictions). The results are shown in termsof separation degree (mass flow of additive in the stream/massflow of additive in the inlet stream times 100). As it can beseen, the results are very different when using UNIFACparameters instead of the ones obtained by fitting experimentaldata.

For synthetic rubber processing, it is recommended to getexperimental VLE or LLE data of mixtures in which heavy polaradditives are involved. UNIFAC properly predicts the behaviorofthesesubstancesonlywhentheyarelightenough.Additive-waterpair interactions seem to have a bigger influence thanadditive-cyclohexane ones over the simulation results. Thiscould be due to hydrogen bonding that it is not taken intoaccount by the UNIFAC model.

4. Conclusions

In this paper we present a new procedure to model theequilibrium-staged operations for synthetic SEBS rubber pro-cessing, with Aspen Plus.

Concerning polymer-solvent mixtures, from the results it canbe seen that it is necessary to carry out experimental measure-ments in the overall polymer composition range.

The results show that all the solvents have a good behaviorin a one stage steam stripping process at moderate temperatureand pressure conditions, cyclohexane being the most suitable.Employing this solvent in the stripping process, the amount ofpolymer in the organic phase is high enough and the steamconsumption is acceptable.

With this modeling procedure, the behavior of some additivesin the separation process can be also analyzed.

But, the most important conclusion is that, by applying themethodology described in the paper, it is possible to estimatethe amount of a component which remains with the polymerafter the separation, in order to assess quality specifications toemploy it, for example, as a recipient for drinks. Anotherapplication could be optimizing the conditions (temperature,pressure, and amount of vapor) of the operation. This is thefirst step todevelopamorecomplexmodelof thepolymer-solventsteam stripping separation process.

Nomenclature

ai ) activity of component iaij ) first NRTL binary interaction parameter of components i and

jbij ) temperature-dependent NRTL binary interaction parameter

of components i and jB11 ) solvent second term of the virial EOS, cm3/molc ) concentration of polymer solution, g/dLfi° ) standard fugacity of the i component, PaF ) carrier gas flow rate, cm3/sj ) retention volume correction factorKH ) Huggins coefficientKK ) Kraemer coefficientMi ) i average molecular weightNA ) Avogadro numberP ) pressure, Pap ) vapor pressure of polymer solution, Pa

Table 8. Simulation Results of the Striping Process for HeavyPolar Modifiers in Terms of Separation Degree (Additive Mass Flowin Each Outlet Stream Divided by Additive Mass Flow in the InletStream), As a Function of the NRTL Parameters Employed forBoth Additive-Cyclohexane and Additive-Water Mixturesa

binary mixtures outlet streams

additiveadd-Chexmodel

add-watermodel

finalpolymer

solvent topwater

bottomwater

TMEDA exp exp 0.6 80.8 11.1 7.5exp UNIFAC 0.9 37.9 23.9 37.3UNIFAC exp 0.6 85.3 6.7 7.4UNIFAC UNIFAC 0.9 45.0 16.8 37.2

4EMORF exp exp 0.8 79.4 8.6 11.2exp UNIFAC 1.0 48.7 11.5 38.6UNIFAC Exp 0.8 75.2 13.2 10.8UNIFAC UNIFAC 1.0 44.1 16.4 38.4

ETE exp exp n/a n/a n/a n/aexp UNIFAC n/a n/a n/a n/aUNIFAC exp 0.3 87.6 11.4 88.0UNIFAC UNIFAC 0.6 94.9 2.1 2.5

THFAM exp exp 0.2 19.5 3.4 76.9exp UNIFAC 0.3 28.6 3.3 67.8UNIFAC exp 0.2 10.7 11.8 77.3UNIFAC UNIFAC 0.3 20.0 12.0 67.7

TEGDME exp exp 3.3 6.9 0.5 89.3exp UNIFAC 6.9 16.9 0.3 75.9UNIFAC exp 3.3 5.0 0.5 91.2UNIFAC UNIFAC 6.9 15.7 1.8 75.7

a Exp parameters obtained from experimental fitting; UNIFACparameters obtained with the UNIFAC group contribution method.

Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009 7721

Pi° ) vapour pressure of component i, Par ) molar volume of polymer to molar volume of solvent ratioR ) ideal gas constantt ) flow time of the polymer solution, sto ) flow time of the pure solvent, stm ) inert component retention time, str ) solvent retention time, sT ) temperature, KVg ) retention volume, cm3/gVm,i ) molar volume of i, cm3/molW ) amount of polymer packed in the column, gx ) liquid phase mass fractiony ) vapour phase mass fractionGreek SymbolsR12 ) nonrandomness parameter of NRTL equationδi ) solubility parameter of component i, MPa0.5

δi∞ ) solubility parameter of component i obtained in infinitedilution conditions MPa0.5

∆sH1 ) solvent heat of solution, kJ/mol∆mixHj 1

∞ ) solvent partial molar heat of mixing, kJ/mol∆vapH1 ) solvent heat of vaporization, kJ/mol ) polymer-solvent interaction parameterH ) enthalpic contribution of polymer-solvent interaction

parameterS ) entropic contribution of polymer-solvent interaction parameterΩi

∞ ) infinite dilution activity coefficient of iFi ) density of i, g/cm3

[η] ) intrinsic viscosity, dL/gηr ) relative viscosityηsp ) specific viscosityS ) entropic contribution of polymer-solvent interaction parameterH ) enthalpic contribution of polymer-solvent interaction

parameter[η] ) intrinsic viscosity at theta conditions, dL/gΦ0 ) universal viscosity constant, 1/molVi ) partial specific volume of iτij ) NRTL binary interaction parameter of components i and jSubscripts1, 2, 3 ) solvent, polymer, waterAbbreViations4EMORF ) 4-ethylmorpholineDIOX ) 1,4-dioxaneEGDME ) ethyleneglycol dimethyletherEOS ) equation of stateETE ) ethyl tetrahydrofurfuryl etherIGC ) inverse gas chromatographyIV ) intrinsic viscosityLF ) lattice fluidLLE ) liquid-liquid equilibriumSAFT ) statistical associated fluid theorySBR ) styrene-butadiene rubberSBS ) styrene-butadiene-styrene rubberSEBS ) styrene-ethylene-butadiene-styrene rubberTEGDME ) triethyleneglycol dimethyletherTHF ) tetrahydrofuranTHFAM ) tetrahydrofurfurylamineTMEDA ) N-N-N’-N’-tetramethylethylene diamineVLE ) vapor-liquid equilibrium

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Accepted June 9, 2009

IE9006497

Ind. Eng. Chem. Res., Vol. 48, No. 16, 2009 7723

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