Continuous Production of Solid Polystyrene in Back-Mixed and Linear-Flow Reactors.

A mathematical model has been developed to predict the steady state performance of a continuous bulk styrene polymerization process with catalytic initiation for solid polystyrene. The polymerization section contains one boiling CSTR, followed by multiple linear-flow reactors. The devolatilization section consists of two polymer pre-heaters and two high-solids flashes. The polymer moment equations were solved simultaneously with the reactor modeling equations. The non-linear algebraic equations were solved by a Newton-Raphson iteration technique to give the steady-state styrene monomer weight fraction in a CSTR. The coupled, non-linear ordinary differential equations were numerically integrated using a single-step, 4th-order Runge-Kutta technique, followed by a multi-step Adams-Moulton technique. The resulting computer simulation model is capable of evaluating how the production rate and product quality are affected by feed composition, temperature, initiator type, initiator concentration, and residence time. Several case studies were given for commercially important crystal-clear and impact-resistant resins. A binary initiation system gives a good balance of monomer conversion, polymer molecular weights, and rubber grafting compared to a single initiation system. The styrene dimer/trimer occur in low concentrations but can be substantially reduced with a low temperature initiator. The ideal mean residence time is approximately one minute or less in a shell-and-tube devolatilization pre-heater. Low flash chamber vacuum is more effective than high polystyrene melt temperature to reduce the volatile content of the final product. The water injected to the low volatile melt shows promising improvement in the second-stage polystyrene devolatilization.

INTRODUCTION

Polystyrene is one of the major commodity thermoplastics in the world. It has a large and growing market compared to other styrenic polymers. Crystal-clear polystyrene and impact-resistant polystyrene are often called solid polystyrene (SPS) to distinguish from expandable polystyrene (EPS). In EPS, the beads are produced via suspension polymerization and then impregnated with a blowing agent such as pentane in a batch reactor. In SPS, a continuous bulk or low solvent process is more effective than a batch suspension process in terms of production flexibility, plant capacity, operating cost, and investment cost. Crystal-clear products are produced mainly from styrene, while impact-modified resins are obtained by polymerizing a homogeneous solution of butadiene rubber, styrene-butadiene block copolymer. or similar elastomers dissolved in styrene. Rubber-modified polystyrene can be produced with toughness in the range of medium-impact, high-impact, or super high-impact by varying the initial rubber content. Newe r specialty impact resins have emerged to bridge the gap between engineering ABS (acrylonitrille-butadiene-styrene) and conventional HIPS (high impact polystyrene).

The continuous bulk styrene polymerization reactors are generally classified into two groups: the back-mixed reactor and the linear-flow reactor (LFR). A continuous stirred-tank reactor (CSTR) is one typical example of a completely back-mixed reactor, while an LFR with recycle (a loop reactor) represents a partially back-mixed reactor. By definition, the LFR has good radial mixing but no or little back-mixing in the axial flow direction. The LFR will approximate a plug-flow or piston-flow reactor in the ideal case. Bulk styrene polymerization is always accompanied with large heat generation and high viscosity. A wide variety of reactor designs depend upon the method of heat removal, the degree of axial mixing, the degree of radial mixing, and the number of reactors in series. The choice of polymerization reactor types depends on the polymer quality/quantity desired. One continuous or batch boiling reactor is efficient in producing a single product. Multiple reactor stages can be tailored in a number of ways t o meet specific product needs. Most polystyrene licensors and/or producers still stay with two or more reactors in series to maintain production flexibility. Major commercial process technologies for continuous production of solid polystyrene have been well described in papers or patents by McDonald et al. [1], Bronstert et al. [2], Carter and Simon [3], McCurdy and Stein [4], Gawne and Ouwerkerk [5], Tauscher [6], Morita et al. [7], Morita and Nakamura [8], and Sugawara et al, [9]. The Nippon Steel/UOP polystyrene process has a new generation of polymerization reactor compared to the conventional CSTR, agitated coil-blade reactor, reflux-cooled LFR, or un-agitated coil-cooled reactor. The stirred plate-blade reactor coupled with a special recipe is capable of producing tough, ultra-high-gloss materials, i.e., advanced styrenic resins. The tougher and glossier HIPS grades offer an excellent alternative to medium-impact, high-gloss ABS plastics by providing a good balance of cost and performance. This speciall y-designed reactor technology has been commercially proven with four production lines at Kimitsu plant in Tokyo, Japan. The first two lines were started-up at a capacity of 75,000 MTA in 1988. The second two lines were commissioned at a larger capacity of 110,000 MTA in 1993. Several potential benefits associated with the Sulzer/Dainippon/Sumitomo (SDS) process are the elimination of agitators and thereby shaft seal problems. The conventional shell-and-tube unit is not suitable for bulk styrene polymerization due to flow instabilities of the polymerizing fluid on the tube side. Larger tube sizes have the potential of run-away reactions. Most static mixers (Chemineer Kenics type, Sulzer SMX type, etc.) are designed only for mixing and are not used as reactors. This may be due to the fact that there is no effective way of removing the reaction heat. The static mixing reactor (SMR) gives, however, simultaneous heat transfer and mixing for the highly viscous polymer solution. The heat transfer oil flows through t he folded tubes to remove the reaction heat. In the meantime, the mixing is accomplished by moving the polymer solution through the outside surface of the tubes. The SMR provides uniform residence time distribution and excellent temperature control. In the coil-blade or plate-blade configuration, there is always the possibility that a moving blade can break any of the coils or plates in the reactor.

A CSTR, an agitated LFR, or an SMR loop reactor has been commonly used as a pre-polymerizer for solid polystyrene to establish key properties. The grafting of styrene to rubber, occluded styrene, phase inversion, and rubber particle sizing are usually accomplished in the same reactor. Unlike crystal polystyrene, the rubber phase morphology is extremely important to HIPS properties. A first patent by Bronstert et al. [2] invented a smaller CSTR for styrene occlusions/grafting prior to a larger CSTR for phase inversion. The pre-inversion reactor also functions as a heat exchanger to advance the rubber solution temperature. The closer the temperature and composition between the pre-inversion reactor and the phase-inversion reactor, the better the morphology of the resulting rubber phase. The concept of separating a pre-inversion reactor from a phase-inversion reactor was later implemented by Sosa and Nichols [10]. The design of finishing reactors is very critical to distinguish one technology from another in a c ontinuous bulk process. Typical reactors for post-polymerization are compared as follows:

1. One or more CSTR's (Emejota, Chevron/Gulf/ Union Carbide, Nova/Huntsman/Shell, Mitsui, Nippon Steel/UOP).

2. A horizontal, boiling stirred-tank with multiple compartments-a reflux-cooled LFR with multiple CSTR stages (Nova/Monsanto, BP).

3. Two or more horizontal, coil-blade reactors-an LFR with many CSTR stages (Fina/Cosden, Nova/Huntsman/American Hoechst, Nova/ Huntsman/Amoco, Atochem, United Sterling, Nova).

4. Two or more vertical coil-blade or plate-blade reactors-an LFR with many CSTR stages (Dow, BASF, Nippon Steel/UOP).

5. A vertical, unagitated tower with internal tubes for heat transfer-an LFR (CdF, Nova, many Asian polystyrene producers).

6. One or more Sulzer/Hoechst type SMR-an LFR (SDS, Nippon Steel/UOP, other polystyrene producers in Asia, Europe, etc.).

In a bulk thermal process, the conversion of styrene to polystyrene are controlled only by reaction temperature and residence time. The polymerization reaction can be, however, manipulated by initiators, reaction temperature, and residence time in a bulk catalytic process. Peroxide initiators are frequently used in the existing polystyrene process for increased reactor throughputs and improved polymer properties. In crystal polystyrene production, a major peroxide effect is the rate of monomer conversion and the molecular weights of polymer. In HIPS production, an additional peroxide effect is the grafting of styrene to the rubber chain. The use of peroxyketals as described in a patent by Sosa and Morris [11] is attractive for continuous production of SPS due to the formation of nonacid decomposition by-products. Drumright et al. [12] studied the decomposition chemistry of 1, l-bis(tertbutylperoxy)cyclohexane, one of cycloalkane perketal initiators, for styrene polymerization. Estenoz et al. [13] investigate d the molecular macrostructure of bulk styrene polymerization initiated by tert-butylperoxy-2-ethylhexanoate or tert-butylperoxy octoate in the presence of butadiene rubber in a batch reactor. Gonzalez et al. [14] conducted different bulk styrene polymerization reactions catalyzed by binary mixtures of mono- and bifunctional initiators in a batch reactor. There has been no detailed disclosure of simulating an industrial continuous SPS process. A recent paper by Chen [15] studied the bulk catalytic SPS polymerization in a cascade of multiple CSTR's. In this paper, a rather comprehensive and flexible computer simulation model will be developed to evaluate the performance of bulk catalytic SPS polymerization in a boiling CSTR, followed by multiple linear-flow reactors. A two-stage flash devolatilization will be included in the study.

PROCESS DESCRIPTION

Figure 1 shows the schematic flow diagram of a continuous bulk styrene polymerization process. The HIPS line is essentially the same as the crystal polystyrene line except for the feed preparation. The polymerization section contains one boiling CSTR in series with four identical SMR's. There are three [3] modules in each SMR and two [2] tube bundles in each module. The total reactor volume can be estimated using the total feed rate to the first reactor multiplied by the total residence time in all reactors. For instance, the polystyrene plant is assumed to be operated at a total feed rate of 10,000 kg/h with a total residence time of 6 hours. The total reactor volume required for the plant is approximately 65 [m.sup.3].

The devolatilization is a required step prior to pelletization (granulation) in the process. The total volatile matter in the pellet is controlled by vapor-liquid equilibrium and equipment efficiency. In high solids flashes, the surface area generation via foaming is necessary for achieving a near-equilibrium flash. All vapor bubbles in a flash chamber will nucleate, grow, and coalesce into an open-celled foam. The criteria for a single flash or two flashes are the solids content exiting from the final reactor. A single flash is adequate if the solids content coming out of the final reactor is 80% or higher. Two flashes in series are generally required if the final reactor effluent contains 70% polymer or less. The solvent concentration entering the second flash chamber may be insufficient to generate an open-celled foam. A liquid is much easier to mix with a polymer melt than a gas. The water in a liquid state has been commonly used as a foaming agent for polystyrene to generate an open-celled foam. In this work, the devolatilization section consists of two polymer solution or melt pre-heaters and two high-solids flashes.

MODEL DEVELOPMENT

A mathematical model will be developed to include polymerization kinetics, polymerization reactors, devolatilization pre-heaters, vapor-liquid equilibrium in a flash chamber, and polymer product properties. The details of the model are as follows:

Kinetic Model

The bulk styrene polymerization catalyzed by initiators will follow the conventional free radical kinetics--initiation, propagation, termination, and chain transfer. In HIPS, the grafting of styrene to butadiene rubber may proceed via allylic hydrogen abstraction.

The carbon-carbon double bonds in the rubber chain are not considered as sites for grafting. The work reported by Brydon et al. [16, 17] extremely favors the allylic hydrogen abstraction mechanism. A direct attack of primary initiator radicals on the rubber is practically the only one at low temperatures. The data reported by Manaresi et al. [18] clearly demonstrate that chain transfer to rubber is also important at temperatures above 100[degrees]C. Thermal initiation becomes substantial at polymerization temperatures above 100[degrees]C. According to the thermal initiation mechanism proposed by Hui and Hamielec [19], the rate of thermal initiation can be represented by a third-order kinetics with respect to the styrene monomer. Watanabe et al. [20] studied the kinetics of bulk styrene polymerization initiated by 2.2-bis[tert-butyldioxy) alkanes. The decomposition of these bifunctional initiators was found to occur by bond fission of one peroxide group rather than simultaneous bond fission of two peroxide gro ups. The formation of diradical species is thus considered negligible. Some simplifications made in this work are:

1. The primary radicals are assumed to be indistinguishable in their activities for styrene polymerization.

2. The thermal stability of undecomposed peroxide groups in temporarily dead polymers is independent of their chain length.

3. The polystyryl radicals with undecomposed peroxides are assumed to have the same propagation, chain transfer, and termination rate constants as the polystyryl radicals without undecomposed peroxides.

4. The graft-polystyryl radicals are assumed to have the same propagation, chain transfer, and termination rate constants as the homo-polystyryl radicals.

5. The chain termination is assumed to occur exclusively by combination. Termination by disproportionation is negligible in styrene polymerization.

6. In crystal polystyrene, chain transfer occurs mainly to AH.

With the above assumptions, the proposed reaction mechanisms for bulk styrene polymerization catalyzed by mono- and bi-functional initiators are shown in Table 1 for crystal-clear polystyrene and in Table 2 for HIPS. In free-radical polymerization at high conversions, the termination reactions involving polymeric radicals become diffusion-controlled and the effective termination rate constant decreases considerably with an increase in monomer conversion. This phenomenon is called the gel (Trommsdorff) effect. The gel effect correlation suggested by Hui and Hamielec [19] for bulk styrene polymerization is given by

= [k.sub.tc] = [k.sub.tc,0] exp[- 2([A.sub.1]X + [A.sub.2][X.sup.2] + [A.sub.3][X.sup.3]) (1a)

with

[A.sub.1] = 2.57 - 5.05 X = 2.57 - 5.05 X [10.sup.-3]T (1b)

[A.sub.2] = 9.56 - 1.76 X [10.sup.-2]T (1c)

[A.sub.3] = - 3.03 + 7.85 X [10.sup.-3]T (1d)

The chain transfer to by-products (such as AH) of thermal initiation is considered to give an effective monomer chain transfer constant. The importance of chain transfer to by-products has been reported by Pryor and Coco [21]. A large portion of the previously reported chain transfer constant of styrene is actually the result of chain transfer to AH:

[([k.sub.tr,m]/[k.sub.p]).sub.apparent] = [([k.sub.tr,m]/[k.sub.p]).sub.actual] + [k.sub.tr,AH]/[k.sub.p] [AH]/[M] (2a)

The observed monomer chain transfer constant suggested by Hui and Hamielec [19] is written as

[([k.sub.tr,m]/[k.sub.p]).sub.apparent] = [([k.sub.tr,m]/[k.sub.p]).sub.actual] + [B.sub.1]X (2b)

with

[B.sub.1] = - 1.013 X [10.sup.-3] log (473.12 - T/202.5),

for T [less than] 473K (2c)

Equation 2b is an empirical form of Eq 2a. Since Eq 2c cannot be solved for temperatures greater than 200[degrees]C, the parameter [B.sub.1] recommended by Husain and Hamielec [22] for use at temperatures of 200[degrees]C and above is given by

[B.sub.1] = 0.01[E.sub.1]/1 + 2[E.sub.1] ; [E.sub.1] = 0.9755

exp[- 12180(1/T - 1/473)], for T [greater than or equal to] 473K (2d)

The long chain approximation is assumed to be valid for monomer consumption. This means that the monomer is considered to be consumed only by propagation reactions. Monomer consumption via thermal initiation, chemical initiation, and chain transfer to monomer is neglected. The rate of polymerization can thus be written as:

For crystal polystyrene:

[R.sub.p] = [k.sub.p]([rho][w.sub.m])[[lambda].sub.o] with monofunctional initiation (3a)

[R.sub.p] = [k.sub.p]([rho][w.sub.m])([[lambda].sub.o] + [[lambda].sub.o]) with bifunctional initiation (3b)

For HIPS:

[R.sub.p] = [k.sub.p]([rho][w.sub.m])([[lambda].sub.o] + B[[lambda].sub.o]) with monofunctional initiation (3c)

[R.sub.p] = [k.sub.p]([rho][w.sub.m])([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o] with bifunctional initiation (3d)

By applying the quasi-steady-state assumption to all radical species, the total concentration of radical species during polymerization can be found as

[[lambda].sub.o] = [square root of]2[k.sub.i,th][[M].sup.3] + 2 f[k.sub.d][I]/[k.sub.tc] (3e)

[[lambda].sub.o] + [lambda] =

[square root of]2[k.sub.i,th][[M].sup.3] + 4f[k.sub.d1][[I.sub.B]] + 2 f [K.sub.d2] [[micro].sub.o] + 4f [k.sub.d2] [[micro].sub.o]/[k.sub.tc] (3f)

[[lambda].sub.o] + B[[lambda].sub.o] = [square root of]2[k.sub.i,th] [[M].sub.3] + 2 f[k.sub.d][I]/[k.sub.tc] (3g)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3h)

Equations 3e-3h indicate that the total rate of initiation is equal to the total rate of termination under steady-state conditions. The associated rate equations for primary radicals, growing radicals, temporarily dead polymers, and dead polymers are derived in the Appendix.

Styrene and methyl methacrylate are the two industrially important monomers that can be polymerized only by heating. Many theories have been proposed to explain the unusually high thermal initiation of styrene. The formation of styrene dimer and trimer via side reactions was outlined by Pryor and Coco [21]. The main by-products during thermal initiation are cis-and trans-1,2-diphenylcyclobutane (DCB) and cyclic trimers (CT). At up to 97% conversion in the temperature range of 100-180[degrees]C, the rate equations of dimer and trimer formation found by Rintelen et al. [23] are

d[dim er]/dt = [k.sub.DCB][([rho][w.sup.m]).sup.2] (4a)

d[trimer]/dt = k[([rho][w.sub.m]).sup.2])/a + b([rho][w.sub.m]) [approximately equals] [k.sub.CT]([rho][w.sub.m])

at high monomer concentration (4b)

[approximately equals] [k.sub.CT][([rho][w.sub.m]).sup.2] at low monomer concentration

The dimer/trimer content is usually reported as the ratio of the amount of dimer/trimer formed to the amount of polystyrene produced. The dimensionless concentration in parts per million (ppm) of styrene dimer and timer is thus written as:

For crystal polystyrene with monofunctional initiation:

[w.sub.DCB] = [dim er]/[[micro].sub.1] + [[lambda].sub.1] X [10.sup.6] (5a)

[w.sub.CT] = [trimer]/[[micro].sub.1] + [[lambda].sub.1] X [10.sup.6] (5b)

For crystal polystyrene with bffiinctional initiation:

[w.sub.DCB] = [dim er]/[[micro].sub.1] + [[micro].sub.1] + [[micro].sub.1] + [[lambda].sub.1] + [[lambda].sub.1] X [10.sup.6] (5c)

[w.sub.CT] = [trimer]/[[micro].sub.1] + [[micro].sub.1] + [[micro].sub.1] + [[lambda].sub.1] + [[lambda].sub.1] X [10.sup.6] (5d)

For HIPS with monofunctional initiation:

[w.sub.DCB] = [dim er]/[[micro].sub.1] + B[[micro].sub.1] + B[[micro].sub.1]B + [[lambda].sub.1] + B[[lambda].sub.1] X [10.sup.6] (5e)

[w.sub.CT] = [trimer]/[[micro].sub.1] + B[[micro].sub.1] + B[[micro].sub.1]B + [[lambda].sub.1] + B[[lambda].sub.1] X [10.sup.6] (5f)

For HIPS with bifunctional initiation:

[w.sub.DCB] = [dim er]/[[micro].sub.1] + [[micro].sub.1] + [[micro].sub.1] + B[[micro].sub.1] + B[[micro].sub.1] + B[[micro].sub.1]B + [[lambda].sub.1] + [[lambda].sub.1] + B[[lambda].sub.1] X [10.sup.6] (5g)

[w.sub.CT] = [trimer]/[[micro].sub.1] + [[micro].sub.1] + [[micro].sub.1] + B[[micro].sub.1] + B[[micro].sub.1] + B[[micro].sub.1]B + [[lambda].sub.1] + [[lambda].sub.1] + B[[lambda].sub.1] X [10.sup.6] (5h)

Reactor Model

1. Polymerization in a CSTR

For isothermal free radical polymerization with mono- and bi-functional initiators in a completely back-mixed reactor of volume V, the steady-state material balances can be written as:

Mass balance for monomer:

[w.sub.m,o] - [w.sub.m] = [R.sub.p](T)V/[F.sub.out] = [R.sub.p](T)[tau]/[rho](T) (6a)

Mass balances for initiators:

[w.sub.I] = [w.sub.I,o]/1+[k.sub.d](T)[V.sub.[rho]](T)/[F.sub.out] = [w.sub.I,o]/1 + [k.sub.d](T)[tau] (6b)

[w.sub.[I.sub.B]] = [w.sub.[I.sub.Bo]]/1 + 2[k.sub.d1](T)[V.sub.[rho]](T)/[F.sub.out] = [w.sub.[I.sub.Bo]]/1 + 2[k.sub.d1](T)[tau] (6c)

Mass balances for dimer and trimer:

[dim er] = [k.sub.DCB][tau] =[([rho][w.sup.m]).sup.2] (6d)

[trimer] = [k.sub.CT] [tau]([rho][w.sub.m]) (6e)

A boiling CSTR is not a full reactor and is usually operated under low vacuum at a constant reaction temperature. The isothermal temperature is maintained using vapor cooling and a lower temperature feed stream. The vacuum pressure is at equilibrium with the vapor pressure of the polymerizing fluid at the reaction temperature. The evaporative cooling removes about 70% of the reaction exotherm, while the lower temperature feed supplies 30% of the cooling load. The external coil of the pre-polymerizer provides a means for heating only during the start-up. During normal operation, the external coil is maintained at the reaction temperature and does not contribute to heat removal. For an auto-refrigerated CSTR, the steady-state energy balance is given by

[q.sub.in] + [q.sub.polymerization] = [q.sub.out] + [q.sub.boiling] (7a)

with

Heat input rate (J/h): [q.sub.in] = [F.sub.in][C.sub.p,in][T.sub.in] (7b)

Heat output rate (J/h): [q.sub.out] = [F.sub.out] [C.sub.p,out] [T.sub.out] (7c)

Heat generation rate (J/h): [q.sub.polymerization] = [F.sub.in][w.sub.m,in]X(- [delta][H.sub.rxn]) (7d)

Heat removal rate (J/h): [q.sub.boiling] (7e)

The evaporative rate of styrene and ethylbenzene can be calculated from the rate of heat removal and the latent heat of vaporization by

m = [q.sub.boiling]/[delta][H.sub.v] + [C.sub.p]([T.sub.boiling] - [T.sub.reflux]) (7f)

With

[delta][H.sub.v] = 3.56 x [10.sup.5] J/kg @ 14.7 psia for styrene (7g)

[delta][H.sub.v] = 3.35 x [10.sup.5] J/kg @ 14.7 psia for ethylbenzene (7h)

On the other hand, the reaction temperature of the polymerizing fluid in a completely full CSTR is controlled primarily by means of internal heat transfer coils (or internal heat transfer plates) and an external jacket. The heat transfer surface area is required for the removal of reaction exotherm.

The non-linear algebraic equations were solved by a Newton-Raphson iteration technique to give the steady-state value of styrene monomer weight fraction in a CSTR.

2. Polymerization in an LFR

In an LFR, the removal of sensible heat is used to control the reaction temperature. For non-isothermal free radical polymerization in an LFR of heat transfer surface area [A.sub.c] and volume V, the steady-state mass and heat balances in the presence of multiple initiators are written as:

Mass balances for initiators:

d[w.sub.I]/dx = -[k.sub.d]t[w.sub.I] (8a)

d[w.sub.IB]/dx = -2[k.sub.d1t[w.sub.IB]] (8b)

Mass balance for monomer:

d[w.sub.m]/dx = -[R.sub.p]t/[rho] (8c)

Mass balances for dimer and timer:

d[dim er]/dx = [k.sub.DCB]t[([rho][w.sub.m]).sup.2] (8d)

d[trimer]/dx = [k.sub.CT]t([rho][w.sub.m]) (8e)

Energy balance:

dT/dx = h[A.sub.c]/[rho][c.sub.p]V([T.sub.w] - T) - [R.sub.p]t[delta][H.sub.rxn]/[rho][C.sub.p] (8f)

The associated initial conditions at x = 0 are

[w.sub.I] = [w.sub.I,in] ; [w.sub.[I.sub.B]] = [w.sub.[I.sub.B,in]] ; [w.sub.m] = [w.sub.m,in];

[dim er] = [[dim er].sub.in] ; [timer] = [[timer].sub.in] T = [T.sub.in] (8g)

The heat transfer coefficient (h) can be estimated from Tien et al. (24)

Nu = hd/k = 2.6[(RePr).sup.0.35] (8h)

with

Re = [rho]ud/[micro] and Pr = [C.sub.p][micro]/k (8i)

The coupled, non-linear ordinary differential equations were numerically integrated. A step-size of [delta]x = 0.005 in marching down an LFR was taken for numerical solutions. The first three points were calculated by means of a single-step, fourth-order Runge-Kutta method. The subsequent points were computed using a multi-step Adams-Moulton method.

Density

The density of the polymerizing fluid will vary with the conversion in the reactor. The density of the styrene/polystyrene reaction mixture is estimated with the density correlation taken from Wallis et al. (25).

[rho] = 845 - (T - 353) + [200 + (T - 353)]X (9)

Monomer Conversion

By definition, the conversion of styrene monomer in the reactor is defined as

X = 1 - [w.sub.m]/[w.sub.m,o] (10)

Molecular Weight Determination

Molecular weight averages and distributions can be calculated using radical and polymer moments. The number-average and weight-average molecular weights of crystal-dear polystyrene are then defined as:

With mono-functional initiation:

[M.sub.n] = 104.15 [[micro].sub.1] + [[lambda].sub.1]/[[micro].sub.o] + [[lambda].sub.o] (11a)

[M.sub.w] = 104.15 [[micro].sub.2] + [[lambda].sub.2]/[[micro].sub.1] + [[lambda].sub.1] (11b)

With bi-functional initiation:

[M.sub.n] = 104.15 [[micro].sub.1] + [[micro].sub.1] + [[micro].sub.1] + [[lambda].sub.1] + [[lambda].sub.1]/[[micro].sub.o] + [[micro].sub.o] + [[micro].sub.o] + [[lambda].sub.o] + [[lambda].sub.o] (11c)

[M.sub.n] = 104.15 [[micro].sub.2] + [[micro].sub.2] + [[micro].sub.2] + [[lambda].sub.2] + [[lambda].sub.2]/[[micro].sub.1] + [[micro].sub.1] + [[micro].sub.1] + [[lambda].sub.1] + [[lambda].sub.1] (11d)

In rubber-modified polystyrene, the number-average and weight-average molecular weights of matrix polystyrene and grafted polystyrene can be calculated, respectively. The molecular weight average of free polystyrene are similarly computed using Eqs 11a-11d. The molecular weight averages of grafted polystyrene are obtained as follows:

With mono-functional initiation:

[M.sub.n,g] = 104.15 B[[micro].sub.1] + B[[lambda].sub.1]/B[[micro].sub.o] + B[[lambda].sub.o] (12a)

[M.sub.w,g] = 104.15 B[[micro].sub.2] + B[[lambda].sub.2]/B[[micro].sub.1] + B[[lambda].sub.1] (12b)

With bi-functional initiation:

[M.sub.n,g] = 104.15 B[[micro].sub.1] + B[[micro].sub.1] + B[[lambda].sub.1]/B[[micro].sub.o] + B[[micro].sub.o] + B[[lambda].sub.o] (12c)

[M.sub.w,g] = 104.15 B[[micro].sub.2] + B[[micro].sub.2] + B[[lambda].sub.2]/B[[micro].sub.1] + B[[micro].sub.1] + B[[lambda].sub.1] (12d)

The crosslinked polystyrene is not included to calculate the molecular weight averages of grafted polystyrene. Both free polystyrene and grafted polystyrene are usually mixed to define the number-average and weight-average molecular weights of impact-modified polystyrene. The ratio of weight-average molecular weight to number-average molecular weight, the polydispersity index (PDI), is usually used to describe the molecular weight distributions in final polymer product.

Grafting of Styrene to Polybutadiene 

In HIPS, the mass of the apparent (observed) rubber is always greater than the mass of actual rubber, that is, the initial rubber content. This is due to the presence of polystyrene in the rubber phase. After the phase inversion, the total mass of polystyrene in the rubber phase may contain grafted polystyrene and occluded polystyrene. For a given HIPS sample, the total mass of polystyrene in the rubber phase can be estimated by subtracting the initial rubber content from the gel content. Mathematically, the degree of styrene grafting to polybutadiene is defined as the ratio of the total mass of polystyrene in the rubber phase to the initial rubber content. In other words, the percent grafting can be expressed as

For mono-functional initiation:

[G.sub.d] = B[[micro].sub.1]/[rho][w.sub.r,o] X 100% (13a)

For bi-functional initiation:

[G.sub.d] = B[[micro].sub.1] + B[[micro].sub.1]/[rho][w.sub.r,o] X 100% (13b)

The crosslinked polystyrene is not included to calculate the graft level of grafted polystyrene.

Viscosity

The viscosity of the reaction mixture is estimated with the zero-shear viscosity correlation developed by Mendelson [26, 27] for 40-100% polystyrene in ethylbenzene at elevated temperatures (60-200[degrees]C):

[micro] = 3.31 X [10.sup.-12] [X.sup.10.7] [[M.sup.3.4].sub.w] exp [([E.sub.a]/[R.sub.g])(1/T - 1/473)],

cp (1 Pa-s = 1.000 cp) (14a)

with

[E.sub.a] = 2300 exp(2.4X) (14b)

Melt Flow Rate, Thermal Properties, and Tensile Strength 

The thermal, rheological or mechanical properties of solid polystyrene may depend upon the residual styrene, dimer, timer, oligomers (methanol solubles), white mineral oil, or polymer molecular weights in the final product. Methanol solubles are low molecular weight species containing up to 15-20 styrene monomer units. The melt flow rate (MFR), Vicat softening point (VSP), heat distortion temperature (HDT). and tensile strength (TS) in crystal polystyrene are estimated with the correlation suggested by Wooden et al. [28]:

In(MFR) = 23.29 - 3.27 In([M.sub.w]/1000) -

0.877 In([M.sub.n]/1000) + 0.233(100[w.sub.oil]) + 0.562[w.sub.m] (15a)

VSP = 227 - 5.71(100[w.sub.oil]) - 16.3[w.sub.m] - 2.8[w.sub.CT] ([degrees]F) (15b)

HDT =

205.2 - 4.74(100[w.sub.oil]) - 15.8[w.sub.m] - 1.77[w.sub.CT] ([degrees]F) (15c)

TS = 8,370 - 151,000/([M.sub.n]/1000) - 298(100[w.sub.oil]),

In the above correlation, we can expect that the higher the molecular weights of the polymer, the lower the flow rates of the melt. Higher mineral oil concentration in the product generally gives lower thermal temperatures, lower tensile strengths, and higher melt flow rates. One can also see that the lower the residual styrene in the product, the higher the thermal temperatures of the polymer.

Devolatilization Pre-heater

A falling strand devolatilizer is a lower-cost, higher-throughput alternative compared to a vented extruder or a wiped-film evaporator. The effluent from the final reactor is a highly viscous polystyrene solution and must be preheated to reach the higher temperatures (230-245[degrees]C) suitable for the effective removal of residual monomer and other volatiles. A shell-and-tube heat exchanger is usually used as a polymer pre-heater in flash or foaming devolatilization. Each tube is often installed with special flow redistribution devices such as static (motionless) mixers to substantially improve the effective heat transfer coefficient between the process fluid and the heat transfer oil. The radial velocity profiles over the tube cross-section are essentially flat and the residence time distribution of the flow is narrow. A plug flow can be assumed. The temperature and concentration gradients in the radial direction are neglected. The design equations as defined above for an LFR can be applied to a devolatili zation pre-heater.

Vapor-Liquid Equilibrium in a Flash Chamber

A flash chamber for polystyrene devolatilization is a vapor-liquid separation vessel under vacuum. The vapor is the solvent and unreacted monomer, while the liquid is the devolatilized polystyrene with residual volatiles. Vapor-liquid equilibrium determines the limiting residual concentration of a volatile component at a given temperature. The activity of the residual volatile components remaining in the polymer exiting the flash tank will be equal to the partial pressure of the same component in the vapor leaving the flash tank. The partial pressure in the vapor is given by Dalton's law 

[p.sub.t] = [y.sub.i] [pi] (16a)

The activity of aromatic solvents in polystyrene is known to be well described by the Flory-Huggins (29) equation

ln [a.sub.i] = ln [p.sub.i]/[[P.sup.0].sub.i] = ln [[phi].sub.i] + [X.sub.ip][[[phi].sup.2].sub.p] + [[phi].sub.p] (16b)

or

[p.sub.i]/[[P.sup.0].sub.i] = [[phi].sub.i] exp[[[phi].sub.p](1.0 + [X.sub.ip][[phi].sub.p])] (16c)

which is often used to find the vapor pressure of a volatile component over a polymer solution. In the case of devolatilization, [[phi].sub.p] approaches one and Eq 16c becomes

[p.sub.i] = [[P.sup.0].sub.i][[phi].sub.i] exp(1.0 + [X.sub.ip]) (16d)

or on a weight fraction basis

[p.sub.t] = [[P.sup.0].sub.t][w.sub.t] [[rho].sub.t]/[[rho].sub.p] exp(1.0 + [X.sub.tp]) (16e)

At equilibrium, the partial vapor pressure of each component in the polymer given by Eq 16e should be equal to the partial pressure of each component in the vapor phase expressed by Eq 16a. Equating Eq 16a and Eq 16e yields

[w.sub.t] = [y.sub.t][pi][[rho].sub.p]/[[P.sup.0].sub.i][[rho].sub.i] exp[1.0 + [X.sub.ip]] (16f)

The weight fraction activity coefficient at infinite dilution is related to the Flory-Huggins interaction parameter by

[[[omega].sup.[infinity]].sub.t] = [[rho].sub.t]/[[rho].sub.p] exp[1.0 + [X.sub.ip]] (16g)

and the equilibrium expression can be rewritten as

[w.sub.t] = [y.sub.t] [pi]/[[P.sup.0].sub.t] [[[omega].sup.[infinity]].sub.t] (16h)

For the polystyrene-ethylbenzene system, the interaction parameter was determined to be 0.35 [plus or minus] 0.01 by Vrentas et al. [30]. According to their studies, the weight fraction activity coefficient at infinite dilution is approximately equal to 5.0 and independent of temperature for benzene, toluene, and ethylbenzene. The activity coefficient data on dimer and trimer are not available, so the [[[omega].sup.[infinity]].sub.t] suggested by Meister and Platt [31] for all components will be approximated as 5.0 in this work.

RESULTS AND DISCUSSION

The model developed earlier was used to determine what effect feed composition, temperature, initiator type, and initiator concentration have on monomer conversion, molecular weight development, grafting of styrene to rubber, formation of dimer/trimer, density, viscosity, melt flow rate, thermal properties, and tensile strength. The model simulations were performed using the numerical values of kinetic parameters and physical property data given in Table 3. The heat of reaction, the specific heat of reaction medium, and the wall temperature are supposed to be constant. The total fresh and recycled feed rate to the CSTR is assumed to be 10,000 kg/h. Two different types of perketal initiators will be included in the simulation. The ethyl 3,3-bis(tert-butylperoxy)butyrate, an acyclic perketal, behaves like a mono-functional initiator and has one-hour half-life at 134[degrees]C. The 1.1-bis(tert-butylperoxy)cyclohexane, a cyclic perketal, is a bifunctional initiator and has one-hour half-life at 115[degrees]C. T he dimensionless concentration in parts per million (ppm) of the initiator is usually reported relative to the fresh monomer feed rate or the polystyrene pellet production rate. Each of the initiators is assumed to have a 50% solution in mineral oil, ethylbenzene, or other diluents. A 300 ppm of 50% initiator solution means a 150 ppm of neat initiator. The polystyrene pellet production rate is estimated as the total monomer feed rate multiplied by the final monomer conversion. The reactor types, dimensions, and volumes used in this work are summarized in Table 4.

Crystal Polystyrene

Major raw materials for crystal polystyrene may be styrene with or without the presence of white mineral oil. Typical additives are zinc stearate (a mold release agent) and blue dye. The acrawax or N,N-ethylene bisstearamide, a fine powder, is used as an external lubricant for easy transport of pellets within a pipe. The tert-butylcatechol (TBC) inhibitor is usually added by monomer manufacturer at 10--15 ppm to prevent the styrene polymerization during shipping and storage. It has been suspected that the residual inhibitor after a TBC removal column may still interact with zinc stearate to give an undesirable color. The blue dye, a powder, is injected into the process in a styrene solution for ease of operation. The crystal-clear products with a blue dye are usually more attractive to customers than the colored or water- white pellets. The following case studies based on three common commercial grades of crystal polystyrene are high-heat, high-molecular-weight grade, medium-flow grade, and high-flow grade. A high-heat, high-molecular-weight grade is used mostly for extrusion. Medium-flow and high-flow grades are used primarily for injection molding. Most crystal polystyrene producers have resins in each of these grades.

High-Heat, High-Molecular-Weight Crystal Grade

The target of a high-heat, high-molecular-weight crystal grade is to produce the polymer with a very low melt flow rate in the range of 1.5-2.5 (g/10 mm.).

The weight-average molecular weight is expected to be in the low 300,000 range, while the number-average molecular weight must be greater than 100,000. Table 5 shows the simulated results of bulk styrene polymerization for a high heat, high molecular weight crystal grade. The feed preparation uses only styrene and no mineral oil. Lower reaction temperatures are usually favorable in all post-reactors. The wall temperatures of the four finishing reactors are 130[degrees]C, 132[degrees]C, 135[degrees]C, and 140[degrees]C, respectively. As can be seen, the polymerizers have a smooth temperature transition in a very narrow range.

In Case A, the polymerization is initiated only with a low temperature bifunctional initiator at 110[degrees]C. The low thermal polymerization rate is accompanied with the high catalytic polymerization rate due to the decomposition of about two thirds of the initiator in the pre-polymerizer. With the instantaneous consumption of the remaining initiator, the reaction rate is quickly increased because of high thermal and catalytic polymerization in the first LFR. Thermal polymerizations at low temperatures will result in low reaction rates in the latter post-reactors. Lower monomer conversion is expected to exit from the final reactor and thus the plant rate is low. The molecular weights of the polymer formed are, however, higher under these conditions. A high molecular weight, low melt flow, crystal polystyrene is a prerequisite in fabricating superior bi-axially oriented polystyrene (BOPS) extruded solid sheet for salad or food containers, cake domes, cookie trays, and other applications. The higher the mole cular weight of the polymer, the higher the strength of the material. This high-strength product is also good to make extruded foam sheet for egg cartons, hot or cold food service, and meat trays. In Case B, the polymerization is catalyzed by a high temperature mono-functional initiator at 128[degrees]C. It is obvious that the initiator is active until the last LFR. The gradual decomposition of an initiator will provide a very uniform reaction rate with a combined thermal and catalytic polymerization in all reactors. Higher monomer conversion is observed to exit from the final reactor and the production rate is thus increased. On the other hand, the molecular weights of the resulting polymer are decreased. In Case C, the polymerization is carried out with a binary initiator mixture. The reaction starts with a low reaction temperature of 110[degrees]C for gradual control of the reaction rate. The low temperature initiator is completely consumed in the first LFR. The high temperature initiator is almost unchang ed in a boiling CSTR and active until the last LFR. The final monomer conversion is approximately in the low 70% range without reducing greatly the molecular weights of the polymer. It is clear that a binary initiation system is more effective to give a good balance of monomer conversion and molecular weights than a single initiation system.

In a boiling CSTR, a decrease in feed temperature from 75[degrees]C to 60[degrees]C will substantially reduce the evaporative cooling duty for the same reaction and reflux temperatures. An increase in reaction temperature requires less vapor cooling for the given feed and reflux temperatures. The mean residence time in a melt pre-heater should be as short as possible at least for a high monomer concentration product exiting from the final reactor. This will minimize the formation of low molecular weight species. The higher the vacuum of the flash chamber, the lower the total volatile content in the product. The residual styrene is observed to decrease by injecting the water into a static dispersion mixer between the first flash chamber and the second polymer pre-heater. With water injection, the calculated equilibrium values of the residual styrene are much lower than the actual data. This may be due to the assumption of a perfect dispersion in water/styrene and the use of Flory-Huggins equation. In real pra ctice, some styrene will still stay with the polystyrene melt because of an excellent solubility. After devolatilization, the high-heat grade has a very low melt flow index, a Vicat softening point of 108[degrees]C, a heat distortion temperature of 96[degrees]C, and a tensile strength of 50 MPa.

Medium-Flow Crystal Grade

The goal of a medium-flow crystal grade is to produce the polymer with an improved melt flow rate in the range of 6--8.5 (g/10 min.). Table 6 shows the simulated results of bulk styrene polymerization for a medium-flow crystal grade. The feed solution consists of 97.25% styrene and 2.75% mineral oil. The initiator type, initiator concentration, and auto-refrigerated CSTR temperature are kept unchanged as those for a high-heat grade. The wall temperatures of four finishing reactors are raised to 138[degrees]C, 144[degrees]C, 157[degrees]C, and 163[degrees]C, respectively. As the temperature is suddenly changed from 110[degrees]C to 138[degrees]C, the low temperature bifunctional initiator is instantaneously consumed. The reaction rate is thus greatly increased in the first LFR. As compared with a high-heat crystal grade, the effluent from the final polymerization reactor has substantially higher styrene monomer conversion because of the increased reaction temperatures in the last two LFR's. As expected, the mo lecular weights of the resulting polymer are significantly reduced. The pellet production rate of a medium-flow grade is approximately 15% higher than that of a high-heat grade. After devolatilization, the medium-flow grade has a melt flow index of 6.5, a Vicat softening point of 100[degrees]C, a heat distortion temperature of 89[degrees]C, and a tensile strength of 43 MPa.

High-Flow Crystal Grade

The objective of a high-flow crystal grade is to produce the polymer with a high melt flow rate in the range of 12-16.5 (g/10 min.). Table 7 shows the simulated results of bulk styrene polymerization for a high-flow crystal grade. The feed solution contains 96.2% styrene and 3.8% mineral oil. The initiator type, initiator concentration, and auto-refrigerated CSTR temperature are the same as those for a high-heat grade. The wall temperatures of four post-reactors are further increased to 143[degrees]C, 146[degrees]C. 165[degrees]C, and 175[degrees]C, respectively. The first increase of the reaction rate is caused by an immediate depletion of the initiator in the first LFR. The second rise of the reaction rate is due to high thermal polymerization at an elevated temperature in the third LFR. It can be seen that a very high monomer conversion exits from the final reactor due to the extremely high polymerization rates in all LFR's. The high thermal polymerization rate will also adversely impact the molecular weig hts of the polymer formed. The weight-average molecular weight has been decreased to the low 200,000 range. The pellet production rate for a high-flow grade is obviously the highest among the three common crystal grades considered in this study. The reaction temperatures for this grade are so high that the polymer solution exiting from the last reactor contains higher concentration of styrene dimer/trimer. After devolatilization, the high-flow grade has a melt flow index of 12.3, a Vicat softening point of 96[degrees]C, a heat distortion temperature of 86[degrees]C, and a tensile strength of 39 MPa.

Impact-Modified Polystyrene

Major raw materials for HIPS may be styrene and rubber. The mineral oil is used as an internal lubricant to modify the melt flow index for production of extrusion or injection-molding grades. Typical additives are antioxidant and zinc stearate. The function of an antioxidant is to protect the rubber molecules from oxygen attack in the manufacturing process and to protect the finished parts fabricated from the pellet. In HIPS polymerization system, the stable state is that a large volume phase occupies the continuous phase and a small volume phase takes the discontinuous phase. The impact strength will be affected by the following important factors:

* Polystyrene occlusions. After the phase inversion, the occluded styrene in the rubber phase continues to be polymerized gradually. This is so-called occluded polystyrene in the rubber phase.

* Grafting of polystyrene to rubber via a chemical bond. The grafting reaction is highly dependent upon the design of polymerization reactors and the type of polymerization initiators. A good linear-flow reactor is better to control the grafting reaction than a conventional CSTR. Owing to the unequal stability of primary initiator radicals, the ability to abstract the allylic hydrogen atoms is obviously different.

* Rubber particle size. The rubber particle size is usually controlled in the phase-inversion reactor by the agitator speed (the shear stress of the agitator), the viscosity in the reactor, and the grafting of polystyrene to the rubber chain. In the phase-inversion reactor, the viscosity of the polymerizing fluid may be affected by reaction temperature, polymer solids content, and ethyl-benzene concentration. The rubber particle size is almost unchanged during and after the phase inversion. The higher the agitator speed, the smaller the rubber particle size. The higher the viscosity, the smaller the rubber particle size.

Heat-Resistant, High-Impact Grade

The purpose of a high-heat, high-impact polystyrene is to develop the HIPS with better heat resistance. Table 8 shows the simulated results of bulk styrene polymerization in the presence of butadiene rubber for a high-heat, high-impact grade. The feed solution contains 90% styrene, 7% rubber, and 3% EB. The initiator type, initiator concentration, and auto-refrigerated CSTR temperature are the same as those for the above-mentioned crystal grades. The reaction temperatures of the four post-reactors are 145[degrees]C, 147[degrees]C, 156[degrees]C, and 159[degrees]C, respectively. Three types of catalytic initiation were considered in this grade. The reaction rates are the highest for all three initiation systems in the first LFR. With bifunctional initiation, the percent grafting is particularly high in the pre-polymerizer. The rate of allylic hydrogen abstraction may be higher than the rate of styrene homo-polymerization in the reactor. The grafting of styrene to butadiene rubber is more effective with bifunctional initiation than with monofunctional initiation. This may be due to the reinitiation of temporarily dead polymer species generated by a bifunctional initiator. The use of a binary initiator mixture provides the best balance of conversion, molecular weights, and rubber grafting among these three initiation systems. The molecular weights of grafted polystyrene are observed to be higher than those of matrix polystyrene. The molecular weights of the resulting HIPS are located between the molecular weights of grafted polystyrene and the molecular weights of matrix polystyrene. The concentration of solvent and un-reacted styrene is not substantially decrea sed by increasing the melt temperature for a given chamber vacuum. In general, the mineral oil can be injected after the first flash chamber to generate another HIPS with the same properties except for the heat distortion temperature and Vicat softening point.

Comparison With Commercial Polystyrene Data

The molecular weight distribution of commercial solid polystyrene will be in the range of 2.0 to 3.0 in all grades. Typical molecular weights of crystal resins are [M.sub.n] = 130,000 and [M.sub.w] = 300,000 for high-heat grade; = 92,000 and = 225,000 for medium-flow grade; [M.sub.n] = 74,000 and [M.sub.w] = 218,000 for easy-flow grade. The melt flow rate can be 1.5, 2.5. 6, 8, 14, 20, etc. depending on product grades. The heat distortion temperature will be 83 to 94[degrees]C (181 to 201[degrees]F) for extrusion grades and 75 to 94[degrees]C (167 to 201[degrees]F) for molding grades. The Vicat softening point will be 100 to 109[degrees]C (212 to 228[degrees]F for extrusion grades and 93 to 109[degrees]C (199 to 228[degrees]F) for molding grades. The simulated results showed very good agreement with the polystyrene plant operation data in conversion, density, heat distortion temperature, Vicat softening point, and tensile strength for approximately the same process conditions. The calculated melt flow index, molecular weights, and viscosity are also comparable with the actual data of real commercial products.

CONCLUSIONS

A comprehensive mathematical model has been developed and solved to simulate a continuous bulk styrene polymerization process with catalytic initiation for crystal polystyrene and HIPS. The resulting computer simulation model is capable of analyzing what effect feed composition, temperature, initiator type, initiator concentration, and residence time have on styrene monomer conversion, polystyrene molecular weights, grafting of styrene to rubber, formation of dimer/trimer, density, viscosity, melt flow rate, thermal properties, and tensile strength. Several case studies were carried out for commercially important crystal-clear and high-impact products. The quality of the polymer produced is in the range of commercial solid polystyrene. In crystal polystyrene, the molecular weight is one of the most important structural factors to tailor a specific product quality. A combined thermal and catalytic polymerization in post-reactors is favorable to decrease further the molecular weights of the polymer formed. The styrene dimer/trimer occur in low concentrations but can be substantially reduced with a low temperature initiator. The vacuum of the flash chamber is more effective in decreasing the residual solvent and un-reacted styrene than the temperature of the polymer melt. The water injected to the low volatile melt in about 1% relative to the mass flow rate exiting from the first flash chamber is adequate to reduce the total volatile matter. A uniform wall temperature was taken in an LFR, but multiple wall temperatures can be used to control the reaction further. The efficiency for primary initiators and temporarily dead polymer species is an important adjustable parameter f or the model.

APPENDIX

A well-established method of solving an infinite set of coupled mass balance equations is to use the method of moments. The kth moments for the chain length distributions of dead (inactive) polymer species, temporarily dead polymer species, and growing (active or live) polymers are defined as:

[[micro].sub.k] = [[[sigma].sup.[infinity]].sub.j=2] [j.sup.k][[P.sub.j]] [[micro].sub.k] = [[[sigma].sup.[infinity]].sub.j=2] [j.sup.k][[P.sub.j]] [[micro].sub.k] = [[[sigma].sup.[infinity]].sub.j=2] [j.sup.k][[P.sub.j]] (A-1)

[B.sub.[[micro].sub.k]] = [[[sigma].sup.[infinity]].sub.j=2] [j.sup.k][[BP.sub.j]] [B.sub.[[micro].sub.k]] = [[[sigma].sup.[infinity]].sub.j=2] [j.sup.k] [[BP.sub.j] [B.sub.[[micro].sub.k]]B = [[[sigma].sup.[infinity]].sub.j=2] [j.sup.k][[BP.sub.j]B] (A-2)

[[lambda].sub.k] = [[[sigma].sup.[infinity]].sub.j=1] [j.sup.k][[R.sub.j]*] [[lambda].sub.k] = [[[sigma].sup.[infinity]].sub.j=1] [j.sup.k][[R.sub.j]*] B[[lambda].sub.k] = [[[sigma].sup.[infinity]].sub.j=1] [j.sup.k][[BR.sub.j]*] (A-3)

The batch rate equations can be developed from the reaction mechanism and the moment definition. The rate expressions for HIPS catalyzed by bi-functional free radical initiators have the following forms:

Primary Radicals

1 d([[R.sub.o]*]V)/V dt =

2 [fk.sub.d1][[I.sub.B]] + [fk.sub.d2] [[micro].sub.o] + 2[fk.sub.d2] [[micro].sub.o] + [fk.sub.d2] [B.sub.[[micro].sub.o]]

- [K.sub.i,1] [[R.sub.o]*][M] - [k.sub.i,2][[R.sub.o]*][BH] (A-4)

1 d)[R.sub.o]*]V)/V dt =

2 [fk.sub.d1][[I.sub.B]] - [k.sub.i,1] [[R.sub.o]*][M] - [k.sub.i,2][[R.sub.o]*][BH] (A-5)

[approximately equals] [k.sub.1,2][[R.sub.o]*][BH] + [k.sub.i,2][[R.sub.o]*][BH] - [k.sub.i,3][M][B*] + [k.sub.tr,r][BH]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-6)

In the above equations, it has been assumed that the initiator efficiency is the same for a bifunctional initiator ([I.sub.B]) and for temporarily dead polymer species ([P.sub.j] and [P.sub.j]).

Growing Polymers

1 d([[R.sub.1]*]V)/V dt =

2[k.sub.i,th][[M].sup.3] + [k.sub.i,1][[R.sub.o]*][M] - [k.sub.p][[R.sub.1]*][M] - [k.sub.tr,m][M][[R.sub.1]*] + [k.sub.tr,m][M]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) - [k.sub.tr,r][BH][[R.sub.1]*] - [k.sub.tc][[R.sub.1]*]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-7)

1 d([[R.sub.j]*]V)/V dt =

[fk.sub.d2][[P.sub.j] + [k.sub.p][M]([[R.sub.j-1]*] - [[R.sub.j]*]) - ([k.sub.tr,m][M] + [k.sub.tr,r][BH])[[R.sub.j]*] - [k.sub.tc][[R.sub.j]*]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]), j [greater than or equal to] 2 (A-8)

1 d([[R.sub.1]*]V)/V dt =

[k.sub.i,1][[R.sub.o]*][M] - [k.sub.p][[R.sub.1]*][M] - [k.sub.tr,m][M][[R.sub.1]*] - [k.sub.tr,r][BH][[R.sub.1]*] - [k.sub.tc][[R.sub.1]*]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-9)

1 d([[R.sub.j]*]V)/V dt =

2[fk.sub.d2][[P.sub.j]] + [k.sub.p][M]([[R.sub.j-1]*] - [[R.sub.j]*]) - ([k.sub.tr,m][M] + [k.sub.tr,r][BH])[[R.sub.j]*] - [k.sub.tc][[R.sub.j]*]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]), j [greater than or not equal to] 2 (A-10)

1 d([[BR.sub.1]*]V)/V dt =

[k.sub.i,3][B*][M] - [k.sub.p][[BR.sub.1]*][M] - [k.sub.tr,m][[BR.sub.1]*][M] - [k.sub.tr,r][[BR.sub.1]*][BH] - [k.sub.tc][[BR.sub.1]*]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-11)

1 d([[BR.sub.j]*]V)/V dt =

[fk.sub.d2][[BP.sub.j]] + [k.sub.p][M]([[BR.sub.j-1]*] - [[BR.sub.j]*]) - ([k.sub.tr,m][M] + [k.sub.tr,r][BH])[[BR.sub.j]*] - [k.sub.tc][[BR.sub.j]*]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]), j [greater than or equal to] 2 (A-12)

The associated zeroth, first, and second moments of growing radicals are then given by

1 d([[lambda].sub.o]V)/V dt =

2[k.sub.i,th][[M].sup.3] + [k.sub.i,1][[R.sub.o]*][M] + [fk.sub.d2][[micro].sub.o] + [k.sub.tr,m][M]([[lambda].sub.o] + B[[lambda].sub.o]) - [k.sub.tr,r][BH][[lambda].sub.o] - [k.sub.tc][[lambda].sub.o]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-13)

1 d([[lambda].sub.o]V)/V dt =

[k.sub.i,1][[R.sub.o]*][M] + 2[fk.sub.d2][[micro].sub.o] - [k.sub.tr,m][M][[lambda].sub.o] - [k.sub.tr,r][BH][[lambda].sub.o] - [k.sub.tc][[lambda].sub.o]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-14)

1 d(B[[lambda].sub.o]V)/V dt =

[k.sub.i,3][B*][M] + [fk.sub.d2]B[[micro].sub.o] - [k.sub.tr,m][M]B[[lambda].sub.o] - [k.sub.tr,r][BH]B[[lambda].sub.o] - [k.sub.tc](B[[lambda].sub.o])([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-15)

1 d([[lambda].sub.1]V)/V dt =

2[k.sub.t,th][[M].sup.3] + [k.sub.t,1][[R.sub.o]*][M] + [fk.sub.d2][[micro].sub.1] + [k.sub.p][M][[lambda].sub.o] - [k.sub.tr,m][M][[lambda].sub.1] - [k.sub.tr,r][BH][[lambda].sub.1] - [k.sub.tc][[lambda].sub.1]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) {A-16)

1 d([[lambda].sub.1]V)/V dt =

[k.sub.i,1][[R.sub.o]*][M] + 2[fk.sub.d2][[micro].sub.1] + [k.sub.p][M][[lambda].sub.o] - [k.sub.tr,r][M][[lambda].sub.1] - [k.sub.tr,r][BH][[lambda].sub.1] - [k.sub.tc][[lambda].sub.1]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-17)

1 d(B[[lambda].sub.1]V)/V dt =

[k.sub.i,3][B*][M] + [fk.sub.d2]B[[micro].sub.1] + [k.sub.p][M]B[[lambda].sub.o] - [k.sub.tr,m][M]B[[lambda].sub.1] - [k.sub.tr,r][BH]B[[lambda].sub.1] - [k.sub.tc]B[[lambda].sub.1]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-18)

1 d([[lambda].sub.2]V)/V dt =

[2k.sub.i,th][[M].sup.3] + [k.sub.i,1][[R.sub.o]*][M] + [fk.sub.d2][[micro].sub.2] + [k.sub.p][M]([[lambda].sub.o] + 2[[lambda].sub.1]) - [k.sub.tr,m][M][[lambda].sub.2] - [k.sub.tr,r][BH][[lambda].sub.2] - [k.sub.tc][[lambda].sub.2]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-19)

1 d([[lambda].sub.2]V)/V dt =

[k.sub.i,1][[R.sub.o]*][M] + 2[fk.sub.d2][[micro].sub.2] + [k.sub.p][M]([[lambda].sub.o] + 2[[lambda].sub.1]) - [k.sub.tr,m][M][[lambda].sub.2] - [k.sub.tr,r][BH][[lambda].sub.2] - [k.sub.tc][[lambda].sub.2]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-20)

1 d(B[[lambda].sub.2] V)/V dt =

[k.sub.1,3][B*][M] + [fk.sub.d2] B[[micro].sub.2] + [k.sub.p][M](B[[lambda].sub.o] + 2B[[lambda].sub.1]) -

[k.sub.tr,m][M]B[[lambda].sub.2] - [k.sub.tr,r][BH]B[[lambda].sub.2] - [k.sub.tc]B[[lambda].sub.2]([[lambda].sub.o] + [[lambda].sub.o] + B[[lambda].sub.o]) (A-21)

Dead or Temporarily Dead Polymers

1 d([[P.sub.j]]V)/V dt = [k.sub.tr,m][M][[R.sub.j]*] +

[k.sub.tr,r][BH][[R.sub.j]*] + 1/2 [k.sub.tc] [[[sigma].sup.j-1].sub.n=1] [[R.sub.j-n]*][[R.sub.n]*] - j [greater than or equal to] 2 (A-22)

1 d([[P.sub.j]]V)/V dt = [k.sub.tr,m][M][[R.sub.j]*] +

[k.sub.tr][BH][[R.sub.j]*] = [k.sub.tc][[[sigma].sup.j-1].sub.n=1] [[R.sub.j-n]*][[R.sub.n]*] - [k.sub.d2][[P.sub.j]] j [greater than or equal to] 2 (A-23)

1 d([[P.sub.j]]V)/V dt = 1/2[k.sub.tc] [[[sigma].sup.j-1].sub.n=1] [[R.sub.j-n]*][[R.sub.n]*] - 2[k.sub.d2][[P.sub.j]], j [greater than or equal to] 2 (A-24)

1 d([[BP.sub.j]]V)/V dt = [k.sub.tr,m][M][[BR.sub.j]*] + [k.sub.tr,r][BH][[BR.sub.j]*] +

[k.sub.tc][[[sigma].sup.j-1].sub.n=1][[BR.sub.j-n]*] [[R.sub.n]*] + [k.sub.tc] [B*][[R.sub.j]*], j [greater than or equal to] 2 (A-25)

1 d([[BP.sub.j]]V)/V dt =

[k.sub.tc][[[sigma].sup.j-1].sub.n=1][[BR.sub.j-n]*][[R.sub.n]*] - [k.sub.d2][[BP.sub.j]] + [k.sub.tc][B*][[R.sub.j]*], j [greater than or equal to] 2 (A-26)

1 d([[BP.sub.j]B]V)/V dt =

1/2 [k.sub.tc] [[[sigma].sup.j-1].sub.n=1] [[BR.sub.j-n]*][[BR.sub.n]*] + [k.sub.tc][B*][[BR.sub.j]*], j [greater than or equal to] 2 (A-27)

The steady-state mass balances for the moments of molecular weight distributions of dead and temporarily dead polymer species in an LFR are:

u d[[micro].sub.o]/dz = [k.sub.tr,m][M][[lambda].sub.o] + [k.sub.tr,r][BH][[lambda].sub.o] + 1/2 [k.sub.tc][[lambda].sub.o][[lambda].sub.o] (A-28)

u d[[micro].sub.o]/dz = [k.sub.tr,m][M][[lambda].sub.o] + [k.sub.tr,r][BH][[lambda].sub.o] + [k.sub.tc][[lambda].sub.o][[lambda].sub.o] - [k.sub.d2][[micro].sub.o] (A-29)

u d[[micro].sub.o]/dz = 1/2[k.sub.tc][[lambda].sub.0][[lambda].sub.0] - 2[k.sub.d2][[micro].sub.o] (A-30)

u dB[[micro].sub.o]/dz = [k.sub.tr,m][M]B[[lambda].sub.o] + [k.sub.tr,r][BH]B[[lambda].sub.o] + [k.sub.tc][[lambda].sub.o](B[[lambda].sub.o]) (A-31)

u dB[[micro].sub.o]/dz = [k.sub.tc][[lambda].sub.o](B[[lambda].sub.o]) - [k.sub.d2]B[[micro].sub.o] (A-32)

u dB[[micro].sub.o]B/dz = 1/2 [k.sub.tc](B[[lambda].sub.o])(B[[lambda].sub.o]) (A-33)

u d[[micro].sub.1]/dz = [k.sub.tr,m][M][[lambda].sub.1] + [k.sub.tr,r][BH][[lambda].sub.1] + [k.sub.tc][[lambda].sub.o][[lambda].sub.1] (A-34)

u d[[micro].sub.1]/dz =

[k.sub.tr,m][M][[lambda].sub.1] + [k.sub.tr,r][BH][[lambda].sub.1] + [k.sub.tc]([[lambda].sub.0][[lambda].sub.1] + [[lambda].sub.1][[lambda].sub.0]) - [k.sub.d2] [[micro].sub.1] (A-35)

u d[[micro].sub.1]/dz = [k.sub.tc][[lambda].sub.o][[lambda].sub.1] - 2[k.sub.d2][[micro].sub.1] (A-36)

u dB[[micro].sub.1]/dz =

[k.sub.tr,m][M]B[[lambda].sub.1] + [k.sub.tr,r][BH]B[[lambda].sub.1] + [k.sub.tc][[lambda].sub.o](B[[lambda].sub.1]) + [k.sub.tc][[lambda].sub.1](B[[lambda].sub.o]) (A-37)

u dB[[micro].sub.1]/dz = [k.sub.tc][[lambda].sub.o](B[[lambda].sub.1]) + [k.sub.tc][[lambda].sub.1] (B[[lambda].sub.o]) - [k.sub.d2] B[[micro].sub.1] (A-38)

u dB[[micro].sub.1]B/dz = [k.sub.tc](B[[lambda].sub.o])(B[[lambda].sub.1]) (A-39)

u d[[micro].sub.2]/dz = [k.sub.tr,m][M][[lambda].sub.2] + [k.sub.tr,r][BH][[lambda].sub.2] + [k.sub.tc] ([[lambda].sub.1][[lambda].sub.1] + [[lambda].sub.o][[lambda].sub.2]) (A-40)

u d[[micro].sub.2]/dz = [k.sub.tr,m][M][[lambda].sub.2] +

[k.sub.tr,r][BH][[lambda].sub.2] + [k.sub.tc] ([[lambda].sub.o][[lambda].sub.2] + 2[[lambda].sub.1][[lambda].sub.1] + [[lambda].sub.o][[lambda].sub.2]) - [k.sub.d2] [[micro].sub.2] (A-41)

u d[[micro].sub.2]/dz = [k.sub.tc]([[lambda].sub.1] [[lambda].sub.1] + [[lambda].sub.o][[lambda].sub.2]) - 2[k.sub.d2] [[micro].sub.2] (A-42)

u dB[[micro].sub.2]/dz = [k.sub.tr,m][M]B[[lambda].sub.2] +

[k.sub.tr,r][BH]B[[lambda].sub.2] + [k.sub.tc][[lambda].sub.o](B[[lambda].sub.2]) + 2[k.sub.tc][[lambda].sub.1] (B[[lambda].sub.1]) + [k.sub.tc] [[lambda].sub.2] (B[[lambda].sub.o]) (A-43)

u dB[[micro].sub.2]/dz =

[k.sub.tc][[lambda].sub.o](B[[lambda].sub.2]) + 2[k.sub.tc][[lambda].sub.1] (B[[lambda].sub.1]) + [k.sub.tc][[lambda].sub.2] (B[[lambda].sub.o]) - [k.sub.d2] B[[micro].sub.2] (A-44)

u dB[[micro].sub.2]B/dz = [k.sub.tc](B[[lambda].sub.1])(B[[lambda].sub.1]) + [k.sub.tc](B[[lambda].sub.o])(B[[lambda].sub.2]) (A-45)

The steady-state material balances for the moments of molecular weight distributions of dead and temporarily dead polymer species in a cascade of multiple CSTR's can be seen in a recent paper by Chen (15) for further details.

NOMENCLATURE 

[A.sub.1], [A.sub.2], [A.sub.3] gel effect coefficients

AH an unstable Diels-Alder adduct 

[A.sub.c] heat transfer surface area, [m.sup.2]

BH butadiene rubber

[BH] butadiene rubber concentration

B* rubber radicals via allyclic hydrogen abstraction

[BR.sub.j]* graft-polystyryl radicals of j degree of propogation

[BP.sub.j] graft-polystyrene chain of j degree of polymerization 

[BP.sub.j] graft-polystyrene chain with one undecomposed peroxide group

[BP.sub.j]B crosslink-polystyrene chain of j degree of polymerization

BB crosslinked butadiene rubber

[c.sub.p] heat capacity, J/kg/K

d insider diameter of the shell in an LFR, m

[dimer] concentration of dimer

[[dim er].sub.in] concentration of dimer at reactor inlet 

[F.sub.in] inlet mass flow rate, kg/h

[F.sub.out] outlet mass flow rate, kg/h

f initiator efficiency, %

[G.sub.d] percent grafting of styrene to butadiene rubber, %

h overall heat transfer coefficient, 1Btu/h/[ft.sup.2]/[degrees]F = 5.6782W/[m.sup.2]/[degrees]C

HOS hot oil supply

HOR hot oil return

I mono-functional initiator

[I.sub.B] bi-functional initiator

k thermal conductivity of polystyrene-styrene solution, W/m/K

[k.sub.styrene] thermal conductivity of styrene, W/m/K

[k.sub.ps] thermal conductivity of polystyrene, W/m/K

[K.sub.DCB] rate constant for dimer formation, ([m.sup.3]/kg)[s.sup.-1]

[k.sub.CT] rate constant for trimer formation, [s.sup.-1]

[k.sub.d] rate constant for the decomposition of a monofunctional initiator, [s.sup.-1]

[k.sub.d1], [k.sub.d2] rate constant for the decomposition of a bifunctional initiator, [s.sup.-1]

[k.sub.i,1],[k.sub.i2] rate constant for initiation by primary radicals, ([m.sup.3]/kg)[s.sup.-1]

[k.sub.i,3] rate constant for reinitiation by rubber radicals, ([m.sup.3]/kg)[s.sup.-1]

[k.sub.i,th] rate constant for thermal initiation, [([m.sup.3]/kg).sup.2][s.sup.-1]

[k.sub.p] rate constant for propogation, ([m.sup.3]/kg)[s.sup.-1]

[k.sub.tc] rate constant for termination at any conversion, ([m.sup.3]/kg)[s.sup.-1]

[k.sub.tc,o] rate constant for termination at zero conversion, ([m.sup.3]/kg)[s.sup.-1]

[k.sub.tr,m] rate constant for chain transfer to monomer, ([m.sup.3]/kg)[s.sup.-1]

[k.sub.tr,AH] rate constant for chain transfer to AH, ([m.sup.3]/kg)[s.sup.-1]

[k.sub.tr,r] rate constant for chain transfer to butadiene rubber, ([m.sub.3]/kg)[s.sup.-1]

L length of an LFR, m

m evaporative rate in a boiling CSTR, kg/h

M styrene monomer

[M] styrene monomer concentration

M* styrene monomer radical

[M.sub.nf] number-average molecular weight for matrix PS in HIPS, g/mol

[M.sub.wf] weight-average molecular weight for matrix PS in HIPS, g/mol

[M.sub.n,g] number-average molecular weight for grafted PS in HIPS, g/mol

[M.sub.w,g] weight-average molecular weight for grafted PS in HIPS, g/mol

[M.sub.n] number-average molecular weight, g/mol

[M.sub.w] weight-average molecular weight, g/mol

Nu Nusselt number 

[P.sub.t] partial pressure in the vapor

[[P.sup.0].sub.i] vapor pressure of pure component at the flash tank temperature

Pr Prandt number

[P.sub.j] homo-polystyrene chain of j degree of polymerization

[P.sub.j] homo-polystyrene chain with one undecomposed peroxide group

[P.sub.j] homo-polystyrene chain with two undecomposed peroxide groups

Re Reynolds number 

[R.sub.g] universal gas constant, 1.987 cal/mol/K or 8.314 J/mol/K

[R.sub.o]* primary radicals without any un-decomposed peroxide group

[R.sub.o]* primary radicals with one un-decomposed peroxide group

[R.sub.j]* homo-polystyryl radicals of j degree of propagation

[R.sub.j]* homo-polystyryl radicals with one un-decomposed peroxide group

[R.sub.p] rate of polymerization, (kg/[m.sup.3])[s.sup.-1] or (%/hour)

[trimer] concentration of trimer

[[trimer].sub.in] concentration of trimer at reactor inlet

t mean residence time in an LFR, s

[T.sub.boiling] temperature of the polymerizing fluid in a boiling CSTR, K

[T.sub.reflux] reflux temperature in a boiling CSTR, K

T temperature of the polymerizing fluid in an LFR, K

[T.sub.in] inlet temperature, K

[T.sub.out] outlet temperature, K

[T.sub.melt] temperature of polystyrene melt, K

[T.sub.w] wall temperature, K

u linear velocity in an LFR, m/s

V net volume of the reactor, [m.sup.3]

[w.sub.i] weight fraction of volatile component

[w.sub.m,o] initial weight fraction of styrene monomer

[w.sub.m,in] inlet weight fraction of styrene monomer

[w.sub.m] weight fraction of styrene monomer in the reactor

[w.sub.I,o] initial weight fraction of a monofunctional initiator

[w.sub.I,in] inlet weight fraction of a mono-functional initiator

[w.sub.I] weight fraction of a mono-functional initiator in the reactor

[w.sub.[I.sub.B],o] initial weight fraction of a bi-functional initiator

[w.sub.[I.sub.B],in] inlet weight fraction of a bi-functional initiator

[w.sub.[I.sub.B]] weight fraction of a bi-functional initiator in the reactor

[w.sub.oil] weight fraction of white mineral oil

[w.sub.r,o] initial weight fraction of butadiene rubber

[w.sub.DCB] weight fraction of styrene dimer

[w.sub.CT] weight fraction of styrene trimer

X styrene monomer conversion in the reactor

x dimensionless axial coordinate, x = z/L

[y.sub.i] mole fraction of component i in the vapor

z axial coordinate, m

Greek Letters 

[micro] viscosity of the polymerizing fluid, Pa-s (1 Pa-s = 10 poise = 1,000 centipoise)

[[micro].sub.k] kth moment of homo-PS chain

[[micro].sub.k] kth moment of homo-PS chain with one undecomposed peroxide group

[[micro].sub.k] kth moment of homo-PS chain with two undecomposed peroxide groups

B[[micro].sub.k] kth moment of graft-PS chain

B[[micro].sub.k] kth moment of graft-PS chain with one undecomposed peroxide group

B[[micro].sub.k]B kth moment of crosslink-PS chain

[[lambda].sub.k] kth moment of homopolystyryl radical chain

[[lambda].sub.k] kth moment of homo-polystyryl radical chain with one undecomposed peroxide group

[B[lambda].sub.k] kth moment of graft-polystyryl radical chain

[tau] space time or mean residence time in a CSTR, s

[rho] density of styrene-polystyrene mixture in the reactor, kg/[m.sup.3]

[[delta]H.sub.rxn] heat of polymerization, J/kg

[[delta]H.sub.v] latent heat of vaporization, J/kg

[[phi].sub.i] volume fraction of volatile component

[[phi].sub.p] volume fraction of polymer

[X.sub.ip], Flory-Huggins interaction parameter between volatile component and polymer

[pi] total pressure in the flash tank, mm Hg or torr 

[[omega].sup.[infinity].sub.i] weight fraction activity coefficient at infinite dilution

REFERENCES

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(5.) G. Gawne and C. Ouwerkerk, U.S. Patent 4,011,284 (to Shell Oil Company), Mar. 8. 1977.

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           Kinetics of Bulk Styrene Polymerization Catalyzed by
                    Mono- and Bifunctional Initiators.
Thermal initiation:
  M + M [right arrow][k.sub.1]/
  [left arrow][k.sub.1] AH
  AH + M [right arrow][k.sub.2] A* +  (slow)
  M*
  A* + M [right                       (fast)
  arrow][k.sub.3][R.sub.1]*
  M* + M [right                       (fast)
  arrow][k.sub.4][R.sub.1]*
  AH + M [right arrow][k.sub.cT]
  cyclic trimers
  M + M [right arrow][k.sub.DCB]      (cis- and
  dimers                              trans-1,2-diphenylcyclobutane)
  Overall : 3M [right arrow]
  [k.sub.i,th] 2[R.sub.1]*
Initiation by peroxide initiators:
  I [right arrow][k.sub.d]2[R.sub.o]* (monofunctional initiators)
  [I.sub.B][right arrow]2[k.sub.d1]
  [R.sub.o]* + [R.sub.o]*             (bifunctional initiators)
  [R.sub.o]* + M [right arrow]
  [k.sub.i,1] [R.sub.1]*              (initiation)
  [R.sub.o]* + M [right arrow]
  [k.sub.i,1] [R.sub.1]*              (initiation)
  [P.sub.j][right arrow][k.sub.d2]
  [R.sub.o]* + [R.sub.j]*             (j [greater than or equal to] 2)
  [P.sub.i][right arrow]2[k.sub.d2]
  [R.sub.o]* + [R.sub.i]*             (j [greater than or equal to] 2)
Propagation:
  [R.sub.j]* + M [right arrow]
  [k.sub.p] [R.sub.i]+1*              (j [greater than or equal to] 1)
  [R.sub.i]* + M [right arrow]
  [k.sub.p] [R.sub.j]+1*              (j [greater than or equal to] 1)
Termination by combination:
  [R.sub.j]* + [R.sub.k]*
  [right arrow][k.sub.tc][P.sub.i+k]  (j, k [greater than or equal to] 1)
  [R.sub.i]* + [R.sub.k]*
  [right arrow][k.sub.tc][P.sub.j+k]  (j, k [greater than or equal to] 1)
  [R.sub.j]* + [R.sub.k]*
  [right arrow][k.sub.tc] [P.sub.j+k] (j, k [greater than or equal to] 1)
Chain transfer to monomer and AH:
  [R.sub.j]* + M [right arrow]
  [k.sub.tr,m][R.sub.1]* + [P.sub.i]  (j [greater than or equal to] 1)
  [R.sub.j]* + AH [right arrow]
  [k.sub.tr,AH][R.sub.1]* + [P.sub.j] (j [greater than or equal to] 1)
  [R.sub.j]* + M [right arrow]
  [k.sub.tr,m][R.sub.1]* + [P.sub.i]  (j [greater than or equal to] 1)
  [R.sub.j]* + AH [right arrow]
  [k.sub.tr,AH][R.sub.1]* + [P.sub.i] (j [greater than or equal to] 1)
             Kinetics of Bulk Styrene Polymerization Catalyzed
                by Mono- and Bifunctional Initiators in the
                        Presence of Butadiene Rubber.
Thermal initiation:
  3M [right arrow][k.sub.I,th]
  2[R.sub.1]*
Initiation by peroxide Initiators:
  I [right arrow][k.sub.d]
  2[R.sub.o]*                          (monofunctional initiators)
  [I.sub.B] [right arrow]2[K.sub.d1]
  [R.sub.o]* + [R.sub.o]*              (bifunctional initiators)
  [R.sub.o]* + M
  [right arrow][k.sub.i,1] [R.sub.1]*;
  [R.sub.o]* + M [right
  arrow][k.sub.i,1]
  [R.sub.1]*                           (initiation)
  [R.sub.o]* + BH [right
  arrow][k.sub.i,2]
  B * + [R.sub.o]H; [R.sub.o]* + BH
  [right arrow][k.sub.i,2] B* +        (allylic hydrogen abstraction)
  [R.sub.o]H
  B* + M [right arrow][k.sub.i,3]      (re-initiation)
  [BR.sub.1]*
  [P.sub.j] [right arrow][k.sub.d2]
  [R.sub.o]* + [R.sub.j]*; [P.sub.j]
  [right arrow]2[k.sub.d2] [R.sub.o]*
  +
  [R.sub.j]*                           (re-initiation) (j [greater
                                       than or equal to 2])
  [BP.sub.j] [right arrow][k.sub.d2]   (re-initiation) (j [greater
  [R.sub.o]* + [BR.sub.j]*             than or equal to 2])
Propagation:
  [R.sub.j]* + M [right
  arrow][k.sub.p]
  [R.sub.j+1]*; [R.sub.j]* + M
  [right arrow][k.sub.p] [R.sub.j+1]*  (j [greater than or equal to] 1)
  [BR.sub.j]* + M [right
  arrow][k.sub.p]
  [BR.sub.j+1]*                        (j [greater than or equal to] 1)
Termination by combination:
  [R.sub.j]* + [R.sub.k]*
  [right arrow][k.sub.tc] [P.sub.j+k];
  [R.sub.j]* + [R.sub.k]*
  [right arrow][k.sub.tc] [P.sub.j+k];
  [R.sub.j]* + [R.sub.k]*
  [right arrow][k.sub.tc] [P.sub.j+k]  (j, k [greater than or equal to] 1)
  [R.sub.j]* + [BR.sub.k]*
  [right arrow][k.sub.tc]
  [BP.sub.j+k];
  [R.sub.j]* + [BR.sub.k]*
  [right arrow][k.sub.tc]              (j, k [greater than or equal to] 1)
  [BP.sub.j+k];
  [BR.sub.j]* + [BR.sub.k]*
  [right arrow][k.sub.tc]              (j, k [greater than or equal to] 1)
  [BP.sub.j+k]B
  [R.sub.j]* + B* [right
  arrow][k.sub.tc]
  [BP.sub.j]; [R.sub.j]* + B*
  [right arrow][k.sub.tc] [BP.sub.j];
  [BR.sub.j]* + B* [right
  arrow][k.sub.tc]
  [BP.sub.j]B                          (j [greater than or equal to] 1)
  B* + B* [right arrow][k.sub.tc] BB
Chain transfer to monomer and AH:
  [R.sub.j]* + M [right
  arrow][k.sub.tr,m]
  [R.sub.1]* + [P.sub.j]; [R.sub.j]* +
  AH
  [right arrow][k.sub.tr,AH]
  [R.sub.1]* +
  [P.sub.j]                            (j [greater than or equal to] 1)
  [R.sub.j]* + M [right
  arrow][k.sub.tr,m]
  [R.sub.1]* + [P.sub.j]; [R.sub.j]* +
  AH
  [right arrow][k.sub.tr,AH]
  [R.sub.1]* +
  [P.sub.j]                            (j [greater than or equal to] 1)
  [BR.sub.j]* + M [right
  arrow][k.sub.tr,m]
  [R.sub.1]* + [BP.sub.j]; [BR.sub.j]*
  + AH
  [right arrow][k.sub.tr,AH]
  [R.sub.1]* +
  [BP.sub.j]                           (j [greater than or equal to] 1)
Chain transfer to polybutadiene
rubber:
  [R.sub.j]* + BH [right
  arrow][k.sub.tr,r]
  B* + [P.sub.j]                       (j [greater than or equal to] 1)
  [R.sub.j]* + BH [right
  arrow][k.sub.tr,r]
  B* + [P.sub.j]                       (j [greater than or equal to] 1)
  [BR.sub.j]* + BH [right
  arrow][k.sub.tr,r]
  B* + [BP.sub.j]                      (j [greater than or equal to] 1)
                 Kinetic Parameters and Physical Property
                      Data Used in Model Simulations.
1,1-Bis(tert-butylperoxy)cyclohexane (Lupersol
331 or Luperox 331; Trigonox 22):
   [k.sub.d1] = 2.115 x [10.sup.16]
   exp( - 17,948/T),[s.sup.-1]                     Villalobos et al. [33]
   [k.sub.d2] = 1.817 x [10.sup.19]
   exp( - 21,361/T),[s.sup.-1]                     Villalobos et al. [33]
   [k.sub.d1] = 5.33 x [10.sup.15]
   exp( - 17,409/T),[s.sup.-1]                     (Elf Atochem)
   [k.sub.d1] = 3.47 x [10.sup.15]
   exp( - 17,128/T),[s.sup.-1]                     (Akzo)
   f = 0.7
Ethyl 3,3-bis(tert-butylperoxy)butyrate
  (Lupersol 233 or Luperox 233):
   [k.sub.d] = 5.48 x [10.sup.15]
   exp( - 18,240/T),[s.sup.-1]                     (Elf Atochem)
   f = 0.7
[k.sub.i,th] = 2.120 x [10.sup.2] exp(- 15,005/T),
[([m.sup.3]/kg).sup.2] [s.sup.-1]                  Peng [32]
[k.sub.i,1] = 8.036 x [10.sup.3] exp( - 2,650/T),
([m.sup.3]/kg)[s.sup.-1]                           Estenoz et al. [13]
[k.sub.i,2] = 5.060 x [10.sup.3] exp( - 2,650/T),
([m.sup.3]/kg)[s.sup.-1]                           Estenoz et al. [13]
[k.sub.i,3] [approximately equals] [k.sub.p]       Peng [32]
[k.sub.p] = 6.346 x [10.sup.3] exp( - 2,600/T),
([m.sup.3]/kg)[s.sup.-1]                           Peng [32]
[k.sub.tc,o] = 1.205 x [10.sup.7] exp( - 844/T),
([m.sup.3]/kg)[s.sup.-1]                           Hui and Hamielec [19]
[k.sub.tr,m] = 2.218 x [10.sup.4] exp( - 6,377/T),
([m.sup.3]/kg)[s.sup.-1]                           Hui and Hamielec [19]
[k.sub.tr,r] = (1.12 x [10.sup.-3])[k.sub.p]       Manaresi et al. [18]
[k.sub.DCB] = 7.6 x [10.sup.4] exp( - 14,087/T),
([m.sup.3]/kg)[s.sup.-1]                           Rintelen et al. [23]
[k.sub.CT] = 1.266 x [10.sup.5]
exp( - 11,078/T),[s.sup.-1]                        Rintelen et al. [23]
[delta][H.sub.rxn] = -  6.7 x [10.sup.5] J/kg      Husain and Hamielec [34]
[C.sub.p] = 1.884 x [10.sup.3] J/Kg/K              Husain and Hamielec [34]
k = [k.sub.styrene](1 - X) + [k.sub.ps]X, W/m/k    Husain and Hamielec [34]
[k.sub.styrene] = [2.72 - 2.8 x [10.sup.-3]
(T - 423) + 1.6 x [10.sup.-5][(T - 423).sup.2]]
4.187 x [10.sup.2]
[k.sub.ps] = [2.93 - 5.17 x [10.sup.-3]            Husain and Hamielec [34]
(T - 353)]4.187 x [10.sup.-2]                      Husain and Hamielec [34]
Trademark names: Trigonox (Akzo); Lupersol or Luperox (Elf Atochem)
                  Reactor Types, Dimensions, and Volumes
                        Used in Model Simulations.
Reactor No.                   R-1           R-2            R-3
Reactor Types             Boiling CSTR      LFR            LFR
Internal Diameter, ID (m)      3             1              1
Tangent-to-Tangent
  (T/T) Length (m)            4.5            --             --
Elliptical Heads           top/bottom        --             --
L (m)                          --            12             12
Shell Volume ([m.sup.3])       --           9.4            9.4
Tube Volume ([m.sup.3])        --           2.3            2.3
V ([m.sup.3])                  39           7.1            7.1
Ac ([m.sup.2])                 --          390.5          390.5
Ac/V                           --            55             55
Liquid Level (%)               85           100            100
Temperature Control by    latent heat  sensible heat  sensible heat
                            removal       removal        removal
Reactor Operation          isothermal  non-isothermal non-isothermal
Reactor No.                    R-4            R-5
Reactor Types                  LFR            LFR
Internal Diameter, ID (m)       1              1
Tangent-to-Tangent
  (T/T) Length (m)              --             --
Elliptical Heads                --             --
L (m)                           12             12
Shell Volume ([m.sup.3])       9.4            9.4
Tube Volume ([m.sup.3])        2.3            2.3
V ([m.sup.3])                  7.1            7.1
Ac ([m.sup.2])                390.5          390.5
Ac/V                            55             55
Liquid Level (%)               100            100
Temperature Control by    sensible heat  sensible heat
                             removal        removal
Reactor Operation         non-isothermal non-isothermal
The volume of an elliptical head space in a vessel
can be estimated as [pi]/24 [(ID).sup.3]
  Simulated Results of a High-Heat, High-Molecular-Weight Crystal Grade.
               (Feed Rate-10,000 kg/h with 99.98% Styrene).
          A. [W.sub.l,o] = 0 ppm; [W.sub.[1.sub.B],o] = 150 ppm;
                    Pellet production rate = 6,085 kg/h
                                          R-1       R-2         R-3
[T.sub.in]([degrees]C)                    60        110         133
[T.sub.reflux] or [T.sub.w]([degrees]C)   40    130-130-130 132-132-132
[T.sub.out] ([degrees]C])                 110       133         134
m(kg/h)                                  2,635      --          --
[W.sub.[I.sub.B]]/[W.sub.I] (ppm)        48/0       0/0         0/0
[rho](kg/[m.sup.3])                       891       902         915
X (%)                                     33       43.5         49
[tau] or t(h)                            2.95      0.63        0.64
[R.sub.p] (%/h)                           11       16.5         8.5
[M.sub.n] (g/mol)                       202,000   180,000     177,000
[M.sub.w] (g/mol)                       365,000   352,000     346,000
Dirner/Trimer (ppm)                     25/181   207/1,249   285/1,665
[micro](Pa-s)                              2        10          40
                                            R-4         R-5
[T.sub.in]([degrees]C)                      134         138
[T.sub.reflux] Or [T.sub.w]([degrees]C) 135-135-135 140-140-140
[T.sub.out] ([degrees]C])                   138         143
m(kg/h)                                     --          --
[W.sub.[1.sub.B]]/[W.sub.l] (ppm)           0/0         0/0
[rho](kg/[m.sup.3])                         927         942
X (%)                                      54.5         61
[tau] or t(h)                              0.65        0.66
[R.sub.p] (%/h)                             8.5         10
[M.sub.n] (g/mol)                         172,000     165,000
[M.sub.w] (g/mol)                         338,000     328,000
Dirner/Trimer (ppm)                      350/2,030   412/2,403
[micro](Pa-s)                               120         400
                                     Pre-heater 1 Flash 1  Pre-heater 2
[T.sub.in] ([degrees]C)                  143                   222
[T.sub.w] ([degrees]C)                   250                   250
[T.sub.out] ([degrees]C)                 222                   241
t (min.)                                  1                     1
[pi] (torr)/[T.sub.melt]([degrees]C]              450/222
[rho](kg/[m.sup.3])                      916       1,037      1,037
Solids Content (%)                       62.2      97.79      97.80
Water Injection (%)
Residual ST/EB (ppm)                              22,106/0
[M.sub.n] (g/mol)                      146,000               146,000
[M.sub.w] (g/mol)                      321,000               321,000
[M.sub.w]/[M.sub.n]                      2.20                  2.20
HDT/VSP ([degrees]C)                               96/108
TS(MPa)                                              51
MFR(g/10 min.)                                      1.3
Dimer/Trimer (ppm)                    538/2,679             542/5,130
[micro](Pa-s)                             70       4,000      2,000
                                     Flash 2 Flash 2
[T.sub.in] ([degrees]C)
[T.sub.w] ([degrees]C)
[T.sub.out] ([degrees]C)
t (min.)
[pi] (torr)/[T.sub.melt]([degrees]C]  5/241   5/241
[rho](kg/[m.sup.3])                   1,045   1,045
Solids Content (%)                    99.98    1.0
Water Injection (%)                     0       1
Residual ST/EB (ppm)                  179/0   49/0
[M.sub.n] (g/mol)
[M.sub.w] (g/mol)
[M.sub.w]/[M.sub.n]
HDT/VSP ([degrees]C)                 96/108
TS(MPa)                                51
MFR(g/10 min.)                         1.3
Dimer/Trimer (ppm)
[micro](Pa-s)                         2,000
          B. [W.sub.l,o] = 150 ppm; [W.sub.[I.sub.B],o] = 0 ppm;
                    Pellet Production rate = 6,932 kg/h
                                            R-1        R-2         R-3
[T.sub.in]([degrees]C)                      60         128        134.5
[T.sub.reflux] or [T.sub.w] ([degrees]C)    40     130-130-130 132-132-132
[T.sub.out] ([degrees]C)                    128       134.5        136
m(kg/h)                                    1,739       --          --
[W.sub.lB]/[W.sub.l] (ppm)                 0/74       0/46        0/26
[rho](kg/[m.sup.3]                          878        897         921
X (%)                                       33         42          52
[tau] or t(h)                              2.91       0.62        0.64
[R.sub.p] (%/h)                             11        14.5        15.5
[M.sub.n] (g/mol)                         153,000    148,000     144,000
[M.sub.w] (g/mol)                         284,000    276,000     271,000
Dimer/Trimer (ppm)                       538/2,752  547/2,771   544/2,788
[micro](Pa-s)                                1          3          30
                                             R-4         R-5
[T.sub.in]([degrees]C)                       136         139
[T.sub.reflux] or [T.sub.w] ([degrees]C) 135-135-135 140-140-140
[T.sub.out] ([degrees]C)                     139        143.5
m(kg/h)                                      --          --
[W.sub.lB]/[W.sub.l] (ppm)                  0/12         0/3
[rho](kg/[m.sup.3]                           943         964
X (%)                                        61          69
[tau] or t(h)                               0.65        0.67
[R.sub.p] (%/h)                              14          12
[M.sub.n] (g/mol)                          141,000     138,000
[M.sub.w] (g/mol)                          267,000     262,000
Dimer/Trimer (ppm)                        536/2,818   532/2,907
[micro](Pa-s)                                200        1,000
                                     Pre-heater 1  Flash 1  Pre-heater 2
[T.sub.in] ([degrees]C)                 143.5                  221.5
[T.sub.w] ([degrees]C)                   250                    250
[T.sub.out] ([degrees]C)                221.5                   241
t (min.)                                  1                      1
[pi] (torr)/[T.sub.melt]([degrees]C)              200/221.5
[rho](kg/[m.sub.3])                      944        1,042      1,042
Solids Content (%)                       70.4       99.00      99.00
Water Injection (%)
Residual ST/EB (ppm)                               9,975/0
[M.sub.n] (g/mol)                      129,000                129,000
[M.sub.w] (g/mol)                      259,000                259,000
[M.sub.w]/ [M.sub.n]                     2.01                   2.01
HDT/VSP ([degrees]C)                               96/108
TS(MPa)                                              50
MFR(g/10 min.)                                       2.9
Dimer/Trimer (ppm)                    596/3,082              597/3,499
[micro](Pa-s)                            100        2,500      1.000
                                     Flash 2 Flash 2
[T.sub.in] ([degrees]C)
[T.sub.w] ([degrees]C)
[T.sub.out] ([degrees]C)
t (min.)
[II] (torr)/[T.sub.melt]([degrees]C)  5/241   5/241
[rho](kg/[m.sub.3])                   1,045   1,045
Solids Content (%)                    99.98    1.0
Water Injection (%)                     0       2
Residual ST/EB (ppm)                  180/0   14/0
[M.sub.n] (g/mol)
[M.sub.w] (g/mol)
[M.sub.w]/ [M.sub.n]
HDT/VSP ([degrees]C)                 96/108
TS(MPa)                                50
MFR(g/10 min.)                         2.9
Dimer/Trimer (ppm)
[micro](Pa-s)                         1,000
          C, [W.sub.l,o] = 50 ppm; [W.sub.[l.sub.B],o] = 150 ppm;
                    Pellet production rate = 6,899 kg/h
                                           R-1       R-2         R-3
[T.sub.in] ([degrees]C)                    75        110         134
[T.sub.reflux] or [T.sub.w] ([degrees]C)   40    130-130-130 132-132-132
[T.sub.out] ([degrees]C)                   110       134         136
m(kg/h)                                   3,266      --          --
[W.sub.lB]/[W.sub.l] (ppm)                48/42     0/27        0/16
[rho](kg/[m.sup.3])                        892       907         926
X (%)                                      33        45          53
[tau] or t(h)                             2.96      0.63        0.64
[R.sub.p] (%/h)                            11        19          12
[M.sub.n] (g/mol)                        200,000   173,000     166,000
[M.sub.w] (g/mol)                        361,000   340,000     327,000
Dimer/Trimer (ppm)                       25/183   199/1,198   257/1,520
[micro](Pa-s)                               2        20          100
                                             R-4         R-5
[T.sub.in] ([degrees]C)                      136        138.5
[T.sub.reflux] or [T.sub.w] ([degrees]C) 135-135-135 140-140-140
[T.sub.out] ([degrees]C)                    138.5        143
m(kg/h)                                      --          --
[W.sub.lB]/[W.sub.l] (ppm)                   0/7         0/2
[rho](kg/[m.sup.3])                          945         963
X (%)                                        61          69
[tau] or t(h)                               0.66        0.67
[R.sub.p] (%/h)                              12          12
[M.sub.n] (g/mol)                          160,000     154,000
[M.sub.w] (g/mol)                          317,000     308,000
Dimer/Trimer (ppm)                        295/1,772   326/2,026
[micro](Pa-s)                                450        1,600
                                     Pre-heater 1 Flash 1 Pre-heater 2
[T.sub.in] ([degrees]C)                  143                  221
[T.sub.w] ([degrees]C)                   250                  250
[T.sub.out] ([degrees]C)                 221                  241
t (min.)                                  1                    1
[pi] (torr)/[T.sub.melt]([degrees]C)              20/221
[rho](kg/[m.sup.3])                      943       1,045     1,045
Solids Content (%)                       70.1      99.90     99.90
Water Injection (%)
Residual ST/EB (ppm)                              1,000/0
[M.sub.n] (g/mol)                      142,000              142,000
[M.sub.w] (g/mol)                      303,000              303,000
[M.sub.w]/[M.sub.n]                      2.13                 2.13
HDT/VSP ([degrees]C)                              96/108
TS(MPa)                                             50
MFR(g/10 min.)                                      1.6
Dimer/Trimer (ppm)                    399/2,229            399/2,234
[micro](Pa-s)                            200       4,000     2,000
                                     Flash 2 Flash 2
[T.sub.in] ([degrees]C)
[T.sub.w] ([degrees]C)
[T.sub.out] ([degrees]C)
t (min.)
[pi] (torr)/[T.sub.melt]([degrees]C)  5/241   5/241
[rho](kg/[m.sup.3])                   1,045   1,045
Solids Content (%)                    99.98    1.0
Water Injection (%)                     0       3
Residual ST/EB (ppm)                  180/0    1/0
[M.sub.n] (g/mol)
[M.sub.w] (g/mol)
[M.sub.w]/[M.sub.n]
HDT/VSP ([degrees]C)                 96/108
TS(MPa)                                50
MFR(g/10 min.)                         1.6
Dimer/Trimer (ppm)
[micro](Pa-s)                         2,000
             Simulated Results of a Medium-Flow Crystal Grade.
    (Feed Rate-10,000 kg/h with 97.25% Styrene and 2.75% Mineral Oil).
           [w.sub.l,o] = 50 ppm; [w.sub.[I.sub.B],o] = 150 ppm;
                    Pellet production rate = 8,047 kg/h
                                           R-1       R-2         R-3
[T.sub.in] ([degrees]C)                    75        110         143
[T.sub.reflux] or [T.sub.w] ([degrees]C)   40    138-138-138 144-144-144
[T.sub.out] ([degrees]C)                   110       143         149
m(kg/h)                                   3,032      --          --
[w.sub.lB]/[w.sub.l](ppm)                 48/43     0/13         0/2
[rho](kg/[m.sup.3])                        890       904         931
X (%)                                      33        47          58
[tau] or t(h)                             2.95      0.63        0.64
[R.sub.p] (%/h)                            11        22          17
[M.sub.n] (g/mol)                        199,000   161,000     146,000
[M.sub.w] (g/mol)                        359,000   324,000     300,000
Dimer/Trimer (ppm)                       25/187   291/1,567   440/2,272
[micro] [Pa-s]                              2        10          100
                                             R-4         R-5
[T.sub.in] ([degrees]C)                      149         162
[T.sub.reflux] or [T.sub.w] ([degrees]C) 157-157-157 163-163-163
[T.sub.out] ([degrees]C)                     162         167
m(kg/h)                                      --          --
[w.sub.lB]/[w.sub.l](ppm)                    0/0         0/0
[rho](kg/[m.sup.3])                          961         987
X (%)                                        70          80
[tau] or t(h)                               0.66        0.68
[R.sub.p] (%/h)                              18          15
[M.sub.n] (g/mol)                          128,000     117,000
[M.sub.w] (g/mol)                          274,000     257,000
Dimer/Trimer (ppm)                        628/3,248   731/4,056
[micro] [Pa-s]                               700        3,000
                                    Pre-heater 1 Flash 1 Pre-heater 2 Flash 2
[T.sub.in] ([degrees]C)                 167                  227
[T.sub.w] ([degrees]C)                  250                  250
[T.sub.out] ([degrees]C)                227                  243
t (min.)                                 1                    1
[pi](torr)/[T.sub.melt]([degrees]C)              20/227                5/243
[rho](kg/[m.sup.3])                     978       1,045     1,045      1,045
Solids Content (%)                      80.6      99.91     99.91      99.98
Residual ST/EB (ppm)                              905/0                174/0
[M.sub.n] (g/mol)                     112,000              112,000
[M.sub.w] (g/mol)                     255,000              255,000
[M.sub.w]/ [M.sub.n]                    2.28                 2.28
HDT/VSP ([degrees]C)                             89/100               89/100
TS(MPa)                                            43                   43
MFR(g/10 min.)                                     6.5                  6.5
Dimer/Trimer (ppm)                   775/4,238            775/4,241
[micro](Pa-s)                           300       2,000      850        850
                                    Flash 2
[T.sub.in] ([degrees]C)
[T.sub.w] ([degrees]C)
[T.sub.out] ([degrees]C)
t (min.)
[pi](torr)/[T.sub.melt]([degrees]C)  8/243
[rho](kg/[m.sup.3])                  1,045
Solids Content (%)                   99.97
Residual ST/EB (ppm)                 278/0
[M.sub.n] (g/mol)
[M.sub.w] (g/mol)
[M.sub.w]/ [M.sub.n]
HDT/VSP ([degrees]C)
TS(MPa)
MFR(g/10 min.)
Dimer/Trimer (ppm)
[micro](Pa-s)
              Simulated Results of a High-Flow Crystal Grade.
     (Feed Rate-10,000 kg/h with 96.2% Styrene and 3.8% Mineral Oil).
            [W.sub.l,o] = 50 ppm; [W.sub.[I.sub.B],o]= 150 ppm;
                    Pellet production rate = 8,559 kg/h
                                           R-1       R-2         R-3
[T.sub.in] ([degrees]C)                    75        110         149
[T.sub.reflux] or [T.sub.w] ([degrees]C)   40    143-143-143 146-146-146
[T.sub.out] ([degrees]C)                   110       149         150
m(kg/h)                                   2,945      --          --
[W.sub.lB]/[W.sub.l] (ppm)                48/43      0/5         0/0
[rho](kg/[m.sup.3])                        890       905         932
X (%)                                      33        48          59
[tau] or t(h)                             2.95      0.63        0.64
[R.sub.p] (%/h)                            11        24          17
[M.sub.n] (g/mol)                        199,000   152,000     139,000
[M.sub.w] (g/mol)                        358,000   313,000     292,000
Dimer/Trimer (ppm)                       25/188   382/1,885   540/2,657
[micro](Pa-s)                               2        20          100
                                             R-4         R-5
[T.sub.in] ([degrees]C)                      150         171
[T.sub.reflux] or [T.sub.w] ([degrees]C) 165-165-165 175-175-175
[T.sub.out] ([degrees]C)                     171         179
m(kg/h)                                      --          --
[W.sub.lB]/[W.sub.l] (ppm)                   0/0         0/0
[rho](kg/[m.sup.3])                          970        1,000
X (%)                                        74          85
[tau] or t(h)                               0.66        0.69
[R.sub.p] (%/h)                              23          16
[M.sub.n] (g/mol)                          114,000     101,000
[M.sub.w] (g/mol)                          256,000     236,000
Dimer/Trimer (ppm)                        835/4,095   989/5,382
[micro](Pa-s)                                800        3,000
                                      Pre-heater 1 Flash 1 Pre-heater 2
[T.sub.in] ([degrees]C)                   179                  230
[T.sub.w] ([degrees]C)                    250                  250
[T.sub.out] ([degrees]C)                  230                  244
t(min.)                                    1                    1
[pi] (torr)/[T.sub.melt] ([degrees]C)              20/230
[rho](kg/[m.sup.3])                       994       1,045     1,045
Solids Content (%)                        85.5      99.91     99.98
Residual ST/EB (ppm)                                860/0
[M.sub.n] (g/mol)                        98,000               98,000
[M.sub.w] (g/mol)                       235,000              235,000
[M.sub.w]/[M.sub.n]                       2.40                 2.40
HDT/VSP ([degrees]C)                                86/96
TS(MPa)                                              39
MFR(g/10 min.)                                      12.2
Dimer/Trimer (ppm)                    1,020/5,551          1,020/5,554
[micro](Pa-s)                             400       1,000      600
                                      Flash 2 Flash 2
[T.sub.in] ([degrees]C)
[T.sub.w] ([degrees]C)
[T.sub.out] ([degrees]C)
t(min.)
[pi] (torr)/[T.sub.melt] ([degrees]C)  5/244  10/244
[rho](kg/[m.sup.3])                    1,045   1,045
Solids Content (%)                     99.98   99.96
Residual ST/EB (ppm)                   171/0   342/0
[M.sub.n] (g/mol)
[M.sub.w] (g/mol)
[M.sub.w]/[M.sub.n]
HDT/VSP ([degrees]C)                   86/96
TS(MPa)                                 39
MFR(g/10 min.)                         12.2
Dimer/Trimer (ppm)
[micro](Pa-s)                           600
         Simulated Results of a Heat-Resistant, High-Impact Grade.
      (Feed Rate-10,000 kg/h with 90% Styrene, 7% Rubber, and 3% EB).
               A. [W.sub.I,o] = 0 ppm; [W.sub.IB,o] = 150 ppm;
                     Pellet production rate = 7,334 kg/h
                                             R-1       R-2         R-3
  [T.sub.in]([degrees]C)                     75        110         149
  [T.sub.reflux] or [T.sub.w] ([degrees]C)   40    145-145-145 147-147-147
  [T.sub.out] ([degrees]C)                   110       149         151
  m(kg/h)                                   2,314      --          --
  [W.sub.IB]/[W.sub.I] (ppm)                48/0       0/0         0/0
  [rho](kg/[m.sup.3])                       883       887         913
  X (%)                                      30        42          52
  [tau] or t(h)                             2.93      0.63        0.63
  [R.sub.p] (%/h)                            10        19          16
  [M.sub.n,f] (g/mol)                      160,000   131,000     119,000
  [M.sub.w,f] (g/mol)                      295,000   266,000     246,000
  [M.sub.n,g] (g/mol)                      188,000   151,000     140,000
  [M.sub.w,g] (g/mol)                      314,000   288,000     273,000
  [M.sub.n] (g/mol)                        163,000   134,000     122,000
  [M.sub.w] (g/mol)                        298,000   271,000     251,000
  [G.sub.d] (%)                              226       108         128
Dimer/Trimer (ppm)                         31/237   458/2,274   681/3,274
  [micro](Pa-s)                               1         2          20
                                               R-4         R-5
  [T.sub.in]([degrees]C)                       151         161
  [T.sub.reflux] or [T.sub.w] ([degrees]C) 156-156-156 159-159-159
  [T.sub.out] ([degrees]C)                     161         163
  m(kg/h)                                      --          --
  [W.sub.IB]/[W.sub.I] (ppm)                   0/0         0/0
  [rho](kg/[m.sup.3])                         943         971
  X (%)                                        64          74
  [tau] or t(h)                               0.65        0.67
  [R.sub.p] (%/h)                             18.5         15
  [M.sub.n,f] (g/mol)                        105,000     97,000
  [M.sub.w,f] (g/mol)                        224,000     210,000
  [M.sub.n,g] (g/mol)                        125,000     114,000
  [M.sub.w,g] (g/mol)                        254,000     239,000
  [M.sub.n] (g/mol)                          108,000     100,000
  [M.sub.w] (g/mol)                          230,000     216,000
  [G.sub.d] (%)                                153         177
Dimer/Trimer (ppm)                          880/4,262   962/4,945
  [micro](Pa-s)                                120         600
                                    Pre-heater 1 Flash 1 Pre-heater 2 Flash 2
[T.sub.in] ([degrees]C)                 163                  215
[T.sub.w] ([degrees]C)                  235                  240
[T.sub.out]([degrees]C)                215                  232
t (min.)                                 1                    1
[pi](torr)/[T.sub.melt]([degrees]C)              20/215                5/232
[rho](kg/[m.sup.3])                     959       1,045     1,045      1,045
Solids Content (%)                      74.4      99.89     99.89      99.98
Residual ST/EB (ppm)                             992/105              188/16
[M.sub.n] (g/mol)                      97,000               97,000
[M.sub.w] (g/mol)                     214,000              214,000
[M.sub.w]/[M.sub.n]                     2.21                 2.21
[G.sub.d](%)                            178                  178
HDT/VSP ([degrees]C)                             96/108               96/108
Dimer/Trimer (ppm)                   998/5,082            998/5,085
[micro](Pa-s)                           120       2,000      800        800
                                    Flash 2
[T.sub.in] ([degrees]C)
[T.sub.w] ([degrees]C)
[T.sub.out] ([degrees]C)
t (min.)
[pi](torr)/[T.sub.melt]([degrees]C) 20/232
[rho](kg/[m.sup.3])                  1,045
Solids Content (%)                   99.92
Residual ST/EB (ppm)                752/66
[M.sub.n] (g/mol)
[M.sub.w] (g/mol)
[M.sub.w]/[M.sub.n]
[G.sub.d](%)
HDT/VSP ([degrees]C)
Dimer/Trimer (ppm)
[micro](Pa-s)
              B. [w.sub.I,o] = 150 ppm: [W.sub.IB,o] = 0 ppm;
                    Pellet production rate = 7,484 kg/h
                                              R-1        R-2         R-3
  [T.sub.in] ([degrees]C)                     75         128         151
  [T.sub.reflux] or [T.sub.w] ([degrees]C)    40     145-145-145 147-147-147
  [T.sub.out] ([degrees]C)                    128        151         151
  m(kg/h)                                    1,485       --          --
  [W.sub.lB]/[W.sub.l] (ppm)                 0/73        0/6         0/0
  [rho](kg/[m.sup.3])                         870        894         923
  X (%)                                       30         45          55
  [tau] or t(h)                              2.90       0.62        0.63
  [R.sub.p] (%/h)                             10         24          16
  [M.sub.n,f] (g/mol)                       127,000    108,000     103,000
  [M.sub.w,f] (g/mol)                       240,000    212,000     204,000
  [M.sub.n,g] (g/mol)                       142,000    125,000     118,000
  [M.sub.w,g] (g/mol)                       256,000    232,000     224,000
  [M.sub.n] (g/mol)                         129,000    110,000     105,000
  [M.sub.w] (g/mol)                         243,000    216,000     207,000
  [G.sub.d] (%)                               70         99          121
Dimer/Trimer (ppm)                         580/3,174  768/3,708   877/4,244
  [micro](Pa-s)                                1          2          20
                                               R-4         R-5
  [T.sub.in]([degrees]C)                       151         161
  [T.sub.reflux] or [T.sub.w] ([degrees]C) 156-156-156 159-159-1 59
  [T.sub.out] ([degrees]C)                     161         162
  m(kg/h)                                      --           --
  [W.sub.lB]/[W.sub.l] (ppm)                   0/0         0/0
  [rho](kg/[m.sup.3])                          950         975
  X (%)                                        66           75
  [tau] or t(h)                               0.65         0.67
  [R.sub.p] (%/h)                              17          13.5
  [M.sub.n,f] (g/mol)                        96,000       92,000
  [M.sub.w,f] (g/mol)                        194,000     187,000
  [M.sub.n,g] (g/mol)                        110,000     102,000
  [M.sub.w,g] (g/mol)                        213,000     203,000
  [M.sub.n] (g/mol)                          98,000       93,000
  [M.sub.w] (g/mol)                          197,000     189,000
  [G.sub.d] (%)                                145         169
Dimer/Trimer (ppm)                          988/4,899  1,034/5,412
  [micro](Pa-s)                                120         500
                                    Pre-heater 1 Flash 1 Pre-heater 2 Flash 2
[T.sub.in] ([degrees]C)                 162                  215
[T.sub.w] ([degrees]C)                  235                  240
[T.sub.out] ([degrees]C)                215                  232
t (min.)                                 1                    1
[pi](torr)/[T.sub.melt]([degrees]C)              20/215                5/232
[rho](kg/[m.sup.3])                     965       1,045     1,045      1,045
Solids Content (%)                       76       99.89     99.89      99.98
Residual ST/EB (ppm)                             989/112              187/17
[M.sub.n] (g/mol)                      91,000               91,000
[M.sub.w] (g/mol)                     188,000              188,000
[M.sub.w]/[M.sub.n]                     2.06                 2.06
[G.sub.d](%)                            170                  1.70
HDT/VSP ([degrees]C)                             96/108               96/108
Dimer/Trimer (ppm)                  1,062/5,530          1,062/5,533
[micro](Pa-s)                           100       1,200      500        500
                                    Flash 2
[T.sub.in] ([degrees]C)
[T.sub.w] ([degrees]C)
[T.sub.out] ([degrees]C)
t (min.)
[pi](torr)/[T.sub.melt]([degrees]C) 20/232
[rho](kg/[m.sup.3])                  1,045
Solids Content (%)                   99.92
Residual ST/EB (ppm)                748/70
[M.sub.n] (g/mol)
[M.sub.w] (g/mol)
[M.sub.w]/[M.sub.n]
[G.sub.d](%)
HDT/VSP ([degrees]C)
Dimer/Trimer (ppm)
[micro](Pa-s)
          C. [W.sub.I,o] = 50 ppm; [W.sub.[I.sub.B],o]] = 150 ppm;
                    Pellet production rate = 7,492 kg/h
                                             R-1       R-2         R-3
  [T.sub.in] ([degrees]C)                    75        110         150
  [T.sub.reflux] or [T.sub.w] ([degrees]C)   40    145-145-145 147-147-147
  [T.sub.out] ([degrees]C)                   110       150         151
  m(kg/h)                                   2,396      --          --
  [W.sub.lB]/[W.sub.l] (ppm)                48/43      0/4         0/0
  [rho](kg/[m.sup.3])                        885       896         923
  X (%)                                      30        45          55
  [tau] or t(h)                             2.93      0.63        0.63
  [R.sub.p] (%/h)                            10        24          16
  [M.sub.n,f] (g/mol)                      158,000   121,000     112,000
  [M.sub.w,f] (g/mol)                      291,000   251,000     234,000
  [M.sub.n,g] (g/mol)                      185,000   142,000     133,000
  [M.sub.w,g] (g/mol)                      310,000   276,000     262,000
  [M.sub.n] (g/mol)                        161,000   125,000     116,000
  [M.sub.w] (g/mol)                        294,000   256,000     240,000
  [G.sub.d] (%)                              227       117         138
Dimer/Trimer (ppm)                         30/236   430/2,142   611/3,025
  [micro](Pa-s)                               1         4          30
                                               R-4         R-5
  [T.sub.in] ([degrees]C)                      151        160.5
  [T.sub.reflux] or [T.sub.w] ([degrees]C) 156-156-156 159-159-159
  [T.sub.out] ([degrees])                     160.5        162
  m(kg/h)                                      --          --
  [W.sub.lB]/[W.sub.l] (ppm)                   0/0         0/0
 [rho](kg/[m.sup.3])                           951         976
  X (%)                                        66          75
  [tau] or t(h)                               0.65        0.67
  [R.sub.p] (%/h)                              17         13.5
  [M.sub.n,f] (g/mol)                        102,000     96,000
  [M.sub.w,f] (g/mol)                        218,000     207,000
  [M.sub.n,g] (g/mol)                        121,000     111,000
  [M.sub.w,g] (g/mol)                        246,000     233,000
  [M.sub.n] (g/mol)                          106,000     98,000
  [M.sub.w] (g/mol)                          223,000     212,000
  [G.sub.d] (%)                                163         187
Dimer/Trimer (ppm)                          774/3,932   850/4,593
  [micro](Pa-s)                                200         800
                                    Pre-heater 1 Flash 1 Pre-heater 2 Flash 2
[T.sub.in] ([degrees]C)                 162                  215
[T.sub.w] ([degrees]C)                  235                  240
[T.sub.out] ([degrees]C)                215                  232
t (min.)                                 1                    1
[pi](torr)/[T.sub.melt]([degrees]C)              20/215                5/232
[rho](kg/[m.sup.3])                     965       1,045     1,045      1,045
Solids Content (%)                       76       99.89     99.89      99.98
Residual ST/EB (ppm)                             989/113              187/18
[M.sub.n] (g/mol)                      96,000               96,000
[M.sub.w] (g/mol)                     210,000              210,000
[M.sub.w]/[M.sub.n]                     2.19                 2.19
[G.sub.d](%)                            187                  187
HDT/VSP ([degrees]C)                             96/108               96/108
Dimer/Trimer (ppm)                   881/4,722            881/4,725
[micro](Pa-s)                           800       2,000      800        800
                                    Flash 2
[T.sub.in] ([degrees]C)
[T.sub.w] ([degrees]C)
[T.sub.out] ([degrees]C)
t (min.)
[pi](torr)/[T.sub.melt]([degrees]C) 20/232
[rho](kg/[m.sup.3])                  1,045
Solids Content (%)                   99.92
Residual ST/EB (ppm)                748/70
[M.sub.n] (g/mol)
[M.sub.w] (g/mol)
[M.sub.w]/[M.sub.n]
[G.sub.d](%)
HDT/VSP ([degrees]C)
Dimer/Trimer (ppm)
[micro](Pa-s)