modeling the dynamics of the xylene soluble fraction (xs) in a bulk propylene polymerization process

Full Paper

Modeling the Dynamics of the Xylene SolubleFraction (XS) in a Bulk PropylenePolymerization Process

Fabricio Machado, Jose Carlos Pinto*

A model is built to describe the dynamic trajectories of the xylene soluble fraction (XS) in anindustrial bulk propylene polymerization process. Emphasis is given to the couplingbetween the XS dynamics and the reactor liquid bleed policy. It is shown that cocatalystrecirculation can affect the dynamics of the cocatalyst/donor ratio and consequently thedynamics of XS during polymerization. Simulationresults indicate that the effect of the reactor liquid bleedoperation and of the cocatalyst/donor ratio upon the XStrajectories can be minimized if PI controllers aredesigned to control the propane concentration and toincrease the speed of the cocatalyst/donor transitions.Finally, it is shown that the model is able to reproducethe dynamic XS profile obtained during a large XStransition at plant site.

Introduction

One of the most important quality properties of the final

polypropylene (PP) product is the xylene soluble fraction

(XS). XS analyses are generally used to provide a rough

evaluation of the atactic fraction, rubbery content, and

polymer material with low molecular weight in the final

polymer resin.[1–9] According to the usual industrial

practice, in order to evaluate the XS, 2 g of polymer are

initially dissolved in 100mL of boiling xylene and then left

at boiling conditions for around 15 min. Afterwards, the

J. C. PintoPrograma de Engenharia Quımica/COPPE, Universidade Federaldo Rio de Janeiro, Cidade Universitaria, CP 68502, Rio de Janeiro21941-972, RJ, BrazilE-mail: [email protected]. MachadoInstituto de Quımica, Universidade de Brasılia, CampusUniversitario Darcy Ribeiro, CP 04478, Brasılia 70910-900, DF,Brazil

Macromol. React. Eng. 2011, 5, 129–139

� 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlin

solution is cooled down to ambient temperature, left at rest

for 30 min, filtrated, and dried under vacuum. Finally, the

solid residual of the liquid phase (XS) and the filtrated solid

powder (insoluble fraction) are weighed and expressed as

fractions of the original polymer sample. Obtained XS

values are then compared to standard operation values and

used to specify the quality of the final product and of the

operation procedures.[1–3]

Xylene soluble fraction (XS) analyses are performed at

plant site to characterize the polymer quality because they

are much simpler and much less expensive than gel

permeation chromatography (GPC) and nuclear magnetic

resonance (NMR) analyses, which can be used for detailed

characterization of molecular weight distributions, degree

of isotacticity, and composition distributions of the

polymer product.[1–3] Besides, XS analyses can be correlated

strongly with the atactic and oligomers content of PP

homopolymer powders and with the rubber content of PP/

PE (polyethylene) copolymers.[1–3] Finally, XS values can

also be correlated stronglywith thefinal end-use properties

of the polymer material, including the rigidity and impact

elibrary.com DOI: 10.1002/mren.201000038 129

Figure 1. Dynamic XS responses to modifications of the COCAT/DONOR ratio, as observed at plant site (full lines emphasize theapparent existence of overshoots). (Due to proprietary reasons,a.u. represents normalized arbitrary units.).

Figure 2. Schematic representation of the process flowsheet.

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F. Machado, J. C. Pinto

strength of PP products.[10] Therefore, the very simple XS

quality test can provide rich amount of information about

the polymer structure and final product performance.

The widespread use of XS analyses to characterize the

final qualityof PP resinsmakes theproperunderstandingof

XS dynamic responses to changes of the operation

conditions very important at plant site. Therefore, under-

standingofXSdynamics canbeof fundamental importance

for development of advanced control schemes and auto-

mation in industrial sites, whenever tight control of XS

values is needed. Surprisingly, though, no information

regardinghowXSvalues respond tomodificationof process

operation conditions can be found in the open literature.

It seems thatMattos Neto and Pinto,[11] Oliveira et al.[12],

and Prata et al.[13–15] were the only ones that attempted to

represent how XS values respond to changes of operation

conditions in real PP plants. In the first case, Mattos Neto

and Pinto developed an empirical equation to correlate the

final XS value with the catalyst and cocatalyst concentra-

tions in slurry andbulkpolymerizationprocesses operating

at steady-state conditions. As a consequence, their

approach cannot be used for independent analysis of the

XS dynamics during transient operation conditions. The

correlation developed by Mattos Neto and Pinto was used

afterwards by Oliveira et al. to simulate the process

behavior in a broader range of steady-state conditions.

Finally, Prata et al. developed a dynamicmodel to represent

variations of XS values but did not perform an independent

study of the XS dynamic responses to changes of operation

conditions. As amatter of fact, XS valueswereusedbyPrata

etal. toallowforparameterestimationandreconciliationof

process data in real time applications.

In the universe of bulk PP technology, it is generically

believed that it is difficult to model the XS dynamics

because of the sluggishness and strong nonlinear behavior

of XS dynamic trajectories, as illustrated in Figure 1. As a

consequence, dynamic trajectories of XS during polymer

grade transitions must be carefully considered in order to

keep thefinal polymer propertieswithin acceptable quality

limits.[16–20] This is particularly true in the liquid pool

propylene polymerization process (LIPP) technology (LIPP-

SHAC Shell Technology), where polymerization is per-

formed in bulk in a single continuous stirred tank reactor

(CSTR) (the PP powder is kept suspended in liquid

propylene), using a high-activity third generation Ziegler-

Natta catalyst (TiCl4/MgCl2 þ PEEB þ TEAL), where

triethylaluminum (TEAL) is a cocatalyst and p-ethoxy-

ethyl-benzoate (PEEB) is an electron donor. The LIPP process

was described in detail by Mattos Neto and Pinto[11] and

is represented in Figure 2.

It is important to observe that in the LIPPprocess theheat

of polymerization is partially removed by condensation of

boiling propylene and partially removed by cooling of a

recycled liquid propylene stream. As variations of liquid

Macromol. React. Eng.

� 2011 WILEY-VCH Verlag Gmb

propane concentration can prejudice polymer productivity

andmodify the quality of the final resin, the recycled liquid

propylene stream is partially bled. Liquid bleed flow rates

must bemanipulated in order keep the propane concentra-

2011, 5, 129–139

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Modeling the Dynamics of the Xylene Soluble Fraction . . .

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tion in the liquid pool (the liquid propylene polymerization

medium) around 10wt.-%. Due to recycling of the liquid

propylene, the characteristic process time of recycled

material can be as large as 48h, although the characteristic

reaction time of this process is around 1h, as polymer is not

recycled through the liquid propylene stream.

In LIPP processes, special attention must be given to the

liquid bleed operation and to XS dynamic responses.

Depending on the liquid bleed operation policy, it can be

very difficult to specify the real steady state operation

conditions, given the large characteristic process times and

the fact that the liquid bleed stream is frequently operated

discontinuously. For this reason, the concentrations of all

chemical species that recirculate through the recycle

stream are allowed to fluctuate during actual plant

operation. As liquid bleed flow rate cycles are usually very

long, concentrations in the liquid pool are allowed to drift

for long periods of time and dynamic trajectories appear to

be sluggish and very complex, as illustrated in Figure 1. As

the XS dynamic behavior seems to present similar dynamic

characteristics, it iswonderedwhether the liquidbleedflow

rate policy might exert any significant effect upon XS

dynamic responses to process operation changes. For this

reason, thedynamicsof the liquidbleedoperationshouldbe

characterized properly.

The main objective of the present work is to study how

XS values respond to changes of the operation conditions

in the LIPP process using a simple mathematical model

to represent the process operation. The model assumes

that the XS fraction can be represented as a pseudo

chemical species and that part of the cocatalyst can be

recirculated through the recycle liquid propylene stream.

As a consequence, the liquid bleed policy can cause drifts

of the XS values during actual process operation and affect

the quality of the final polymer product. This work also

presents real industrial operation data, which seemingly

indicate that the liquid bleed flow rate policy can be

important indeed for the proper modeling of the XS

dynamics.

Process Modeling

Describing Xylene Soluble Fraction (XS) as a Lump

As stated previously, XS analyses are used to provide

a rough evaluation of the atactic fraction, of rubbery

content and of polymer material with low molecular

weight in the final polymer resin.[1–9] Particularly, Matos

et al.[1–3] showed that the XS fraction is constituted by

a complex mixture of polymer chains with different

molecular structures (different isotactic indices and

ethylene contents, in the case of ethylene/propylene

copolymers) and sizes (broad molecular weight distribu-

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tions, although shifted to smaller sizes when compared

to the overall resin). In spite of that, the XS is used to

characterize the quality of the final polymer at plant site

as a lump and not in terms of the individual molecular

characteristics of its constituents. Matos et al.[1–3] also

showed that the obtained XS values depend essentially

on the analyzed polymerization conditions and not on

the polymer productivity, as supported by extensive

plant experience. This can certainly be supported by

sound kinetic reasoning, if one assumes that the XS

material is produced in catalyst sites through simple

mechanistic steps (for instance, when the probability to

produce atactic defects and to transfer chain activity

to chain transfer agents remain constant with time)

and when the relative polymerization activities of the

distinct catalyst sites do not change significantly with

time. Therefore, there are incentives to describe the

XS fraction as a pseudo-byproduct (lump or pseudo-

component) of the polymerization mechanism, as

extensively used in the petroleum literature to describe

oil fractions (which actually are complex mixtures of

distinct substances).

It is very important to emphasize thatXS values reported

throughout this paper were obtained as described pre-

viously, using samples of dry PP powder withdrawn from

the line that connects the solid–gas separator and themain

powder storage silos, as illustrated in Figure 2.

Modeling Cocatalyst (COCAT) Recirculation

Although liquid bleed flow rates must be manipulated to

control the propane concentration in the liquid pool,

significant changes of the liquid bleed flow rates may

occur during actual operation practice, independently from

the values of measured propane concentrations in the

liquid pool. As already said, it can be very difficult to specify

the real steady state operation conditions at the production

site, given the large characteristic process timesand the fact

that the liquid bleed stream is frequently operated

discontinuously. Inaddition, if oneassumes that significant

amounts of the cocatalyst can be recirculated through the

recycle liquid propylene stream, then important interac-

tions between the dynamics of the liquid bleed operation

and the dynamics of XS responses can occur, as the ratio

between the cocatalyst and the electron donor (DONOR)

concentrations control the XS at steady-state condition,[11]

affecting the final polymer quality. Recirculation of

cocatalyst (usually TEAL) through the recycle stream is

indeedveryplausible, given theveryhighvolatility of these

organometallic compounds at usual operation conditions.

Besides, when samples of the recirculating liquid stream

are withdrawn at plant site, one can always observe the

characteristic development of fumes, due to the contact of

the organometallic compound with the atmospheric

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oxygenandhumidity. (Itmustbeobserved that samplingof

the pressurized recirculating liquid stream is not possible

on a regular basis, given the high risk of the operation.) On

the other hand, recirculation of electron donors is not

plausible, as these compounds (such as PEEB) are solid at

usual operation conditions.

Based on the previous remarks and assuming that the

perfect mixing hypothesis is valid, mass balance equations

can be written as:

Propylene Mass Balance

d

dPe

dt¼ me�Rpol�

Pe

Peþ Pa

� �mo (1)

Propane Mass Balance

dPa

dt¼ wame�

Pa

Peþ Pa

� �mo (2)

Polymer Mass Balance

dPol

dt¼ Rpol�mpol (3)

DONOR Mass Balance

dCOC

dDONOR

dt¼ mDONOR�

DONOR

Pol

� �mPol (4)

d
COCAT Mass Balance
COCAT

dt¼mCOCAT�

COCATPolPol

� �mPol�

COCATRecPeþ Pa

� �mo

(5)

dCO

d

where Pe is themass of propylene inside the reactor vessel;

Pa is the mass of propane in the reactor vessel; Pol is the

mass of PP inside the reactor vessel; DONOR is the mass of

electron donor inside the reactor vessel; COCAT is themass

of cocatalyst inside the reactor vessel;me is the feed rate of

fresh propylene; RPol is the rate of polymerization;mo is the

liquid bleed flow rate; wa is the weight fraction of propane

in the feed stream; mPol is the mass rate of polymer

removal;mDONOR is the feed rate of electron donor;mCOCAT

is the feed rate of cocatalyst; and COCATPol and COCATRecare the amounts of cocatalyst in the solid polymer powder

and in the recycle stream respectively. In all cases the

reactor contents are expressed in kg, while flow rates are

given in kg �h�1.

Assuming that polymer accumulation inside the reactor

vessel does not occur (due to proper control of the slurry

concentration) and that the solid concentration is constant

and equal to 0.40 (usually named the slurry concentration

and given as the ratio between the polymer mass and the



overall slurry mass), it is possible to write:

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RPol ¼ mPol (6)

Pol

Polþ Peþ Pa¼ 0:40 ! Pol ¼ 2

3Peþ Pað Þ (7)

These two assumptions are very good at normal

operation conditions, although Equation (7) can be easily

relaxed to accommodate for other solids concentration

values. Assuming additionally that the reactor level is

controlled properly as usual at plant site, then

1þ wað Þme ¼ mo þmPol (8)

Inserting Equation (6–8) into Equation (1–5)

dPe

dt¼ 1

1þ wa

� �mPol þmoð Þ�mpol�

Pe

Peþ Pa

� �mo

(9)

dPa

dt¼ wa

1þ wa

� �mPol þmoð Þ� Pa

Peþ Pa

� �mo (10)

dDONOR

dt¼ mDONOR�1:5

DONOR

Peþ Pa

� �mPol (11)

AT

t¼ mCOCAT�1:5

COCATPolPeþ Pa

� �mPol�

COCATRecPeþ Pa

� �mo

(12)

Finally, assuming that a certain partition coefficient (K)

can be used to describe partitioning of COCAT between the

polymer and the recycle streams, it is possible to write;

COCATRecPeþ Pa

¼ KCOCATPol

Pol! COCATRec

¼ 1:5K COCATPol (13)

as

COCATRec þ COCATPol ¼ COCAT

!COCATRec ¼

1:5KCOCAT

1þ 1:5K

COCATPol ¼COCAT

1þ 1:5K

8><>: (14)

Inserting Equation (14) into Equation (12)

CAT

t¼ mCOCAT� 1�að Þ COCAT

Pol

� �mPol�a

COCAT

Peþ Pa

� �mo

(15)

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1


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where a is a recirculation factor, defined as

0.6

0.8

(a.u

.)

www.M

a ¼ 1:5K

1þ 1:5K

� �(16)

0

0.2

0.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

XS
Modeling Xylene Soluble Fraction (XS) Dynamics
In order to investigate the main characteristics of the XS

dynamic responses to changes of the COCAT/DONOR feed

ratio, the XS balance is then written as:
COCAT/DONOR Feed Ratio (a.u.)
Figure 3. Steady-state XS responses to modifications of theCOCAT/DONOR ratio. (Due to proprietary reasons, a.u. standsfor a normalized arbitrary units, which measures the difference

d PolXSð Þdt

¼ �mPolXSþ RPolXSi (17)

between themeasured XS and the XS obtained when the COCAT/DONOR ratio is equal to zero.).

where XSi is the instantaneous XS value of the polymer

being produced inside the reactor vessel. Equation (17)

assumes that the XS fraction can be described as a pseudo

chemical species and can also be written as:

Pold XSð Þdt

þ XSd Polð Þdt

¼ �mPolXSþ RPolXSi (18)

Inserting Equation (3) into Equation (18)

Pold XSð Þdt

þ XS RPol�mPolð Þ ¼ �mPolXSþ RPolXSi (19)

which leads to

d XSð Þdt

¼ RPol

PolXSi�XS� �

(20)

Finally, data collected after the introduction of a

sequence of small step changes of the COCAT/DONOR ratio

during 5 d of continuous operation were used to build an

empirical steady-state model for XS in the form:

XS�XSR

COCAT=DONOR�1¼ 5:56 (21)

where XSR¼ 4.83 is the reference value for a COCAT/

DONOR feed ratio. Figure 3 illustrates the quality of the

proposed steady-state model fit. Equation (21) indicates

that a constant linear gain model can be used to describe

fluctuations around nominal steady-state operation condi-

tions. Assuming that Equation (21) is also valid to describe

the instantaneous XS value of the produced polymer

material during transient operation conditions, then

d XSð Þdt

¼ RPol

PolXSR þ KXS

COCAT

DONOR�1

� ��XS

� �(22)

which shows that the polymer production rate should also

be expected to influence the dynamics of XS. Then, the XS

model comprises Equation (1–5) and Equation (22).

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Controller Design

In order to minimize possible undesired interactions

between the liquid bleed policy and the remaining

operation variables, control strategies were also studied

for regulatorycontrolofpropaneconcentration in the liquid

pool and servo control of the COCAT/DONOR ratio in the

reactor vessel. Assuming that simple proportional-integral

(PI) controllers canbeused to control these variables, then it

is possible to write:

Propane Concentration Controller

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mo ¼ mSSo þ Kp w�wset

� �þ 1

tP

Zw�wset� �

dt (23)

COCAT/DONOR Ratio Controller

mCOCAT ¼ f að Þ�Kt R�Rset� �

(24)

where mSSo is the reference steady-state liquid bleed flow

rate; Kp is the proportional gain for control of the propane

concentration; w is the measured weight fraction of

propane; wset is the set-point value for the propane

concentration; tP is the characteristic integral time

constant for control of the propane concentration; Kt is

the proportional gain for control of the COCAT/DONOR

ratio; R is the inferred COCAT/DONOR ratio in the reaction

environment; Rset is the set-point value for the COCAT/

DONOR ratio; and f(a) is a reference value which can

depend on the recirculation factor as:

f að Þ ¼ mDONOR Rset 1:5mpol�a 1:5mpol þmo

� �1:5mpol

� �

ffi mDONOR Rset 1�a½ � (25)

The propane concentration was measured in the

recirculating line online and in real time, with the help

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of a sampling device used to feed a standard gas

chromatograph. Parameters of the propane concentration

andCOCAT/DONORratio controllersweredeterminedwith

the well-known internal model control (IMC) methodo-

logy.[21,22] According to this procedure Kp, tP, and Kt

were found to be equal to 104 kg/min, 625min2/kg and

40 kg/min, respectively.

Equation (25) indicates explicitly that the desired COCAT

feed rate can depend on the recirculation factor, as the

increase of a leads to the increase of the COCAT/DONOR

ratio inside the reactor vessel. Therefore, as a increases,

lower COCAT feed rates are required to keep the COCAT/

DONOR ratio constant. Despite that, in a given process

configuration, a should be regarded as a constant, as shown

in Equation (16).

Equation (23–25) assume that propane concentrations

respond much slower to process perturbations than the

COCAT/DONOR ratio, as propane can only be removed

through the liquid bleed stream, while DONOR and part of

the COCAT are removed through the polymer stream. As

a consequence, adjustment and control of the COCAT/

DONOR ratio is expected to be much simpler than

adjustment and control of the propane concentration, as

also observed at plant site.

Figure 4. (A) Liquid bleed flow rates and (B) propane concen-trations, as measured at plant site. (Due to proprietary reasons,a.u. represents normalized arbitrary units.).

Figure 5. Propane concentrations in the liquid pool, as measuredat plant site. (Due to proprietary reasons, a.u. represents normal-ized arbitrary units.).

Results and Discussion

First, Equation (9–16) are used to represent the dynamic

behavior of the COCAT/DONOR ratio. During the simula-

tions, mo was allowed to vary at random, as observed at

plant site and illustrated in Figure 4. According to Figure 4,

the bleed flow rates are not kept constant and do not follow

a deterministic operation policy, fluctuating around

normalized average value equal to 0.695with a normalized

characteristic variance equal to 0.150. In order to under-

stand this unusual operation policy, it is necessary to

remember that the characteristic circulation time is very

large, so that one cannot guarantee that the inlet propane

concentrations are kept constant during the operation. As

the inlet propane concentrations are very low (below 0.5%

inmolar basis), small changes of the feed purity can lead to

significant modification of the propane concentration

trajectories when the liquid bleed flow rates are kept

constant. As measurement of propane concentrations are

frequently performed only at the lab after sampling, bleed

rate values frequently are manipulated discontinuously to

avoid that the propane concentration fall below a specified

minimum limit and increase above a specified maximum

limit. Specification of both limits depends on the process

economics.

Figure 5 shows real operation data obtained for the

propane concentration in the liquid pool when the liquid

bleed rate was allowed to vary as described in Figure 4.



Figure 6 shows calculated propane concentrations in the

liquid pool when it is assumed that a random liquid bleed

rate policy is performed. Figure 6A was built by assuming

that liquid flow rates were allowed to fluctuate between

two characteristic maximum and minimum values and

that the operation timewas subject to normal fluctuations,

with the same average and variance of the real operation

values.Asonecanobserve inFigure5and6B,both the range

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Figure 6. (A) Liquid bleed flow rates and (B) propane concentrationsin the liquid pool, as obtained through simulation. (Due to pro-prietary reasons, a.u. represents normalized arbitrary units.).

Figure 7. Dynamics of the COCAT/DONOR ratio for differentvalues of a. (A) a¼0.20; (B) a¼0.60, as obtained throughsimulation. (Due to proprietary reasons, a.u. represents normal-ized arbitrary units.).


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of variation of the propane concentration and the

characteristic oscillatory patterns of propane concentra-

tions and liquid bleed rates are very similar to the actual

operation data displayed in Figure 4 and 5. Therefore,

simulation studies performed below assume that the bleed

flow rates are changed from minimum to maximum

allowed values with a characteristic frequency that is

subject to normal perturbations, as described previously.

The characteristic recirculation factor a was allowed to

vary in the range [0,1] in all simulations in order to analyze

the influence of the recirculation factor upon the COCAT/

DONOR ratio inside the reactor vessel. Figure 7 shows that

the COCAT/DONOR ratio in the reactor vessel oscillates

with increasing amplitude as the recirculation factor

increases even when the COCAT/DONOR ratio is kept

constant in the freshmonomer feed.When the recirculation

factor is equal to 0.2 (K¼ 0.16), the oscillatory response of

the COCAT/DONOR ratio would certainly cause observable

XS fluctuations, given the high steady-state XS gain, as

presented in Equation (21). The increase of a also shifts the

steady-state COCAT/DONOR ratio to higher values. There-

fore, it is clear that the liquid bleed flow rate policy can




influence theXSdynamics if COCAT is partially recirculated

through the recycle stream, even if the COCAT/DONOR feed

ratio is kept constant.

Figure8 showsdynamic responses of theCOCAT/DONOR

ratio when modifications of the COCAT/DONOR feed ratio

and the liquid bleed flow rate occur simultaneously.

Figure 8A shows that the simultaneous modification of

bothoperationvariablesmaybesynchronized to induce the

development of apparent overshoots and apparent slow

dynamic responses, as frequently reported at plant site.

Therefore, if partial COCAT recirculation does occur, then it

is possible to conclude that the execution of grade

transitions might lead to strange XS dynamics, when the

liquidbleedflowratesareallowedtovary independently, as

normally practiced at the production site. Figure 8B shows

that the COCAT/DONOR ratio responds relatively fast to

changes of the feed conditions when the liquid bleed

operation is kept constant. Therefore, according to the

model, sluggish and strong nonlinear dynamics should be

expected only when simultaneous and uncontrolled

variations of the bleed and feed operations take place.

2011, 5, 129–139


Figure 8. Dynamic responses of the COCAT/DONOR ratio tosimultaneous changes of the liquid bleed flow rate andCOCAT/DONOR feed ratio, as obtained through simulation. (A)a¼0.4; (B) a¼0.20. Initially, bleed flow rates are at the maxi-mum allowed value. (Due to proprietary reasons, a.u. representsnormalized arbitrary units.).

Figure 9. Performance of the proposed control scheme during theregulatory control of propane concentration. (A) Liquid bleed flowrates; (B) Propane concentrations. (Due to proprietary reasons,a.u. represents normalized arbitrary units.).

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Figure 9 shows simulation results regarding the perfor-

manceof theproposed control schemeduring the regulatory

control ofpropane composition, obtainedwhen thepropane

concentration inthe feedstreamisallowedtovary. Figure10

shows simulation results obtainedwhen a set-point change

is introduced in the desired COCAT/DONOR ratio. In the first

case, it may be observed that proper control of the propane

composition is achievedwithoutmuchdifficulty for feasible

valuesof the liquidbleedflowrate. In thesecondcase, itmay

be observed that implementation of the controller leads to

much faster grade transition dynamics than the traditional

open-loop grade transition strategy.

Figure 11 shows that XS dynamic responses can be

indeed very fast at certain operation conditions. Results

were obtained during a large XS transition in industrial

plant. Fast XS responses and fast stabilization of XS values

can be observed. As samples were measured with a

frequency of 1 h�1, no more than a couple of hours are

needed for XS values to reach the new steady-state



conditions, which is in good agreement with the char-

acteristic residence timeof 1 h in the reactor vessel. It is also

interesting to observe that XS values seem to oscillate after

the final stabilization of the COCAT/DONOR feed ratio. It is

important to emphasize that liquid bleed flow rates and

propane feed concentrationswere kept constant during the

analyzed grade transition, indicating once more that

strange nonlinear dynamic responses can probably be

related to the liquid bleed policy. As one can also observe in

Figure 11, model predictions agree fairly well with the

available XS data in this example. In this particular case,

values estimated for the linear XS gain and for the

recirculation factor were equal to 4.6 and 0.6, respectively.

The first value is in very good agreement with the previous

result presented in Equation (21), which demonstrates the

consistency of the proposed parameter estimation proce-

dure. The second value seems very high, indicating that

significant amounts of COCAT can indeed recirculate in the

system, as assumed previously.

Figure 12 illustrates the process behavior when the

polymerization system is subject to successive changes of

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Figure 10. Performance of the control scheme for servo control ofthe COCAT/DONOR ratio. Linear fit represents the absence ofproportional control action. (Due to proprietary reasons, a.u.represents normalized arbitrary units.).

Figure 11. Dynamic XS transition, as observed at plant site whenthe bleed flow rate and the propane feed concentrationwere keptconstant. (Vertical bars indicate the 95% range of experimentalerror). (Due to proprietary reasons, a.u. represents normalizedarbitrary units.).

Figure 12. Performance of the control scheme for regulatorycontrol of propane concentration: (A) propane concentration inthe feed stream; (B) liquid bleed flow rate response. (Due toproprietary reasons, a.u. represents normalized arbitrary units.).


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the propane concentration, as analyzed through simulation.

It was assumed that the propane concentration of the feed

stream was allowed to vary 12.5% in respect to the initial

value. Figure 12B shows how the controller responds to the

process variations in order to keep the propane concentra-




tion in the reaction medium at the desired value. Figure 13

shows how the COCAT/DONOR ratio and the XS respond to

reductionofthebleedflowrate,duetothesuddenincreaseof

the propane feed concentration, when the proposed

controller scheme is used and when it is not used after

the first step disturbance of the propane concentration. As

one can observe, the proposed controller is able tomaintain

the XS at the desired set-point value and avoid the XS drift

induced by the modification of the COCAT/DONOR ratio

after the decrease of the bleed flow rate. On the other hand,

when the XS values and COCAT/DONOR ratio are not

controlled, very significantdrifts of both theCOCAT/DONOR

ratio and of the XS values are expected to occur, due to the

modification of the bleed flow rates.

Figure 14 illustrates how XS values respond to modifica-

tion of the set-point values of the COCAT/DONORwhen the

2011, 5, 129–139


Figure 13. Performance of the control scheme for the simultaneousregulatory control of propane concentration and COCAT/DONORratio: (A) COCAT/DONOR ratio; (B) XS response. (Due to proprietaryreasons, a.u. represents normalized arbitrary units.).

Figure 14. Performance of the control scheme for the servo controlof the COCAT/DONOR ratio and XS during XS transitions: (A)COCAT/DONOR ratio; (B) XS responses. (Due to proprietaryreasons, a.u. represents normalized arbitrary units.).

138

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controller is used to manipulate the liquid bleed flow rate

and the cocatalyst feed rates. Simulations were performed

by assuming that the propane feed concentrations were

allowed to vary, as illustrated in Figure 12. As shown in

Figure 14, XS values can be controlled effectively and the

proposed controller schemefilters the process disturbances

effectively, allowing for faster grade transition.

Conclusion

A mathematical model was built to describe the effects of

changing operation conditions upon the trajectories of the

XS in a real industrial bulk propylene polymerization

process, assuming that the XS fraction can be treated as a

pseudo chemical species. Special emphasiswas given to the



coupling that exists between the XS dynamics and the

reactor liquid bleed policy. It was shown that cocatalyst is

likely to recirculate through the recycle stream, which can

exert significant influence on the dynamics of the

cocatalyst/donor ratio andofXSduring thepolymerization.

Particularly, itwasshownthat theproposedmodel isable to

reproduce actual dynamic XS profiles obtained during

grade transitions at plant site and that estimated model

parameters support the assumption that significant

recirculation of cocatalyst does occur at plant site through

the recirculation monomer stream.

Obtained simulation results indicated that the charac-

teristic sluggishness of XS transitions observed at plant site

are probably due to the strong coupling between the feed

propane concentrations, liquid bleed flowrate policies, and

recirculation of cocatalyst through the recycle stream. For

2011, 5, 129–139



www.mre-journal.de

this reason, a standardPI controllerwasdesigned to remove

process disturbances and used to perform simulations.

Simulation results indicated that the effect of the reactor

liquid bleed operation and of the cocatalyst/donor ratio

upon the XS trajectories can be minimized if PI controllers

are designed to control the propane concentration in the

reactor and to increase the speed of the cocatalyst/donor

transitions.

Acknowledgements: The authors thank Polibrasil Resinas S.A.(Brazil) for technical and financial support. The authors thankCNPq (Conselho Nacional de Desenvolvimento Cientıfico e Tecno-logico, Brazil) for scholarships and financial support.

Received: July 24, 2010; Revised: October 15, 2010; Publishedonline: December 27, 2010; DOI: 10.1002/mren.201000038

Keywords: bulk polymerization; modeling; poly(propylene) (PP);process control; xylene soluble fraction (XS)

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modeling the dynamics of the xylene soluble fraction (xs) in a bulk propylene polymerization process

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