Accepted Manuscript

Title: Dynamic simulation of liquid polymerization reactors inSheripol process for polypropylene

Author: Shin Hyuk Kim Seung Won Baek Jae Cheol LeeSeong Uk Hong Min Oh

PII: S1226-086X(15)00462-1DOI: http://dx.doi.org/doi:10.1016/j.jiec.2015.10.017Reference: JIEC 2686

To appear in:

Received date: 19-8-2015Revised date: 13-10-2015Accepted date: 14-10-2015

Please cite this article as: S.H. Kim, S.W. Baek, J.C. Lee, S.U. Hong, M.Oh, Dynamic simulation of liquid polymerization reactors in Sheripol processfor polypropylene, Journal of Industrial and Engineering Chemistry (2015),http://dx.doi.org/10.1016/j.jiec.2015.10.017

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Dynamic simulation of liquid polymerization reactors in Sheripol process

for polypropylene

Shin Hyuk Kima, Seung Won Baeka, Jae Cheol Leeb, Seong Uk Honga*, Min Oha*aDepartment of Chemical Engineering, Hanbat National University, 125 Dongseo-daero, Yuseong-gu,

Daejeon 305-719, KoreabSchneider-electric Co., Ltd., 13F, Jei Platz, 186, Digital 1st, Geumcheon-gu, Seoul, Korea

Abstract

This work executed mathematical modelling and dynamic simulation of a polyolefin process with

pre-polymerization and two loop reactors. Transient changes occurring within the reactors were

simulated based on a one-dimensional plug flow assumption. Temperature control in the reactors is

germane to the realization of the desired products because of the exothermic reactions, and this was

accounted for using cooling jackets. The gPROMS package was utilized as a software platform for

modelling and simulation.

The results identified the physicochemical changes in each reactor. Molecular weight and

polydispersity were predicted. Simulation results were validated with commercial data and agree well.

Keywords: Polymerization, Polypropylene, Polyolefin, Ziegler Natta, Loop reactor, Simulation

Corresponding authors:

Tel.: +82 42 821 1535; E-mail address: minoh@hanbat.ac.kr (Min Oh)

Tel.: +82 42 821 1536; E-mail address: suhong@hanbat.ac.kr (Seong Uk Hong)

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NOMENCLATURE

Symbol Name Unit

Area of tube m2

Co-catalyst

Heat transfer area m2

Concentration of component i mol m-3

Active catalyst

Inactive catalyst

Heat capacity J kg-1K-1

Dispersion coefficient m2 s-1

Activation energy J mol-1

Hydrogen

Reaction constant

Frequency factor

m3 mol-1s-1

or s-1

Heat dispersion coefficient J m-1s-1K-1

Mass kg

Mass flow rate kg s-1

Monomer

Number average molecular weight g mol-1

Weight average molecular weight g mol-1

Molecular weight g mol-1

Molecular weight of monomer g mol-1

Molecular weight of polymer chain n g mol-1

Active polypropylene of chain i

Inactive polypropylene of chain i

Heat of transfer with cooling jacket J s-1

Ideal gas constant J mol-1K-1

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Energy source term of polymerization J m-3s-1

Mass source term of component i mol m-3s-1

Temperature K

Velocity m s-1

Volume of reactor

Greek Notations

Density kg m-3

Density by thermal dynamic kg m-3

Partial

Active mis-insertion polymer

Indices

Deactivation

Initiation

Number of polymer chain

Propagation

Secondary insertion

Chain transfer after mis-insertion

Cooling jacket tube

Simulation time index

Transfer to co-catalyst

Transfer to hydrogen

Transfer to monomer

Dimension index

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Introduction

Mathematical modelling and simulation of the polypropylene reactors covered in this project has

been carried out previously with most of these works focused on liquid-polymerization reactors [1~3].

These researchers modeled loop reactors as a continuous stirred tank reactor (CSTR), and this

approximation of loop reactors works fairly well in regimes with high recycle ratios. In practice, loop

reactors can exhibit outlet polymer concentrations that differ significantly from concentrations inside

the reactor as explained by Ferrero and Chiovetta (1990) [4~6].

Discrepancy in the CSTR assumption has been elucidated through their prediction of end-use

polymer properties via steady-state as well as dynamic simulations [7, 8]. Development of computer

and mathematical analysis tools has enabled the simulation and analysis of loop reactors on a multi-

dimensional scale. Zacca and Ray (1993)[9] predicted physical changes occurring within a loop

reactor using a one-dimensional model; but this work could not reflect molecular weight (MW),

which decides the property of a polymer made from the prediction of physical changes and is the most

important property for deciding polymer characteristics. Many researchers propose the method of

most probable distribution (MPD) to overcome this difficulty [10, 11]; however, the MPD method,

which is an expression of MW based on statistics, cannot reflect the variables of mathematical models

so that it is not acceptable for dynamic simulation expression. A reactor based on the commercial

process data designed and simulated was investigated in 2007 and 2010 [12, 13]. Although they found

that the technology of polymer simulation could be used for real process design, they maintained the

CSTR assumption.

Olefin polymerization normally requires catalysts. The composition and structure of the catalyst used

directly affects polymer properties and characteristics [14, 15]; therefore, catalyst selection is an

important factor. Despite the broad spectrum of high mileage catalyst systems that have been available

in recent times, use of Ziegler-Natta catalysts has dominated propylene production processes. The

1970s witnessed probing research into reaction mechanisms involving Ziegler-Natta catalysts [2,

16~18]. This culminated in the suggestion of a kinetic mechanism that involves a consideration of the

elementary reaction with a catalyst [19]. Since then, many researchers have developed the universal

kinetics of polypropylene synthesis on the basis of Hutchinson’s idea.

A review of previous works reveals the absence of a multiscale model that adequately accounts for a

realistic reactor mode and rigorous mathematical description of MW distribution. Most works employ

the plug flow assumption and account for MW via statistics, while rigorous mathematical modelling

of MW is often seen to be accompanied by the CSTR approximation based on high recycle ratios.

This unravels the necessity of dynamic simulation based on a rigorous mathematical model for the

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performance, analysis, and optimization of the process.

In this work, rigorous mathematical modelling involving the polymerization mechanism and balance

equations for all chemical species is used in predicting the properties of each polymer chain and

changes occurring in the one-dimensional model of the loop reactors instead of a widespread

statistical approach. The polymerization loop reactor in the Spheripol process, being comprised of

three reactors (pre-polymerization reactor, two loop reactors), was employed as a target process. The

simulation was carried out and validated with data from an existing commercial plant. The gPROMS

package was utilized as a software platform for modelling and simulation [20].

Model description and mathematical modelling

Description of reactors

The polymer reactor (Fig. 1) is a thin-walled tubular reactor surrounded by external cooling jackets

for heat exchange to induce the growth of macromolecules because of the temperature sensitivity of

the polymerization reaction. Sufficient circulation is also required in the loop reactor because of its

susceptibility to space alteration.

Fig. 1. Block diagram of the loop reactor structure

A summary of some important design parameters of the pre-polymerization and loop reactors is

shown in Table 1. Very high recycle ratios and cooling water rates are required in the loop reactors to

avoid thermal runaways compared with those required in the pre-polymerization reactor.

Table 1. Design parameters of polymerization reactors

Mathematical modelling of reactors

The loop reactor has been modeled as a one-dimensional plug flow reactor, and the resulting

changes in concentration and heat of reaction are represented as source terms in the following

mathematical formulations. Continuity assumption underscores the mathematical models presented

below.

Reactor

Mass balance

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(1)

(2)

where is the concentration of component i, is the velocity, is the dispersion coefficient,

is the mass source term of component I and is calculated from momentum balance equation

in reactor model. is calculated by reaction mechanism using the Arrhenius equation and reaction

constant.

Momentum balance

where , are density and density by thermal dynamic, respectively. Momentum balance is

considered continuity equation under some assumption.

Energy balance

where is the heat capacity, is the heat dispersion coefficient, is the energy source term

of polymerization, q is the heat of transfer with cooling jacket, T is the temperature in reactor and V is

the volume of reactor. T is dynamically changed by energy source and heat transfer.

Molecular weight

Where is the molecular weight of polymer chain n, is the molecular weight of

monomer, is the weight average molecular weight and is the number average molecular

weight.

(3)

(4)

(5)

(6)

(7)

(8)

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Cooling jacket

Mass balance

where is the density and is the velocity in cooling jacket tube. There variable value are from

momentum balance in cooling jacket model.

Momentum balance

Energy balance

where is the heat capacity, is the temperature and is the volume of cooling jacket. is

also dynamically changed by heat transfer.

Heat transfer with reactor

Where is the overall heat transfer coefficient and is the heat transfer area.

Description of reaction kinetics in polymerization

A detailed mechanism for the radical polymerization reaction employing Ziegler-Natta catalysts in

the loop reactors is shown in Table 3. This involves initiation, propagation, transfer, and deactivation

steps. Rate constants of the various steps can be determined using the Arrhenius equation.

(9)

(10)

(11)

(12)

(13)

(14)

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where reaction constant, is the frequency factor and E is the activation energy.

Table 2. Ziegler-Natta reaction mechanism for PP polymerization

The activation energies E and frequency factors k0 of the reaction steps in Table 3 are shown in Table

4 [10].

Table 3. Ziegler-Natta reaction constant for PP polymerization

Usually, heat of reaction only occurs in the propagation step when catalysts are employed. In the

case of PP, a value of 8.635×104 J mol-1 is evolved.

Description of loop reactor section in Spheripol process

A detailed flow chart is represented in Fig. 2. R1~R3 represent the three reactors employed in the

process. The pre-polymerization reactor is designated R1 and the two loop reactors are denoted by R2

and R3.

Fig. 2. Schematic diagram of liquid polymerization reactors

Result and discussion

Dynamic behavior of reactors

Liquid polymerization of polypropylene begins with the pre-polymerization step. Pre-polymerization

occurs in a reactor with a height of about 45 m and a diameter of 0.168 m. Better control of operating

conditions can be achieved in the pre-polymerization reactor compared with the main polymerization

step. The first loop reactor functions to grow the pre-polymerization product. The first loop reactor is

50 times larger than the pre-polymerization reactor, allowing for a longer residence time while being

quite difficult to control. The existence of active catalysts and live polymer from the first loop reactor

is exploited by a second loop reactor, which is similar in size and operating conditions to the first. The

only notable difference between them is the amount of control action required to maintain temperature

at set-point. A rapid temperature rise occurs in the second loop reactor compared with the first.

The monomer concentration in the reactors decreased exponentially and attained a steady-state value

after about 10000 s (Fig. 3). The zenith and nadir of the graph correspond to concentrations of

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11064.69 mol m-3 and 10081.42 mol m-3 respectively. The monomer concentration in the first loop

reactor took 26000 s to decrease from 11065.25 to 6511.77 mol m-3 at a temperature of 343.15K. The

rate of polymerization is rapid after about 10000 s as illustrated in Fig. 3 (b), while a constant

temperature was maintained in the reactor by the recycle stream. The longer duration taken for the

process to reach steady state can be accounted for by two reasons: first, the temperature difference

between the influx and operating condition and, second, the reactor size. In the second loop reactor,

the feed concentration of the monomer decreased from 11065.41 mol m-3 to 6143.68 mol m-3. There is

a striking similarity between the concentration profiles of Fig. 3 (b) and Fig. 3 (c). Reactions in the

second loop reactor take longer (27000 s) to reach steady state because of the difficulty in contact

between the active polymer and the active sites of the catalysts.

Fig. 3. Monomer concentration profile with time and space: (a) pre-polymerization reactor, (b) 1st loop

reactor, (c) 2nd loop reactor.

A decrease in monomer concentration results in generation of the desired products. A plot of polymer

concentration in the pre-polymerization reactor (Fig. 4 (a)) shows that a maximum concentration of

3.81 mol m-3 is achieved at equilibrium with living polymers accounting for about 90%. The results of

the generation of polymer in the first loop reactor with emphasis placed on the percentage of living

and dead polymer (Fig. 4 (b)) show that dead polymer accounts for about 80% of the total polymer

produced. From this percentage of dead polymer obtained, it can be deduced that the decisive point of

polymer growth is the first loop reactor. The second loop reactor leads to a 7% increase in dead

polymer with a 34% decrease in live polymer as illustrated in Fig. 4 (c).

Fig. 4. Polymer concentration profile of live polymer and dead polymer with time at reactor exit: (a)

pre-polymerization reactor, (b) 1st loop reactor, (c) 2nd loop reactor.

Temperature change in the pre-polymerization reactor is shown in Fig. 5 (a). The temperature

increased by 293.25 K because of the exothermic polymerization reaction. A cooling jacket was used

to maintain normalcy by providing adequate amelioration of detrimental temperature effects because

increasing temperature is catastrophic to the process. Temperature in the first loop reactor increased

from about 316 K and was maintained at 343.25 K after 10000 s of operation with the aid of the PI

controller because of the high heat of reaction (Fig. 5 (b)). Temperature rose at a faster rate in the

second loop reactor compared with the first, taking about 9100 s to reach the operating temperature

(Fig. 5 (c)), because the two reactors operate in series.

Fig. 5. Temperature profile with time at reactor exit: (a) pre-polymerization reactor, (b) 1st loop reactor,

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(c) 2nd loop reactor.

Polymerization reactors are susceptible to dynamic shock from the heat of reaction. This temperature

sensitivity requires a control action. The controller was assumed to be applicable to a flowrate 10

times larger than the designed flowrate. The control action is illustrated in Fig. 6. An actuating signal

allowing for an abrupt change in flowrate to 870 kg s-1 was issued by the controller at about 10000 s

when the temperature exceeded 343.15 K (Fig. 6 (a)). A stable operating temperature was maintained

with a cooling water flowrate of 228 kg s-1. In the case of the second loop reactor (Fig. 6 (b)), cooling

water was maintained at 1490 kg s-1 by the controller. This amount is 1.7 times larger than that used in

the preceding reactor, an indication of the relative amounts of heat generated. Cooling water

temperature varied from 327.2 K at the inlet to 331.15 K at the cooling jacket outlet.

Fig. 6. Controlled rate of inflow in cooling jacket: (a) 1st loop reactor, (b) 2nd loop reactor.

The velocity profile of the pre-polymerization reactor (Fig. 7 (a)) shows that the velocity changed

from 3.55 m s-1 at the onset of the process to 3.14 m s-1 at steady state under the influence of

concentration and temperature. This corresponds to a volume flowrate of 250.45 m3 hr-1, which is

similar to a flowrate of 250 m3 hr-1 obtained from commercial data. The outlet flowrate obtained from

our simulations deviate from the actual value by less than 0.2%. The recycle ratio is a key factor that

enables the approximation of flow patterns in the loop reactor. In this project, a recycle ratio of 153.3

was maintained in the first loop reactor with circulation velocity decreasing from 9.52 m s-1 upon

entry to 6.84 m s-1 at exit. The exit velocity compares well with an actual velocity of 6.88 m s-1 in the

process as shown in Fig. 7 (b). The operating conditions of the two loop reactors are similar in all

respects with slight variations in certain steady-state variables such as a velocity. In the second loop

reactor, a steady state value of 6.91 m s-1 is predicted (Fig. 7 (c)) instead of the 6.84 m s-1 predicted in

the first loop reactor.

Fig. 7. Velocity profile with time and space: (a) pre-polymerization reactor, (b) 1st loop reactor, (c) 2nd

loop reactor.

Mn, Mw and PD and PD of the growing polymer increased with time (Fig. 8). The polymer

produced in the pre-polymerization reactor possesses Mn and Mw of 27000 g mol-1 and 51000 g mol-1

respectively and a PD of 1.98, which lies between the PD of 1.5 and 2.5 of the polymer produced

from the existing plant. It is evident that an increase in polymer growth was achieved in the first loop

reactor from a quick comparison with the Mn of 205746 g mol-1 and Mw of 398085 g mol-1 of the

issuing pre-polymerization products, which resulted in a PD of 1.93 (Fig. 8 (b)). A plot of these values

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from the simulation of the Spheripol process is shown in Fig. 8 (c). Inferring from this graphical

representation indicate values of 215053 g mol-1 and 412558 g mol-1 for Mn and Mw respectively

with a PD of 1.92. The PD and MW in the second reactor remained almost constant. The second loop

reactor increased the yield of polymer as reflected in an increase in the polymer flow rate from

16860.42 kg hr-1 to 27181.42 kg hr-1 (Table 4) despite the constancy in PD and MW.

Fig. 8. Average molecular weight and polydispersity profile of produced polymer: (a) pre-

polymerization reactor, (b) 1st loop reactor, (c) 2nd loop reactor.

Validation of simulation

Simulation results shown in Table 4 predict conversions of 17.56%, 52.4%, and 54.91% in the pre-

polymerization, R1, and R2 respectively. Comparing these conversions with conversions achieved

from an existing plant under the same operating conditions in the bar chart of Fig. 9 below shows

absolute errors of 1.90 %, 1.69 %, and 3.02 % in the pre-polymerization, R1, and R2 respectively.

These are errors less than 10 % and considered acceptable for engineering applications.

Table 4. Material balance of simulation result

Fig. 9. Comparison and validation of polymer conversion rate for each reactor

Conclusion

A plethora of factors such as operating conditions, processing methods, catalysts, and the choice of

reactors influence the quality and efficiency of polymer processes. This difficulty has led to the

development of model based analysis of the Spheripol process for polyolefin production, particularly

in consideration of steady and dynamic state simulation. Deductions and conclusions from the work

carried out are as follows:

First, rigorous mathematical modeling of the reactors, namely the pre-polymerization reactor, first

loop reactor, and second loop reactor, was carried out to provide an accurate description of

physicochemical changes by way of conservation equations, polymerization reaction kinetics,

methods of moment, and population balance. Important process variables such as concentration,

density, temperature, and mass flow rate as well as MW and growth of the polymer chains were

considered in the formulation of the mathematical models.

Second, based on the developed mathematical model, a dynamic simulation was executed using

commercial operating and design data to identify the dynamic behavior of the process. The simulation

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results were compared with commercial data to verify the accuracy and effectiveness of this research.

The simulation predicted an overall conversion of 54.91 % with an associated error of 3.02 %. It is

concluded that this study can be extended for design and operational optimization of polyolefin

processes as well as other polymerization process without considerable modifications.

Acknowledgement

This research is funded by the LINC Program of Hanbat National University (2015) and the authors

would like to acknowledge for the assistance.

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REFERENCE

[1] B. A. Uvarov, V. I Tsevetkova, Polim. Protsessy Appar. Tecnol. Oformlenie Mat. Model

(1974), 165-168

[2] D. M. Lepski, A. M. Inkov, Sb. Tr. Vses. Ob’edin. Meftekim 13 (1977), 34-45

[3] M. A. Ferrero, M. G. Chiovetta, Polym.-Plast. Technol. Engng 29 (1990), 263-287

[4] J. R. Fried, Polymer Science and Technology, PrenticeHallPTR, (1996)

[5] N. G. McCrum, C. P. Buckley, C. B. Bucknall, second edition, Oxford, (1998)

[6] KOSHA, KOREA OCCUPATIONAL SAFETY & HEALTH AGENCY,

<www.kosha.or.kr/cms/board/Download.jsp?fileId=58539>

[7] A. G. Mattos Neto, J. C. Pinto, Chemical Engineering Science, 56 (2001), 4043-4057

[8] E. A. de Lucca, R. M. Filho, P. A. Melo, J. C. Pinto, Macromol. Symp. 271 (2008), 8-14

[9] J. J. Zacca, W. H. Ray, 48 (1993), 3743-3765

[10] T. J. Crowley, K. Y. Choi, Ind. Eng. Chem. Res., 36 (1997), 1419-1423

[11] D. W. Van Krevelen, Properties of Polymers, Elsevier, (2009)

[12] Z. H. Luo, Y. Zheng, Z. K. Cao, S. H. Wen, POLYMER ENGINEERING AND SCIENCE, (2007),

1643-1649

[13] Z. H. Luo, P. L. Su, W. Wu, Ind. Eng. Chem. Res., 49 (2010), 11232-11243

[14] Z. Liu, X. Zhang, H. Huang, J. Yi, W. Liu, W. Liu, H. Zhen, Q. Huang, K. Gao, M. Zhang, W.

Yang, Journal of Industrial and Engineering Chemistry, 18 (2012), 2217–2224

[15] J. Pinyocheep, S. K. Ayudhya, B. Jongsomjit, P. Praserthdam, Journal of Industrial and

Engineering Chemistry, 18 (2012), 1888–1892

[16] D. R. Burfield, I. D. Mckenzie, P. J. T. Tait, Polymer, 13 (1972), 303-326

[17] L. L. Bohm, Polymer, 19 (1978), 545-552

[18] J. Boor, Academic Press, New York

[19] H. M. Hutchinson, Ph.D. thesis, University of Wisconsin, Madison.

[20] PSE. <http://www.psenterprise.com>, (2015)

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List of Figures

Fig. 1. Block diagram of the loop reactor structure

Fig. 2. Schematic diagram of liquid polymerization reactors

Fig. 3. Monomer concentration profile with time and space: (a) pre-polymerization reactor, (b) 1st loop

reactor, (c) 2nd loop reactor.

Fig. 4. Polymer concentration profile of live polymer and dead polymer with time at reactor exit: (a)

pre-polymerization reactor, (b) 1st loop reactor, (c) 2nd loop reactor.

Fig. 5. Temperature profile with time at reactor exit: (a) pre-polymerization reactor, (b) 1st loop reactor,

(c) 2nd loop reactor.

Fig. 6. Controlled rate of inflow in cooling jacket: (a) 1st loop reactor, (b) 2nd loop reactor.

Fig. 7. Velocity profile with time and space: (a) pre-polymerization reactor, (b) 1st loop reactor, (c) 2nd

loop reactor.

Fig. 8. Average molecular weight and polydispersity profile of produced polymer: (a) pre-

polymerization reactor, (b) 1st loop reactor, (c) 2nd loop reactor.

Fig. 9. Comparison and validation of polymer conversion rate for each reactor

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List of Tables

Table 1. Design parameters of polymerization reactors

Table 2. Ziegler-Natta reaction mechanism for PP polymerization

Table 3. Ziegler-Natta reaction constant for PP polymerization

Table 4. Material balance of simulation result

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Table 1. Design parameters of polymerization reactor

Parameter Pre-polymerization reactor Polymerization loop reactor

Length of reactor 45 m 190 m

Diameter of tube 0.168 m 0.6 m

Diameter of jacket 0.273 m 0.8 m

Recycle ratio 75 153.3

Flowrate of cooling water

11.11 kg/s 222.22 kg/s

Table 2. Ziegler-Natta reaction mechanism for PP polymerization

Initiation

Propagation

Chain transfer to hydrogen

Chain transfer to monomer

Chain transfer to co-catalyst

Deactivation reactions

Spontaneous deactivation

Table 3. Ziegler-Natta reaction constant for PP polymerization

Reaction constant

kin : Initiation 4.97×104 m3 mol-1 s-1 50000 J mol-1

kp : Propagation 4.97×104 m3 mol-1 s-1 50000 J mol-1

ktr,H : Transfer to hydrogen 4.4×103 m3 mol-1 s-1 50000 J mol-1

ktr,M : Transfer to monomer 6.16 m3 mol-1 s-1 50000 J mol-1

ktr,A : Transfer to co-catalyst 7.04×10-1 m3 mol-1 s-1 50000 J mol-1

kd : Deactivation 7.92×103 s-1 50000 J mol-1

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Table 4. Material balance of simulation result

Streamnumber

101 102 103 104 105 106 107 108 109

Description Catalysts Propylene R1outlet Propylene R2outlet Propylene R3outlet Top Bottom

Fraction kg h-1 kg h-1 kg h-1 kg h-1 kg h-1 kg h-1 kg h-1 kg h-1 kg h-1

Catalysts 12.35

Hydrogen 0.07 0.07 1.13 0.64

Propylene 1719.64 1396.02 27391.29 12240.54 15681.14 17586.29 15208.35 2377.94

Propane 180.29 180.49 2871.72 3075.53 1644.02 4734.58 4053.75 680.88

Polymer 335.77 16860.42 27181.42 27181.42

Total 12.35 1900 1912.35 30264.14 32176.49 17325.8 49502.29 19262.1 30240.19

T (℃) 10 10 20.3 45 70.1 45 70.2 70 70

P (bar) 40 35 35 35 35 35 35 18.4 2

ρ(kg m-3) 512 578 512 714 512 725

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*Graphical Abstract

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Figure 1

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Figure 2

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Figure 3(a)

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Figure 3(b)

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Figure 3(c)

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Figure 4(a)

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Figure 4(b)

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Figure 4(c)

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Figure 5(a)

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Figure 5(b)

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Figure 5(c)

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Figure 6(a)

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Figure 6(b)

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Figure 7(a)

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Figure 7(b)

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Figure 7(c)

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Figure 8(a)

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Figure 8(b)

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Figure 8(c)

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Figure 9