Reactor modeling and physicochemical properties characterization for a polyethylene fluidized bed reactor

Reactor modeling and physicochemical properties characterization for a polyethylene fluidized bed reactor

F. A. N. FERNANDES and L. M. F. LONA BATISTA

Departamento de Processos Químicos, Faculdade de Engenharia Química, Universidade Estadual de Campinas, UNICAMP, 13081-970, Campinas - SP, BRAZIL

[e-mail]

(Received: July 29, 1999; Accepted: September 9, 1999)

Abstract - A new steady state model for the fluidized bed reactor and a physicochemical characterization model were developed for the simulation of polyethylene production using gas-phase technology. The association of these models was done in order to predict the characteristics of the polymer produced in the fluidized bed reactor (molecular weight, polydispersity, melt index, and other characteristics) throughout the reactor and also to predict the growth of the polymer particle.

Keywords: modeling, polyethylene, fluidized bed reactor.

INTRODUCTION

Although the fluidized bed reactor technology for producing polyethylene was invented in the 50’s, and its commercial use has been increasing since the last decade, still little is known about its behavior regarding temperature, concentration, yield and polyethylene physicochemical properties gradients inside the reactor.

In the last few years, some researchers have focused their attention on the modeling of these polyethylene gas-phase processes (Choi & Ray, 1985; McAuley et al., 1994); however, these models are based on strong assumptions such as the existence of well-mixed emulsion phase, which can easily be disproven when considering a low degree of or no prepolymerization. In the latter cases, heat and mass transfer resistances become significant and the polymerization rate for young particles can cause overheating.

In order to create a more reliable model for the fluidized bed reactor, a steady state model incorporating interactions between separate bubble and emulsion phases inside the reactor bed was developed. A polymer physicochemical characterization model was also developed, and the two models were adjoined and studied.

MODEL DEVELOPMENT

The assumptions that were made in the development of the model are summarized below.

(a) The fluidized bed comprises two phases: bubble and emulsion phases.

(b) Polymerization reactions occur only in the emulsion phase.

(c) The emulsion phase is at minimum fluidizing conditions.

(d) The emulsion phase is not well mixed.

(e) Gas in excess of that required to maintain the minimum fluidizing condition passes through the bed as the bubble phase.

(f) Bubbles are spherical and of uniform size throughout the bed, reaching a maximum stable size.

(g) Bubbles travel up through the bed at a constant velocity in a plug-flow regime.

(h) There are negligible radial temperature and concentration gradients in the bed, due to the agitation produced by the up-flowing gas.

(i) There is negligible resistance to heat and mass transfer between gas and solids in the emulsion phase.

(j) There is no agglomeration of polymer particles within the bed.

(k) Elutriation of fine particles from the bed are not considered.

(l) The polymer particle grows and segregates inside the reactor.

(m) The gas phase is composed of ethylene, 1-butene, 1-hexene, nitrogen and hydrogen.

All mass and energy balances were given in the differential form in order to account for gas concentrations (ethylene, 1-butene, 1-hexene, hydrogen and nitrogen) and temperature axial gradients throughout the reactor in both phases. This means that the reagent gases are in a plug-flow regime but at different velocities for the bubble and emulsion phases.

Bubble-Phase Material and Energy Balances

Emulsion-Phase Material and Energy Balances

The new approach presented in this study relies on the average weight fraction of catalyst in the polymer, which is not constant throughout the reactor and has also been expressed as a differential equation that depends mainly on polyethylene yield. In this way it is possible to simulate a high catalyst/polymer mass weight fraction at the top of the reactor and a low mass weight fraction at the base, which is in accordance with the fact that there is a degree of segregation of the different polyethylene particle sizes in the fluidized bed reactor.

Average Mass Weight Fraction of Catalyst in the Polyethylene

The advantage of having this new variable is that it allows the use of a more complex reaction mechanism, which is summarized in Table 1. It provides strong support in the prediction of the growth of polyethylene particles throughout the fluidized bed.

Table 1: Reaction Mechanism and Kinetic Parameters

Reaction			Catalytic Site 1	Catalytic Site 2
formation [s-1]		kf	1	1
initiation		ki1	1	1
[L.mol-1.s-1]		ki2	0.14	0.14
		kh1	1	1
		kh2	0.1	0.1
		khr	20	20
propagation		kp11	85	85
[L.mol-1.s-1]		kp12	2	15
		kp21	64	64
		kp22	1.5	6.2
chain transfer		kf11	0.0021	0.0021
[L.mol-1.s-1]		kf12	0.006	0.11
		kf21	0.0021	0.001
		kf22	0.006	0.11
		kfh1	0.088	0.37
		kfh2	0.088	0.37
		kfr1	0.024	0.12
		kfr2	0.048	0.24
		kfs1	0.0001	0.0001
		kfs2	0.0001	0.0001
deactivation [s-1]		kds	0.0001	0.0001

The mathematical solution of the model took into account the physical design of the reactor, where the gas and polymer particles flow in countercurrent, the gas is fed in at the base and the catalyst at the top portion of the reactor, as shown in figure 1. This design configuration implies having boundary conditions at the base and top of the reactor, which resulted in an iterative solution of the system till all base and top boundary conditions were satisfied. The final reactor model was composed of ten differential equations, plus accessory equations for the calculation of particle growth throughout the reactor.

Figure 1
: Fluidized bed Reactor for Polyethylene Production.

The reaction mechanism used in this work is the same as that described by Kissin (1987), de Carvalho et al. (1989) and McAuley et al. (1990). In general, this mechanism is based upon the coordination copolymerization of ethylene using Ziegler-Natta catalyst with two different catalyst sites. Each site is associated with different rate constants for formation, initiation, propagation and chain transfer. Only the effects of the terminal monomers on the reaction rates were considered.

Alongside the reactor model, the method of moments (Zabisky et al., 1992) was used to create a new mathematical model capable of predicting the physicochemical properties of the polyethylene (average molecular weight, density, polydispersity, melt index, etc.) throughout the reactor height and also polymer particle growth. The guidelines followed by Zabisky et al. (1992) were adapted to the case of the coordination copolymerization reaction mechanism outlined by McAuley et al. (1990) and to the dynamics along the reactor height. Equations for polymer moments are shown in Table 2. The model consisted of 36 differential equations corresponding to the material balances of the components and the live and dead polymer moments, plus accessory equations for calculating polydispersity, density, comonomer incorporation in the polymer chain and other properties.

Table 2: Polymer Moments

To combine the results from the reactor model (temperature, concentration and production profiles obtained as a function of the height position) with the results from the method of moments predictions (concentration, yield and quality profiles obtained as a function of the time), an iterative process was created. Outputs from the reactor model served as inputs for the physicochemical model, and vice-versa, so that operational parameters could be adjusted in both models, till the profiles obtained matched in terms of ethylene and comonomer concentrations and yield of polyethylene. The problem with this operation was that it relied on the different integration variables (time and position) of the two models, which hinders the convergence of the system to a single matching result.

RESULTS

The data obtained with the reactor model showed interesting results concerning the temperature and concentration gradients in the reactor, specially in the catalyst feeding region, where the reaction rate is higher due to the higher temperature and the greater influence of the catalyst in the formation and early development of young polymer particles. The case illustrated by figure 2 shows typical temperature and concentration gradient profiles given for the production of polyethylene in a fluidized bed reactor with no prepolymerization. The data used in the model simulations are shown in table 3 and are typical operational conditions for industrial reactors.

Figure 2:
Ethylene concentration and temperature gradients for the production of polyethylene in a fluidized bed reactor with no prepolymerization. Simulation data from table 3.

Table 3: Operational conditions and reactor data used in the simulations

Ethylene feed rate	0.50 mol/L	1-Butene feed rate	0.20 mol/L
Hydrogen feed rate	0.05 mol/L	Inert feed rate	0.00 mol/L
Catalyst feed rate	0.20 g/s	Cocatalyst feed rate	0.01 mol/L
Gas feed temperature	316 K	Room temperature	340 K
Catalyst density	2.38 g/cm3	Catalyst diameter	0.05 mm
Activation energy	37620 J/mol	DH	-3829 J/g
Reactor diameter	396 cm	Reactor height	1097 cm
d	0.214	emf	0.50
Umf	7.0 cm/s	Ue	34.8 cm/s
Ub	114.0 cm/s	Bubble diameter	15 cm

As can be seen in figure 2, the top portion of the reactor requires special attention in order not to form hot spots or even melt the polymer. According to the parametric study of the system, this situation can be avoided by controlling gas feed velocity and temperature.

Polyethylene production can be enhanced by elevating the gas feed temperature and by decreasing the gas feed velocity. It was observed that an increase of 15K in the gas feed temperature can multiply the yield of polyethylene by up to 50% (not shown), without jeopardizing the properties and integrity of the polyethylene.

The physicochemical model alone shows that the average molecular weight of the polymer increases more rapidly at the beginning of the polymerization period and slows down after a period of time. Polydispersity shows the same increase profile. Density and comonomer incorporation in the polymer remains practically constant during the entire polymerization process.

Figure 3 shows a simulation of the polyethylene physicochemical properties inside the fluidized bed reactor, obtained by linking the reactor and the physicochemical characterization models. The simulation shows that there is a highly active reaction zone at the top of the reactor, which is in accordance with the reactor model. Beneath this highly active zone is a less active zone responsible for refining the polymer properties.

Figure 3:
Average molecular weight (M_n and M_w), accumulated polyethylene production and particle diameter profiles inside the fluidized bed reactor. Simulation data from table 3.

The upper and highly reaction-active zone tends to be less evident when prepolymerization of the polyethylene particles is employed.

The assumption that the polymer particles segregate inside the reactor still holds up, with fine particles found at the reactors’ top and heavier particles distributed along the reactor height.

CONCLUSIONS

In this work new reactor and physicochemical properties characterization models were developed and combined to provide a complete understanding of the fluidized bed reactor for polyethylene production.

The reactor model developed permits the use of a more complex reaction mechanism and the prediction of the polymer average particle diameter and polymer/catalyst weight fraction. But above all, it also extends the possibility of simulation of reactor operation with a low degree of or no prepolymerization, a case which the models based on the well-mixed emulsion phase theory are incapable of predicting correctly.

When combined the two models become a very useful tool for performing a complete optimization of the fluidized bed reactor for the production of polyethylene. This coupling makes it possible to optimize reactor conditions in an attempt to increase the rate of polyethylene production and at the same time discover how changes in the operational conditions of the reactor influence the grade of the polymer being produced.

From the industrial point of view, these more reliable copolymerization models are capable of simulating the synthesis conditions of polyethylene and permit the study of new copolymers prior to industrial tests. In this way, new polymer grades can be developed more easily, and existent grades can be optimized in order to produce high quality resins.

NOTATION

A sectional area of the reactor

C_ij concentration of component j in the i phase

c_pgj^* molar heat capacity of gas component j

c_ps mass heat capacity of the solids

D diameter of the fluidized bed reactor

DH heat of reaction

H^* molecular hydrogen

H_m heat transfer coefficient

K_mj mass transfer coefficient of component j

M_W molecular weight of ethylene

NC number of components

P(r) nonreactive polymer with chain-length size r

q_cat catalyst feeding rate

R^* potentially active site

R_i(r) live polymer with terminal monomer i and chain-length size r

Rp’ rate of polyethylene production

T_i temperature of the i phase

T_ref reference temperature

U_i velocity of the i phase

U_h wall heat transfer coefficient

X cocatalyst

z height above the distributor

d volumetric fraction of bubble in the bed

e_mf minimum fluidized porosity

c catalyst/polymer average weight fraction

Subscripts

1 ethylene

2 1-butene

b bubble phase

e emulsion phase

mf minimum fluidizing condition

T total (sum of all components)

ACKNOWLEDGEMENTS

The authors would like to thank the São Paulo State Research Aid Foundation - FAPESP, for the scholarship and their financial support of this research.

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Publication Dates

• Publication in this collection
  01 Mar 2000
• Date of issue
  Dec 1999

History

• Received
  29 July 1999
• Accepted
  09 Sept 1999