Article pubs.acs.org/IECR
Experimental and Modeling Analysis of Propylene Polymerization in a Pilot-Scale Fluidized Bed Reactor Ahmad Shamiri,† M. A. Hussain,†,* Farouq Sabri Mjalli,‡ Mohammad Saleh Shafeeyan,† and Navid Mostoufi§ †
Department of Chemical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia Petroleum and Chemical Engineering Department, Sultan Qaboos University, Muscat 123, Oman § Process Design and Simulation Research Center, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran ‡
ABSTRACT: A pilot-scale fluidized bed reactor was built and used to study and gain a better understanding of the propylene polymerization process at conditions similar to those of industrial fluidized-bed reactors. Propylene polymerization reaction was carried out continuously in the reactor and dynamic temperatures, and propylene and hydrogen concentrations data were collected. Simulated dynamic profiles of the two-phase model and the well-mixed model were compared with the actual plant data. It was found that predictions of the two-phase model were in better agreement with the pilot plant data at typical industrial operating conditions. This agreement is due to the realistic assumptions of the two-phase model as compared to the well-mixed model. The maximum deviations between the pilot plant data and the two-phase model prediction for the propylene, hydrogen concentrations, reactor temperature, and polypropylene production rate were about 3.4 mol %, 0.15 mol %, 2.4 °C, and 0.8 g/s, respectively. framework to represent the transient behavior of a fluidized bed propylene polymerization reactor. Shi et al.13 developed a three-dimensional computational fluid dynamics (CFD) model to present the gas−solid two-phase flow in fluidized bed polymerization reactors. They used an Eulerian−Eulerian twofluid model which includes the kinetic theory of granular flow. In addition, the distribution of solid holdup, the behavior of bubbles and the velocity vectors of solid particles in free and agitated fluidized bed polymerization reactors were described in details by them. Khare et al.14 proposed a model for steadystate and dynamic propylene polymerization in a gas phase stirred-bed reactors. In their model, they considered a set of reaction kinetic equations for Ziegler−Natta catalyst as well as thermodynamic parameters that accurately define the polymer properties. However, all these previous studies were theoretical in nature and lack the necessary experimental validation. To the best of our knowledge, only one experimental study has been published concerning gas-phase propylene homopolymerization in a fluidized bed reactor in which propylene polymerization was carried out in a batch reactor for which a simplified single-phase dynamic model was proposed by Meier et al.15 They extended a compartment reactor model based on the small-scale reactor. This model is able to determine temperature and concentration profiles inside the reactor as well as molecular-weight distribution of the polymer. They studied vertical particle mixing and segregation in a pressurized pilot-scale fluidized bed reactor and proposed a simplified dynamic model to compare the measured temperature and
1. INTRODUCTION Fluidized bed reactors are widely used in the polymer industries due to their capability in carrying out a variety of chemical reactions and their high heat and mass transfer rates with uniform particle mixing.1−6 Therefore, development of accurate and rigorous models for the kinetics of heterogeneous polymerization, mass and heat transfer, and hydrodynamic characteristics in the fluidized bed is essential for understanding the ongoing phenomena in the reactor and for designing more productive reactors. Mass and heat transfer restrictions, especially in the presence of highly reactive catalyst particles, can become considerable at the particle level.7 Model development for investigating industrial polymerization processes, reactor design, and operation need an integrated approach comprising of kinetics, reactor hydrodynamics, as well as heat and mass transfer processes. Different modeling approaches have been proposed in the literature to describe the hydrodynamics, mass and heat transfer characteristics, and chemical reactions in fluidized bed polyolefin reactors. Choi and Ray8 proposed a dynamic twophase model in which the reactor consists of the emulsion and bubble phases. They considered the polymerization reaction only in the emulsion phase, assuming that the bubbles are solidfree. McAuley et al.9 presented a dynamic model to describe the olefin polymerization in a gas-phase fluidized-bed reactor. They considered the fluidized bed polyolefin reactor as a well-mixed reactor. A mathematical model consisting of bubble, emulsion, and particulate phases with plug flow behavior was developed by Fernandez and Lona.10 Hatzantonis et al.11 considered the reactor to consist of a perfectly mixed emulsion phase and a bubble phase divided into several solid-free well-mixed compartments in series. Harshe et al. 12 developed a comprehensive mathematical model based on a mixing cell © 2014 American Chemical Society
Received: Revised: Accepted: Published: 8694
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Figure 1. Schematic of pilot scale fluidized bed propylene polymerization reactor.
were continuously charged into the reactor to produce a broad distribution of polymeric particles during contact with reactants. The Ziegler−Natta catalyst contains titanium as the active metal and polymerization reaction occurs on the catalyst active sites. As the reaction proceeds, catalyst portions are scattered and particles grow into the final polypropylene product.16 Reactants (i.e., propylene and hydrogen) and nitrogen act as the fluidization gas as well as the heat transfer medium. Solid particles are separated from the unreacted gases in the disengaging zone. The recycled gas is mixed with the makeup gas after heat removal and is fed back to the reactor inlet. The polymer particles were continuously withdrawn from a position above the distributor. The detailed design summary of the pilot scale fluidized bed reactor is given in Table 1. The reactor (R 01) includes a fluidized bed and a disengagement zone. The inner diameter of the reactor is 10 cm, and the height of the fluidized bed zone is 150 cm. Height and diameter of the disengagement zone are both 25 cm. Catalyst particles were injected into the bed at a point 9 cm above the gas distributor. Product samples were withdrawn from three different locations, i.e., 16, 26, and 40 cm above the distributor plate. The produced polymer can be discharged semicontinuously by opening a valve connected to the product vessel at a point 5 cm above the gas distributor. The gas distributor was a stainless steel perforated plate of 100mesh size. Temperature in the reactor was measured at 6 different positions, starting at 16 cm above the distributor. Radial temperature gradients in the reactor can be neglected due to the agitation produced by the up-flowing gas and small diameter of the reactor. Temperature uniformity is a wellknown advantage of fluidized bed reactors. In fact, the solid circulation rate inside the bed is high enough that it can
concentration profiles with the model results. The polymerization reactor was considered to be well-mixed and singlephase in which the particulate phase remains at minimum fluidizing conditions. In addition, the kinetic model involved only the propagation and deactivation of the catalyst reactions. They used metallocene rac-Me2Si[Ind]2ZrCl2 as a catalyst and triisobutylaluminum (TIBA) as a cocatalyst to increase the catalyst activity. The main focus of this work is to implement a comprehensive model for a continuous gas-phase propylene polymerization with heterogeneous Ziegler−Natta catalyst in a pilot scale fluidized-bed catalytic reactor (FBR) and to validate the two-phase model along with the comprehensive two-site kinetic scheme through a real-time study. A unique and novel fluidized bed pilot plant, resembling an industrial unit, was designed and built for this purpose. The pilot-scale fluidized bed reactor was simulated using a two-phase model and the results were compared with the experimental data in terms of the reactor temperature, concentration profiles of propylene and hydrogen and polypropylene production rate. In addition, the experimental and calculated temperatures were compared for different polypropylene grades.
2. EXPERIMENTAL STUDIES 2.1. Experimental Setup. A pilot-scale fluidized bed reactor was constructed in the Pilot Plant Laboratory at the University of Malaya. The main objective for employing such a setup was to study the catalytic polymerization of olefins at high pressure and operating conditions close to the industrial units. Figures 1−3 illustrate the schematic, picture, and detailed drawing of the pilot scale fluidized bed reactor, respectively. Ziegler−Natta catalyst and triethyl aluminum as the cocatalyst 8695
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Figure 2. Fluidized bed propylene polymerization reactor detailed drawing.
temperature entering the reactor at start up to enable the reactants to reach the required reaction temperature. An airdriven piston gas booster compressor (P101) was used to compensate the pressure drop through the loop. A buffer vessel, installed downstream the compressor, was used to damp pressure fluctuations. Flow of gas through the reactor was controlled by a control valve (FCV301) and was measured by a flow meter (FT301) that is located just before the reactor. An important requirement of a fluidized bed reactor is that the velocity of the recycle stream must be sufficient to keep the bed
disperse the heat generated by the reaction instantaneously. Therefore, the radial temperatures of the reactor were not taken but only temperatures at different levels in the reactor were measured. One cyclone and four filters were placed to separate entrained solid particles from the exiting gas. The gas leaving the reactor was cooled by a shell and tube heat exchanger (E-401). A control valve (TCV101) was used to manipulate the reactor gas inlet temperature. Heat was removed from the reactor by cooling the gaseous recycle stream outside the reactor. A heater was used to control the gas 8696
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Figure 3. Picture of the pilot scale fluidized bed polypropylene reactor in this study.
content of the gas was measured continuously by the online hygrometer. A gas sample flow from the reactor was analyzed continuously by a Perkin-Elmer Clarus 580 gas chromatograph (GC) to measure and regulate the gas composition inside the reactor. Due to agitation produced by the up-flowing gas as well as the small height and diameter of the pilot scale reactor, which ensure uniformity of reactants in the bed ,and also because the presence of solid particles throughout the bed would choke the gas line, only one gas sample was taken from the top of the reactor and analyzed continuously by an online Perkin-Elmer Clarus 580 gas chromatograph (GC) to measure and regulate the gas composition inside the reactor. The threecolumn model Arnel 1117PPC provided a guaranteed analysis of hydrogen, nitrogen, and propylene in approximately 8.5 min using a flame ionization detector (FID) and two thermal conductivity detectors (TCD/TCD). Three columns were installed in the GC. Column A used nitrogen as the carrier gas, while columns B and C used hydrogen. Column A performed a full-range hydrogen analysis on the gas samples using a TCD with nitrogen carrier gas. Oxygen, nitrogen, carbon monoxide and carbon dioxide were analyzed by the fixed gas column (B) using a TCD with hydrogen carrier gas. The hydrocarbon column (C) was used to analyze propylene using a FID with hydrogen carrier gas. Columns A and B were linked electronically and eluted to the data handling system as one response and appear as one column. Therefore, only two columns of data handling were required. All three columns could be run simultaneously or independently. Highly pure raw materials are required for catalytic olefin polymerization to avoid poisoning the catalyst. Propylene, hydrogen, and nitrogen gases were purified in separate purification systems (Entegris GateKeeper gas purifiers) to remove traces of oxygen, water vapor, and carbon monoxide. Three mass flow meters (Brooks) were used in the fresh feed
Table 1. Detail Design Parameters of the Pilot Scale Fluidized Bed Reactor parameters
value
catalyst type Ziegler−Natta catalyst density ρc 2370 kg/m3 average catalyst particle diameter dp 80 μm maximum catalyst feed rate ṁ cat 3.02 g/h minimum fluidization velocity Umf 0.1 ms−1 maximum bubble size dBv max 0.0008 m Reactor Design reaction zone inner Di,RZ 0.1016 m diameter 0.00785 m2 crossARZ sectional area height HRZ 1.5 m volume VRZ 0.011775 m3 disengagement inner Di,DZ 0.25 m zone diameter 0.0490625 m2 crossADZ sectional area height HDZ 0.25 m volume VDZ 0.0097 m3 reactor volume Vreactor 0.0215 m3 maximum pressure drop across Δpbed 0.0325 atm fluidized bed Distributor Plate Design distributor plate type stainless steel perforated plate 100-mesh size
in a fluidized state. This was ensured by monitoring and stabilizing the flow of the gaseous stream. The Easidew online hygrometer (MICHELL, EA2-MON-100) was used to measure the moisture content of the gas within the reactor. In this experiment, two gas samples for humidity measurement were taken from inlet and outlet of the reactor and the moisture 8697
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stream to measure the flow of propylene (FT302), hydrogen (FT304), and nitrogen (FT303). For injecting a small amount of Ziegler−Natta catalyst into the reactor, a continuous feeding system was developed. A ball valve, installed under the catalyst container, was used as the dosing device. A small flow of pressurized high purity nitrogen was permanently kept in the whole injection system to feed the catalyst into the reactor through the ball valve and stop gas leakage into the injection system. A kill gas injection system, composed of CO2 gas, was installed for terminating the polymerization reaction at emergency conditions, such as power failure, to stop or reduce the polymerization reaction, or to maintain the reactor bed temperature below the sintering temperature of the polymer. It was injected manually into the system in case these emergency conditions took place. The system was designed to work at a maximum pressure of 30 bar and temperature of 100 °C. The reactor differential pressure indicator (DPT211), thermocouples, and pressure indicators located inside the reactor in different places were utilized to monitor temperatures and pressures of the system. In the event of a measured value indicating a dangerous situation, the experiment was stopped. A rupture disc and a pressure relief valve were installed on top of the reactor and set to a relief pressure of 30 and 32 bar, respectively, to protect the reactor from overpressure. 2.2. Experimental Procedure. The reactor was charged with 2 kg of a polypropylene powder with an average particle size of 500 μm before the startup. The system must be free of contaminants such as moisture, oxygen, carbon monoxide, or carbon dioxide before polymerization takes place in the reactor. This was achieved by purging the system with high purity liquefied nitrogen. The reactor was always exposed to air and moisture and consequently needed to be purged with high purity nitrogen until the moisture level dropped to less than10 ppmv prior to charging the Ziegler−Natta catalyst. Triethylaluminum (TEAL) was used to further scavenge impurities such as moisture and oxygen from the reactor. TEAL removes catalyst poisons from the reactor and thereby maximizing the catalyst activity and productivity. TEAL diluted in hexane was then injected to the reactor until the moisture level further dropped to less than 1 ppmv. The setup ran with gas inlet temperature of 60 °C, measured by the temperature transmitter TT101 (Figure 1). When the system was at the required operating conditions (Table 2), the system was regarded as being ready to start the catalyst
injection. After eliminating the catalyst poisons from the system in the beginning of the experiment, a low amount of catalyst was injected into the reactor. Inlet temperature and fluidization velocity were kept constant during the experiments. However, total and partial pressures were changing because injection of the fresh gas was not done continuously. Temperature and concentration of gas components inside the reactor were monitored continuously with the instruments mentioned in section 2.1. This pilot plant was equipped with a local/remote control system. Monitoring and data acquisition were performed through a PC-based software system which included various capabilities such as trending, monitoring, recording and printing of process data as well as process control variables. The full SCADA is illustrated in Figure 4. Control of the heat exchanger unit was also carried out through the use of this software.
3. MATHEMATICAL MODELING In the present study, the kinetic model of propylene homopolymerization over Ziegler−Natta catalyst was combined with the dynamic single-phase and two-phase hydrodynamic models. The strength of the heterogeneous Ziegler−Natta catalysts to generate polymers with broad molecular weight distributions has long being identified. The single type of active center kinetic model is not adequate to define the kinetic behavior of propylene homopolymerization. Therefore, two types of active sites were considered for the catalyst in the present work. The kinetic scheme, comprising of a series of elementary reactions, and the rate parameters, used for the two models, are listed in Table 3. The reaction rate constants used in this work are given in Table 4. The model consists of mass balances on the species presented in the reactor which are written as a series of algebraic and differential equations. Consumption rate of each component (monomer and hydrogen) and the polymer production rate were modeled using population balance and the method of moments. The corresponding moment equations are given in Table 5. Details of the kinetic model are reported by Shamiri et al.17 Based on the assumption that the only significant consumption of propylene monomer is by the propagation reaction, where the consumption of hydrogen gas occurs via transfer to hydrogen, the following equations for the consumption rate of monomer and hydrogen can be stated: For monomer:
Table 2. Operating and Gas Composition Conditions and Physical Properties Used in the Experimental Study
NS
Ri =
∑ [Mi]Y (0, j)k p(j), i = 1 (1)
j=1
operating conditions
physical properties
Tin (K)=333.15 Tref (K) = 342.15 Tw(K) = 350.15 D (m) = 0.1016 H (m) = 1.5 V (m3) = 0.0215 P (bar) = 22 propylene concentration (mol %) = 59.18 hydrogen concentration (mol %) = 6.46 nitrogen concentration (mol %) = 33.7 propane concentration (mol %) = 0.47 C6+ concentration (mol %) = 0.19
dp (m) = 500 × 10−6 μ (Pa·s) = 1.14 × 10−4 ρg (kg/m3) = 23.45 ρpol (kg/m3) = 910 εmf = 0.45
For hydrogen: NS
Ri =
∑ [Mi]Y (0, j)k fh(j), i = 2 (2)
j=1
The total polymer production rate for each phase can be calculated from 2
Rp =
∑ MwiR i i=1
(3)
where Ri is the instantaneous rate of reaction. 8698
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Figure 4. Software-based control and data acquisition system (SCADA) for the pilot scale fluidized bed polypropylene reactor.
Table 3. Elementary Chemical Reactions of Propylene Homo-polymerization reaction k f (j)
N *(j) + cocatalyst ⎯⎯⎯→ N (0, j)
Table 4. Rate Parameters Used for the Two-Phase and WellMixed Models (Obtained at 69 °C)
description reaction
formation of active sites
formation initiation
rate constant kf(j) ki(j)
k i(j)
initiation of active sites
k p(j)
propagation
kh(j)
k fm(j)
chain transfer to monomer
kh
N (0, j) + M ⎯⎯⎯→ N (1, j) N (r , j) + M ⎯⎯⎯⎯→ N (r + 1, j) N (r , j) + M ⎯⎯⎯⎯⎯→ N (1, j) + Q (r , j) k fh(j)
N (r , j) + H 2 ⎯⎯⎯⎯→ NH(0, j) + Q (r , j)
propagation
transfer to hydrogen
activation energy transfer
k h(j)
NH(0, j) + M ⎯⎯⎯⎯→ N (1, j) kh r(j)
NH(0, j) + AlEt3 ⎯⎯⎯⎯⎯→ N (1, j)
kp(j)
kfm(j)
transfer to cocatalyst
kfh(j)
k fs(j)
spontaneous transfer
kfr(j)
kds(j)
deactivation reactions
kfs(j)
k fr(j)
N (r , j) + AlEt3 ⎯⎯⎯⎯→ N (1, j) + Q (r , j) N (r , j) ⎯⎯⎯⎯→ NH(0, j) + Q (r , j)
N (r , j) ⎯⎯⎯⎯→ Nd(j) + Q (r , j)
deactivation
kds(j)
N (0, j) ⎯⎯⎯⎯→ Nd(j)
kds(j)
unit s−1 m3 kmol−1 s−1 m3 kmol−1 s−1 m3 kmol−1 s−1 m3 kmol−1 s−1 kcal kmol−1 m3 kmol−1 s−1 m3 kmol−1 s−1 m3 kmol−1 s−1 m3 kmol−1 s−1 −1 s
site type 1
site type 2
1 22.9
1 54.9
0.1
0.1
20 208.6 7200
20 22.9 7200
0.046
0.253
7.54
7.54
0.024
0.12
0.0001
0.0001
0.00034
0.00034
kds(j)
NH(0, j) ⎯⎯⎯⎯→ Nd(j)
The number-average molecular weight and the weightaverage molecular weight, M̅ n and M̅ w, can be determined using the method of moments as follows: 8699
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Table 5. Moment correlations
Table 6. Hydrodynamic Correlations and Equations Used for the Two-Phase Model
dY (0, j) = [M]{k i(j)N (0, j) + k h(j)NH(0, j)} + NH(0, j)k hr(j)[AlEt3] dt ⎧ ⎪ ⎪ Rv ⎫ ⎬ ( )[H ] ( ) ( ) k j k j k j − Y (0, j)⎨ + + + fh 2 fs ds ⎪ ⎪ V ⎩ p⎭
parameter
formula
Minimum fluidization velocity Bubble velocity
dY (1, j) = [M]k i(j)N (0, J ) + NH(0, J ){k h(j)[M] + k hr(j)[AlEt3]} dt
Bubble rise velocity Emulsion velocity
+ Y (0, j){k fm(j)[M] + k fr(j)[AlEt3]} + [M]k p(j)Y (0, j) ⎧ ⎪ k (j)[M] + k fr(j)[AlEt3] + k fh(j)[H 2] + k fs(j) − Y (1, j)⎨ ⎪ fm ⎩
Bubble diameter
25
Ub = U0 − Ue + ubr
26 26
1/2
ubr = 0.711(gdb) Ue =
27
U0 − δUb 1−δ
28
db = db0[1 + 27(U0 − Ue)]1/3 (1 + 6.84H ) db0 = 0.0085 (for Geldart B)
⎪ R ⎫ + kds(j) + v ⎬ Vp ⎪ ⎭
mass transfer coefficient
26
−1 ⎛ 1 1 ⎞ Kbe = ⎜ + ⎟ Kce ⎠ ⎝ Kbc
dY (2, j) = [M]k i(j)N (0, j) + NH(0, j){k h(j)[M] + k hr(j)[AlEt3]} dt
⎛ D 1/2g 1/4 ⎞ ⎛U ⎞ g ⎟ Kbc = 4.5⎜ e ⎟ + 5.85⎜⎜ 5/4 ⎟ ⎝ db ⎠ ⎝ db ⎠
+ Y (0, j){k fm(j)[M] + k fr(j)[AlEt3]}
⎛ Dg εeubr ⎞ Kce = 6.77⎜ ⎟ ⎝ db ⎠
+ [M]k p(j){2Y (1, j) + Y (0, j)} − Y (2, j) ⎧ ⎪ ⎨ k (j)[M] + k fr(j)[AlEt3] + k fh(j)[H 2] + k fs(j) + kds(j) ⎪ fm ⎩ +
ref
Remf = [(29.5)2 + 0.357Ar ]1/2 − 29.5
heat transfer coefficient
⎪ Rv ⎫ ⎬ Vp ⎪ ⎭
26
−1 ⎛ 1 1 ⎞ Hbe = ⎜ + ⎟ Hce ⎠ ⎝ Hbc
⎛ Ueρg Cpg ⎞ (kgρg Cpg)1/2 g 1/4 ⎟⎟ + 5.85 Hbc = 4.5⎜⎜ db5/4 ⎝ db ⎠
dX(n , j) = Y (n , j){k fm(j)[M] + k fr(j)[AlEt3] + k fh(j)[H 2] + k fs(j) dt R + kds(j)} − X(n , j) v Vp
⎛ ε u ⎞1/2 Hce = 6.77(ρg Cpgkg)1/2 ⎜ e 3br ⎟ ⎝ db ⎠
n = 0, 1, 2
bubble phase fraction
29
⎛ ∑NS (X(1, j) + Y (1, j)) ⎞ j=1 ⎟ M̅ n = Mw⎜ NS ⎜ ∑ (X(0, j) + Y (0, j)) ⎟ ⎝ j=1 ⎠
⎡ ⎛ U − Umf ⎞⎤ ⎟⎥ δ = 0.534⎢1 − exp⎜− 0 ⎝ ⎣ 0.413 ⎠⎦
emulsion phase porosity
⎛ U − Umf ⎞ ⎟ εe = εmf + 0.2 − 0.059 exp⎜− 0 ⎝ 0.429 ⎠
29
bubble phase porosity
⎛ U − Umf ⎞ ⎟ εb = 1 − 0.146 exp⎜− 0 ⎝ 4.439 ⎠
29
volume of polymer phase in the emulsion phase volume of polymer phase in the bubble phase volume of the emulsion phase volume of the bubble phase
VPe = AH(1 − εe)(1 − δ)
18
VPb = AH(1 − εb)δ
18
Ve = AH(1 − δ)
18
Vb = AδH
18
⎛ ∑NS (X(2, j) + Y (2, j)) ⎞ j=1 ⎟ M̅ w = Mw⎜ NS ⎜ ∑ (X(1, j) + Y (1, j)) ⎟ ⎝ j=1 ⎠
(4)
(5)
The polydispersity index (PDI) is defined by the ratio of weight-average to number-average molecular weights: M̅ PDI = w M̅ n
(6)
[Mi]b,(in) UbAb − [Mi]b UbAb − R vεb[Mi]b
3.1. Dynamic Two-Phase Model. Based on the dynamic two-phase model, polymerization reactions were considered to occur in the bubble phase and the emulsion phase. The heat loss through the reactor wall to the surroundings due to the absence of insulation was also considered in the model. Poisoning reactions were neglected because it was assumed that the feed gas was free of impurities. Elutriation of solid particles from the reactor was also neglected. The required correlations for the dynamic two phase model are given in Table 6. Based on the above assumptions, the following dynamic material balances were derived:18−23 For bubbles:
− Kbe([Mi]b − [Mi]e )Vb − (1 − εb) =
Ab VPFR
∫ R i dz b
d (Vbεb[Mi]b ) dt
(7)
For emulsion: [Mi]e,(in) UeAe − [Mi]e UeAe − R vεe[Mi]e ⎛ δ ⎞ ⎟ − (1 − ε )R + Kbe([Mi]b − [Mi]e )Ve⎜ ie e ⎝1 − δ ⎠ d = (Veεe[Mi]e ) dt
(8)
Moreover, the energy balances can be written as 8700
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• Homogeneous composition and temperature throughout the bed were considered. • The feed gas is free of impurities, thus, poisoning reactions were neglected. • No elutriation of solid particles occurs from the reactor. Based on the above assumptions, the following dynamic material and energy balance equations can be derived:19 The molar balance is given by
For bubbles: m
UbAb(Tb,(in) − Tref ) ∑ [Mi]b,(in) Cpi − UbAb(Tb − Tr ef ) i=1
m
∑ [Mi]b Cpi i=1 m
−R v(Tb − Tref )(∑ εbCpi[Mi]b + (1 − εb)ρpol Cp,pol) i=1
A ΔH + (1 − εb) b R VPFR
(Vεmf )
∫ R pbdz
d[Mi] = U0A([Mi]in − [Mi]) − R vεmf [Mi] dt − (1 − εmf )R i
m
d +Hbe(Te − Tb)Vb − Vbεb(Tb − Tr ef ) ∑ Cpi ([Mi]b ) d t i=1
(15)
The energy balance is written as m
[∑ [Mi]CpiVεmf + V (1 − εmf )ρpol Cp,pol]
m
d =(Vb(εb ∑ Cpi[Mi]b + (1 − εb)ρpol Cp,pol)) (Tb − Tref ) dt i=1
i=1
m
dT dt
= U0A ∑ [Mi]Cpi(Tin − Tref )
(9)
i=1
For emulsion:
m
−U0A ∑ [Mi]Cpi(T − Tr ef )
m
UeAe(Te,(in) − Tref ) ∑ [Mi]e,(in) Cpi − UeAe(Te − Tref )
i=1
i=1
m
m
− R v[∑ [Mi]Cpiεmf + (1 − εmf )ρpol Cp,pol](T − Tref )
∑ [Mi]e Cpi
i=1
i=1
+(1 − εmf )ΔHR R p − πDHhw (Te − Tw )
m
−R v(Te − Tref )(∑ εeCpi[Mi]e + (1 − εe)ρpol Cp,pol)
(16)
The initial conditions are as follows:
i=1
− (1 − εe)R peΔHR ⎛ δ ⎞ ⎟(T − T ) − V ε (T − T ) −HbeVe⎜ b e e e ref ⎝1 − δ ⎠ e m ∑ Cpi d ([Mi]e ) − πDHhw(1 − δ)(Te − Tw)= dt i=1 m
(Ve(εe ∑ Cpi([Mi]e ) + (1 − εe)ρpol Cp,pol)) i=1
(10)
The initial conditions are given by (11)
[Mi]e, t = 0 = [Mi]in
(12)
Tb(t = 0) = Tin
(13)
Te(t = 0) = Tin
(14)
(17)
T (t = 0) = Tin
(18)
4. RESULTS AND DISCUSSION In the present study, the two-phase model along with the comprehensive two-site kinetic scheme, discussed in section 3 was validated with the actual pilot plant data. The operating conditions and gas composition for producing polypropylene in this work are listed in Table 2. A comparative study with the actual dynamic pilot plant data in terms of reactor temperature, propylene gas concentration and polypropylene production rate was conducted to validate the two-phase model for propylene homopolymerization in the gas phase fluidized bed reactor. Comparison between the results of two-phase and conventional well-mixed models with the pilot plant data in terms of the propylene concentration inside the reactor is illustrated in Figure 5. As can be seen in Figure 5, predicted data of the two-phase model are in good agreement with the experimental data, especially at longer elapsed times. Based on considering the presence of solids in the bubbles and the emulsion phase being at conditions beyond the minimum fluidization the two-phase model provides more realistic results. However, the two-phase model under-predicts the experimental data at shorter elapsed time. This is mainly due to very high rate of mass and heat transfer between the bubbles and the emulsion phase at the very beginning of the process startup at which the concentration difference between the two phases is maximum. This situation during the initial stages of fluidization makes the hydrodynamics of the reactor approach the well-mixed condition. However, this mechanism is definitely unrealistic later in the reaction as more bubbles are
d (Te − Tref ) dt
[Mi]b, t = 0 = [Mi]in
[Mi]t = o = [Mi]in
Solving the above set of equations, changes in concentration and temperature inside the reactor can be obtained. 3.2. Well-Mixed Model. For the sake of comparison, formulation of the well-mixed model is discussed briefly in this section. In the simplified well-mixed model proposed by McAuley et al.,9,24 the following simplifying assumptions were made: • Due to the absence of insulation, the heat loss through the reactor wall to the surroundings was considered. The polymerization reactor is considered to be a well-mixed reactor due to high mass and heat transfer rates between bubble and emulsion phases.4,19,21 • The emulsion phase remains at minimum fluidization. 8701
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Figure 7. Comparison between experimental data and calculated temperatures.
Figure 5. Comparison between experimental data and calculated propylene concentration.
formed and rates of mass and heat transfer are reduced. The maximum difference between the experimental data and predictions of the two-phase and well-mixed models are about 3.4 and 5 mol %, respectively. These differences are further due to the effect of inert gas on the hydrodynamic behavior of the fluidized bed reactor. Concentration profiles of inert gases versus time are shown in Figure 6. When the polymerization reaction starts, propylene
reactor occurs between the temperature transmitter TT102 at the bottom and TT107 at the top of the reactor at about 7 °C. The maximum temperature observed in this experiment was about 87.5 °C sensed by TT102. Since it was the closest sensor to the catalyst injection point, the presence of a higher amount of catalyst causes a higher reaction rate and consequently higher temperature. Nevertheless, the average bed temperature was used for comparison with predictions of the theoretical models. The figure also shows good agreement between the calculated and experimental average bed temperature profiles. As time evolves, predictions of the two-phase model become closer to the average bed temperature than does the well-mixed model. It should be noted that considering more realistic assumptions of the two-phase model, results obtained by this model are closer to real values compared to the well mixed model. At the start of reaction, the well-mixed model shows a close dynamic response to the average bed temperature. However, upon reaching a temperature of about 81 °C, this model begins to deviate considerably with time due the fact that it was assumed that the bubbles are solid-free and the emulsion stays at minimum fluidization, interchanging heat and mass with the bubble phase at uniform rates at all operating conditions. It is obvious that due to these simplified assumptions, it is not capable to accurately describe the dynamics of gas−solid distribution on the chemical reaction and rate of heat and mass transfer in the fluidized bed reactors by the well-mixed model. The maximum difference between the pilot plant temperature data and that of the two-phase and well-mixed models were about 2.4 and 3.5 °C, respectively. A comparison between the results of two-phase model with the pilot plant data in terms of the polypropylene production rate is illustrated in Figure 8. As shown in Figure 8, the twophase model predictions are in good agreement with the experimental data. However, the two-phase model overpredicts the experimental values within the initial reaction time range of 0−2000 s. This is mainly due to very high rate of polymerization reaction as well as mass and heat transfer at the beginning of the process startup. The maximum difference between the experimental data and predictions of the twophase model is about 0.8 g/s. Hydrogen gas is used to regulate the molecular weight and its distribution as well as grade transition of product in a pilot-scale propylene polymerization plant. Hydrogen concentration
Figure 6. Concentration profile of inert gas versus time inside of reactor.
concentration is reduced due to its conversion to polypropylene. By this decrease in the propylene concentration during the polymerization reaction, an expected increase in the concentration of inert components (nitrogen, propane, ethane, and C6+) in the system was observed. This is similar to what happens in an industrial scale polymerization reactor. Experimental reactor temperatures obtained at different levels of the fluidized bed and those obtained based on the two-phase and well-mixed models are presented in Figure 7, demonstrates that the temperature starts rising rapidly after injection of the catalyst and reaches its steady value after about 2 h. As expected in this system, the reactor temperature increases as the polymerization reaction starts due to progress of the exothermic reaction of propylene polymerization. During a single experiment, the largest temperature gradient inside the 8702
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Figure 10. Evolution of number and weight-average molecular weights and PDI with the time in the reactor (propylene = 60 mol %, hydrogen = 0.5 mol %, and nitrogen = 39.5 mol %).
Figure 8. Comparison between experimental data and calculated production rate using the two-phase model.
indicates that the weight-average molecular weight, numberaverage molecular weight and PDI of the polymer increase rapidly at the beginning of the polymerization and eventually stabilize within less than half an hour of the process startup. The final value of the number-average molecular weight, weight-average molecular weight and PDI, under the conditions of this modeling, are close to 28900, 145000, and 5, respectively. This indicates that the produced polypropylene attains a broad molecular weight distribution. A comparison between actual reactor temperatures and those calculated based on the model presented in this work is shown in Figure 11. The gas composition conditions for producing
profile versus time is shown in Figure 9. It is obvious that the hydrogen concentration decreases at the start of the polymer-
Figure 9. Concentration profile of hydrogen versus time inside of reactor.
ization reaction due to its consumption via the mechanism of transfer to hydrogen reaction. The simulation results based on the two-phase model were found to be in a close agreement with the experimental data in terms of hydrogen concentration profile. As discussed before, this is mainly due to the sensible assumption and correlation coefficient considered in the twophase model. The maximum difference between the pilot plant data and the two phase model prediction for the hydrogen concentration was as little as 0.15 mol %. The over prediction of the two-phase model can be attributed to the effect of inert gas on the process hydrodynamics which is neglected in this work. The polymer molecular weight and its distribution affect most of the essential properties of the polymer, such as tensile strength, thermal stability, stiffness, hardness, softening point and impact strength significantly. While the PDI represents the distribution of individual molecular masses in a batch of polymers and is used as a measure of the width of the molecular weight distribution. Figure 10 shows the polypropylene molecular weight distribution as a function of time. This figure
Figure 11. Comparison between experimental data and calculated temperatures using the two-phase model at different polypropylene grades.
different polypropylene grades employed in this study are listed in Table 7. As can be seen in Figure 11, there is a good agreement between the calculated and pilot plant temperatures. The maximum difference between the industrial data and the model prediction is 1.5 K for polypropylene grade B type. The differences between predicted and industrial temperatures are due to the effect of inert gas, particle size distribution, and solid entrainments on the hydrodynamic behavior of the fluidized bed reactor. 8703
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Table 7. Gas Composition Conditions for Producing Different Grades of Polypropylene gas
unit
A
B
C
D
E
F
propylene concn hydrogen concn nitrogen concn
mol % mol % mol %
64.945 4.85 29.95
59.18 6.46 33.71
54.9 4.83 39.96
49.95 4.1 45.71
44.96 3.9 50.9
40.04 3.8 55.93
cloud to emulsion heat transfer coefficient (W/m3·K) spontaneous deactivation rate constant for a site of kds (j) type j kf (j) formation rate constant for a site of type j kfh (j) transfer rate constant for a site of type j with terminal monomer M reacting with hydrogen kfm (j) transfer rate constant for a site of type j with terminal monomer M reacting with monomer M kfr (j) transfer rate constant for a site of type j with terminal monomer M reacting with AlEt3 kfs (j) spontaneous transfer rate constant for a site of type j with terminal monomer M kh (j) rate constant for reinitiating of a site of type j by monomer M kh (j) rate constant for reinitiating of a site of type j by cocatalyst ki (j) rate constant for initiation of a site of type j by monomer M kp (j) propagation rate constant for a site of type j with terminal monomer M reacting with monomer M Kbc bubble to cloud mass transfer coefficient (s−1) Kbe bubble to emulsion mass transfer coefficient (s−1) Kce cloud to emulsion mass transfer coefficient (s−1) M monomer (propylene) [Mi] concentration of component i in the reactor (kmol/ m3) [Mi]in concentration of component iin the inlet gaseous stream Mw monomer molecular weight (kg/kmol) N(0, j) uninitiated site of type j produced by formation reaction N(r,j) living polymer molecule of length r, growing at an active site of type j, with terminal monomer M NH(0,j) uninitiated site of type j produced by transfer to hydrogen reaction r number of units in polymer chain Ri instantaneous rate of reaction for monomer i (kmol/ s) Remf Reynolds number of particles at minimum fluidization condition Rp production rate (kg/s) Rpb bubble phase production rate (kg/s) Rpe emulsion phase production rate (kg/s) Rv volumetric polymer phase outflow rate from the reactor (m3/s) Tin temperature of the inlet gaseous stream (K) Tw wall temperature (K) U0 superficial gas velocity (m/s) Umf minimum fluidization velocity (m/s) V reactor volume (m3) Vp volume of polymer phase in the reactor (m3) VPFR volume of PFR (m3) X(n,j) nth moment of chain length distribution for dead polymer produced at a site of type j Y(n,j) nth moment of chain length distribution for living polymer produced at a site of type j
5. CONCLUSIONS A two-phase model was used for simulating the propylene polymerization in a pilot-scale fluidized bed reactor. The model was validated with data generated in a pilot plant designed to study olefin polymerization reactions. To achieve a better insight on the reactor performance, the hydrodynamics of the fluidized bed reactor of propylene polymerization, based on the dynamic two-phase flow structure, was coupled with the kinetic model. Moreover, the polymerization reaction was considered to take place in both the bubble phase and the emulsion phases in the two-phase model. Comparative studies were performed using two-phase and well-mixed models versus the pilot plant data. A good agreement was observed between the prediction of the twophase model and that of the pilot plant. The maximum differences between the pilot plant data and the two phase model prediction for the propylene and hydrogen concentrations, reactor temperature and polypropylene production rate were about 3.4 mol %, 0.15 mol %, 2.4 °C, and 0.8 g/s, respectively. The well-mixed model was found to underestimate the propylene concentration and emulsion phase temperature. Furthermore, a comparison between actual reactor temperatures and those calculated based on the two-phase model using different gas composition or polypropylene grades was carried out and good agreement was also achieved with an average error of 0.22%.
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Hce
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected];
[email protected]. Tel: +60-379677657. Fax: +60-379675319. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful to the University of Malaya and the Ministry of Higher Education of Malaysia (MOHE) for supporting this research project via the research grant UM.C/ 625/1/HIR/MOHE/ENG/25 which made possible the publication of this paper.
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NOMENCLATURE A cross-sectional area of the reactor (m2) AlEt3 triethyl aluminum Ar Archimedes number Cpi specific heat capacity of component i (J/kg·K) Cp,pol specific heat capacity of solid product (J/kg·K) db bubble diameter (m) dp polymer particle diameter (m) D bed diameter (m) hw wall heat transfer coefficient (W/m2·K) H bed height (m) Hbe bubble to emulsion heat transfer coefficient (W/m3· K) Hbc bubble to cloud heat transfer coefficient (W/m3·K) 8704
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Greekletters
ΔHR εmf μ ρg ρpol
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heat of reaction (J/kg) void fraction of the bed at minimum fluidization gas viscosity (Pa.s) gas density (kg/m3) polymer density (kg/m3)
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