Steady-State and Dynamic Modeling of the Basell Multireactor Olefin

Dec 1, 2010 - Limited of China National Petroleum Company, Lanzhou 730060, China. In this work, we developed the steady-state and dynamic models for t...
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Ind. Eng. Chem. Res. 2011, 50, 322–331

Steady-State and Dynamic Modeling of the Basell Multireactor Olefin Polymerization Process Zu-Wei Zheng,† De-Pan Shi,† Pei-Lin Su,† Zheng-Hong Luo,*,† and Xiao-Jun Li‡ Department of Chemical and Biochemical Engineering, College of Chemistry and Chemical Engineering, Xiamen UniVersity, Xiamen 361005, China and Polyolefin Department of Lanzhou Petrochemical Company Limited of China National Petroleum Company, Lanzhou 730060, China

In this work, we developed the steady-state and dynamic models for the commercial polypropylene process of Basell Spheripol technology, involving fundamental chemical engineering principles and advanced software tools, i.e., Polymers Plus and Aspen Dynamics. The models considered the important issues of physical property and thermodynamic model selection, catalyst characterization, and reactor model. Besides, a multisite catalyst with traditional Ziegler-Natta polymerization kinetics was introduced to describe the broad molecular weight distribution of the polymers produced in this polypropylene technology. Both the continuous stirred tank reactor model and the combined plug flow reactors model were proposed to simulate the reactors. Furthermore, we validated the models using industrial data and demonstrated application of the dynamic model to grade change, start up, and shut down at a certain emergent accident. 1. Introduction 1.1. Scope. The Basell Spheripol technology is one of the most widespread commercial methods to produce polypropylene. Commonly, its key parts are two loop reactors and one or two fluidized bed reactors (FBRs). Among them, the loop reactors are used to produce homopolypropylene, ethylene-propylene random copolymer, and ethylene-propylene-1-butene copolymer, and the FBR is used to produce impact polypropylene.1,2 It is well acknowledged that the loop reactor is one of the best choices for the preparation of homopolypropylene due to its high mixing capability as well as high heat transfer/exchange rate.1 The objective of this work is to discuss the considerations and techniques needed to develop a comprehensive model for the polypropylene process of the Spheripol technology. Generally, an excellent polymerization process model needs accurate description of physical and thermodynamic properties, phase equilibrium, and polymerization kinetics, all of which were discussed in our previous work.2 In addition, both steady-state and dynamic models for the commercial bulk polypropylene process of HYPOL technology were developed in our previous work.2 To date, there have also been many other models describing the olefin polymerization process.3-19 For instance, Khare et al.3 presented a model for the gas-phase polypropylene process using a stirred-bed reactor, which was approximated as a series of continuous stirred-tank reactors (CSTRs). Detailed modeling methodologies, especially the reactor modeling, were provided. Khare et al.4 also simulated slurry high-density polyethylene processes. The nonequilibrium behavior in ethylene/polyethylene flash separators was detected in their work.6 Chatzidoukas et al.5 developed a dynamic model for the commercial polypropylene process of Borstar technology, wherein a comprehensive kinetic model for the ethylene-1butene copolymerization based on a two-site catalyst was employed. The Sanchez-Lacombe equation of state (S-L-EoS) was employed for the thermodynamic properties and the phase * To whom correspondence should be addressed. Tel.: +86-5922187190. Fax: +86-592-2187231. E-mail: [email protected]. † Xiamen University. ‡ China National Petroleum Company.

equilibrium calculations in the process units.5 As a whole, there are many methodologies proposed in the literature,1-27 which succeed in developing a comprehensive model for polyolefin processes. These methodologies include model selection and parameter tuning for physical and thermodynamic properties, catalyst characterization, and polymer properties in addition to the single and multiple site of traditional Ziegler-Natta polymerization kinetics. However, most of the preceding works have focused on the polyethylene process and the gas-phase polypropylene process. To the best of our knowledge, there is no comprehensive model of the commercial bulk polypropylene process of the Spheripol technology in the literature prior to our work. In this work, both steady-state and dynamics models for the polypropylene process of Spheripol technology are developed using fundamental chemical engineering principles and advanced software tools, i.e., Polymers Plus and Aspen Dynamics. We focus not only on the accurate modeling of the reactors and polymerization kinetics but also on the thermodynamic understanding and, moreover, discuss the limitation of thermodynamics and suggest the proper efforts needed for development of the process model. 1.2. Commercial Polypropylene Process of Spheripol Technology. Spheripol technology was first industrialized by Montedison in 1983. The second-generation technology was developed by Montell in 1995, which is also called Basell technology at present.28,29 An application of this Spheripol technology in a chemical plant in China was studied here. Figure 1 shows a schematic flow chart for a typical polypropylene process of the Spheripol technology. The process includes bulk polymerization, degasification, gas-phase copolymerization, steaming, and drying. The prepolymerization is carried out under mild operating conditions to prevent particle overheating and generation of fine powder. The main polymerization then proceeds in two liquid-phase tubular loop reactors. In the case of production of impact copolymer, the polymerization reaction will be continued in FBR. The technology uses a titanium-based catalyst and an aluminum-alkyl-based cocatalyst, which are titanium tetrachloride (TiCl4) and triethyl aluminum [Al(C2H5)3], respectively. Besides, hydrogen along with the propylene feed is used as the molecular-weight control agent to produce various

10.1021/ie101699b  2011 American Chemical Society Published on Web 12/01/2010

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Figure 1. Simplified flow chart for a polypropylene process of the Spheripol technology.

Figure 2. Spheripol loop process (A, catalyst; B, propylene; C, hydrogen; D, product; E, coolant; 1, P200, pump; 2, P201, pump; 3, P202, pump; 4, R200, prepolymerization reactor; 5, R201, main polymerization reactor; 6, R202, main polymerization reactor).

grades of polypropylene, and the tacticity control agents fed along with the catalyst are commonly used to increase the isotactic content of the polypropylene. Figure 2 shows a simplified diagram of the Spheripol technology using three liquid-phase tubular loop reactors for production of homopolypropylene, ethylene-propylene random copolymer, and ethylene-propylene-1-butene copolymer. The temperature for the prepolymerization reactor is controlled at 20 and 70 °C for the main polymerization reactor. The pressure of those three reactors can range from 3.4 to 4.5 MPag, and it is 4.0 MPag in this discussion. The axial flow pumps are used to provide the driving force for circulation and help to mix the slurry well in the reactors. Cooling jackets possess high heat transfer rates due to their high aspect ratio. 1.3. Modeling Technique. As reported in refs 2-4 the model integrates the fundamental chemical engineering principles and advanced software tools to simulate both steady-state and dynamic processes. For the modeling part, there were mass and energy balances, physical properties, phase equilibrium, polymerization kinetics, and reactor modeling. We used Polymers Plus and Aspen Dynamics developed by Aspen Tech. Co. to simulate the process. 2. Physical and Thermodynamic Properties 2.1. Introduction. We used the PC-SAFT equation of state (EOS) to predict the physical and thermodynamics properties for components involved in the polypropylene process. The PCSAFT EOS,7,8 regarded as an extension of the well-known SAFT EOS, was developed specifically for polymer systems by Gross and Sadowski. For more information on the PC-SAFT EOS, readers are encouraged to refer to refs 2, 3, 6-8, and 19. In this work, most of pure-component parameters except for polypropylene involved in the process were taken directly from refs 2, 3, 7, and 8. The applied pure-component parameters for the PC-SAFT EOS are listed in Table 1.

Table 1. Pure-Component Parameters for the PC-SAFT Equations no. 1 2 3 4 5 6 7 8 9

component

m

hydrogen 0.8285 ethylene 1.559 ethane 1.607 propylene 1.960 propane 2.002 polypropylene catalyst 25.0 cocatalyst 25.0 electron donor 25.0

σ (A) ε/kB (K) r (mol/g) refs 2, 3, 7 2.973 3.434 3.521 3.536 3.618 4.147 2.668 2.668 2.668

12.53 179.4 191.4 207.2 208.1 294.0 198.8 198.8 198.8

0.0228

2, 3 2, 3 2, 3, 7 2, 3, 7 2, 3, 7 2, 3, 8 2, 3 2, 3

On the other hand, it is wellknown that the density of slurry in the tubular loop reactor not only affects the residence time of the reagents but also is one of the most important control factors for protection of axial flow pump. However, we found that using the parameters of polypropylene from the literature2,3,7,8 would always lead to overpredicting the density in the tubular loop reactors. Therefore, we adjusted the pure-component parameters for polypropylene and changed the mixture rule for liquid mixture molar volume (VLMX), a submodel in PC-SAFT EOS for calculation of the density of the liquid mixture. Figures 3 and 4 show comparisons of the polypropylene density and heat capacity data obtained via the PC-SAFT EOS and that from experiment.23 We could find that the parameters used in this work provide a better prediction for the polypropylene density and almost the same precision for polypropylene heat capacity in the literature. Furthermore, the ideal mixing model (VL2IDL) was used for VLMX for a better prediction of the liquid mixture density in the tubular loop reactor. By using the ideal mixing model, the pure-component mole volume was calculated by PCSAFT EOS and the liquid mixture mole volume was calculated by VL2IDL. 2.2. Polymer Properties. In this work, critical polymer properties that are involved in the process are molecular weight distribution and melt index. They were investigated in our

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Figure 3. Density of polypropylene.

Figure 4. Heat capacity of polypropylene.

previous work.2,21,26 Here, the same simulation method and similar equations were adopted. 3. Reactor Modeling For modeling the tubular loop reactor, many researchers20,21 considered that the reactor could be treated as a continuous stirred tank reactor (CSTR) when the recycle ratio is high. In this work, we will discuss the effect of recycle ratio on reactor operation and explore whether the tubular loop reactor can be treated as a CSTR. As shown in Figure 5, the whole tubular loop reactor has four vertical pipes with cooling jackets which are connected by four adiabatic elbows. Correspondingly, the combined plug flow reactor model is comprised of four plug flow reactors with cooling jackets connected by four adiabatic plug flow reactors. Here, we chose the RPlug module in Aspen Plus to represent a plug flow reactor. Figure 6 shows a schematic representation of the combined plug flow reactor model. R201-A, R201-B, R201-C, and R201-D represent the four RPlugs with cooling jackets, and R201-1, R201-2, R201-3, and R201-4 are four adiabatic RPlugs. The prepolymerization slurry is introduced between R201-B and R201-2; the fresh propylene is fed between R201-A and R201-1. Pump P201 here is used for modeling the axial flow pump in the tubular loop reactor, with which we can balance the pressure in the reactor. OUT-SPLI is a stream splitter module, through which we can model the reactor at different recycle ratios by adjusting the output fraction in OUT-SPLI.

Figure 5. Tubular loop reactor. The locations of the monomer/prepolymer feed streams and polymer product stream on the reactor are similar to those on R202 described in Figure 2.

The above model was then compared with a CSTR model, the other alternative for tubular loop reactor modeling. For modeling the fluidized bed reactor R401, we considered it as a CSTR, which was the same as the one in our previous work,2 where the RCSTR module in Aspen Plus was chosen. 4. Polymerization Kinetics 4.1. Introduction. The polymerization kinetics for ZieglerNatta catalysts has been studied extensively.12-15,27 Due to the multisite nature of the catalysts, it can produce polyolefin with a broad molecular weight distribution (MWD). In this work, we developed a multisite kinetic model for the homopolypropylene process and three steps were put forward in the polymerization kinetics. First, a base set of the single-site reaction mechanism and kinetic parameters was developed based on the literature. Second, the kinetic parameters were finely tuned to match the polymer production rate and average number of polymerization degree (DPn). Finally, the single-site kinetic model was extended to multisite kinetic model using MWD deconvolution to match the polymer polydispersity index (PDI). 4.2. Homopolymerization Kinetic Scheme. According to the literature,12-15 a subset of Ziegler-Natta reactions listed in Table 2 was used to describe homopolymeriztion reactions, as follows.

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Figure 6. Schematic flow sheet representation of the combined plug reactor model.

where kini,i is the rate constant of chain initiation at the ith site type and P1,i is an initiated catalyst site of type i with a single monomer attached to it. 4.2.3. Chain Propagation. The polymer chains grow when the monomer continues to attach to the active catalyst sites

Table 2. Reaction Subset Used for Homopolymerization Kinetics reaction no.

description

1 2 3 4 5

catalyst site activation chain initiation chain propagation chain transfer catalyst site deactivation

kp,i

Pn,i + M 98 Pn+1,i

4.2.1. Catalyst Activation. In the polypropylene process of the Spheripol technology, there is premixing of catalyst and cocatalyst before being put into the reactor. Therefore, catalyst activation by cocatalyst was not considered in this study. Only activation of catalyst by monomer and hydrogen were considered in this work and the reactions are as follows kacm,i

CATi + M 98 P0,i

kach,i

CATi + H2 98 P0,i

(1)

(2)

where kacm,i and kach,i are the rate constants for activation of catalyst at the ith site type by monomer and hydrogen, respectively. A “max sites” parameter was employed to represent the number of catalyst sites per unit mass of catalyst within Polymer Plus. The value of this parameter may range from 1.0 × 10-5 to 1.0 × 10-3 mol of sites per gram of catalyst. We can adjust the production rate without affecting the molecular weight by adjusting this parameter. 4.2.2. Chain Initiation. An active site can be initiated by reacting with the monomer kini,i

P0,i + M 98 P1,i

(3)

(4)

where kp,i is the rate constant for chain propagation at the ith site type and Pn,i and Pn+1,i are polymer chains of length n and n + 1 attached to site type i, respectively. The chain propagation rate constant plays a key role in the polymer molecular weight. In addition, with the increase of the rate constant, the polymer molecular weight increases linearly. 4.2.4. Chain Transfer. A chain transfer reaction will lead to disengaging of the growing polymer chain from the catalyst active site. Accordingly, a dead polymer chain and an empty active site or an initiated active site will form. Hydrogen is always used as a chain transfer agent in the polyolefin process, and monomer will also cause the chain transfer reaction. On the basis of the above description, the chain transfer reactions are as follows kth,i

Pn,i + H2 98 Dn + P0,i ktm,i

Pn,i + M 98 Dn + P1,i

(5)

(6)

where kth,i and ktm,i are the rate constants for chain transfer to hydrogen and monomer at the ith site type, respectively, and Dn is a dead polymer chain. We adjusted these two kinetic constants to match the polymer number-average molecular weight. 4.2.5. Spontaneous Catalyst Deactivation. The catalyst active sites can undergo spontaneous deactivation to form dead

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Pn,i Dn + DCATi

(8)

where kds,i is the rate constant of deactivation for the ith site type and DCATi is a deactivated site for the ith site type. In addition, production of the polymer decreases with the increase of this deactivation rate constant. 4.3. Determination of Kinetic Parameters. In order to accomplish the process simulation, the kinetic constants must be obtained in advance. We suggested the determination program/method in our previous study.2 Here, the same determination method was applied and has not been described yet due to limited space. However, the main steps were listed.

Figure 7. Deconvolution of a representative MWD results using five-site model. Table 3. Deconvolution Results for a Representative Polypropylene Sample site type

polymer weight fraction

Mn

1 2 3 4 5

0.1677 0.3595 0.0934 0.3352 0.0442

29 550 78 740 599 580 208 590 8810

sites with no activity, and the corresponding reaction equations are as follows kds,i

(7)

P0,i DCATi

To simplify the parameters’ determination for highly coupled polymerization kinetics of the Ziegler-Natta catalyst, first, we assume the catalyst contains a single site type which is capable of modeling the polymerization rate and Mn but not Mw or equivalently PDI; second, we deconvolute GPC data to confirm the appropriate number of active site types and then determine the relative amount of polymer and the corresponding Mn produced by each site type. Appendix A (Supporting Information) describes the input variables, and Appendix B (Supporting Information) describes the initial kinetic parameters for the single-site model. Simulation targets for models with single and multisite types catalyst are listed in Table 6 (Supporting Information). There are five site types used in this work, and the representative sets of the results are shown in Figure 7 and Table 3. In addition, the reaction rate constants for multisite Ziegler-Natta catalyst employed in this study are listed in Table 4.

Table 4. Reaction Rate Constants for Multisite Ziegler-Natta Catalyst reaction

site no.

comp l

comp 2

pre-exp

activation energy (kcal/mol)

order

reference temp. (°C)

act-H2 act-H2 act-H2 act-H2 act-H2 act-mon act-mon act-mon act-mon act-mon chain-ini chain-ini chain-ini chain-ini chain-ini propagation propagation propagation propagation propagation chat-mon chat-mon chat-mon chat-mon chat-mon chat-H2 chat-H2 chat-H2 chat-H2 chat-H2 deact-spon deact-spon deact-spon deact-spon deact-spon

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

catalyst catalyst catalyst catalyst catalyst catalyst catalyst catalyst catalyst catalyst C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6

H2 H2 H2 H2 H2 C3H6 C3H6 C3H6 C3H6 C3H6

0.002677 0.002677 0.002677 0.002677 0.0018 1.00 × 10-6 1.00 × 10-6 1.00 × 10-6 1.00 × 10-6 1.00 × 10-7 125.775 269.625 70.05 251.4 33.15 125.775 269.625 70.05 251.4 33.15 0.075 0.061 0.0021 0.022 0.067 7.5 6.1 0.21 2.2 6.7 2.30 × 10-5 2.30 × 10-5 2.30 × 10-5 2.30 × 10-5 2.30 × 10-5

6.4 6.4 6.4 6.4 6.4 7.64 7.64 7.64 7.64 7.64 5.52 5.52 5.52 5.52 5.52 5.52 5.52 5.52 5.52 5.52 65.42 65.42 65.42 65.42 65.42 10.7 10.7 10.7 10.7 10.7 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.5 0.5 0.5 0.5 0.5 1 1 1 1 1

69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69

C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 C3H6 H2 H2 H2 H2 H2

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Figure 8. Simple control schematic for the bulk polymerization unit.

5. Dynamic Modeling 5.1. Introduction. The dynamic model is developed by exporting the steady-state model from Polymer Plus into Aspen Dynamics with complementary information, for example, reactor and some other vessels dimensions and geometries. Meanwhile, the default PID control schemes are configured. Some additional control schemes are needed for reliable modeling of the dynamic process, including setup, grade transition, and the emergent shut down. Furthermore, the CSTR model which was used in the steady-state model had been discussed earlier. Therefore, the CSTR used in the dynamic model is not discussed here. 5.2. Main Control Scheme. Figure 8 shows an illustrative control schematic for the bulk polymerization reactors. It included the following controllers. (1) Level and temperature controllers were used for the three tubular loop reactors. The lever controllers kept the reactors level by adjusting the output of the slurry. The temperature controllers adjusted the heat capacity of the reactors to keep the reactor at constant temperature. (2) As for R201 and R202, density control was very important for these two reactors and propylene feed rate was adjusted instead of the reactor density to control the polymer mass fraction of the output stream of the reactors. (3) Total polymer production rate was controlled by adjusting the catalyst feed flow rate. (4) Three FSplit modules (Sp0, Sp1, Sp2) after three tubular loop reactors were used to split the slurry from the three reactors to the high-pressure blow-down vessel (D601) in the case of emergent shut down. 6. Simulation Results 6.1. Reactor Models. In this work, both the CSTR model and the combined PFR model for reliable modeling of the tubular loop reactors were first developed. Results from the combined PFR model were discussed and compared with those from the CSTR model. Figure 9 shows the temperature distribution along the loop reactor. From Figure 9 one can find that the temperature increased obviously at four adiabatic elbows of R201-1, R2012, R201-3, and R201-4 due to high reaction heat. As for the other four vertical pipes with cooling jackets, R201-D was positioned as the inlet of cooling water, the temperature

Figure 9. Temperature distribution along the tubular loop reactor.

decreased along the pipe obviously at this section due to the significant temperature difference between reactant and cooling water. As the temperature of the cooling water became higher, the above temperature difference became smaller, which is shown in Figure 10. In addition, the decrease of the reactant temperature along the pipe became less evident, even increased at R201-A. Therefore, it is noted that that a good control of the temperature and flow rate of cooling water is very important for reactor temperature control. From Figure 9 one can also find that there was an obvious temperature decrease at the following two positions: the first one was between R201-A and R201-1 because of the feed of fresh propylene, and the second one was between R201-B and R201-2 because of the feed of prepolymerization slurry from R200. Furthermore, from Figure 9 one knows that the temperature scale on the y axis showed that the data varied only from about 69.950 to 70.175 °C over a distance of 230 m. From an engineering point of view, this result showed effectively a totally isothermal reactor for all practical purposes. The fact that the temperature profile is totally isothermal is helpful to produce a resin with excellent inherent properties, i.e., Melt Index, MWD, etc. Figures 11-13 described the effect of recycle ratio on the reactor operation. According to Figure 11, one can obtain that the temperature distribution was uneven at a low recycle ratio;

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Figure 10. Coolant temperature distribution along the tubular jacket.

Figure 11. Effect of the recycle ratio on the loop reactor temperature distribution.

however, when the recycle ratio reached 20, the temperature distribution would become uniform. In practice, at low slurry recycle flow rate, the fresh propylene feed affected the reactor temperature greatly and a sharp decrease of temperature can be found from 71 to 66 °C. Meanwhile, at the adiabatic elbows the temperature increased obviously due to the long residence time. On the contrary, the temperature decreased dramatically at the vertical pipes with cooling jackets because of the smaller reaction heat along with the lower recycle flow rate. Figure 12 shows the effect of the recycle ratio on the polymer molecular weight distribution. When the recycle ratio was 5, the MWD was obviously different from that obtained from the CSTR model. When the recycle ratio was up to 20, the MWD calculated by the combined PFR model was always consistent with the increase of the recycle ratio but there were are still some differences from the result of the CSTR model. The

Figure 12. Effect of the recycle ratio on the polymer molecular weight distribution.

differences were caused not only by the temperature contrast but also by the hydrogen concentration difference between the two models. Figure 13 shows the effect of the recycle ratio on the hydrogen concentration distribution; the same tendency with Figure 12 can be found. With the increase of the recycle ratio, the hydrogen concentration obtained from the combined PFR models approached that obtained from the CSTR model. Figure 14 presents the effect of the recycle ratio on the polymer production rate and DPn. From Figure 14 one knows that with the increase of the recycle ratio the polymer producing rate increased but the DPn decreased. In practice, at a high recycle ratio the residence time distribution of polymers is close to that in CSTR, which leads to the decrease of the breakage possibility of catalyst.2 Accordingly, catalysis activity can be released efficiently and the polymer producing rate increases. In addition, the change of the DPn was the same with the MWD shown in Figure 12.

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Figure 13. Effect of the recycle ratio on the hydrogen molar fraction distribution.

Figure 14. Effect of the recycle ratio on the polymer production rate and DPn. Table 5. Comparison of the Modeling Results with the Data from Plant R201

R202

properties

predicted

plant

predicted

plant

density (kg/m3) Mn Mw PDI

545.5 66 557 325 207 4.89

546.7 65 300 317 700 4.86

583.7 48 604 253 413 5.21

584.8 49 000 259 400 5.29

As a whole, by using the combined PFR model, one can obtain some detailed information on the reactors and it is useful for design of the reactor. However, as for process modeling, the CSTR model can be used to get appropriate results such as the polymer production rate and MWD. Therefore, the following process modeling results were based on the CSTR model for saving the simulation time. 6.2. Model Validation. In our investigation, the plant data have been used to fit the kinetic parameters. The polymer properties obtained from polymer samples were also incorporated to validate our model. Table 5 shows the comparison of the modeling results with the plant data in terms of slurry density, MW, PDI, and MI in the reactors, demonstrating that the simulated results agree well with the data obtained from the plant. 6.3. Model Application. Several typical dynamic processes, i.e., grade transition, start up, and shut down at certain emergent accidents, were simulated via the dynamic model. For the grade transition process, we considered a step increase of the hydrogen feed rate, and the simulation results are shown

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Figure 15. Polymer grade-transition strategy preformed by a step change in hydrogen flow rate.

Figure 16. Heat duty of the two reactors in the start-up process.

in Figure 15. From Figure 15 one observes that the polymer Mn in each reactor stepped to a smaller stage. Due to a lower hydrogen concentration in R201, a larger polymer Mn can be obtained, which is in line with the reality of the plant observation. Besides, as the hydrogen concentrations in the two reactors were adjusted simultaneously and separately, it took almost the same time for the two reactors to achieve steady state. The model can be used to optimize the grade transition process to minimize the transition time and the amount of offspecification polymer produced by adjusting the control strategy. As for the start-up process, a step feed of catalyst was considered. It is very important to control the reactor temperature in the start-up process. Figure 16 shows the demanding heat duties of R201 and R202. It was a positive value at the initial period of the start-up process, as the reaction heat was not sufficient due to a low catalyst concentration; the hot water was required to sustain the reactor’s temperature at 70 °C. As the process proceeded, the catalyst concentration increased and the reaction rate became larger; meanwhile, cold water was then needed, and the value of heat duty changed to negative. Besides, the heat duties were almost the same for the two reactors because of the same polymer production rate as shown in Figure 17. Here, we also point out that the polymer producing rates shown in Figure 17 were the total polymer flow rate from the two reactors. The polymer from R202 was produced by both R201 and R202, and we can see it was almost twice as much as the polymer producing rate of R201. Therefore, the polymer production rate was almost the same in the two reactors.

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kinetics models based on single and multisite catalyst were established by fitting plant data and GPC deconvolution results. With conceptual control schemes added to the well-established steady-state modules, the enhanced model system can be used to simulate the dynamic behavior. Though the modeling results were in good agreement with the plant data, more data of different scenarios or product grade were still important for further validation and improvement of the flexibility of our models. The model was used to simulate dynamics behavior such as grade transition, start up, and emergent shut down. Those applications could potentially benefit operators as well as process engineers. Acknowledgment Figure 17. Polymer production of the two reactors in the start-up process.

The authors gratefully acknowledge China National Petroleum Corporation, China Lanzhou Petrochemical Company, China Lanzhou Petrochemical Company Research Institute (particularly Zhao, X. T., the Senior President; Zhu, B. C., the Senior Associate President), and Dalian Nationalities University (particularly Dr. Li B.H.) for supporting this work. We also thank the anonymous referees for comments on this manuscript. The simulation work was implemented by advanced software tools (Polymers Plus and Aspen Dynamics) provided by China Lanzhou Petrochemical Company Research Institute and Dalian Nationalities University. Supporting Information Available: Appendix A (input variables and simulation targets for models for catalysts with single and multiple site types); Appendix B (initial Kinetic Parameters for the Single-site Model). This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 18. Flare gas flow rate in the shut-down process.

In addition, the shut-down process at a certain emergent accident was also simulated via our dynamic model in order to find out the flare line load when the plant was at certain emergent accident. The “disable reactions” option in the reactor module was selected to stop the reaction by modeling the injection of reaction terminating agent carbonic oxide, and the reactant in the tubular loop reactors was discharged to the highpressure discharge vessel D601 in 20 min. According to the industrial data collected from a chemical plant in China, injection of carbonic oxide is in order to stop polymerization in the reactor for a little poison lead to greatly decrease the catalyst activity. Therefore, the above section/option was reasonable for the shutdown simulation. Figure 18 shows the flare flow rate during the shut-down process in the emergent accident. From Figure 18 one can find that when the emergent shut-down began at 1 h, the flare flow rate grew rapidly and the maximum flow rate can reach 90 T/h. After all of the slurry in the tubular loop reactors was discharged to D601, the flare flow rate dropped rapidly. The flare flow rate grew again at about 1.5 h. That is because of the heating and steaming of D601. The nitrogen gas was used to dry the polypropylene at about 4 h, and the flare gas flow rate grew again. 7. Conclusions In this work, we described the strategy and methodology for modeling the polypropylene process of the Spheripol technology. The improved PC-SAFT EOS was used to predict the thermophysical properties and phase equilibrium of the system, and both CSTR and the combined PFR model were developed for modeling the tubular loop reactor. In addition, polymerization

Nomenclature CATi ) inactive catalyst site of type i Cp ) heat capacity, kJ/kg Dn ) inactive polymer chain containing n monomer segments DPn ) number average of the polymer degree of polymerization DPw ) weight average of the polymer degree of polymerization DCATi ) deactivated catalyst site of type i kach,i ) rate constants for the activation of catalyst at the ith site type by hydrogen, s-1 kacm,i ) rate constants for the activation of catalyst at the ith site type by monomer, s-1 kds,i ) rate constant for spontaneous deactivation of catalyst site type i, s-1 kini,i ) rate constant for active site initiation at site type i, L/mol · s kp,i ) rate constant for initiated active site propagation at site type i, L/mol · s kth,i ) rate constant for chain transfer to hydrogen for site type i, L/mol · s ktm,i ) rate constant for chain transfer to monomer for site type i, L/mol · s M ) monomer component MI ) melt index, g/10 min MWD ) molecular-weight distribution Mn ) number-average molecular weight, g/mol Mw ) weight-average molecular weight, g/mol n ) number of monomer segments in the polymer (degree of polymerization) PDI ) polymer polydispersity index P0,i ) activated catalyst site of type i P1,i ) initiated catalyst site of type i Pn,i ) live polymer chain containing n segments attached to catalyst site type i

Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011 r ) size parameter for polymer species in the PC-SAFT EOS; ratio of the characteristic chain length to the number-average molecular weight, mol/g T ) temperature, °C VL2IDL ) the ideal mixing model for liquid mixture molar volume VLMX ) liquid mixture molar volume, m3/kg ε/k ) the segment energy parameter in the PC-SAFT EOS, K σ ) the segment diameter in the PC-SAFT EOS, Å

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ReceiVed for reView August 10, 2010 ReVised manuscript receiVed October 11, 2010 Accepted November 12, 2010 IE101699B