Accepted Manuscript. Modified Two-Phase Model with Hybrid Control for Gas Phase Propylene Copolymerization

Transcription

1 Accepted Manuscript Modified Two-Phase Model with Hybrid Control for Gas Phase Propylene Copolymerization in Fluidized Bed Reactors Ahmad Shamiri, Suk Wei Wong, Mohd Fauzi Zanil, Mohamed Azlan Hussain, Navid Mostoufi PII: S (14) DOI: Reference: CEJ To appear in: Chemical Engineering Journal Received Date: 11 August 2014 Revised Date: 19 November 2014 Accepted Date: 23 November 2014 Please cite this article as: A. Shamiri, S.W. Wong, M.F. Zanil, M.A. Hussain, N. Mostoufi, Modified Two-Phase Model with Hybrid Control for Gas Phase Propylene Copolymerization in Fluidized Bed Reactors, Chemical Engineering Journal (2014), doi: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

2 Modified Two-Phase Model with Hybrid Control for Gas Phase Propylene Copolymerization in Fluidized Bed Reactors Ahmad Shamiri a, Suk Wei Wong a, Mohd Fauzi Zanil b, Mohamed Azlan Hussain a*, Navid Mostoufi c a Department of Chemical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia b Chemical & Petroleum Engineering, Faculty of Engineering & Built Environment, UCSI University, Kuala Lumpur, Malaysia. c Process Design and Simulation Research Center, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran ABSTRACT In order to explore the dynamic behavior and process control of reactor temperature, a modified two-phase dynamic model for gas phase propylene copolymerization in a fluidized bed reactor is developed in which the entrainment of solid particles is considered. The modified model was compared with well-mixed and two-phase models in order to investigate the dynamic modeling response. The modified two-phase model shows close dynamic response to the well-mixed and two-phase models at the start of the polymerization, but begins to diverge with time. The proposed modified two-phase and two-phase models were validated with actual plant data. It was shown that the predicted steady state temperature by the modified two-phase model was closer to actual plant data compared to those obtained by the two-phase model. Advanced control system using a hybrid controller (a simple designed Takagi-Sugeno fuzzy logic controller (FLC)) integrated with the adaptive neuro-fuzzy inference system (ANFIS) controller was implemented to control the reactor temperature and * Corresponding author. mohd_azlan@um.edu.my (Fax: ) 1

3 compared with the FLC and conventional PID controller. The results show that the hybrid controller (ANFIS and FLC controller) performed better in terms of set point tracking and disturbance rejection compared to the FLC and conventional PID controllers. Keywords: Olefin polymerization; Dynamic two-phase model; Entrainment; Adaptive neurofuzzy inference system; Fuzzy logic controller 1. Introduction Polymerization is an important process in the petrochemical and polymer industries. It is a complicated process with complex chemical kinetics and physical mechanisms [1, 2], thus making its modeling and control a very challenging task. There are a number of papers about successful modelling and controlled of polymerization processes [3-19]. However, few attemps have been reported on modelling and the control of polypropylene (PP) copolymerization in fluidized bed reactors (FBR). Copolymerization is a process in the production of polymers from two (or more) different types of monomers which are linked in the same polymer chain. In the industrial PP copolymerization, the most commonly used reactor configuration is the FBR [20-22]. With this reactor configuration, shown schematically in Fig. 1, catalyst (Ziegler-Natta and triethyl aluminium) and reactants (propylene, ethylene and hydrogen) are fed continuously into the reactor with nitrogen as the carrier gas. Conversion of monomers is low for a single pass through the FBR and it is necessary to recycle the unreacted monomers. Unreacted monomer gases are removed from the top of the reactor. A cyclone is used to separate the solid particles (i.e., catalyst and low molecular weight polymer particles) from the gas in order to prevent them from damaging the downstream compressor or heat exchanger. Monomer gases are then recompressed, cooled and recycled back into the FBR. 2

4 The product (PP) is gradually removed from the bottom of the reactor as soon as a reasonable conversion is achieved. Several models have been proposed to describe the behavior of olefin polymerization in FBR [23-27]. Choi and Ray [23] applied a simple two-phase model, known as the two-phase constant bubble size model, in which the bubble phase is considered to move in plug flow with constant bubble size and emulsion phase is completely mixed. It is also assumed in this model that the polymerization only occurs in the emulsion phase. On the other hand, Mcauley et al. [5] and Xie et al. [27] considered a well-mixed model for this process (known as the well-mixed model). They found that the well-mixed model estimates temperature and monomer concentration by 2-3 K and 2 mol %, respectively, less than the constant bubble size model. Hatzantonis et al. [24] refined the two-phase model by including the effects of bubble size on the steady-state and dynamic behavior of the reactor. The bubble phase is separated in this model into a number of segments in series and the emulsion phase is assumed to be in a perfect mixing condition. This model is known as the bubble growth model. Later, Fernandes and Lona [25] developed a heterogeneous three-phase model (gas in emulsion, bubble and solid particles, all in plug flow) whereas Ibrehem et al. [9] proposed a four-phase model (bubble, cloud, and emulsion with solid phase). All these models were developed for the production of polyethylene (PE). For homopolypropylene production, Shamiri et al. [13] developed a simple two-phase model by considering the progress of the polymerization reaction in both bubble and emulsion phases. They adopted this modified two-phase model to describe the gas phase propylene homopolymerization to produce PP in a FBR and compared its results with the two-phase constant bubble size model and the wellmixed model. They found that the two-phase constant bubble size model overpredicted the conversion of propylene and temperature of the emulsion phase. Meanwhile, the two-phase model and the well-mixed model were in better agreement at the same operating condition. 3

5 The propylene polymerization reaction is highly exothermic. To maintain the polypropylene production rate at the desired condition, it is essential to keep the reactor temperature greater than the dew point of reactants in order to avoid condensation of gas within the reactor. It is also important to keep the temperature lower than the melting point of the polymer in order to prevent particle melting, agglomeration and subsequently reactor shut down. Therefore, an efficient temperature control system is required to address this issue. Choi and Ray [23] showed that a simple PI controller could only be used to control transients with limited recycle gas cooling capacity. Ghasem [28] also investigated the performance of a PI controller, FLC based on Mandani and Takagi-Sugeno (TS) inference method as well as a hybrid Mamdani-PI controller and a hybrid TS-PI controller for controlling the temperature in a polyethylene fluidized bed reactor. It was shown that the hybrid Mamdani-PI controller and the hybrid TS-PI controller performed better compared to the PI controller. Besides, Ibrehem et al. [10] were able to control the system with a neural network based predictive controller. They showed that the advanced controller works better than the PID controller. On the other hand, Shamiri et al. [29] implemented a model predictive control (MPC) technique to control the temperature of a two-phase model for propylene homopolymerization and compared its performance with PI controllers tuned by using the Internal Model Control (IMC) strategy and Ziegler-Nichols (Z-N) strategy. In another study of PP reactor, the Adaptive Predictive Model-Based Control (APMBC) method, a hybrid of generalized predictive control (GPC) algorithm and recursive least squares algorithm (RLS), was proposed by Ho et al. [15] to control the reactor temperature and polymer production rate by using the model developed by Shamiri et al. [13]. The APMBC performed excellent set point tracking and disturbance rejection of the superficial gas velocity and monomers concentration changes when compared with IMC strategy and PID strategy. 4

6 In all above mentioned models, it was assumed that solid entrainment is negligible at the top of the reactor. However, it was shown that solid entrainment did exist during the polymerization process [30]. Therefore, in this work, the two-phase model of Shamiri et al. [13] was modified by incorporating it with solid entrainment in order to consider the losses of entrained catalyst and polymer particles from the fluidized bed. A two-site copolymerization kinetic scheme for propylene and ethylene were used in this study in order to have a clearer picture of copolymerization over a heterogeneous Ziegler Natta catalyst in a FBR. Then, a comparative study of the results by using the well-mixed, two-phase and modified two-phase models for PP copolymerization in FBR was carried out. The modified two-phase model and the two-phase model were also validated with actual plant data. Furthermore, advanced controllers using the Takagi-Sugeno based fuzzy logic controller (FLC) controller as well as the hybrid adaptive neuro fuzzy inference system (ANFIS) and Takagi-Sugeno based fuzzy logic controller (FLC) were implemented on the proposed modified two-phase model to control the reactor temperature for set point tracking and disturbance rejection, as shown in Fig. 2, to ensure a better performance of the FBR with safety consideration. To the best of our knowledge, this is the first time that such a modified copolymerization of propylene model and its controlling system is implemented on the propylene copolymerization system. Lastly, these controllers were compared with the conventional PID controller for the set-point tracking and disturbance rejection. 2. Modeling 2.1 polymerization mechanisms In the copolymerization reaction, there are two types of monomer forming a polymer while in homopolymerization, only one monomer is involved in the production of the polymer. In the current study, an extensive mechanism was employed to explain the kinetics 5

7 of copolymerization of propylene and ethylene over two sites of Ziegler Natta catalyst, using the kinetic model developed by Decarvalho et al. [4] and Mcauley et al. [31]. Reactions, including formation, initiation, propagation, transfer and deactivation of active sites, are listed in Table 1, based on which the moment equations, shown in Table 2, were derived. The index j in these tables refers to the type of the active site and i refers to the type of monomer. Rate constants of each reaction for each site type were taken from the literature and given in Table 3. By assuming that monomers are consumed mainly through the propagation reactions, the consumption rate equation for each component is shown as below after the moment equations are solved [31]: R =M Y(0,j)k,k=1,2 (1) where ns is the number of each type of active site and m is the number of each type of monomer. Then, the total polymer production rate can be obtained from: R =mw R (2) 2.2. Hydrodynamic modeling Well-mixed model It is assumed in the well-mixed model, proposed by Mcauley et al. [5], that the FBR is a single-phase, continuously stirred tank reactor. They further assumed that: 1. Bubbles are small. Therefore, heat and mass transfer between bubble and emulsion phases are fast, thus, the reactor can be considered a well-mixed reactor (single phase). 2. Temperature and concentrations throughout the bed are uniform. 3. The emulsion phase is maintained at minimum fluidization. 6

8 [24]: With the assumptions above, the material balance and energy balance can be written as Vε d[m ] dt =U A([M ] [M ]) R ε [M ] (1 ε )R (3) [M ]C Vε +V(1 ε )ρ C, ] dt dt =U A[M ]C (T T ) U A[M ]C (T T ) R [[M ]C ε +(1 ε )ρ C, (T T ) +(1 ε ) H R (4) Equations (3) and (4) can be solved with the following initial conditions: [M ] =[M ] T =T (5) (6) Two-phase model In the dynamic two-phase model it is assumed that the polymerization reaction occurred in both emulsion and bubble phases. Table 4 shows the equations used for calculating velocities in emulsion and bubble phase, heat and mass transfer coefficients as well as other required parameters in the two-phase model. Assumptions used in deriving the material and energy balances of the two-phase model are summarized below [13]: 1. The emulsion phase is assumed to be completely mixed and not at the minimum fluidization condition. 2. Polymerization reactions are considered to take place in both emulsion and bubble phases. 3. The bubbles are considered to be a sphere of constant size and pass through the bed at plug flow condition with uniform velocity. 4. Heat and mass transfer resistances between solid and gas in bubble and emulsion phases are ignored. 7

9 5. Radial gradients of temperature and concentration in the reactor are neglected due to severe agitation induced by the up-flowing gas. 6. Solids elutriation at the upper part of the bed is ignored. 7. Uniform particle size is considered throughout the bed. Based on the above assumptions, the following material balances can be obtained: For the emulsion phase: [M ],() U A [M ] U A R [M ] +([M ] [M ] )V (1 ε )R = (V ε [M ] ) (7) For the bubble phase: [M ],() U A [M ] U A R ε [M ] K ([M ] [M ] )V (1 ε ) Ri dz= (V ε [M ] ) (8) Also, the energy balances for emulsion and bubble phases are as follows: For the emulsion phase: U A T.() T [M ],() C U A (T T ) [M ] C R (T T ) ε C [M ] +(1 ε )ρ C. +(1 ε )R H H V (T T ) V ε (T T ) C ([M ] )=(V (ε C [M ] +(1 ε )ρ C. )) (T T ) (9) For the bubble phase: U A T.() T [M ],() C U A (T T ) [M ] C R (T T ) ε C [M ] +(1 ε )ρ C. +(1 ε ) R dz+h (T T )V 8

10 V ε (T T ) C ([M ] )=(V (ε C [M ] +(1 ε )ρ C. )) (T T ) (10) where U = (11) U =U U +u (12) U =0.711(gd ) / (13) δ= exp (14). ε =ε exp(-. ) (15) ε = exp (. ) (16) V =AH(1 ε )(1 δ) (17) V =AH(1 ε )δ (18) V = AH(1 δ) V = AδH (19) (20) Equations (7) to (10) can be solved by MATLAB, with the following initial conditions. [M ], =[M ] T (t=0)=t [M ], =[M ] T (t=0)=t (21) (22) (23) (24) The proposed modified two-phase model In the present work, the two-phase model (described in section 2.2.2) was further improved to consider solid entrainment at the top of the reactor for the cases where elutriation 9

11 rate cannot be ignored. In general, coarse particles stay in the bed whereas small particles will be entrained and pushed off from the system. However, where velocities are several times greater than the terminal velocity, coarse particles can also be entrained from the bed [30]. Therefore, in the present study, solid entrainment was considered in the model. Mass balances obtained based on the assumptions of this model are as follows: For the emulsion phase: [M ],() U A [M ] U A R [M ] +([M ] [M ] )V (1 ε )R [ ] = (V ε [M ] ) (25) For the bubble phase: [M ],() U A [M ] U A R ε [M ] K ([M ] [M ] )V (1 ε ) Ri dz [ ] = (V ε [M ] ) (26) The energy balances are expressed as: For the emulsion phase: U A T.() T [M ],() C U A (T T ) [M ] C R (T T ) ε C [M ] +(1 ε )ρ C. +(1 ε )R H H V (T T ) V ε (T T ) C ([M ] ) K A /W (T T ) ε C [M ] +(1 ε )P C. )=(V (ε C [M ] +(1 ε )ρ C. )) (T T ) (27) For the bubble phase: 10

12 U A T.() T [M ],() C U A (T T ) [M ] C R (T T ) ε C [M ] +(1 ε )ρ C. +(1 ε ) R dz+h (T T )V V ε (T T ) C ([M ] ) K A /W (T T ) ε C [M ] + (1 ε )ρ C. )=(V (ε C [M ] +(1 ε )P C. )) (T T ) (28) In the above mass and energy balances, solid elutriation rate constant were obtained from [30]: K =23.7ρ U exp. (29) K =23.7ρ U exp. (30) W =AH(1 ε )ρ (31) W =AH(1 ε )ρ (32) U =U μρ ρ ρ g / (33) U =18d +( )d. (34) for 0.5< 1, d =d μ ρ ρ ρ g (35) Similar initial conditions as shown in Equations (21) to (24) were applied and the set of equations were solved by MATLAB. 3. Control strategy Most of the studies on the control of temperature of the polymerization process suggest that advanced control schemes, such as FLC (fuzzy logic controller), MPC (model predictive controller) and adaptive predictive model-based control (APMBC), exhibit better 11

13 performance than conventional PI or PID controllers [15, 16, 28]. Besides these advanced controllers, Ghasem [28] showed that a hybrid controller incorporating FLC and PI controllers performs better than a regular PI controller. However, for such a control system the predictive based and adaptive based methods rely heavily on the accuracy of the model and are also tedious to be implemented online. At the same time the use of the FLC can also be cumbersome due to trial and error methods for obtaining the fuzzy rules especially for complex nonlinear systems. This problem can be alleviated by using the ANFIS based controller. Therefore, advanced control employing a hybrid controller (a simple designed Takagi-Sugeno FLC integrated with an ANFIS controller), was used in this study for controlling the temperature of the reactor by manipulating the cooling water flow rate, F, as the manipulated variable (see Fig. 2). The hybrid controller was then compared with FLC and conventional PID controllers Hybrid FLC-ANFIS controller Fuzzy logic requires a good understanding of the process characteristic and has the capacity to reason with the condition of the inputs and deliver the conclusion collectively. The technique has been introduced to improve machine reasoning in decision making which is natural for human brain to correlate the action-conclusion relation. This technique has a tremendous influence on the various applications in engineering including process control systems for chemical reactors. Since the nonlinearity and uncertain complexity of this polypropylene reactor can be appropriately handled by this methodology, the standard steps of fuzzification, fuzzy rules, fuzzy inference system, and defuzzification mechanisms have been applied in this control system [37]. 12

14 The diagram in detail can be seen in Fig. 3 with 2 inputs and 3 triangular membership functions. The rules are designed in the form of IF (CONDITION) then (ACTION). This expression correlates the relation between a set of condition parameters for the appropriate control action. Each fuzzy rule is evaluated as shown in Table 5 based on the error and rate of error condition. ANFIS controllers are mainly employed in processes that encounter unpredictable variation in process parameters where complete information of the parameters are unavailable [38]. ANFIS uses a hybrid learning algorithm, least square method and back propagation descent, to generate a fuzzy inference system where the membership functions are iteratively altered according to the given input and output data. The FIS structure with 3 membership functions for each input, as shown in Fig. 3, was generated in MATLAB. Because of the nonlinear, process condition and model complexity, the action signals and set-point error relationship will vary and the appropriate output signals are very hard to determine. This will lead to a bad controller performance and therefore, an inverse correlation is introduced inside the main controller to integrate the empirical model technique (ANFIS controller). The ANFIS controller was designed based on the historical value of the successful control system with several process conditions setup. The outcome of the ANFIS controller will reflect the inverse response of set-point error (input) and the cooling water flow rate (as an output). These integration setups are to provide a guarantee that the controller will give a sufficient and appropriate action signal for any reactor conditions. The propose hybrid controller requires additional inputs such as U 1, U 2 and U 3 to the fuzzy logic controller. Inputs are from the state parameters that significantly influence the response of the reactor dynamics. The rules in Table 5 are shown in Fig. 3 where they are dependent on the inputs U 1, U 2 and U 3 concurrently. When the error e is negative, the process 13

15 variable is actually greater than the set-point value and the three corresponding connections will trigger three different fuzzy rules, as can be seen in Fig. 3 as well as Table 5. System identification was used to design ANFIS controller to obtain the inverse dynamic response of the reactor and it involves similar methodology such as neural networks inverse plant model development [39]. For the servo system, process variable is driven to the desired set-point when error is negative/positive and change of error is decline/incline. The key factor for the fuzzy controller is the output value of membership function named GOOD. When process error equals to zero, the inverse response from ANFIS will decide the output value of GOOD and send the signal to the manipulate control variable. In the case of error close to zero but no progression to the set-point, this approach will bring the process variable to set-point since the other output membership function ( CLOSE / OPEN ) will infer the decision of GOOD and adjust the final manipulated variable signal accordingly. Propylene concentration, superficial gas velocity, catalyst flow rate and temperature are used as input data whereas the output data is the cooling water flow rate in this work. Fig. 4 shows the fuzzy logic framework that was used to couple with the ANFIS inverse response controller. 4. Results and discussion 4.1. Comparison of models Dynamic modeling and simulation studies of the gas phase propylene and ethylene copolymerization in the FBR was conducted using the modified two-phase model and results were compared with results of two-phase and well-mixed models incorporated with a comprehensive two-site kinetic scheme. Simulations were performed at the operating 14

16 conditions given in Table 6. One of the main issues of olefin polymerization in fluidized bed reactor is the solids entrainment. Considering particle entrainment is crucial since this phenomenon affects the particle size distribution, agglomeration, polymer properties, polymer production rate as well as the bed hydrodynamics. In addition, it is a key parameter in design and control of a fluidized bed reactor. Therefore, in the present work, solids elutriation is considered in the modified two-phase model in order to predict the dynamic behavior of the process and control the reactor effectively. Evolutions of the emulsion phase temperature against time for the modified two-phase, two-phase and well-mixed models are illustrated in Fig. 5, and evolutions of propylene and ethylene concentrations in the emulsion phase for these models are shown in Figs. 6 and 7, respectively. In this case, the reactor starts to operate when the catalyst is fed into the reactor. It can be seen in these figures that the response for each of these variables (temperature and concentrations) is the same at the starting point until they reach the steady state after about 4 hours. However, the final steady state values for each responding variable of modified two-phase, two-phase and well-mixed models are different. The final temperatures in modified two-phase, two-phase and wellmixed models are 354 K, K and K, respectively. It is shown that the proposed modified two-phase model exhibits an emulsion phase temperature which is 2.83 K lower than the two-phase model and 17.8 K higher than the well-mixed model. Loss of catalyst and polymer particles by carryover in an actual or commercial polypropylene fluidized bed reactor results in a lower reaction rate, thus, lower reactor temperature since the reaction is exothermic. It can be seen in figure 5 that the reactor temperature predicted by the modified model is lower than that obtained by the two-phase model. This is mainly due to considering the solids elutriation in the modified two phase model which results in a lower reaction rate, thus, lower reactor temperature, which is in accordance with the performance of an actual polypropylene fluidized bed reactor. Propylene and ethylene concentration profiles for the 15

17 proposed modified two-phase model lie in between those of two-phase and well-mixed models. As shown in Figs. 5, 6 and 7, the well-mixed model shows a larger deviation from the two-phase model compared to the modified two-phase model. This is mainly due to the simplified assumptions of the well-mixed model. The modified two-phase model shows closer behavior to the two-phase model compared to the well-mixed model due to considering the distribution of catalyst between emulsion and bubble phases which takes into account polymerization reaction in both bubble and emulsion phases. The reactor temperatures and concentrations predicted by the modified model were lower and higher than those obtained by the two-phase model, respectively. This is mainly due to considering the solid elutriation in this model which results in lower a reaction rate, thus, lower monomer conversion, due to the loss of entrained catalyst and polymer particles from fluidized bed. Generally, the modified two-phase model shows the same dynamic behavior as the two-phase and well-mixed models at the beginning of polymerization and starts to differ over time Superficial gas velocity is an important operating parameter in FBR operation. Therefore, the effect of this parameter, which is directly related to the monomer residence time in the reactor on propylene concentration, was verified by various models and is shown in Fig. 8. All the three models predict that propylene concentration increases with increasing superficial gas velocity. In fact, increasing the superficial gas velocity decreases the monomer residence time, leading to a decrease in the reaction rate and consequently the monomer conversion. The propylene concentration as predicted by the improved two-phase model was greater than the two-phase model. This is mainly due to considering particle entrainment in the modified two-phase model. In addition, the high gas velocity reduces the monomer mean 16

18 residence time, leading to a lower reaction rate and monomer conversion per pass through the fluidized bed. It also leads to greater elutriation of polymer particles from the bed Validation with actual plant data The proposed modified two-phase and two-phase models were validated with the steady state actual plant data. The operating conditions and gas composition conditions for producing different polypropylene grades employed in this study are listed in Tables 7 and 8, respectively. Comparison between results of the proposed modified two-phase and two-phase models with the actual plant data in terms of temperature are shown in Fig. 9. As can be seen in this figure, there is a good agreement between predicted and industrial data on temperatures in both models. However, the data predicted by the proposed modified twophase model is closer to the actual plant data compared to those predicted by the two-phase model. The maximum difference between the industrial data and the proposed modified twophase model prediction for the temperature is 0.96 K whereas this difference is 1.59 K for the two-phase model. Therefore, it can be concluded that the modified two-phase model performance is closer to the realistic condition Controlling Non-linearity analysis of the propylene copolymerization reactor The proposed modified two-phase model was used in this section for the control studies since it is closer to the actual process as discussed previously. To demonstrate the non-linear behavior of the propylene copolymerization reactor, the process was simulated for a step change in the superficial gas velocity and catalyst feed rate, as process key parameters, on the reactor temperature. The open-loop simulation results are shown in Figs. 10 and

19 In Fig. 10 the superficial gas velocity was changed after the reactor reached the steady state at superficial gas velocity of 0.35 m/s. The superficial gas velocity has a considerable impact on the reactor temperature. This figure clearly indicates that negative steps in the superficial gas velocity have more remarkable effect on the reactor temperature than the corresponding positive steps and non-symmetric responses are produced. In other words, reactor temperature changes nonlinearly with the superficial gas velocity. For such a nonlinear behavior, using conventional controllers leads to poor control of the process variables. This justifies the implementation of a more efficient control system to sufficiently regulate the effect of superficial gas velocity on the process variable. The effect of step changes in the catalyst feed rate on reactor temperature is illustrated in Fig. 11. The catalyst feed rate was changed from its nominal value (0.3 g/s) by increments of 0.05 g/s in positive and negative directions. It can be seen in this figure that a small change in the catalyst feed rate leads to a considerable change in the reactor temperature. The slightly symmetric nature of these profiles due to the systematic positive and negative variations in the catalyst flow rate indicates the slightly nonlinear relation with the reactor temperature. The open loop analysis presented in this work and in a previous work [15] reveals the nonlinear behavior of the propylene polymerization in fluidized bed reactors, justifying the use of an advanced control algorithm for efficient control of process variables. In this case, the adaptive neuro-fuzzy inference system (ANFIS) controller (hybrid neuro-fuzzy model) and combination of ANFIS and simple Takagi-Sugeno fuzzy logic controller (FLC) were implemented to control the reactor temperature by manipulating the cooling water flow rate. Set-point tracking and disturbance rejection were carried out to examine the performance and feasibility of the controllers. The optimum temperature for the best performance of the polymerization reaction is between 343K and 353K. 18

20 Set-point tracking Fig. 12 shows the set point from K to 351 K tracked by FLC, hybrid and PID controllers at s. This figure shows that these three controllers are able to track the setpoint. Although the PID controller achieves the set-point almost at the same period with the FLC controller (4000 s), but the FLC controller performance is better than the PID controller as it does not exhibit overshoot. However, the hybrid controller exhibits a performance superior to that of FLC and PID controllers since the system returns to the set point in half of the time required by other two models (2000 s) with a very small overshoot. The controller moves for PID, FLC and hybrid FLC-ANFIS controllers in tracking set point change in the reactor temperature are shown in Fig. 13. It is found that the starting point of cooling water flow rate for the PID controller is zero while tracking the set-point of 351 K. This is because the temperature change is high (6.5 K). However, the PID controller exhibits a final response almost similar to the FLC controller after the temperature is tracked. On the other hand, the hybrid FLC-ANFIS controller shows an oscillatory behavior when the set point is K. This small slew rates, however, is still acceptable since the cooling water valve for an oscillation is about 4 minutes which means that the proposed hybrid controller is sensitive enough to operate the control valve in such a rapid opening or closing time in this simulation. However, when dealing with a real plant, this sensitivity might not be acceptable due to the limitation of the control valve with its small rangeability and the tolerance of the resistor used for the data acquisition system. In order to increase the sensitivity, a resistor of lower tolerance number is required in practical implementations. After tracking the set-point of 351 K, the valve opening response is similar to the PID controller but the response is twice as fast as the PID controller Disturbance rejection 19

21 In order to make sure that a controller can be used practically in the industry, it also must be able to cope with regulatory problems effectively. In this study, disturbances such as superficial gas velocity, catalyst feed rate and monomer concentration (propylene) were imposed onto the system with an increment of 10% of each respective nominal value. Figs show the temperature response controlled by the three controllers with an increment of 10% of each parameter. These figures clearly show that the hybrid FLC-ANFIS controller is able to reject the disturbance in a more efficient manner as compared to other two controllers although it exhibits a small oscillation at the start of disturbance. As shown in Fig. 14, FLC controller and PID controller are able to reject the disturbance within s and s, respectively, whereas the hybrid controller brings the system back to the stable set-point within 2500 s which is a very short time compared to the other two controllers. It can be seen in Fig. 15 that the catalyst feed rate has the highest temperature effect on the system in the 10% increment. Therefore, all controllers take longer time to track back the set-point. The FLC controller and PID controller are able to reject the disturbance of the catalyst feed rate within s whereas the hybrid controller brings the system back to the stable set-point within 7000 s. Furthermore, FLC and PID controllers are able to reject the disturbance of propylene concentration within s and s, respectively, whereas the hybrid controller is able to bring the system back to the stable set-point within 5000 s, as illustrated in Fig. 16. This figure shows that the PID controller is able to track back to the normal condition faster than the FLC controller but the response of the PID controller is larger than the effect of FLC controller. In the above analyses, the integral absolute error for each controller in both set-point tracking and disturbance rejection was calculated and shown in Table 9. Error values in this table also show that the hybrid controller exhibited a better performance compared to the 20

22 other two controllers since the IAE value for the hybrid controller is the lowest in both setpoint tracking and disturbance rejection studies. 5. Conclusions A two-phase model was developed and adopted for modeling of propylene copolymerization in FBRs. The model takes into account the entrainment of solids into the FBR modeling. This hydrodynamic model was combined with a kinetic copolymerization model (propylene and ethylene) to provide a better understanding of the reactor performance. Comparative simulations were carried out using the modified two-phase model, the twophase model and the well-mixed model in order to investigate their dynamic responses and the effect of different operating parameters (superficial gas velocity and catalyst feed rate) on the performance of the reactor. The proposed modified two-phase model showed the same response as two-phase and well-mixed models in the start of polymerization but started to diverge over time. The modified model exhibited a steady state reactor temperature which was 2.83 K and 17.8 K lower than the two-phase model and higher than the well mixed model, respectively. Propylene and ethylene concentration profiles for the proposed modified two phase model lie between those of two-phase and well-mixed models. The proposed modified two-phase and two-phase models were validated with actual plant data. It was shown that the performance of the modified two-phase model was closer to the real condition. The temperature predicted by the proposed modified two-phase was closer to the actual plant data compared to those predicted by the two-phase model. The maximum temperature difference between the industrial data and proposed modified two-phase model was 0.96 K. This value was lower than the temperature difference between that calculated by the two-phase model and industrial data which was 1.59 K. 21

23 The modified two phase model was adopted to carry out control studies. A proper selection of controller for industry uses was implemented in order to handle the servo and regulatory problems effectively. Results showed that the hybrid FLC-ANFIS controller performs better in terms of set point tracking and disturbance rejection compared to FLC and PID controllers. Acknowledgement The authors would like to thank the support of the Research Council of the University of Malaya under research grant (UM.C/HIR/MOHE/ENG/25). 22

24 Nomenclature A Cross sectional area of the reactor (m ) ALEt Triethyl aluminum cocatalyst Ar B Archimedes number Moles of reacted monomer of type i bound in the polymer in the reactor C Specific heat capacity of component i (J/kg K) C specific heat capacity of gaseous stream (J/kg K) C, Specific heat capacity of product (J/kg K) C Specific heat of component i (J/kmol K) d d d d D D Bubble diameter (m) Initiate bubble diameter (m) Particle diameter (m) Dimensionless particle size gas diffusion coefficient (m /s) Reactor diameter (m) F Catalyst feed rate (kg/s) f Fraction of total monomer in the reactant gas which is monomer M g Gravitational acceleration (m/s ) H Height of the reactor (m) H Bubble to emulsion heat transfer coefficient (W/m K) H Bubble to cloud heat transfer coefficient (W/m K) H Cloud to emulsion heat transfer coefficient (W/m K) H I Hydrogen Impurity such as carbon monoxide 23

25 i J kf(j) kh ( j ) kfm ( j) Monomer type Active site type Formation rate constant for a site of type j Transfer rate constant for a site of type j with terminal monomer M Reacting with hydrogen Transfer rate constant for a site of type j with terminal monomer M Reacting with monomer M kfr ( j ) kfs ( j ) Transfer rate constant for a site of type j with terminal monomer M Reacting with Aiet Spontaneous transfer rate constant for a site of type j with terminal monomer M k Gas thermal conductivity (W/m K) kh Rate constant for reinitiation of a site of type j by monomer M (j) kh Rate constant for reinitiation of a site of type j by cocatalyst ( j ) ki ( Rate constant for initiation of a site of type j by monomer M j ) kp (j) Propagation rate constant for a site of type j with terminal monomer Mire acting with monomer M kp propagation rate constant (m /kmol.s) K Elutriation constant in bubble phase (kgm s ) K Bubble toemulsionmasstransfercoefficient (s ) K Bubble to cloud mass transfer coefficient (s ) 24

26 K Cloud to emulsion mass transfer coefficient (s ) K Elutriation constant in emulsion phase (kgm s ) mw molecular weight of monomer i (g/mol) M Concentration of component i in reactor (kmol/m ) [M ] Concentration of component i in the inlet gaseous stream N Potential active site of type j (j) N Uninitiated site of type j produced by formation at sites of type j reaction (0, j) N Spontaneously deactivated site of type j ( j) N, Impurity killed sites of type j (0,j) N Uninitiated site of type j produced by transfer to hydrogen reaction (0.j) N (r, j ) Q Living polymer molecule of length r, growing at an active site of type j, with terminal monomer m Dead polymer molecule of length r produced at a site of type j (r. j ) P PP Pressure (Pa) Polypropylene 25

27 R Number of units in polymer chain T T R R R Re T T U U U U U U U Instanstaneous consumption rate of monomer i (kmol/s) Production rate (kg/s) Volumetric outflow rate of polymer (m /s) Reynolds number of particles at minimum fluidization condition Time (s) Temperature (K) Temperature of the inlet gaseous stream (K) Reference temperature Bubble velocity (m/s) Bubble rise velocity (m/s) Emulsion gas velocity (m/s) Superficial gas velocity (m/s) Minimum fluidization velocity (m/s) Terminal velocity of falling particles ( m/s) Dimensionless terminal falling velocity coefficient V Reactor volume (m ) V Volume of polymer phase in the reactor (m ) W W Weight of solids in the bubble phase (kg) Weight of solids in the emulsion phase (kg) Y (n,j) X (n,j ) N-th moment of chain length distribution for living polymer produced at a site of type j Nth moment of chain length distribution for dead polymer produced at a site of type j 26

28 Greek letters H R ε δ ε ε μ Heat of reaction (J/kg) Void fraction of bubble for Geldart B particles Volume fraction of bubbles in the bed Void fraction of emulsion for Geldart B particles Void fraction of the bed at minimum fluidization Gas viscosity (Pa.s) ρ Gas density (kg/m ) ρ Polymer density (kg/m ) Sphericity for sphere particles Subscripts and superscripts 1 Propylene 2 Ethylene I In J mf pol ref Component type number Inlet Active site type number Minimum fluidization Polymer Reference condition 27

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33 Figure captions Fig. 1. Schematic of an industrial fluidized bed polypropylene reactor Fig. 2. Simplified schematic of the temperature control loop for the gas phase propylene copolymerization in FBR. Fig. 3. Fuzzy Logic Controller; 2 inputs with 3 triangular membership-functions. Fig. 4. Simplify structure arrangement of the propose hybrid ANFIS-FLC controller. Fig. 5. Evolution of the temperature in the emulsion phase over time for the modified twophase, two-phase and well-mixed models Fig. 6. Evolution of the propylene concentration in the emulsion phase over time for the modified two-phase, two-phase and well-mixed models. Fig. 7. Evolution of the ethylene concentration in the emulsion phase over time for the modified two-phase, two-phase and well-mixed models Fig. 8. Effect of superficial gas velocity on the propylene concentration calculated by the modified two-phase, two-phase and well-mixed models. Fig. 9. Comparison between actual plant temperature and predicted temperature by using the two-phase and modified two-phase models. Fig. 10. Effect of step change in the superficial gas velocity on the reactor temperature (catalyst feed rate (Fcat=0. 2 g/s). Fig. 11. Effect of step change in the catalyst feed rate (Fcat) on the reactor temperature (U 0 =0. 35 m/s). 32

34 Fig. 12. Comparison of the performance between the hybrid FLC-ANFIS controller, FLC controller and PID controller (Kc=1.277, =0.0029, = ) in tracking set point change in the reactor temperature. Fig. 13. Comparison between controller moves (cooling water flow rate) in percentage (a) FLC (b) PID (c) hybrid FLC-ANFIS controller in set point tracking of reactor temperature. Fig. 14. Comparison of the performance between hybrid FLC-ANFIS controller, FLC controller and PID controller in rejecting the effect of superficial gas velocity on the emulsion phase temperature. A 10% increment from 0.35m/s to 0.385m/s in the superficial gas velocity is introduced at 60,000 s. Fig. 15. Comparison of the performance between the hybrid FLC-ANFIS controller, FLC controller and PID controller in rejecting the effect of catalyst feed rate on the emulsion phase temperature. A 10% increment from 5g/s to 4.5g/s in the catalyst feed rate is introduced at 50,000 s. Fig. 16. Comparison of the performance between the hybrid FLC-ANFIS controller, FLC controller and PID controller in rejecting the effect of propylene concentration on the emulsion phase temperature. A 10% increment from 1 mol/l to 0.9 mol/l in the propylene concentration is introduced at 50,000 s. 33