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1 Computers and Chemical Engineering 36 ( Contents lists available at ScienceDirect Computers and Chemical Engineering jo u rn al hom epa ge : Improved single phase modeling of propylene polymerization in a fluidized bed reactor Ahmad Shamiri a,b, Mohd Azlan Hussain a,, Farouq Sabri Mjalli c, Navid Mostoufi d a Department of Chemical Engineering, University of Malaya, 563 Kuala Lumpur, Malaysia b Training Center, Razi Petrochemical Company, P.O. Box 161, Bandar Imam, Iran c Petroleum & Chemical Engineering Department, Sultan Qaboos University, Muscat 123, Oman d Process Design and Simulation Research Center, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran a r t i c l e i n f o Article history: Received 27 July 21 Received in revised form 13 July 211 Accepted 25 July 211 Available online 9 August 211 Keywords: Mathematical modeling Polymerization Fluidized bed reactor Polypropylene Ziegler Natta catalyst a b s t r a c t An improved model for the production of polypropylene in a gas phase fluidized bed reactor was developed. Comparative simulation studies were carried out using the well-mixed, constant bubble size and the improved models. The improved model showed different prediction characteristics of polymer production rate as well as heat and mass transfer behavior as compared to other published models. All the three models showed similar dynamic behavior at the startup conditions but the improved model predicted a narrower safe operation window. Furthermore, the safe ranges of variation of the main operating parameters such as catalyst feed rate and superficial gas velocity calculated by the improved and well mixed models are wider than that obtained by the constant bubble size model. The improved model predicts the monomer conversion per pass through the bed which varies from.28 to 5.57% within the practical ranges of superficial gas velocity and catalyst feed rate. 211 Elsevier Ltd. All rights reserved. 1. Introduction The various advantages of fluidized bed reactors (FBR such as their ability to carry out a variety of multiphase chemical reactions, good mixing of particles, high rate of mass and heat transfer and their ability to operate in continuous state have made it one of the most widely used reactors for polyolefin production. Consequently, considerable attention has been paid to model propylene polymerization in fluidized bed reactors. Fig. 1 illustrates the schematic of an industrial gas-phase fluidized bed polypropylene reactor. As shown in this figure, small particles of Ziegler Natta catalyst and triethyl aluminum co-catalyst are charged continuously to the reactor and react with the reactants to produce a broad distribution of polymer particles. The catalyst particles are porous and are composed of small sub-fragments containing titanium active metal. As the monomer diffuses through the porous catalyst, it polymerizes by reaction on the active sites of the catalyst surface. The catalyst fragments become dispersed during the polymerization and the particles grow into the final polymer product (Zacca, Debling, & Ray, The feed gas, which consists of propylene, hydrogen and nitrogen, provides the fluidization through the distributor, acts as the heat transfer medium and supplies the reactants for Corresponding author. Fax: address: mohd azlan@um.edu.my (M.A. Hussain. the growing polymer particles. The fluidized particles disengage from the unreacted gases in the disengaging zone. The solid-free gas is combined with fresh feed after heat removal and recycled back to the gas distributor. The polypropylene product is continuously withdrawn from near the base of the reactor and above the gas distributor. The unreacted gas is recovered from the product which proceeds to the finishing section of the plant. In heterogeneous systems, polymerization occurs in the presence of different phases with inter-phase mass and heat transfer and chemical reaction. Phenomena such as complex flow of gas and solids, kinetics of heterogeneous polymerization and various heat and mass transfer mechanisms must be incorporated in a realistic modeling approach. Several different methods for describing the hydrodynamics of the fluidized bed polyolefin reactor have been proposed in the literature. McAuley, Talbot, and Harris (1994 and Xie, McAuley, Hsu, and Bacon (1994considered the fluidized bed polyolefin reactor as a well mixed reactor. They compared the simple two-phase and the well mixed models at steady state conditions and showed that the well mixed model does not exhibit significant error in the prediction of the temperature and monomer concentration in the reactor as compared with the simple two-phase model at steady state conditions. Choi and Ray (1985 presented a simple two-phase model in which the reactor consists of emulsion and bubble phases. They assumed that the polymerization reaction occurs only in the emulsion since the bubbles are solid-free. Fernandes and Lona (21 proposed a heterogeneous three-phase /$ see front matter 211 Elsevier Ltd. All rights reserved. doi:1.116/j.compchemeng

2 36 A. Shamiri et al. / Computers and Chemical Engineering 36 ( Nomenclature A cross sectional area of the reactor (m 2 AlEt 3 triethyl aluminum co-catalyst Ar Archimedes number B moles of reacted monomer bound in the polymer in the reactor B w mass of resin in the reactor (kg C pi specific heat capacity of component i (J/(kg K C pg specific heat capacity of gaseous stream (J/(kg K C p,pol specific heat capacity of solid product (J/(kg K D g gas diffusion coefficient (m 2 /s D t reactor diameter (m k g gas thermal conductivity (W/(m K d b bubble diameter (m d p particle diameter (m Fcat catalyst feed rate (kg/s F in (j molar flow rate of potential active sites of type j into the reactor H 2 hydrogen H height of the reactor (m H be bubble to emulsion heat transfer coefficient (W/(m 3 K H bc bubble to cloud heat transfer coefficient (W/(m 3 K H ce cloud to emulsion heat transfer coefficient (W/(m 3 K I m impurity such as carbon monoxide (kmol/m 3 j active site type k di (j deactivation by impurities rate constant for a site of type j k ds (j spontaneous deactivation rate constant for a site of type j k f (j formation rate constant for a site of type j k fh (j transfer rate constant for a site of type j with terminal monomer M reacting with hydrogen k fm (j transfer rate constant for a site of type j with terminal monomer M reacting with monomer M k fr (j transfer rate constant for a site of type j with terminal monomer M reacting with AlEt 3 k fs (j spontaneous transfer rate constant for a site of type j with terminal monomer M k h (j rate constant for reinitiating of a site of type j by monomer M k hr (j rate constant for reinitiating of a site of type j by cocatalyst k i (j rate constant for initiation of a site of type j by monomer M k p (j propagation rate constant for a site of type j with terminal monomer M reacting with monomer M K bc bubble to cloud mass transfer coefficient (s 1 K be bubble to emulsion mass transfer coefficient (s 1 K ce cloud to emulsion mass transfer coefficient (s 1 M monomer (propylene M i concentration of component i in the reactor (kmol/m 3 M i in concentration of component i in the inlet gaseous stream M i the ith component M n number average molecular weight of polymer (kg/kmol M w weight average molecular weight of polymer (kg/kmol Mw monomer molecular weight (kg/kmol N * (j potential active site of type j N(, j uninitiated site of type j produced by formation reaction N(1, j living polymer chain of type j with length one N(r, j living polymer molecule of length r, growing at an active site of type j, with terminal monomer M N d (j spontaneously deactivated site of type j N di (, j, N dih (, j impurity killed sites of type j N H (, j uninitiated site of type j produced by transfer to hydrogen reaction NS number of active site types P pressure (Pa PDI polydispersity index PP polypropylene Q(r, j dead polymer molecule of length r produced at a site of type j r number of units in polymer chain R instantaneous consumption rate of monomer (kmol/s R i instantaneous rate of reaction for monomer i (kmol/s R(j rate at which monomer M is consumed by propagation reactions at sites of type j Re mf Reynolds number of particles at minimum fluidization condition R p production rate (kg/s R v volumetric polymer phase outflow rate from the reactor (m 3 /s t time (s T temperature (K T in temperature of the inlet gaseous stream (K U superficial gas velocity (m/s U b bubble velocity (m/s U e emulsion gas velocity (m/s U mf minimum fluidization velocity (m/s V reactor volume (m 3 V b volume of the bubble phase V e volume of the emulsion phase volume of polymer phase in the reactor (m 3 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 Z axial position (m Greek letters H R heat of reaction (kj/kg ı volume fraction of bubbles in the bed ε b void fraction of bubble for Geldart B particles ε e void fraction of emulsion for Geldart B particles ε ave average void fraction of the bed ε mf void fraction of the bed at minimum fluidization gas viscosity (Pa s density (kg/m 3 g gas density (kg/m 3 pol polymer density (kg/m 3 Subscripts and superscripts 1 propylene 2 hydrogen b bubble phase e emulsion phase

3 A. Shamiri et al. / Computers and Chemical Engineering 36 ( Polymerization mechanism g gas mixture property i component type number in inlet j active site type number mf minimum fluidization pol polymer ref reference condition model that considers bubble, emulsion and particulate phases with plug flow behavior. Hatzantonis, Yiannoulakis, Yiagopoulos, and Kiparissides (2 considered the reactor being comprised of perfectly mixed emulsion phase and a bubble phase divided into several solid-free well-mixed compartments in series. Alizadeh, Mostoufi, Pourmahdian, and Sotudeh-Gharebagh (24 proposed a tanks-in-series model to represent the hydrodynamics of the reactor. Harshe, Utikar, and Ranade (24 developed a comprehensive mathematical model based on the mixing cell framework to simulate transient behavior in the fluidized bed polypropylene reactors. This dynamic model was coupled with a steady state population balance equation. Rigorous multi-monomer, multisite polymerization kinetics was incorporated in the model. Ibrehem, Hussain, and Ghasem (28 proposed a fluidized bed comprising of bubble, cloud, emulsion and solid phases and considered the polymerization reactions occurring in the emulsion and solid phases. Their model also accounts for the effect of catalyst particles type and porosity on the rate of reaction. In the present study, these previous works on the modeling of gas-phase olefin polymerization fluidized-bed reactors were extended to account for the dynamic behavior of propylene polymerization in fluidized bed reactors. To describe the homopolymerization of propylene over a heterogeneous Ziegler Natta catalyst, a two-site homopolymerization kinetic scheme was employed. Extensive simulations were carried out to determine the influence of key process parameters (such as superficial gas velocity, catalyst feed rate, feed composition and feed temperature on the dynamic response of the reactor. In order to obtain a better understanding of the reactor performance, a comparative study between the well-mixed, constant bubble size and improved model was carried out. Similar methodology as of McAuley, MacGregor, and Hamilec (199, Kissin (1985, and de Carvalho, Gloor, and Hamielec (1989 were employed and the following mechanism scheme was developed for the homopolymerization of propylene over the Ziegler Natta catalyst containing multiple active sites. Mass and heat transfer resistances and existence of multiple active sites are two factors responsible for exhibiting broad molecular weight distribution using Ziegler Natta catalyst. It has been shown that under most polymerization conditions, the effect of multiple active site types to produce polymers with broad molecular weight distribution is more important than that of transport resistances (Khare, Luca, Seavey, & Liu, 24; Soares & Hamielec, The singlesite kinetic model is also not capable of describing the kinetic behavior, production rate and molecular weight distribution of propylene homopolymerization. Therefore, a two-type active site is considered in the present study. Each site type is associated with different rate constants for formation, initiation, propagation and chain transfer. Elementary polymerization reactions on the Ziegler Natta multi-site catalyst used in the present study are summarized in Table 1 (Shamiri, Hussain, Farouq, & Mostoufi, Kinetic model A mathematical kinetic model based on the mechanism described in the previous section was derived in the present study. This model consists of mass balances on the species presented in the reactor which are represented by a series of algebraic and differential equations as described in the next section. Characterization of polymer properties was modeled using the population balance and the method of moments. Application of population balance and the method of moments allows for the prediction of the physiochemical characteristics of the polymer such as molecular weight, polydispersity index (PDI, melt flow index (MFI, density, polymer production rate, monomer conversion and active site information Mass balance equations for active sites and reacted monomers The mass balance on the number of moles of potential active sites N * (j in the reactor is given by: Fig. 1. Schematic of an industrial fluidized bed polypropylene reactor.

4 38 A. Shamiri et al. / Computers and Chemical Engineering 36 ( Table 1 Elementary chemical reactions of propylene homopolymerization system. Reaction Description N (j + Cocatalyst k f N(, (j j Formation of active sites N(, j + M k i N(1, (j j Initiation of active sites N(r, j + M N(r kp(j + 1, j Propagation N(r, j + M k fm (j N(1, j + Q (r, j Chain transfer to monomer k N(r, j + H fh (j 2 N H(, j + Q (r, j Transfer to hydrogen N H(, j + M k h N(1, (j j k N H(, j + AlEt hr (j 3 N(1, j k fr (j N(r, j + AlEt 3 N(1, j + Q (r, j Transfer to co-catalyst N(r, j k fs N (j H(, j + Q (r, j Spontaneous transfer N(r, j k ds (j N d (j + Q (r, j Deactivation reactions N(, j k ds (j N d (j N H(, j k ds (j N d (j k N(r, j + I di (j m N dih (, j + Q (r, j Reactions with poisons k N H(, j + I di (j m N dih (, j k N(, j + I di (j m N di (, j dn (j = F in (j k f (jn (j N (j R v (1 The molar flow rate of potential active sites into the reactor, F in (j, is proportional to the mass feed rate of the catalyst. Here R v is the volumetric flow rate of the polymer product from the reactor and is the total volume of the polymer in the reactor. Similarly, the following equations can be written for the number of moles of initiation sites N(, jand N H (, j: dn(, j =k f (jn (j N(, j dn H (, j k i (jm + k ds (j + k di (ji m + R v (2 = Y(, jk fh (jh 2 + k fs (j N H (, j k h (jm + k ds (j + k hr (jalet 3 + k di (ji m + R v In these equations M is the molar concentration of monomer (propylene and H 2 is the concentration of hydrogen. Y(, j is the zeroth moment of the living polymer chain length distribution given as: Y(, J = N(r, j = N(1, j + N(r, j (4 r=1 r=2 The population balance for living chains growing on active sites of length r = 1 is given by: dn(1, j = k i (jn(, jm + N H (, jk h (jm + k hr (jalet 3 + Y(, jk fm (jm + k fr (jalet 3 N(1, j k p (jm + k fm (jm + k fh (jh 2 + k fr (jalet 3 + k fs (j + k ds (j + k di (ji m + R v For the living chains with length greater than 1 (i.e., r 2 the equivalent population balance is: (3 (5 dn(r, j = k p (jmn(r 1, j N(r, j k p (jm + k fm (jm + k fr (jalet 3 + k fh (jh 2 + k fs (j + k ds (j + k di (ji m + R v (6 Population balances for dead chains (for r 2 can be expressed as follows: dq(r, j = N(r, j{mk fm (j + H 2 k fh (j + AlEt 3 k fr (j + k fs (j + k ds (j + k di (ji m } R v Q (r, j (7 By combining Eqs. (4, (5 and (6 and summing over all r values, the following mass balance on Y(, j can be obtained: dy(, j = M{k i (jn(, j + k h (jn H (, j} + N H (, jk hr (jalet 3 { } Y(, j k fh (jh 2 +k fs (j+k ds (j+k di (ji m + R v (8 Mass balances on the first and second moments of the living polymer can be determined ( as follows: dy(1, j = d r=1 rn(r, j = dn(1, j + r dn(r, j r=2 = Mk i (jn(, J + N H (, J{k h (jm + k hr (jalet 3 } + Y(, j{k fm (jm + k fr (jalet 3 } + Mk p (jy(, j { Y(1, j k fm (jm + k fr (jalet 3 + k fh (jh 2 + k fs (j } + k ds (j + k di (ji m + R v (9 where r{n(r 1, j} = (r + 1N(r, j = Y(1, j + Y(, j (1 r=2 r=1 Noting that: r 2 {N(r 1, j} = r=2 Thus: dy(2, j (r N(r, j = Y(2, j + 2Y(1, j + Y(, j r=1 = d ( r=1 r2 N(r, j = dn(1, j + r 2 dn(r, j r=2 = Mk i (jn(, j + N H (, j{k h (jm + k hr (jalet 3 } + Y(, j{k fm (jm + k fr (jalet 3 } + Mk p (j{2y(1, j { + Y(, j} Y(2, j + k fs (j + k ds (j + k di (ji m + R v } (11 k fm (jm + k fr (jalet 3 + k fh (jh 2 (12 The moments of the dead polymer distribution are defined by: X(n, j = r n Q (r, j (13 r=1

5 Similar equations can be derived for the nth moments of the chain length distributions for dead polymer: dx(n, j = Y(n, j{k fm (jm + k fr (jalet 3 + k fh (jh 2 + k fs (j + k ds (j + k di (ji m } X(n, j R v (14 For determining the homo-polymer composition in the reactor at any time, mass balances for the reacted monomers were developed on the number of moles of each type of monomer bound in the polymer particles given by: db = R i B R v (15 where B is the number of moles of the monomer, which are incorporated into the polymer in the reactor and R i is the instantaneous consumption rate of monomer to form polymer. Assuming that the only significant consumption of monomers is by propagation, the following expression for the consumption rate of component (monomer and hydrogen can be obtained: For monomer: NS R i = M i Y(, jk p (j, i = 1 (16 j=1 For hydrogen: NS R i = M i Y(, jk fh (j, i = 2 (17 j=1 The total polymer production rate can be calculated from: R p = 2 Mw i R i (18 where R i is the instantaneous rate of reaction for monomer and hydrogen Homopolymer properties The number average and weight average molecular weights can be determined using the method of moments as follows: ( NS j=1 M n = Mw (X(1, j + Y(1, j NS (19 j=1 (X(, j + Y(, j A. Shamiri et al. / Computers and Chemical Engineering 36 ( ( NS j=1 M w = Mw (X(2, j + Y(2, j NS j=1 (X(1, j + Y(1, j (2 The polydispersity index, PDI, is defined by the ratio of weight average to number average molecular weights: PDI = M w (21 M n 3.3. Kinetic model simplification and reaction rate constants In the present work, due to the lack of a unique source that covers all the kinetic parameters for propylene polymerization, the reaction rate constants were taken from different sources in literature on similar reactive systems (Luo, Su, Shi, & Zheng, 29; McAuley et al., 199. The reaction rate constants of formation, initiation, chain transfer and deactivation reactions were taken from the polyethylene system. The rate of these reactions are mainly related to the catalyst and not affected directly by the type of monomer. Furthermore, it was shown that changes in the rate constants of formation, initiation, transfer to cocatalyst, spontaneous transfer and spontaneous catalyst deactivation reaction has marginal influence on the model predictions (McAuley et al., 199. Therefore, assuming similar values for these rate constants as the case of polyethylene is reasonable. The rate constants considered in this study are given in Table 2. Moreover, effect of temperature (thus, activation energies on the polymerization kinetics was considered only for propagation step. It has been established that under various conditions, when the catalyst particles are sufficiently small and the catalyst activity is not extremely high (low to moderate polymerization rates, mass and heat transfer resistances inside the polymer particle and between the gas and the solid polymer particles do not play an important role and will not significantly affect the dynamic behavior of the reactor and the overall properties of the polyolefin (Floyd, Choi, Taylor, & Ray, 1986; Hutchinson, Chen, & Ray, 1992; Shamiri et al., 21; Zacca et al., Therefore, the temperature inside the particles (where the reactions take place is practically the same as the bed temperature. 4. Modeling of fluidized bed reactor Complex mixing and contacting flow patterns, transport phenomena and polymerization reactions make the fluidized bed reactors non-ideal and difficult to characterize. Many studies have attempted to model such non-ideality using various mixing models to describe the behavior of fluidized bed reactors. A combination of kinetics, hydrodynamics and transport phenomena is required for modeling the non ideal fluidized bed reactor. Table 2 Reactions rate constants. Reaction Rate constant Unit Site Type 1 Site Type 2 Reference Formation k f (j s McAuley et al. (199 Initiation k i (j l mol 1 s Luo et al. (29 k h (j l mol 1 s McAuley et al. (199 k hr l mol 1 s McAuley et al. (199 Propagation k p(j l mol 1 s Luo et al. (29 Activation energy kcal mol Transfer k fm (j l mol 1 s Luo et al. (29 k fh (j l mol 1 s Luo et al. (29 k fr (j l mol 1 s McAuley et al. (199 k fs (j l mol 1 s McAuley et al. (199 Deactivation k ds (j s Luo et al. (29 k di (j l mol 1 s McAuley et al. (199

6 4 A. Shamiri et al. / Computers and Chemical Engineering 36 ( The simple two-phase flow structure for the gas-phase olefin polymerization model has been previously used by Choi and Ray (1985, McAuley et al. (1994, Hatzantonis et al. (2 and Harshe et al. (24. In this model, it is assumed that the bubbles are solidfree bubbles while the emulsion remains at minimum fluidization conditions. McAuley et al. (199, 1994 proposed a simplified wellmixed model by assuming the entire contents of the fluidized bed treated as well mixed and the emulsion phase remains at minimum fluidization condition. However, in reality, the voidage of the emulsion phase may differ far from that at the minimum fluidization and the bubbles may contain different portions of solid particles (Cui, Mostoufi, & Chaouki, 2; Cui, Mostoufi, & Chaouki, 21. In the modified model developed in this work, a unified modeling approach is adopted for the gas-solid fluidization, in which the well mixed model (CSTR is developed to describe the dynamic behavior of the polypropylene gas phase fluidized bed reactor. For comparison purpose we described these conventional models in the next section before describing our proposed model Well-mixed model A simplified well-mixed model is obtained by assuming that bubbles are very small or unrestricted mass and heat transfer between the bubble and emulsion phases and the temperature and composition are uniform in the gas phase throughout the bed proposed by McAuley et al. (199, The following assumptions were made for the well mixed model: Mass and heat transfer rates between emulsion and bubble phase are very high or bubbles are sufficiently small; therefore the polymerization reactor is considered to be a single phase (emulsion phase well mixed reactor (Alizadeh et al., 24; McAuley et al., The emulsion phase remains at minimum fluidization. Uniform temperature and composition throughout the bed. Mass and heat transfer resistances between the gas and the solid polymer particles in the emulsion phase are negligible (i.e., small catalyst particles, low to moderate catalyst activity or polymerization rates (Floyd et al., Dynamic material and energy balance equations can be written for the monomer and hydrogen based on the previously mentioned assumptions (Hatzantonis et al., 2. The dynamic molar balance is written as: (Vε mf dm i = U A(M i in M i R v ε mf M i (1 ε mf R i (22 The dynamic energy balance is given by: m dt M i C pi Vε mf + V(1 ε mf pol C p,pol m m = U A M i C pi (T in T ref U A M i C pi (T T ref R v m M i C pi ε mf + (1 ε mf pol C p,pol (T T ref + (1 ε mf H R R p (23 The internal energy of the monomer is considered to be negligible in the energy balance equation. The initial conditions for the solution of model equations are as follows: M i t= = M i in (24 T(t = = T in (25 The well mixed model is an oversimplification of what actually happens in the fluidized bed since it considers the emulsion stays at minimum fluidization conditions at all operating conditions and it takes the voidage over the whole bed at minimum fluidization conditions (ε bed = ε mf. Consequently, this model is incapable of predicting the transfer and reaction rates in the practical process properly The two phase constant bubble size model assumes that the emulsion (or dense phase is at minimum fluidization conditions (Choi & Ray, This model has been adopted by many previous studies for the gas-phase olefin polymerization (Choi & Ray, 1985; Harshe et al., 24; Hatzantonis et al., 2; McAuley et al., 1994; Shamiri, Hussain, Mjalli, Mostoufi, & Shafeeyan, 211. The assumptions made for the constant bubble size model are as follows: The fluidized bed comprises of two phases, bubble and emulsion. Reactions occur only in the emulsion phase. The emulsion phase is considered to be perfectly mixed, at minimum fluidization, interchanging heat and mass with the bubble phase at uniform rates over the bed height. The bubbles are spherical with uniform size and in plug flow at constant velocity. Mass and heat transfer resistances between the gas and the solid polymer particles in the emulsion phase are negligible (i.e., small catalyst particles, low to moderate catalyst activity or polymerization rates (Floyd et al., Using these assumptions, steady-state mass and energy balances can be derived to describe the variation of the monomer concentration and temperature in the bubble phase (Hatzantonis et al., 2. The mole balance for monomer and hydrogen can be written as follows: dm i b dz = K be(m i e M i b U b (26 By integrating the local monomer concentration M i b with respect to the bed height, one can calculate the mean concentration of the ith monomer in the bubble phase: M i b = 1 H M H i b dh = M i e + (M i e,(in M i e U b K be H ( ( 1 exp K beh U b (27 The bubble phase energy balance is expressed by the following equation: m dt M i b C b pi dz = H be (T U b T e (28 b The mean temperature in the bubble phase can be calculated by integrating Eq. (48 over the total bed height: T b = 1 H ( ( T H b dh=t e +(T in T e U b C p 1 exp H beh (29 H be H U b C p where Nm C p = M i b C pmi (3 is the average heat capacity of the reacting monomers.

7 A. Shamiri et al. / Computers and Chemical Engineering 36 ( Table 3 Correlations and equations used in the constant bubble size model. Parameter Formula Reference Minimum fluidization velocity Re mf = ( Ar 1/ Lucas, Arnaldos, Casal, and Puigjaner (1986 Bubble velocity U b = U U mf + u br Kunii and Levenspiel (1991 Bubble rise velocity u br =.711(gd b 1/2 Kunii and Levenspiel (1991 Emulsion velocity U e = U mf ε mf (1 ı Kunii and Levenspiel (1991 Bubble diameter d b = d b (U U e 1/3 ( H d b =.85 (for Geldart B Hilligar and Werther (1986 Mass transfer coefficient K be = ( K bc Kce 1 K bc = 4.5( Ue d b K ce = 6.77( Dg εeu br ( 1 Heat transfer coefficient H be = H bc Hce d b d b ( D 1/2 g g 1/4 d 5/4 b Kunii and Levenspiel (1991 Kunii and Levenspiel (1991 H bc = 4.5( Ueg Cpg (kg g Cpg 1/2 g 1/4 d 5/4 b ( 1/2 H ce = 6.77( gc pgk g 1/2 εeu br d 3 b Bubble phase fraction ı = U U mf U b Kunii and Levenspiel (1991 Emulsion phase porosity ε e = ε mf Volume of polymer phase in the = AH(1 ε e(1 ı emulsion phase The dynamic molar balance for the ith monomer in the emulsion phase can be written as: (V e ε mf dm i e = U e A e ε mf (M i e,(in M i e + V eık be 1 ı ( M i b M i e R v ε mf M i e (1 ε mf R i The dynamic emulsion phase energy balance can be written as: m dt e V e ε mf M i e C pi + V e (1 ε mf pol C p,pol m dm = V e ε mf C i e pi (T e T ref m + U e A e ε mf M i e,(in C pi (T e,(in T ref m U e A e ε mf M i e C pi (T e T ref V eıh be (1 ı (T e T b ( m + R v (1 ε mf pol C p,pol + ε mf M i e C pi (31 (T e T ref + (1 ε mf H R R p (32 The correlations required for estimating the bubble volume fraction in the bed, the voidage of the emulsion phase and bubble phases, the emulsion phase and bubble phases gas velocities and mass and heat transfer coefficients for the constant bubble size model are summarized in Table 3. The boundary and initial conditions for solving the model equations are as follows: M i b,z= = M i in (33 T b (z = = T in (34 M i e,t= = M i in (35 T e (t = = T in (36 The constant bubble model, although is an improvement in some respect to the well mixed model, it is still far from reality since it is assumed in this model that the bubbles are solid-free and the emulsion stays at minimum fluidization at all operating conditions The conventional models assume that the emulsion is at minimum fluidization (ε e = ε mf and bubbles are solid-free (ε b = 1. These assumptions are not able to predict the effect of the dynamic gas solid distribution on the apparent reaction and heat/mass transfer rate in the fluidized beds properly and is limited to lowvelocity bubbling fluidization. However, existence of solid particles in the bubbles has been proven both experimentally and theoretically and the emulsion also does not remain at minimum fluidization conditions and it may contain more gas at higher gas velocities (Cui et al., 2, 21. Since the assumption of minimum fluidization condition for the emulsion phase in the polypropylene reactor (simple two-phase model is not realistic (Alizadeh et al., 24, the hydrodynamic structure proposed by Cui et al. (2, 21 was used in this study for improving the single phase model. The improved model also takes into account the average bed voidage that considers the presence of solids in the bubbles and that the emulsion phase does not remain at minimum fluidization conditions. These facts have already been supported by many experimental and theoretical works (Alizadeh et al., 24. Cui et al. (2 reported the constants of their hydrodynamic model for FCC and sand as representative of Geldart A and Geldart B particles. Polypropylene particles (d p = m and s = 91 kg/m 3 are Geldart B, thus, the constants of this type of particles were chosen and shown in Table 4. It is worth noting that the same approach was adopted in similar modeling attempts (Alizadeh et al., 24; Jafari, Sotudeh-Gharebagh, & Mostoufi, 24; Kiashemshaki, Mostoufi, & Sotudeh-Gharebagh, 26. These studies showed that this model provides good predictions of the reactor performance. In the improved model, it is also assumed that there are negligible mass and heat transfer resistances between the emulsion gas and solid polymer particles as well as that between the bubble and emulsion phases. Therefore, a pseudo-homogeneous singlephase model can be used. Based on these model assumptions and

8 42 A. Shamiri et al. / Computers and Chemical Engineering 36 ( Table 4 Correlations and equations used in the improved and well mixed models. Parameter Formula Reference Minimum fluidization velocity Re mf = ( Ar 1/ Lucas et al. (1986 Bubble velocity U b = U U mf + u br Kunii and Levenspiel (1991 Bubble rise velocity u br =.711(gd b 1/2 Kunii and Levenspiel (1991 Emulsion velocity U e = U ıu b 1 ı Kunii and Levenspiel (1991 Bubble diameter d b = d b (U U e 1/3 ( H d b =.85 (for Geldart B Hilligar and Werther (1986 Emulsion phase porosity for Geldart B particles ε e = ε mf exp Bubble phase porosity for Geldart B particles ε b = exp Bubble phase fraction for Geldart B particles ı = exp ( ( ( U U mf U U mf.413 U U mf.429 Cui et al. (2 Cui et al. (2 Cui et al. (2 Average bed voidage ε ave = (1 ıε e + ıε b Alizadeh et al. (24 Volume of polymer phase in the bed = Ah(1 ε ave Bubble velocity Not applicable Emulsion velocity U e = U Bubble diameter Not applicable Emulsion phase porosity for Geldart B particles ε e = ε mf =.45 Bubble phase porosity for Geldart B particles Not applicable Bubble phase fraction for Geldart B particles Not applicable Average bed voidage Not applicable Volume of polymer phase in the bed = Ah(1 ε mf the hydrodynamic sub-model as described above, the following dynamic material and energy balance with hydrodynamic equations can be written for all of the compositions in the bed. Monomer and hydrogen dynamic molar balance is written as: (AHε ave dm i = U e A(M i in M i R v ε ave M i (1 ε ave R i (37 The dynamic energy balance is given by following equation: m dt M i C pi AHε ave + AH(1 ε ave pol C p,pol m m = U e A M i C pi (T in T ref U e A M i C pi (T T ref m R v ε ave M i C pi + (1 ε ave pol C p,pol (T T ref + (1 ε ave H R R p (38 The dynamic monomer internal energy was considered to be negligible in the energy balance. Better mixing of the two phase results in more solid particles entering the bubbles and more gas entering the emulsion phase when the superficial gas velocity increases in a fluidized bed. Cui et al. (2, 21 considered the effect of particles in the bubbles and excess gas in the emulsion phase and they derived the hydrodynamic correlations based on this concept and this was used in this study. The correlations required for evaluating the average bed voidage and other hydrodynamic correlations used in the improved model and comparison with the well mixed model are summarized in Table 4. The initial conditions for the solution of the model equations are as follows: M i t= = M i in (39 T(t = = T in (4 Table 5 Operating conditions and physical parameters considered in this work for modeling fluidized bed polypropylene reactors. Operating conditions Physical properties V (m 3 = 5 (Pa s = T ref (K = g (kg/m 3 = T in (K = s (kg/m 3 = 91 P (bar = 25 d p (m = Propylene concentration (mol/l = 1 ε mf =.45 Hydrogen concentration (mol/l =.15 Catalyst feed rate (g/s =.2 5. Results and discussion To investigate the effect of different hydrodynamic sub-models on the dynamic response and grade transition, dynamic modeling of the process was carried out using the three hydrodynamic sub-models described above along with the reaction sub-model. Comprehensive simulations were carried out in order to evaluate the effect of the key process parameters such as catalyst feed rate, superficial gas velocity, propylene feed concentrations and carbon monoxide on the polymer production rate, emulsion phase temperature and monomer concentration in the polypropylene reactor. In order to demonstrate the predictive capabilities of the proposed model, simulations were carried out at the operating conditions shown in Table 5. Overall production rate of polymer against time at various catalyst feed rates calculated by the three models are shown in Fig. 2. It should be noted that the initial condition (zero time of the reactor was assumed to be a bed of inert polymer powder and circulating gas before injection of the catalyst particles. It can be seen in this figure that the polymer production rate predicted by the well mixed model is higher than that by the constant bubble size and improved models. This is due to the assumption that the fluidized bed reactor plus recycling system are regarded as a CSTR comprising a well-mixed solid phase interacting with a wellmixed gas phase (McAuley et al., 199. The polymer production rate predicted by the improved model is lower than the conventional models since the excess gas increases the void fractions of the emulsion phase and bed. This fact reduces the polymer production

9 A. Shamiri et al. / Computers and Chemical Engineering 36 ( Production rate (g/s Fcat=.3 g/s Fcat=.2 g/s Production rate (g/s Time (s Catalyst feed rate (g/s.4.5 Fig. 2. Evolution of the polymer production rate over the time in the reactor at various catalyst feed rates (U =.35 m/s. rate compared to the conventional models which assume that the emulsion phase remains at minimum fluidization condition. Fig. 2 also indicates that the improved model, constant bubble size and well mixed models predict similar dynamic behavior at the reactor start-up. However, this behavior change as time evolves. The improved model shows a closer behavior to the constant bubble size model in terms of the production rate. Fig. 3a and b illustrates the emulsion phase temperature and propylene concentration transients in the reactor predicted by the three models. The improved model shows lower emulsion phase temperature and higher monomer concentration compared to the Emulsion phase temperature (k Emulsion phase propylene concentration (mol/lit Time (s 8 (a (a (b 1 Fig. 3. Evolution of reactor behavior against time predicted by the three models (Fcat =.3 g/s and U =.35 m/s: (a temperature and (b propylene concentration. Fig. 4. Effect of catalyst feed rate on polymer production rate at U =.35 m/s. conventional well mixed model due to higher void fraction and lower reaction rate of the emulsion phase. The constant bubble size model shows higher emulsion phase temperature and lower monomer concentration compared to the other models. Constant bubble size model shows that the assumptions of steady-state mass and energy balances and considering mean concentration and temperature over the bed height for the bubble phase may result in an over-prediction of the temperature and propylene conversion in the emulsion phase. Fig. 3a and b also reveals that the improved model shows the same dynamic trend behavior in the evolution of temperature and concentration as the constant bubble size and well mixed models at the beginning of polymerization and start-up conditions of the reactor. However, these transients settle at different final steady-state values. Comparing the temperature profiles with monomer concentration profiles reveals the reverse relationship between these two variables in the reactor. The consumption of monomer increases with the reaction and consequently increases the temperature as well Effect of catalyst feed rate The catalyst contains multiple active sites and each site type is associated with different rate constants for formation, initiation, propagation, chain transfer and deactivation reactions. The molar flow rate of potential active sites into the reactor is proportional to the mass feed rate of the catalyst. This makes the later an important operating parameter in polypropylene fluidized bed reactors. Fig. 4 shows the effect of catalyst feed rate on the polypropylene production rate. It is clear that the polymer production rate is directly proportional to the catalyst feed rate. As the catalyst feed rate increases, so does the polymer production rate. This is due to the increase in the available reaction sites. The improved model shows lower production rate compared to the conventional well mixed and constant bubble size models since it predicts higher void fraction of the bed. In fact, the improved model considers the excess gas entering the emulsion phase which increases the average bed void fraction which leads to reduction in the polymerization rate compared to the conventional models that assume the emulsion phase is at minimum fluidization condition. Fig. 5 illustrates the effect of step changes in the catalyst feed rate on the dynamic behavior of the three models in terms of emulsion phase temperature. The initial catalyst feed rate was assumed to be.3 g/s and when the emulsion phase temperature reached steady state, the catalyst feed rate was changed by ±.1 g/s. As can be seen in Fig. 5, the catalyst feed rate strongly affects the emulsion phase temperature and a small step change in the catalyst feed

10 44 A. Shamiri et al. / Computers and Chemical Engineering 36 ( Emulsion phase temperature (k Safety limit 1 2 Fcat=.3g/s 3 Fcat=.4g/s Time (s Fcat=.2g/s Emulsion phase temperature (k Safety limit U =.4m/s Time (s 7 U =.3m/s U =.5m/s Fig. 5. Effect of step change in the catalyst feed rate from.3 g/s to.2 or.4 g/s on the emulsion phase temperature calculated by the three models at U =.35 m/s. Fig. 7. Effect of step change in U from.4 m/s to.5 or.3 m/s on the emulsion phase temperature calculated by the three models at Fcat =.3 g/s. rate changes the temperature of the reactor. Emulsion temperature predicted by the improved model lies between the temperatures predicted by the other two models and shows an intermediate behavior. The constant bubble size model shows a higher deviation. It should be pointed out that when the catalyst feed rate is changed from.3 g/s to.4 g/s, the constant bubble size model predicts a temperature overshoot of about 2.5 K above the accepted industrial safety limit of 8 C (Meier, Weickert, & Van Swaaij, 21. Working above this critical temperature may lead to particle agglomeration in the reactor Effect of superficial gas velocity The superficial gas velocity is directly related to the monomer residence time in the reactor, heat removal rate from the reactor and fluidization conditions. Consequently it is very important to investigate its effect on these process variables. Effect of superficial gas velocity on the polymer production rate predicted by various models is illustrated in Fig. 6. This figure illustrates that all three models predict that the polymer production rate decreases by increasing the superficial gas velocity. In fact, by increasing the superficial gas velocity (at constant monomer concentration in the feed and catalyst feed rate, gas passes faster through the bed. As a result, some monomers may bypass the catalyst, therefore, reducing the reaction extent which leads to a reduction in the polymer Production rate (g/s U (m/s Fig. 6. Effect of superficial gas velocity on the product rate at Fcat =.2 g/s..6.7 production rate. The production rate predicted by the improved model is less than that of the conventional models since based on the improved hydrodynamic correlations, an increase in the superficial gas velocity increases the average bed void fraction which leads to reducing the volume of solids in the reactor. Therefore, the monomer contact with growth sites is reduced, resulting in decreasing the total monomer conversion and polymer production rate compared to the conventional models. Fig. 7 demonstrates the effect of step changes in the superficial gas velocity on the emulsion phase temperature predicted by the three models. In all cases, the total feed component concentration was kept constant as the superficial gas velocity was changed from.4 m/s to.5 m/s and.4 m/s to.3 m/s respectively. As can be seen in this figure, the superficial gas velocity has a significant effect on the emulsion phase temperature which indicates that it is an important parameter for the heat removal and control of the reactor temperature. Increasing the superficial gas velocity results in a higher convective cooling capacity of the gas which results in a lower temperature for the emulsion phase and vice versa. The improved model temperature prediction lies between predictions of the other two models. By introducing step changes in the superficial gas velocity, the constant bubble size model shows higher temperature compared to the other models. Moreover, as the superficial gas velocity is decreased to.3 m/s the constant bubble size model predicts a temperature overshoot of about 2 K which might lead to particles agglomeration problems while the improved model and well mixed models have lower predicted temperature and do not undergo temperature runaway similar to that encountered by the constant bubble size model. The dynamic response of the emulsion phase temperature to step changes in the superficial gas velocity calculated by the three models show different dynamic behavior and sensitivities which is mainly due to the different assumptions imposed on these models. Moreover, this can be also related to the differences in the bed voidage correlations used in these models. Fig. 8 illustrates the effect of superficial gas velocity on the propylene conversion per pass through the bed predicted by the improved model at various catalyst feed rates. As discussed before, increase in the superficial gas velocity results in decreasing the contact of monomer with growth sites which leads to decreasing the monomer conversion. Fig. 8 shows that in the practical range of superficial gas velocities of.25 to.6 m/s and using different catalyst feed rate, the monomer conversion per pass through the bed can vary from.28 to 5.57%.

11 A. Shamiri et al. / Computers and Chemical Engineering 36 ( Monomer conversion (% Fcat=.2 g/s Fcat=.3 g/s Fcat=.4 g/s Fcat=.5 g/s PDI H 2 =.15 mol/lit H 2=.1mol/lit H 2=.2 mol/lit U (m/s Time (s Fig. 8. Effect of gas velocity on the propylene conversion per pass through the bed predicted by the improved model at different catalyst feed rates. Fig. 1. Effect of step change in the hydrogen concentration on PDI of the polymer predicted by the three models (Fcat =.2 g/s and U =.35 m/s Effect of feed composition Varying monomer and carbon monoxide concentrations have significant effect on the propylene polymerization. The effect of feed propylene concentration on the production rate predicted by the three models is shown in Fig. 9. At low propylene concentration, all models predict similar production rate. As propylene concentration in the feed increases, the production rate profiles for different models start to divert from each other. This can be mainly attributed to the different production levels of polymerization for those models due to the hydrodynamic considerations, discussed in the previous section. The polydispersity index (PDI indicates the distribution of individual molecular masses in a batch of polymers and used as a measure of the breah of the molecular weight distribution. In the industrial polypropylene production process, the most effective technique to control the molecular weight distribution and grade transition is by varying hydrogen concentration. Therefore, a step change in the hydrogen concentration feed was introduced to the system in order to monitor the dynamic response of the different hydrodynamic models in terms of the PDI values. Effect of a step change in the hydrogen concentration in the feed on the PDI of the polymer predicted by the three models is shown in Fig. 1. The initial hydrogen feed concentration was set to.15 mol/l. The propylene concentration in the feed was kept constant at 1 mol/l, while the hydrogen concentration was changed from.15 to.2 and.15 to.1 mol/l respectively. It is clear that the hydrogen concentration strongly affects the PDI of the polymer. Fig. 1 demonstrates that the hydrogen concentration is inversely related to the polymer PDI and this is due to the change in both weight average and number average molecular weight. Transition in molecular weight takes more than 9 h. The reason for such a long transition time is that during the grade transition, new polymer is produced in the reactor and hence the cumulative properties of the polymer such as molecular weight take a long time to reach the new target. As shown in Fig. 1, different hydrodynamic models show similar behavior in the change of polymer properties and approach the steady state values in almost the same time. Catalyst activity is very sensitive to impurities such as carbon monoxide that poison the active sites of the catalyst. Effect of a step change in carbon monoxide concentration on the production rate predicted by the three models is shown in Fig. 11. This figure demonstrates that injection of.2 ppm carbon monoxide to the reactor significantly decreases the production rate. Even low amounts of carbon monoxide may cause a nearly instantaneous reduction in the production rate since the adsorption of carbon monoxide onto a catalyst site deactivates it and results in an instantaneous drop in the propagation rate. Fig. 11 shows that all Production rate (g/s Propylene concentration (mol/lit.9 1. Production rate (g/s CO injection Time (s Fig. 9. Effect of inlet propylene concentration on the product rate (Fcat =.2 g/s and U =.35 m/s. Fig. 11. Effect of step change in the carbon monoxide concentration (.2 ppm on the production rate (Fcat =.2 g/s and U =.35 m/s.

12 46 A. Shamiri et al. / Computers and Chemical Engineering 36 ( Emulsion phase temperature (K Carbon monoxide concentration (ppm levels of carbon monoxide in the reactor, when the reactor works at above the maximum safe bed operation temperature, can reduce the risks of particle melting, agglomeration and subsequent reactor shutdown. Based on the advantages of the improved model, it can be expected that the improved model provide a more realistic result. In fact, even though the model has not been validated experimentally, the recommendations of previous experimental findings have been taken into consideration in the improved model. Although the authors were not able to find or generate experimental data of propylene polymerization for validation of the improved model, the same modeling approach was adopted for polyethylene production and was compared with steady state industrial data in terms of met flow index (Alizadeh et al., 24, molecular weight distribution, polymer production rate, reactor temperature and polydispersity index (Kiashemshaki et al., 26 in which the results showed that the model is in good agreement with the industrial data. Fig. 12. Effect of carbon monoxide concentration on the emulsion phase temperature (Fcat =.2 g/s and U =.35 m/s. models behave similarly in predicting the effect of catalyst poisoning. Fig. 12 illustrates the effect of carbon monoxide on the emulsion phase temperature. The emulsion phase temperature rate sharply decreases by the presence of carbon monoxide due to deactivation of the catalyst sites. Effect of a step change in carbon monoxide concentration on the emulsion phase temperature calculated by the three models is shown in Fig. 13. As shown in this figure, the three models predict a temperature above the accepted industrial safety limit of 8 C at the catalyst feed rate of.5 g/s and superficial gas velocity of.3 m/s. Working above this critical temperature may lead to particle melting, agglomeration and subsequent reactor shutdown. At this condition, the injection of.45 ppm of carbon monoxide to the reactor presents a significant effect on the reactor temperature. In such a condition, the temperature of the emulsion predicted by the three models is decreased by more than 2 K which brings the final temperature below the maximum safe temperature for bed operation which reduces the risks mentioned above. Fig. 13 illustrates that the constant bubble size model shows the most significant change compared to the other two models. The improved model shows closer behavior to the constant bubble size model compared to the well mixed model. This difference can be related to the differences in the bed voidage predicted by these models, as discussed before. It can be concluded that the presence of very low Emulsion phase temperature (k Safety limit CO injection Time (s Fig. 13. Effect of step change in the carbon monoxide concentration (.45 ppm on the emulsion phase temperature calculated by the three models (Fcat =.7 g/s and U =.3 m/s. 6. Conclusions An improved dynamic model for the production of polypropylene in a gas phase fluidized bed reactor was developed to describe the behavior of the fluidized bed reactor of polypropylene production. Comparative simulation studies were carried out using the well-mixed, constant bubble size and the improved models in order to investigate the effects of the mixing, operating conditions, kinetic and hydrodynamic parameters on the reactor performance. The improved model showed different prediction characteristics of polymer production rate as well as heat and mass transfer behavior as compared to other published models. All the three models showed similar dynamic behavior at the startup conditions. But the improved model predicted a narrower safe operation window. Furthermore, the safe ranges of variation of the main operating parameters such as catalyst feed rate and superficial gas velocity calculated by the improved and well mixed models are wider than that obtained by the constant bubble size model. The superficial gas velocity and catalyst feed rate have a strong effect on the hydrodynamics and reaction rate which results in a greater variation in the total production rate. Based on the improved model, by considering the practical range of superficial gas velocity and different catalyst feed rate, the monomer conversion per pass through the bed varies from.28 to 5.57%. The presence of carbon monoxide in the feed resulted in the reduction of polypropylene production rate and reactor temperature due to catalyst deactivation which highlights the importance of including a purification facility in the process. On the other hand, injection of low amount of carbon monoxide to the reactor may prevent particle melting, agglomeration and subsequent reactor shutdown when the reactor is about to work at above the maximum safe bed operating temperature. Acknowledgments The authors would like to thank the support of the Research Council of the University of Malaya under research grant (No. RG54/9AET and the Petroleum and Chemical Engineering Department at Sultan Qaboos University and the School of Chemical Engineering, College of Engineering, University of Tehran for their support to this research. References Alizadeh, M., Mostoufi, N., Pourmahdian, S., & Sotudeh-Gharebagh, R. (24. Modeling of fluidized bed reactor of ethylene polymerization. Chemical Engineering Journal, 97, Choi, K. Y., & Ray, W. H. (1985. The dynamic behavior of fluidized bed reactors for solid catalyzed gas phase olefin polymerization. Chemical Engineering Science, 4,