Chemical Engineering Communications ISSN: 0098-6445 (Print) 1563-5201 (Online) Journal homepage: http://www.tandfonline.com/loi/gcec20 Continuous Dosing of Fast Initiator during Suspension Polymerization of Vinyl Chloride for Enhanced Productivity; Mathematical Modeling and Experimental Study Mohammad Javad Bijhanmanesh, Nasrin Etesami & Mohsen Nasr Esfahany To cite this article: Mohammad Javad Bijhanmanesh, Nasrin Etesami & Mohsen Nasr Esfahany (2016): Continuous Dosing of Fast Initiator during Suspension Polymerization of Vinyl Chloride for Enhanced Productivity; Mathematical Modeling and Experimental Study, Chemical Engineering Communications, DOI: 10.1080/00986445.2016.1205981 To link to this article: http://dx.doi.org/10.1080/00986445.2016.1205981 Accepted author version posted online: 05 Jul 2016. Published online: 05 Jul 2016. Submit your article to this journal View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=gcec20 Download by: [Library Services City University London] Date: 07 July 2016, At: 03:50 Continuous Dosing of fast Initiator during Suspension Polymerization of Vinyl Chloride for Enhanced Productivity; Mathematical Modeling and Experimental study Mohammad Javad Bijhanmanesh1, Nasrin Etesami1, Mohsen Nasr Esfahany1 1 Department of Chemical Engineering, Isfahan University of Technology, Isfahan, Iran E-mail: netesami@cc.iut.ac.ir Abstract Chemical Engineering Communications An adopted mathematical model was developed to reduce the batch time required for the suspension polymerization of vinyl chloride in order to improve productivity by continuous dosage of a fast initiator during polymerization reaction. The model was accompanied by a particle swarm optimization (PSO) algorithm so as to optimize the initiator dosage rate during the process for a certain conversion. A pilot scale reactor was employed to verify the mathematical model predictions. This showed that the model predictions are in very good agreement with the experimental data. A proper initiator dosage trajectory during the course of the reaction was obtained in such a way that the reaction rate over the course of polymerization was constant and corresponded to the maximum rate in the conventional case (non-continuous addition of a mild initiator). The maximum reduction in reaction time relative to conventional polymerization for the predefined conversion was 53%. Analyzing the molecular characteristics of the samples showed that the molecular characteristics of the final PVC product remained relatively unchanged under an optimum initiator dosage trajectory compared with the conventional process. 1 KEYWORDS: PVC, Suspension polymerization, Mathematical modeling, Optimization, Fast initiator, Continuous dosage INTRODUCTION Poly (vinyl chloride) (PVC) is a versatile plastic which is often produced through the suspension polymerization technique. The VCM suspension polymerization is typically carried out in an isothermal batch-wise process (Saeki and Emura, 2002). The monomer is initially dispersed in droplet form in the size range of 50–500 μm using the combined Chemical Engineering Communications action of agitation and surface active agents. In the conventional process for VCM polymerization, the initiator is entirely added to the reactor at the beginning of the reaction. Polymerization begins by decomposing monomer-soluble initiators in the droplets at reaction temperature converting the liquid droplets into rigid, porous polymer particles (Feldman et al., 1977). In such polymerization systems, an auto-acceleration of the reaction rate occurs. The maximum cooling capacity of the reactor corresponds with the maximum rate of the heat release at the exothermic peak (Pinto and Giudici, 2001). In this case, the full capacity of the cooling system remains unutilized most of the time during the course of the polymerization, particularly at the beginning of the reaction. The activity of the initiator and the polymerization temperature are strategic factors that can be manipulated to control the rate at its maximum constant value, and hence to reduce the batch time of the polymerization reaction (Darvishi et al., 2015; Feldman et al., 1977; Meulenbrugge et al., 2007; Pinto, 1990; Pinto and Giudici, 2001; Van Swieten et al., 2002, 2003; Westmijze et al., 2012; Westmijze et al., 2013). The ways of implementing these strategies involve applying a temperature program, a cocktail of initiators and an 2 initiator dosage system in such a way that the polymerization rate is kept constant at the desired value. Achieving the constant maximum reaction rate and hence using from the full capacity of the cooling system during the polymerization time is possible by means of continuous dosing of a fast initiator during the polymerization reaction. The continuous initiator dosage allows for the spreading of heat the reaction over the course of the time during which polymerization occurs, which allows for a higher degree of control of the Chemical Engineering Communications polymerization rate. This process was found to solve a number of drawbacks which originate when using mild initiators, such as poor initiator efficiency and high residual initiator levels in the resin produced. Akzo Nobel Company (Netherlands) suggested a process in which initiators having a half-life in the range of 0.0001-1.0 hour at the polymerization temperature are dosed to the reaction mixture so as to improve productivity (Teiji et al., 1986; Van Swieten et al., 2002, 2003; Westmijze et al., 2012; Westmijze et al., 2013). However, the study did not consider how to optimize the rate of initiator dosage as well as the effects on the properties of the final product. However, because of the time consuming nature of the batch polymerization of PVC, the determination of an optimal initiator dosing regimen for the best enhanced productivity is very difficult to establish experimentally. Therefore, the use of modeling and simulation to obtain an optimal initiator dosing rate is ineviTable . Up to the present, various 3 mathematical models have been developed for regular polymerization process of VCM, but no such models have yet been adopted for a continuous initiator dosage system (Alexopoulos and Kiparissides, 2007; Kiparissides et al., 1997; Krallis and Kiparissides, 2007; Olaj, 1977; Suresh and Chanda, 1982; Ugelstad, 1977; Xie et al., 1991a). In this paper, a mathematical model for the suspension polymerization of VCM with continuous dosages of initiator is developed in which adjusTable parameters are specified using experimental data. The model is then optimized using a PSO algorithm (Eberhart Chemical Engineering Communications and Kennedy, 1995) to achieve an optimal dosing trajectory of the fast initiator with a predefined reaction rate and VCM conversion. The model is validated against the experimental data obtained from performing the suspension polymerization experiments in the pilot-scale reactor. The effect of a continuous dosage initiator on polymerization time and molecular characteristics of the final PVC resin (MW, K value and MWD) are also investigated using several simulation runs. MATERIALS AND METHODS Model Development Our simulations rely on a mathematical model which is a combination of the models provided by Xie, et al., and Kiparissides, et al., in which the polymerization reaction was considered in both monomer and polymer phases (Kiparissides et al., 1997; Xie et al., 1991a). Accordingly, the two-phase based reaction rate can be expressed by differential equations as follows: 4  dX 1  K p1M1  R 1  K p 2 M 2  R  2 dt M 0  (1) where, Mo is the initial mass of VCM (g), Kp, M and [R•] are the propagation rate constant (l mol-1 s-1), the masses of monomer (g) and the radical concentrations in the monomer and polymer phases (mol l-1), respectively. In the current study, subscripts 1 and 2 represent the monomer and the polymer phase, respectively. Given that free-radical polymerization of VCM is accompanied by some physical Chemical Engineering Communications transitions which influence the reaction phases, the model divides the course of polymerization into three stages. During the first stage, conversion is very low (X<0.001) and there is no separate polymer phase as yet, the reaction occurs merely in monomer phase. Monomer mass distributions in two phases will be given by: M1  M 0 (1  X )  M g  M w ; M 2  0.0 (2) where Mg and Mw are the masses of monomer in gaseous and aqueous phases and will be expressed by (Xie et al., 1991a): XM 0 1/ Dm  1/ Dp   MWm Pm0  Mg  (1  W1 )Vr   RT  1  Dg 0 / Dm  M w  KWw (3) (4) where, MWm is the monomer molecular weight (g mol-1), Pm0 is the saturation pressure of the monomer (atm), W1 is the initial fillage factor of reactor, Vr is the reactor volume (l), Dm, Dp and Dgo are the densities of monomer, polymer and monomer vapor (g l-1), K is the monomer solubility constant in water at polymerization temperature 5 ( K  0.0472  11.6 / T ) and Ww is the water mass in the continuous phase (g). The reaction rate equation for the first stage, therefore, becomes (Xie et al., 1991a);  dX 1  K p1   1/2 M1 RI 1  dt M 0  Kt1  X  0.001 (5) where, Kt and RI are termination rate constant (l mol-1 s-1) and initiation rate (mol l-1 s-1). The second stage starts with X>0.001 to the critical conversion (Xf) at which the pressure in the reactor started to drop due to monomer starvation. During this stage, the polymer Chemical Engineering Communications phase appears and the polymerization reaction continues in both the polymer and the monomer phases at different rates. During this stage, the transfer of VCM from the monomer to the polymer phase takes place continually, so that the polymer phase will be evenly saturated with monomer. The following equations can be written for monomer mass distribution in each phase as (Kiparissides et al., 1997; Xie et al., 1991a): M1  M 0 (1  X )  M g  M w  M 2 M2   X M 0 (1  X f )  M gXf  M w Xf (6)  (7) where MgXf is the mass of monomer in gaseous form at Xf and Xf given by (Kiparissides et al., 1997; Xie et al., 1987): Xf  M 0   Dg 0 (1  W1 )Vr  KWw  1 1   ( ) D  g 0  D (1   ) D  Dp 2  M 0 1  m  m Dg 0 2 D p   1    Dm   6 (8) where, φ2 is the volume fraction of polymer in polymer-rich phase. φ2 is related to the ratio of the partial pressure of VCM (Pm) to its saturated value (Pm0) at the reactor temperature and can be obtained by Flory-Huggins equation (Kiparissides et al., 1997; Xie et al., 1991a): P  ln  m   ln 1  2   2  22  Pm0  (9) where χ is VCM-PVC interaction parameter at polymerization temperature (T) that will Chemical Engineering Communications be given by (Xie et al., 1991a):  1286.4  3.02 T (10) A separate monomer phase is available (in the second stage), and the polymer-rich phase remains thermodynamically in equilibrium with monomer. Therefore, the monomer vapor pressure will be equal to its saturated value, (Pm=Pm0). The reaction rate for the second stage can be expressed by (Xie et al., 1991a): dX 1  K P1 ( J12  4Kt1 J 2  J1 )M1   dt M 0  2Kt1    V J1 1 ( J12  4Kt1 J 2  J1 )    K V V2  M 2   P12  R12 (1  Kde )  K  RI 1 1     2 Kt 1 V2 Kt22       (11) 0.001  X  Xf where, V1 and V2 are the volumes of monomer and polymer phases in the reaction, ' respectively, Kde is the desorption rate constant of radicals from polymer phase (s-1), K  is a precipitation constant for polymer radicals and J1 and J2 are defined parameters in 7 Xie’s model, depending on desorption and precipitation rate of radicals from/into polymer phase (Xie et al., 1991a). The third stage is related to the conversions higher than Xf (Xf<X <1.0) in which the monomer completely disappears as a separate phase and as a monomer-swollen polymer phase. After this point, the polymerization will proceed in the polymer phase under diffusion-control reactions (at initiation, termination, and propagation steps) which were modeled with a free volume approximation. Monomer mass weight in each phase, and Chemical Engineering Communications the reaction rate for the third stage, will be given by (Kiparissides et al., 1997; Xie et al., 1991a): M1  0.0; M 2  M 0 (1  X )  M g  M w Mg  (12)  1 Dg 0   1  MWm Pm  X X   (1  W1 )Vr  M 0   f  RT  Dm  Dg 0    Dm Dp    dX 1  K p 2 M R  2 2 I 1/2  dt M 0  Kt 2 (13) XXf (14) The total rate of initiator decomposition can be expressed by (Kiparissides et al., 1997; Xie et al., 1991a): d[ I ]  2 f kd  I  dt (15) where, f, kd and [I] are the efficiency, initiation rate constant and concentration of the initiator. 8 In the method of continuous dosing of initiator during polymerization process, the mole of the fast initiator at each time step (in numerical solution of the discretized equations) is also calculated using the following equation: t I t  I add  I t t exp(kd t ) (16) where, ∆t represents the time step size in numerical solution and t I add is the mole of initiator dosed up at each time step. It is obvious that in a conventional polymerization system in which the initiator is entirely added to the reactor at the beginning of the Chemical Engineering Communications process, the value of t I add will be zero. Since dosing the initiator during the course of the polymerization causes the initiator [ I ]2 partition coefficient (K = [ I ]1 ) to vary, it is taken as an adjusTable parameter in the I kinetic model which is derived from appropriate experimental data. The number and weight averaged molecular weight ( M n and M w ) are calculated using moment methods. The ith moments for the dead and live polymer distribution Qi and Yi are defined as (Kiparissides et al., 1997; Xie et al., 1991b): Qi  r 1 r i Pr (17) Yi   r 1 r i Rr (18)    where, r is the chain length, Pr and Rr are the concentration of live and dead macromolecules with chain length of r, respectively. The remainder of polymerization 9 kinetic equations and molecular weight are used to calculate the average molecular weight and molecular weight distribution are the same as those provided by Xie, et al. (Xie et al., 1991b). Fikentscher's K-values as a molecular characteristic (Fikentscher, 1932) can be evaluated by solving the equation which is related to relative viscosity (ηrel) according to:  75K 2  106  log(rel )    K  103   C 3  1  1.5 C K  10  (19) Chemical Engineering Communications where, C is the concentration of dilute solution of PVC in Cyclohexanone (0.2% W/V). The relative viscosity is evaluated by an empirical correlation according to (Xu et al., 1989) as: []  rel  1  3Ln (rel ) 4C (20) Where intrinsic viscosity is related to weight molecular weight by (Xie et al., 1991b):   5.30 105 Mw0.828 (21) According to (Xie et al., 1991a) Kinetic parameters of VCM polymerization that are used in the model contain:  E Kd1  K0 exp    RT  Kt1 1.3  1012 exp( (22) 4200 ) RT K p1 10.4 Kt10.5 exp( (23) 1902 ) T (24) 10 These kinetic parameters for diffusion controlled conditions are modeled using thefree volume theory as follows (Xie et al., 1991b)   1 1    Kd 2  Kd1 exp  C   V Vf     fp (25)   1 1  Kt 2  Kt1 exp   A     V fp V f ,crit    (26) Chemical Engineering Communications   1 1  K p 2  K p1 exp   B     V fp V f    (27)   1 1  K p 2 f 1/2  ( K p1 f 1/2 ) Xf exp   D    V Vf     fp (28) Where, A  6.64  106 exp(4986 / T ) (29) B 1.85  103 exp(2595 / T ) (30) C  4.77  102 exp(2291/ T ) (31) D  4.01  104 exp(3464 / T ) (32) The free volume fraction of the polymer-monomer mixture Vf, pure polymer Vfp and pure monomer Vfm are calculated by (Xie et al., 1991b): V f V fp 2 V fm (1  2 ) (33) V fp  0.025   p (T  Tgp ) (34) V fm  0.025   m (T  Tgm ) (35) 11 The polymer volume fraction ϕ2 at the glassy transition state can be expressed as: 2   m (T  Tgm )  m (T  Tgm )   p (T  Tgp ) (36) The critical free volumeis given by: V f ,crit  0.8V fm (37) The glassy state transition temperature and the thermal expansion factors (α) for VCM and PVC as follows: Chemical Engineering Communications Tgm  70 ( K ) (38) Tgp  87.1 0.132T (C) (39) m  9.98  104 ( K 1 ) (40)  p  5.47  104 ( K 1 ) (41) Model Solution As mentioned, the aim of this work is to determine an initiator dosage trajectory for reducing batch time by which the conversion and the product specifications (MW and MWD) which are obtained are identical to those achieved by the conventional polymerization. The initiator dosage trajectory that provides both the highest reaction rate and a given conversion must be determined such that for every instant of time during the batch processing, the heat released does not exceed the maximum heat removal capacity of the reactor. A 4th order Rung-Kutta algorithm was applied to solve first order ordinary 12 differential equations (ODEs). The step time size was specified 60s to produce a convergent solution. Optimization Approach Given that PVC polymerization process is time-consuming and the experimental determination of an optimal initiator dose is difficult, estimation of the optimum continuous dosage trajectory can be conducted more readily using an optimization algorithm. Such optimization algorithms allow researchers to determine an optimal Chemical Engineering Communications initiator trajectory in which the reaction rate at any time establishes its maximum permission value more readily than is the case when using a trial and error method. Particle Swarm Optimization algorithm (PSO) is one of the latest evolutionary optimization methods developed by Eberhart and Kennedy (Eberhart and Kennedy, 1995). PSO can optimize the solution to a problem by maintaining a population of candidate solutions (particles) and moving these particles within the search-space (Santos et al., 2012). PSO initially selects candidate solutions randomly and this is initialized with a group of random particles (solutions) followed by searching for optima by updating generations. At any iteration, each particle is updated by following two best values. The first one is the best fitness (pbest). Another best value that is tracked by the particle swarm optimizer is the best value obtained so far by any particle in the population. This best value is a global best and called gbest (Abdel-Magid and Abido, 2004). 13 After determining the two best values, the particle updates its velocity and positions using its current position and velocity according the following equations (Shi and Eberhart, 1998): Vi t 1  wVi t  C1 rand (0,1)( pbesti  X it )  C2 rand (0,1)( gbestt  X it ) X it 1  X it  Vi t 1 (42) (43) where, Vit and Vit+1 are the current and the new velocity of particle i, and Xit and Xit+1 are the current and the new positions of particle i. The pbest and gbest are defined as stated Chemical Engineering Communications above. The rand is a random number between (0, 1). C1 andC2 are learning factors and the "w" is inertia weight used to ensure convergence (Panda and Padhy, 2008). It should be noted that the random parameters terms (rand) in the velocity formula guarantee reaching the global optimum point(Hassan et al., 2005). As regards Eq. (42), the current velocity in a PSO consists of three parts: momentum, cognitive, and social. The balance of these three parts allow for obtaining a high performance PSO algorithm, and this depends on the values of parameters w, C1and C2(Panda and Padhy, 2008). Although the values of 1, 2 and 2 were used in the original PSO algorithm for w, C1, and C2, respectively, Eberhart and Kennedy suggested the ranges of 0.4 to 1.4, 1.5 to 2, and 2 to 2.5 for them (Eberhart and Kennedy, 1995). In general, the values of these parameters depend upon the problem under consideration. In this study, the appropriate values of parameters C1, C2 and w are ultimately considered to be 0.9 and 1.8 and 0.5 respectively. The operational target is achieving the minimum of the overall batch time of polymerization for a certain limiting conversion and reaction rate, which would increase 14 the productivity. In this case, the initiator concentration during the process is the value which should be optimized. The important constraints in the operation are the limitation of maximum reaction rateand final conversion, both of which are determined by the user. The maximum capacity of the cooling system of the reactor is dependent on the reaction Chemical Engineering Communications rate and can be calculated from:   dX  Qmax   H M 0    dt max where, ∆H and  dX    dt  max (44) are the enthalpy of reaction and the possible maximum reaction rate, respectively. It is obvious that the reaction rate at any time during polymerization must not exceed the maximum value, as shown below:  dX   dX       dt at any time  dt  max (45)  dX    where, dt at each stage is obtained from Eqs. (5, 11 and 14). Material In order to validate the model predictions, suspension polymerization experiments were carried out in a 48 L stainless steel-jacketed reaction vessel equipped with four tubular baffles and an agitator consisting of two six-flat-blade turbines. The temperature of the 15 mixture in the reactor was kept constant at the desired value, via flowing cold water in the jacket. The temperature of the reaction mixture, jacket input/output and reactor pressure were recorded by data logger. A special sampler device was designed for extracting samples during the process. Fig. 1 illustrates a schematic diagram of polymerization reactor. The materials used are listed in Table І. Diisobutyryl peroxide is a fast initiator synthesized according to US 70,053,161(2006), using Potassium Hydroxide (KOH), Hydrogen peroxide (H2O2), Isobutyryl Chloride (i- Chemical Engineering Communications BuCl) and n-Hexane (all from Merck Co.). Diisobutyryl peroxide is obtained with a purity of 29.7 wt% in n-Hexane and active oxygen of 2.73%. The physical and chemical properties of obtained Diisobutyryl peroxide is equivalent to Trigonox 187-C30 produced by the Akzo Nobel company. Polymerization Procedure Suspension polymerizations of VCM were carried out under two procedures for initiator addition: a conventional process (in a commercial producing plant), wherein a mild initiator (Perkadox 26) is entirely charged at once at the beginning of the polymerization and a new process in which a fast initiator (Diisobutyryl peroxide) is dosed to a reactor during the course of the polymerization reaction. The reactor was charged with 12200g of VCM, 18500g DM Water, 235g HPC and 245g HPMC (3.5wt. % solution in water) as the primary suspending agents and 16.7g Span 20 as a nonionic secondary suspending agent. The reactor temperature was controlled by adjusting the water flow rate of a circulator into the jacket. In a conventional experiment, the amount of initiator, Perkadox 16 1 15 1 26 (Dimyristyl peroxydicarbonate, A  2.82 10 s , Eactivation 124.1kJ mol ), was 14.3g, which was added to the reactor before the VCM charging. The mixture of reaction was heated up to the polymerization temperature of 52 °C in ≈20 min by flowing hot water in the jacket. In the new process, after reaching the polymerization temperature, 1 14 1 12g Diisobutyryl peroxide ( A  3.37 10 s , Eactivation 109.06 kJ mol ) as a fast initiator, was dosed to the reaction mixture during the process. In all experiments, the temperature in the reactor was regulated to a value of 52 °C with an accuracy ± 0.3oC Chemical Engineering Communications until reaching a sharp pressure drop in the reactor and a significant reduction in the reaction rate of polymerization (critical conversion). The reaction mixture was then heated to 62 °C to remove unreacted VCM. Sampling was carried out during the polymerization course using a sampler device. At the end of the process, the reactor was rapidly cooled to 30°C, followed by the condensation of the remaining VCM in a storage vessel. Slurry obtained was filtered and dried at 55° C for 24 hours in an oven preparing PVC grains. Characterization Of The S-PVC Particles The final conversion was calculated by gravimetry of the dried PVC grains. The conversion during the process was obtained using two methods: weighing the extracted samples, and energy balance around the isolated reactor. The conversion versus time relationship was obtained by weighing each sample, according to: X mp (1  f r ) mt f r (26) 17 where mP is the mass of dried polymer in the sample, mt is the total mass of sample, fr is the VCM/water mass ratio initially present in the reactor. Another method of measurement of the conversion is energy balanced around the isolated reactor, according to (Nagy and Agachi, 1997): Vmix mixCpmix dT dX   H M0 U (T  Tj ) dt dt (27) where, Vmix, ρmix and Cpmix are the volume, density and specific heat of the mixture in the reactor, Tj is jacket average temperature recorded by the data logger and U is the overall Chemical Engineering Communications heat transfer coefficient at the walls of the reactor which was obtained experimentally. The K value as a molecular characteristic was calculated using the dilute-solution viscosity measurements of the PVC samples via a viscometer (LAUDA, Proline, pv15) according to (ISO D3105-1994). The MWs of the samples were measured using gel permeation chromatography (GPC Agilent 1100) with PLgel, 10μm, 300×7.5 mm columns, a Tetrahydrofuran (THF) solution of PVC at 30oC, and a 1 ml/min flow rate. RESULTS AND DISCUSSION Model Validation The model results (conversion, K-value and average molecular weight) were verified by the experimental data. We sought to evaluate the predictions of the model at various doses of the initiator in the method of continuous dosing of the initiator as well as at regular initiator addition. Two mentioned procedures in the polymerization process for adding the initiator were applied; in the first procedure, according to a conventional process, total mild initiator, Perkadox 26, was added to the reactor at the beginning of the 18 process. In the second procedure, the dosage of the fast initiator (Diisobutyryl peroxide) 1 was first kept constant at about 0.36 g min for 20 min, and was then decreased to 1 1 0.0686 g min from 21 to 56min, and once again was decreased to 0.04 g min within a 60-minute time period. The implementation of such an optimal initiator dosage strategy caused the polymerization rate to be kept constant during the time of the polymerization. It should be noted that the reason for dosing the initiator in three successive steps, instead of the optimum dosage rate predicted by the model (using particle swarm optimization Chemical Engineering Communications (PSO) algorithm), is facilitation during the dosing operation. In the other words, the used initiator dosage policy is the average of optimum initiator trajectory during three stages of time. The initiator dosage was stopped at a critical conversion (Xf). The predicted and used optimum trajectories of the fast initiator dosage are shown in Fig. 2. Fig. 3 compares the model predictions and experimental data for conversion during the process in both experiments: continuous dosage of the fast initiator and non-continuous of Perkadox 26. The results obtained from the energy balance method are compared to above data in the Fig. 3. It can be seen that the present model predictions are in good agreement with the experimental data and energy balance results for both experiments. In this model, efficiency of Perkadox 26 and Diisobutyryl peroxide were adjusted to be 0.8 and 0.6, respectively. Traveling through a long path in the continuous aqueous phase and crossing from the VCM droplets/water interface by a fast initiator in process with continuous dosage system leads to decrease initiator efficiency (Mrázek et al., 1991). 19 Also, adsorption of the fast initiator on the surfaces of formed particles alters the initiator partition coefficient between the monomer and polymer phases such that most of the initiator remains in polymer phase. This reason is also corroborated by the known affinity peroxy initiators for PVC chains (Mrázek et al., 1991). The initiator partition coefficient (KI) for a continuous dosage system was estimated by fitting the model with conversiontime data (KI=0.9). A value of 0.77 has been determined by Xie, et al. for conventional system (Xie et al., 1991a). Chemical Engineering Communications Figs. 4 and 5 also show the comparison between the experimental data and model results for K value and average molecular-weights of both experiments. Once again, there is a reasonable agreement between the model and the experimental results. Effect Of Continuous Dosage On PVC Process The goal of the work is to find an optimal trajectory for initiator dosages in order to establish a balance between the maximum permissible cooling capacity of the reactor and minimum batch time. In this regard, the dose level of the initial stage of the fast initiator dosage as the most important dosage step, and the dose level during the process were optimized by the particle swarm optimization (PSO) algorithm in which several attempts were made to find a continuous initiator dosage trajectory by use of simulations so as to minimize the polymerization time for the final conversion of 80% (the reaction rate does not exceed the pre-defined value at any time). In the initial stage, the initiator was dosed in such a way that the reaction rate changed from zero to the desired value. While the time required for the initial stage of the initiator dosage for all of the pre-defined reaction 20 rates was found to be 20 minutes, the dose level of the initiator increases with increasing pre-defined reaction rates. In order to clarify this subject, several runs with different initial stage duration are compared as illustrated in Fig. 6. Once the dosing comprises an initial stage having a duration that is less than 20 minutes (i.e. 10 min), more amount of initiator is required to achieve the desired reaction rate (here 0.61%/min as the maximum permissible reaction rate) which this causes an excess initiator to remain in the process and to affect the reaction rate over the next steps. This level of the initiator with very low half-life leads to produce high radical concentration and a sensible acceleration of the Chemical Engineering Communications reaction and causing the reaction rate to exceed from the maximum permissible reaction rate. On the other side, when the initial stage of initiator dosing is more than 20 minutes (35 min- Fig.6), the desired reaction rate is delayed and hence the time of polymerization process is increased. As a result, an initiator dosing trajectory with a 20 minutes initial stage is considered to balance between the maximum permissible reaction rate and minimum polymerization process time. In order to evaluate the influence of continuous dosage of a fast initiator (Diisobutyryl peroxide) on the suspension polymerization of VCM and the resin properties, several simulation runs were conducted and then compared to the case in which a mild initiator (Perkadox 26) was added at the beginning of the polymerization (conventional process). The results obtained from different runs are presented in Table II. The evaluation of conversion during the polymerization process and the reaction rate of the polymerization in respect to conversion for the aforementioned runs are shown in 21 Figs. 7 and 8, respectively. The maximum reaction rate and conversion for run 1 (conventional run as a reference run) obtained 0.61 percent/min and 80%, respectively. It is now tried to find an initiator dosage trajectory minimizing the polymerization time for the final conversion identical to Run 1 (80%), by simulations. This would be obviously obtained if the reaction rate was kept constant over the entire course of the polymerization at a constant value. In order to study the effect of the maximum permissible reaction rate on resin properties, runs 2-4 were performed at three different Chemical Engineering Communications allowable reaction rates, i.e. lesser, larger and identical to that of conventional process (0.61 %/min). These Runs show that if we allow to choose the maximum cooling capacity of the reactor respect to the permissible reaction rate, what affect on polymerization time and resin properties. Such trajectories are shown in Fig. 9. In all these trajectories, the initiator dosing comprises a first stage which lasted 20 min during which the level of dosage remains constant and the reaction rate reaches to permissible value. Just after that a second stage begins, during which the dosage of the initiator decreases until the level of dosage reaches zero to keep the reaction rate in constant amount. As shown in Fig. 8, by continuous dosage of a fast initiator (in different allowable reaction rates), the reaction rate remained constant during the course of polymerization processes. The results illustrate that applying a continuous dosage mode of a fast initiator leads a 31-65% reduction in the total polymerization time required for a given conversion, as compared to the case in which only one mild initiator was added at the 22 beginning of the process. The higher permissible maximum reaction rates the more reaction rate and thus, the further of the reactor cooling capacity is used, resulting in the lower reaction time. It can be observed in Figs. 7 and 8 that a twofold increase in the maximum permissible reaction rate (it can be achieved by increasing the amount of the initiator), reduces total polymerization time up to 50%. Chemical Engineering Communications Run 5 correspond to a comparative case in which the total amount of the initiator (identical to that of Run1) is added at the beginning of the polymerization reaction. In this case, initiator decomposition occurs rapidly and thus, the free radical source is no longer available to continue polymerization, and it finishes at the middle of the process, resulting in the lowest final conversion level (see Fig. 8). Fig. 10 indicates the molecular characteristics of the final product, in terms of the weightaverage molecular weights. As it is known that the molecular weight of PVC is little affected by type and concentration of the initiator (Kiparissides et al., 1997; Xie et al., 1991b), molecular specifications decrease slightly with the reaction rate. Continuous fast initiator dosage started at the beginning of the process increases the production of free radicals and the subsequent termination rate leading a molecular weight difference with Run1. This phenomenon is more pronounced during the early stage of conversions where monomer phase is predominant and polymerization occurs homogenously. 23 The evolution of the residual level of initiator for different initiator dosage trajectories are shown in Fig. 11. This figure shows while in Run1 some amount of initiator residue finally, initiator residual in a continuous dosing of very fast initiators during polymerization reactions reach zero. Therefore, residual initiator in processes with Diisobutyryl peroxide as a fast initiator (Runs 2-5), is much less than in a process with Perkadox 26 acting as a mild initiator (Run 1). Using a very efficient dosage of a fast initiator, render a resin after polymerization with very low residual initiator levels. Chemical Engineering Communications CONCLUSION The adopted model using PSO algorithm was applied to predict an optimal initiator dosage trajectory in vinyl chloride suspension polymerization, and this validated by experimental data. The model predictions suggest that applying an initiator dosage system in a proper trajectory can dramatically improve productivity by reducing the polymerization time for a certain final conversion compared to regular reactions in which the total amount of initiator is added at the beginning of the polymerization process. The experimental and theoretical model results show that the use of an optimal continuous dosage trajectory during the polymerization (Run 3) decreases total polymerization time up to 53% for given polymer specifications, in comparison with the conventional case. It was shown that as initiator doses are increased, the required heat removal rate increases and the polymerization time reduces to a remarkable degree, and polymer specifications such as K value and average molecular weight only slightly decrease. The morphology and molecular characteristics of PVC grains produced under an initiator dosage system is currently under examination and the results will be presented in forthcoming papers. 24 ACKNOWLEDGMENTS Partial financial support of Petrochemical Research and Technology Company, through Contract 870429202 is gratefully appreciated. REFERENCES bdel-Magid, Y., Abido, M. (2004). Robust coordinated design of excitation and TCSCbased stabilizers using genetic algorithms,Pow. Syst. Res., 69, 129-141. Chemical Engineering Communications Alexopoulos, A.H., Kiparissides, C. (2007). On the prediction of internal particle morphology in suspension polymerization of vinyl chloride. Part I:: The effect of primary particle size distribution,Chem. Eng. Sci., 62, 3970-3983. Darvishi, R., Nasr Esfahany, M., Bagheri, R. (2015). Nonisothermal suspension polymerization of vinyl chloride for enhanced productivity,J. Vinyl Addit. Technol. Eberhart, R.C., Kennedy, J.(1995). A new optimizer using particle swarm theory, Proceedings of the sixth international symposium on micro machine and human science, New York, NY, 39-43. Feldman, D., Macoveanu, M., Robila, G. (1977). Suspension Polymerization of Vinyl Chloride with Programmed Temperature: Morphological Characteristics and Thermal Stability of Polyvinyl Chloride),J. Macromol. Sci., Chem., 11, 1333-1348. Fikentscher, H. (1932). Cellul. Chem., 13, 58-64. 25 Hassan, R., Cohanim, B., De Weck, O., Venter, G. (2005). A comparison of particle swarm optimization and the genetic algorithm, Proceedings of the 1st AIAA multidisciplinary design optimization specialist conference, 1-13. Kiparissides, C., Daskalakis, G., Achilias, D., Sidiropoulou, E. (1997). Dynamic simulation of industrial poly (vinyl chloride) batch suspension polymerization reactors,Ind. Eng. Chem. Res., 36, 1253-1267. Krallis, A., Kiparissides, C.(2007). Mathematical modeling of the bivariate molecular weight—Long chain branching distribution of highly branched polymers.: A population Chemical Engineering Communications balance approach,Chem. Eng. Sci., 62, 5304-5311. Meulenbrugge, L., Van Swieten, A.P., Vanduffel, K.A.K., Westmijze, H.(2007). suspension polymerization of vinyl chloride; temperature control,U.S. Patent, 7,173,095 B2. Mrázek, Z., Lukáš, R., Ševčík, S. (1991). On gradual dosage of the initiator in the suspension polymerization of vinyl chloride,Polym. Eng. Sci.31, 313-320. Nagy, Z., Agachi, Ş. (1997). Model predictive control of a PVC batch reactor,Comput. Chem. Eng., 21, 571-591. Olaj, O. (1977). Kinetic Models for Bulk Polymerization of Vinyl Chloride and Their Rate Expressions, J. Macromol. Sci., Chem., 11, 1307-1317. Panda, S., Padhy, N.P. (2008). Comparison of particle swarm optimization and genetic algorithm for FACTS-based controller design,Appl. Soft comput., 8, 1418-1427. Pinto, J. (1990). Vinyl chloride suspension polymerization with constant rate. A numerical study of batch reactors,J. Vinyl Technol., 12, 7-12. 26 Pinto, J.M., Giudici, R. (2001). Optimization of a cocktail of initiators for suspension polymerization of vinyl chloride in batch reactors,Chem.Eng. sci., 56, 1021-1028. Saeki, Y., Emura, T. (2002). Technical progresses for PVC production,Prog. Polym. Sci., 27, 2055-2131. Santos, L., Biscaia Jr, E., Pagano, R., Calado, V. (2012). CFD-optimization algorithm to optimize the energy transport in pultruded polymer composites,Braz. J. Chem. Eng., 29, 559-566. Shi, Y., Eberhart, R. (1998). A modified particle swarm optimizer, Evolutionary Chemical Engineering Communications Computation Proceedings, 1998, IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on. IEEE, 69-73. Suresh, A., Chanda, M. (1982). A new kinetic model for bulk polymerization of vinyl chloride based on two-phase hypothesis,Eur. Polym. J., 18, 607-616. Ugelstad, J. (1977). Model for Kinetics of Vinyl Chloride Polymerization,J. Macromol. Sci. Chem., 11, 1281-1305. Van Swieten, A.P., Westmijze, H., Schut, J. (2002). Accurate control of rate; organic peroxide; vinylchloride polymers; 0.5-1.0 hour halflife,U.S. Patent, 6,384,155 B1. Van Swieten, A.P., Westmijze, H., Schut, J. (2003). Forming polyvinyl chloride using organic peroxides to control rate of polymerization; half-life,U.S. Patent 6,639,037 B2. Westmijze, H., Meulenbrugge, L., Vanduffel, K.A.K., Van Swieten, A.P. (2012). Increased polymerization reactor output by using a specific initiator system,U.S. Patent, 8,283,431 B2. 27 Westmijze, H., Van Swieten, A.P., Meulenbrugge, L., Vanduffel, K.A.K. (2013). Continuous dosing of extremely fast initiators during polymerization reactions, U.S. Patent, 8,367,784 B2 (2013). Xie, T., Hamielec, A., Wood, P., Woods, D. (1987). Experimental investigation of vinyl chloride polymerization at high conversion—temperature/pressure/conversion and monomer phase distribution relationships,J. Appl. Polym. Sci., 34, 1749-1766. Xie, T., Hamielec, A., Wood, P., Woods, D. (1991a). Experimental investigation of vinyl chloride polymerization at high conversion: mechanism, kinetics and modelling,Polym., Chemical Engineering Communications 32, 537-557. Xie, T., Hamielec, A., Wood, P., Woods, D. (1991b). Experimental investigation of vinyl chloride polymerization at high conversion: molecular-weight development,Polym., 32, 1098-1111. Xu, P., Zhou, D., Zhao, D. (1989). Studies of the thermal stability of poly (vinyl chloride)–II. Influence of molecular weight on the thermal stability of PVC,Eur. polym. J., 25, 581-583. 28 Table І. Materials Used in the Suspension Polymerization of Vinyl Chloride. Name Role Trade Manufacturer Chemical Engineering Communications name Vinyl Chloride (VC) Monomer Arvand Petrochemical Co., Iran Hydroxypropylmetyl Primary suspending Methocel Shin-Etsu Chemical Co., Tokyo, cellulose (HPMC) agent 65SH-50 Japan Hydroxylpropyl Primary suspending Klucle J Hercules International, Ltd., cellulose (HPC) agent Sorbitanmonolaurate Secondary suspending Huntington, WV Span 20 agent Beckmann Chemikalien KG (Becksurf 7125), Bassum, Germany Dimyristyl Initiator peroxydicarbonate Perkadox Akzo Nobel Co.(Amersfoort, 26 The Netherlands) (MYPC) Diisobutyryl peroxide Initiator Petrochemical Research & Technology Co. 29 Table II. Effect of continuous dosage of fast initiator on S-PVC polymerization and comparing with non-continuous dosage of initiator. Initiator type Dosage Initia Convers Poly. Maximum ent 1 Run Perkadox 26 type Non- tor 14.3 ion (%) 80 time 320 reaction rate 0.61 Run 2 Diisobutyryl Continuous 8.25 80 220 0.41 Run 3 Diisobutyryl Continuous 12 80 150 0.61 Run 4 Diisobutyryl Continuous 14.65 80 110 0.81 Run 5 Diisobutyryl Non- 12 30.8 151 0.65 Chemical Engineering Communications Experim 30 Chemical Engineering Communications Figure 1. Schematic diagram of polymerization reactor. 31 Figure 2. Predicted and used optimum trajectories of the fast initiator dosage Chemical Engineering Communications (Diisobutyryl peroxide). 32 Figure 3. Comparison between experimental data (sampling and energy balance) and model predictions for conversion during process for continuous dosage of Diisobutyryl Chemical Engineering Communications peroxide and non-continuous of Perkadox 26. 33 Figure 4. Comparison between experimental data and model predictions for K value vs. conversion at two runs; for continuous dosage of Diisobutyryl peroxide and non- Chemical Engineering Communications continuous of Perkadox 26. 34 Figure 5. Comparison between experimental data and model predictions for molecular weights during process at (a): continuous dosage of Diisobutyryl peroxide and (b): non- Chemical Engineering Communications continuous of Perkadox 26. 35 Chemical Engineering Communications Figure 6. Reaction rate vs. time for different duration of initial stage in initiator dosing. 36 Chemical Engineering Communications Figure 7. Conversion during process for different simulation runs. 37 Chemical Engineering Communications Figure 8. Reaction rate of polymerization vs. conversion for different simulation runs. 38 Chemical Engineering Communications Figure 9. Initiator dosage trajectory of Diisobutyryl peroxide during simulation runs 2-4. 39 Figure 10. weight-average molecular weights of PVC vs. conversion for different Chemical Engineering Communications simulation runs. 40 Chemical Engineering Communications Figure 11. Residual level of initiator for different simulation runs. 41