Polymerization of styrene in a continuous filled tubular reactor

Free radical solution polymerization of styrene has been studied using a binary mixture of symmetrical bifunctional initiators in a filled tubular reactor packed with static mixers. Owing to intensive radial mixing induced by the static mixers, a near plug flow pattern was obtained in the reactor with some axial dispersion effect. The axial mass dispersion coefficient was determined from the residence time distribution experiment and a dynamic axial dispersion model has been developed and solved to investigate steady state and transient behavior of the filled tubular reactor. With a solvent volume fraction of 0.3, the monomer conversion up to 70% was obtained without fouling problems in the temperature range 90 to 120°C. The experimental filled tubular reactor was operated under various reaction conditions and a reasonably good agreement between the model and the experimental data was obtained without using any adjustable parameters.     

Modeling of a Buss‐Kneader as a polymerization reactor for acrylates. Part I: Model validation

The Buss‐Kneader is generally known as a compounding device. Although a reasonable number of papers have been published on extruders as polymerization reactors, only little is known about the behavior of the Buss‐Kneader when used as a polymerization reactor. Its good mixing properties in the radial and axial directions make it a suitable reactor for exothermal polymerization reactions. This paper describes experiments with the co‐polymerization of n‐butyl acrylate and hydroxyethyl methacrylate in a Buss‐Kneader. For model calculations the Buss‐Kneader was treated as a plug flow reactor with axial dispersion. Experimental results on axial temperature profile, monomer conversion and molecular weight are compared with model calculations. Model parameters are based on independently measured data on the heat transfer coefficient, axial dispersion and polymerization kinetics.     

管式反应器中苯乙烯连续本体热聚合过程模型化和数值模拟

建立了管式层流反应器中苯乙烯本体热聚合过程的模型。数值模拟了反应介质流速和温度沿反应器的轴向和径向的分布,考察了反应器的几何尺寸、壁温、反应介质入口温度和流量对反应器出口转化率和产物相对分子质量的影响。结果表明,反应器的几何尺寸和反应器壁温及进料质量流量对单体转化率影响较大,而入口温度影响不大。     

Application of optimal temperature trajectory to batch PMMA polymerization reactor

A mathematical model is developed for the polymerization of methyl methacrylate (MMA) in a batch reactor. The model includes chain transfers to the monomer and solvent and termination by both combination and disproportionation and also takes into account the density change of the reactor contents and the gel effect. The usual pseudo-steady-state assumption is relaxed here. The validity of the proposed model is tested by an isothermal experiment of batch PMMA polymerization. Indeed, the experimental results show that the proposed model can describe the real polymerization system very well in view of both monomer conversion and average molecular weights. The optimal control theory is applied together with Pontryagin's minimum principle to calculate the optimal temperature trajectory for a batch polymerization reactor system which would lead to a polymer product having the desired properties set a priori. The performance index of the control system is composed of three factors—the desired monomer conversion and number- and weight-average molecular weights. The desired values of number- and weight-average molecular weights are obtained at a specified monomer conversion within acceptable error ranges. Control experiments are conducted to track the optimal temperature trajectory obtained from the model and the results are found to be in good agreement with the desired values. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 59–68, 1998     

Experimental investigation of vinyl chloride polymerization at high conversion—reactor dynamics

A series of suspension polymerizations of vinyl chloride monomer (VCM) was carried out in a 5-L pilot plant reactor over the temperature range, 40–70°C. The reactor pressure and monomer conversion were monitored simultaneously every 7–8 min. The critical conversion X_f, at which the liquid monomer phase is consumed, was considered to occur when the reactor pressure fell to 98% of the vapor pressure of VCM for suspension at the polymerization temperature. The reactor model predictions of pressure are in excellent agreement with the experimental data over the entire conversion and temperature ranges studied. The mechanism of reactor pressure development for VCM suspension polymerization is discussed herein in some detail. For isothermal batch polymerization, the reactor pressure falls in two stages due to the effect of polymer particle morphology on pressure drop. The first stage is due to the volume increase of the vapor phase as a result of volume shrinkage due to conversion of monomer to polymer. The monomer phase is not yet consumed at this stage, but it is trapped in the interstices between primary particles creating a mass transfer resistance; therefore, the reactor pressure drops slowly. The second stage is due to both the volume increase of the vapor phase and to the monomer in the vapor phase diffusing into the polymer phase because of the subsaturation condition with respect to monomer in the polymer phase. The reactor pressure drops dramatically with an increase in monomer conversion at this stage. The present model can be used to predict reactor dynamics during suspension polymerization under varying temperature and pressure conditions.     

Finite volume method as the numerical method for new emulsion polymerization tubular reactor with internal angle baffles

A finite volume method is used to solve a determinist mathematical model and to analyze the performance of an alternative design for an emulsion polymerization reactor with internal angular baffles as static mixer. It is assumed to be a steady‐state, cylindrical one‐dimensional model having a fully developed laminar plug flow. The Smith‐Ewart model is used to estimate the monomer conversion, the kinetics is of Arrhenius type, and laminar finite‐rate model is assumed to compute chemical source terms. The objective of this work is to develop the finite volume method for the new emulsion polymerization tubular reactor with internal angle baffles. The performance of the alternative reactor is compared with continuous tubular reactor with constant reaction temperature. The simulations were validated with experimental results for the isothermal and tubular reactor, with a good concordance. The results with baffles were better than without baffles in relation to desired properties such as particle size and viscosity. The problem is sufficiently well solved by finite volume method. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 6037–6048, 2006     

Simulation of bulk free radical polymerization of styrene in tubular reactors

A model that takes into consideration radial and axial changes in velocity in a tubular reactor for the thermal polymerization of styrene is used to simulate the effect of changes in inlet tube wall temperature and tube radius. The reactor performance is sensitive to the changes of these parameters. The method of orthogonal collocation is used to discretize the modeling equation in the radial direction and Gear method to solve the resulting stiff differential equations in the axial direction. It is found that reducing the wall temperature and the tube radius along the direction of the flow of the monomer reduces the variation in conversion between the tube center and tube wall and thus are advantageous.     

Continuous polymerization of methyl methacrylate in a taylor‐couette reactor. I. Influence of fluid dynamics on monomer conversion

A Taylor‐Couette reactor offers certain advantages for continuous polymerization over other reactor types. These advantages are its rather narrow residence time distribution (series of vortices) and its good heat transfer characteristics. Hydrodynamics in this type of reactor can be controlled by its geometry (diameter, gap, width, length) and its operational parameters (rotational speed, mean residence time, viscosity). In this article, a model is presented which is suited to answer the question of how hydrodynamics influences the productivity of a continuously operated Taylor‐Couette polymerization reactor. To this end, productivity is quantified by the rate of monomer conversion. The model is specified and experimentally validated for the free radical polymerization of methyl methacrylate with the solvent xylene and 2,2‐azoisobutyronitrile as the initiator. The model considers the following four phenomena: (i) Macromixing between the vortex cells is accounted for by an axial dispersion model. (ii) The dependence of viscosity on monomer conversion along the reactor is described by a viscosity model. (iii) Polymerization kinetics and its dependence on hydrodynamics are correlated from experimental data. (iv) The dependence of segregation index I_s on the local energy dissipation is used to characterize micromixing within the vortices. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Steady state multiplicity behavior of an isothermal axial dispersion fixed-bed reactor with nonuniformly active catalyst

An isothermal, heterogeneous fixed-bed reactor packed with nonuniformly active catalyst pellets where a biomolecular Langmuir-Hinshelwood reaction occurs, is studied using an axial dispersion model. A catalyst activity distribution given by a Dirac delta function, where the active catalyst is deposited at a specific location within the pellet, is considered. This includes the common case of externally coated pellets with external mass transfer resistance. The steady state multiplicity behavior of this reactor, and its limiting cases: CSTR, PFR and pseudohomogeneous axial dispersion, are examined in detail. The nonlinearity of the reaction kinetics provides two sources of multiplicity, through the heterogeneous nature of the reactor and the presence of axial dispersion in the fluid phase. Their roles in determining reactor multiplicity behavior are fully explored. It is shown that this system can admit at most nine steady state solutions. The limiting behavior of the heterogeneous axial dispersion model as Pe → 0 or ∞ is not represented fully by the CSTR or PFR models because of ignition phenomenon. Finally, the effects of mixing on reactor conversion are discussed.     

Dynamics of a continuous stirred tank reactor for styrene polymerization initiated by a binary initiator mixture. II: Effect of viscosity dependent heat transfer coefficient

The dynamic behavior of the solution polymerization of styrene in a continuous stirred tank reactor is analyzed with a mixture of tert-butyl perbenzoate and benzoyl peroxide as an initiator system. In the modeling of the reactor, a viscosity dependent reactor wall heat transfer coefficient is used to account for the changing heat transfer efficiency as monomer conversion and polymer molecular weight increase. The steady state and bifurcation behaviors have been investigated with the reactor residence time, initiator feed composition, initiator concentration, feed solvent volume fraction, and coolant temperature as bifurcation parameters. Unlike the reactors with constant heat transfer coefficient, the present system exhibits relatively simple steady state and dynamic bifurcation behaviors. Oscillatory behavior is observed only when the solvent volume fraction in the feed exceeds 0.2. The dynamic simulation of the reactor also indicates that a feedback temperature controller may fail to maintain the reactor temperature when the heat transfer coefficient changes as a result of process disturbances.     

Experimental study of traveling waves in nonadiabatic fixed bed reactors for the oxidation of carbon monoxide

An experimental study of axial temperature profiles in a nonadiabatic tubular fixed bed reactor has been made under the transient operation. The catalytic carbon monoxide oxidation occuring on a Pt/alumina catalyst has been used. Unlike the adiabatic conditions the velocity of a traveling temperature wave in a nonadiabatical arrangement depends on its axial position. In certain regions of inlet concentration multiple temperature fronts have been observed. For low inlet CO concentration a downstream temperature wave results and the lower (kinetic) steady state is dominant. For high inlet CO concentration an upstream propagating front results and the upper steady state is dominant. For a downstream moving wave oscillations of wave velocity, hot spot temperature and exit conversion have been measured. For certain operating conditions periodic behavior of temperature profiles in the reactor has been observed.     

Modelling of a continuous kneader reactor for the polymerization of partially neutralized acrylic acid

A mathematical model and analysis of the continuous polymerization of partially neutralized acrylic acid (AA) in a continuous kneader reactor is presented here as an initial attempt to simulate the synthesis of a superabsorbent polymer. A detailed kinetic model has been used to describe the copolymerization of AA and sodium acrylate (NaA) in aqueous medium. This model is used to describe batch and continuous operations. The polymerization is initiated by a mixture of potassium persulphate (K₂S₂O₈, KPS) and hydrogen peroxide (H₂O₂) as oxidizing agent and ascorbic acid (AsA) as reducing agent. A novel set of kinetic parameters has been estimated by fitting experimental data from different literature sources. The operation of a continuous kneader reactor modelled as a plug-flow reactor with axial dispersion is theoretically investigated to predict temperature profile, total and individual monomer conversion, consumption of KPS, H₂O₂, and AsA, and polymer average molecular weights. The simulation results show the presence of a hot spot close to the reactor entrance that could be potentially severe during startup and could have a detrimental impact on polymer quality. This model is a first step in the direction of achieving optimal operating protocols and exploring improved polymerization reactor designs.     

“饥饿”反应器中自由基聚合动力学(Ⅰ)──关于长链假定适用性的讨论

在建立自由基聚合动力学模型时，由于聚合度很大，通常假定聚合速率等于链增长速率，认为用于链引发所消耗的单体量极少，将其忽略不计，即所谓的长链假定．本文对这一假定进行了详尽的分析，通过计算表明：在高温或／和高引发剂浓度下，特别是在“饥饿”反应器中，长链假定不再适用，建立更为精确的聚合动力学模型时，须考虑长链假定适用性．     

EXPERIMENTAL APPLICATION OF GENERALIZED PREDICTIVE CONTROL OF THE TEMPERATURE IN A POLYSTRENE POLYMERIZATION REACTOR

The performance of generalized predictive control (GPC) was examined and compared with conventional control applied to the temperature of as free radical solution polymerization of styrene in a jacketed batch reactor. Optimal conditions were obtained at different initiator concentrations by applying Lagrange's multiplier to the relevant polymerization reactor. The use of the polynomial ARIMAX model related with reactor temperature and heat input was emphasized. Model parameters were determined using the Kalman algorithm. A pseudo random binary sequence (PRBS) signal was employed in order to operate the system. The GPC control method was based on the ARIMAX model. The performance criteria of GPC in evaluating the temperature control results were the required monomer conversion and molecular weight.     

EFFECT OF PARTIAL WETTING ON TRICKLE-BED REACTOR PERFORMANCE

Analysis of trickle-bed reactor data is almost always done by assuming that the catalyst particles are completely covered by a liquid film. The effect on reactor performance from violations of this assumption is demonstrated. The hydrodesulfurization of benzothiophene was simulated with the feed consisting of 10%, by weight, benzothiophene and 90% decalin. The temperature and pressure were held constant at 630 K and 68 atm. The results show that the exit conversion is strongly affected by the wetting efficiency.     

EFFECT OF PARTIAL WETTING ON TRICKLE-BED REACTOR PERFORMANCE

Analysis of trickle-bed reactor data is almost always done by assuming that the catalyst particles are completely covered by a liquid film. The effect on reactor performance from violations of this assumption is demonstrated. The hydrodesulfurization of benzothiophene was simulated with the feed consisting of 10%, by weight, benzothiophene and 90% decalin. The temperature and pressure were held constant at 630?K and 68?atm. The results show that the exit conversion is strongly affected by the wetting efficiency.     

Optimization of the coordination–insertion ring‐opening polymerization of poly(p‐dioxanone) by programmed decreasing reaction temperatures

The optimization of the synthesis of poly(p‐dioxanone), by ring‐opening polymerization with tin II bis(2‐ethylhexanoic acid) as the catalyst, was conducted by a new method in which programmed decreasing reaction temperatures were employed. The results were compared with those obtained for polymerization reactions performed at constant temperatures in the 80–180°C range. In the novel method, the temperature was gradually reduced, as the reaction proceeded, to maintain a maximum polymerization rate and monomer conversion as the monomer was consumed. The experiments performed at constant temperatures confirmed previous reports that the bulk polymerization of 1,4‐dioxan‐2‐one is an equilibrium polymerization reaction. With increasing polymerization temperature, the initial rate of polymerization increased, but the monomer conversion, reaching equilibrium, decreased. High conversions were obtained at low temperatures and long reaction times. Therefore, reducing the reaction temperature, to ensure working conditions that guaranteed the maximum polymerization rate and monomer conversion, could optimize the polymerization process. These conditions were calculated under the assumption of equilibrium polymerization reaction kinetics. With our proposed method, a 71% conversion was achieved in half the time needed when the polymerization was performed at a constant temperature of 120°C. Similarly, a 78% conversion was obtained with our proposed method in only a third of the time employed when the reaction was carried out at a constant temperature of 80°C. Our method guarantees high conversions in shorter times and a gradual reduction of the polymerization temperature. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 659–665, 2005     

Optimal temperature profiles for nylon 6 polymerization in plug-flow reactors

Optimal temperature profiles for nylon 6 polymerization in plug-flow reactors have been obtained under different conditions using a reasonable objective function which gives more flexibility to a designer than those studied earlier. Computations suggest that the temperatures at the feed end of the reactor must be maintained at the highest permissible level (determined by the boiling point of the ?-caprolactam) so as to force the degree of polymerization rapidly to the desired value. Thereafter, the temperatures should be reduced in order to minimize the undesirable cyclic dimer concentration, and, finally, near the exit of the reactor, the temperature must once again be increased in order to attain higher monomer conversion. The effect of a systematic change of values of the various design variables, one by one, is studied. The profile obtained differs substantially from those obtained by earlier workers because of the difference in the objective function as well as in the kinetic mechanism associated with the formation of the cyclic oligomer. Attempts are also made to obtain a global optimal scheme to produce a polymer of a desired degree of polymerization.     

Hierarchical control of a train of continuous polymerization reactors

A multilayer control scheme is synthesized for a series of polymerization stirred tank reactors to control the monomer conversion over the reactor line. In this work two layers of control are implemented. In the' first level digital PI or self-tuning regulators (STR) are used to control the reaction temperature of each reactor in the series by manipulating the flowrates of the coolant streams. In the second layer, a locally linear state space model, that can predict the monomer concentration in each reactor, is derived based on steady-state energy balances. A quadratic performance index is then minimized to obtain the optimal reaction profile that will bring the monomer distribution over the reactor line to its desired target value.