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.     

Optimization of nonvaporizing nylon 6 reactors with stopping conditions and end-point constraints

In this study, optimal temperature profiles (or histories),T(t), are obtained for nonvaporizing plug-flow (or batch) Nylon 6 reactors using the minimum principle. Two objective functions are studied, one in which the monomer conversion, conv_tf, is maximized, and the other in which the undesirable side product (cyclic dimer) concentration in the output stream, [C₂]_tf, is minimized. The control variable, temperature, is constrained to lie between 220°C and 270°C in order to ensure single phase polymerization. The most significant difference between this study and earlier ones is that the residence (or reaction), time t_f, is not specified a priori, but is determined optimally by the use of a ‘stopping’ condition such that the polymer product has a number-average chain length, μ_n, equal to some desired value μ_n.d. Simultaneously, an end-point constraint is used, which, depending on the objective function used, forces either the cyclic dimer concentration or the monomer conversion at the end of the reactor to lie at a specified value, [C₂]_d or conv_d. Thus, this algorithm incorporates stopping conditions as well as end-point constraints and so is more complex than earlier ones, but the results are more meaningful. Different nonisothermal optimal temperature profiles are obtained for the two objective functions studied, depending on the values of μ_n.d, conv_d, [C₂]_d, and the feed water concentration, representing the complex interplay of several opposing factors.     

Multiobjective optimization of an industrial nylon‐6 semi batch reactor using the a‐jumping gene adaptations of genetic algorithm and simulated annealing

The elitist nondominated sorting genetic algorithm (NSGA‐II) and multiobjective simulated annealing (MOSA) with the robust fixed‐length jumping gene adaptation (aJG) are used to solve three computationally intensive multiobjective optimization problems for an industrial semi batch nylon‐6 reactor. In Problems 1 and 2, the batch time and the final concentration of the undesirable side‐product (cyclic dimer) are minimized while maintaining desired values of the degree of polymerization of the product and the monomer conversion (monomer conversion is maximized as a third objective in Problem 3). The histories of two decision variables, pressure [or vapor release rate] and jacket fluid temperature, are used to obtain the Pareto optimal fronts. The study predicts considerable improvement over earlier results when (i) a single‐stage steam jet ejector is used to create subatmospheric pressures in the reactor, (ii) when the jacket fluid temperature is taken as a function of time, and (iii) when some amino caproic acid (from the depolymerization of scrap nylon‐6) is added to the feed. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Optimization of nonvaporizing nylon 6 reactors with stopping conditions

In this study, optimal temperature profiles or histories T(t) are obtained for nonvaporizing plug-flow or batch Nylon 6 reactors using the minimum principle. Two objective functions are studied, one in which the monomer conversion is maximized, and the other in which the undesirable cyclic dimer concentration in the product stream is minimized. The control variable, temperature, is constrained to lie between 220 and 270°C in order to ensure single-phase polymerization. The most significant difference between this study and earlier ones is that the residence or reaction time t_f is not specified a priori, but is determined optimally by the use of a “stopping” condition such that the polymer product has a number-average chain length μ, equal to some desired value μ_n,d. This makes the algorithm considerably more complex, but the results are more meaningful. Qualitatively different optimal temperature profiles are obtained for the two objective functions studied, representing the complex interplay of several opposing factors in determining optimal conditions. This study also lays the foundation for even more complex, but relevant, optimization studies.     

Vinyl chloride suspension polymerization with constant rate. A numerical study of batch reactors

Based on the analysis of a simple mathematical model, different temperature profiles are generated in order to provide vinyl chloride (VCM) suspension polymerization with constant reaction rates in batch reactors. In order to reproduce these temperature profiles in industrial-scale reactors, some process variables, such as coolant temperature, initiator concentration, and rate of water and monomer condensation, have to be manipulated. It is shown that those temperature practices can almost never be applied to large-scale reactors if the jacket temperature is the only variable that can be manipulated. It is also shown that developing an initiator feed procedure or using a reflux condenser may be advantageous.     

Design and optimisation of batch and semi-batch reactors

This paper addresses a systematic methodology for batch and semi-batch reactor design and optimisation for both ideal and non-ideal mixing. It can be applied to non-isothermal and multiphase systems. The method starts from a general representation in the form of a temporal superstructure based on the similarity of between plug flow reactors and ideal batch reactors. The temporal superstructure of a batch reactor exists in both the space and time dimensions. For non-ideal mixing, this paper addresses a mixing compartment network model to represent mixing inside reactors. The mixing compartment network is then included into the temporal superstructure to model non-ideally mixed batch reactors and the mixing pattern optimised with the other variables. Besides the operation variables for batch reactors, this method can also suggest the optimum mixing pattern and promising reactor configurations for mechanical design. A profile-based approach is proposed to make a search of the profiles for temperature, pressure and feed addition. This approach starts from a set of initial profiles of temperature, pressure and feed addition. Then the performance of the batch reactor is evaluated against the objective function under different profiles. An optimal set of profiles is then found by this profile searching process. A stochastic optimisation technique based on simulated annealing is employed to obtain optimal solutions. This method is also extended to multiphase reaction systems based on the concept of shadow reactor compartments. A number of case studies are presented to illustrate the use of the proposed methodology.     

Simulation of nylon 6 polymerization in tubular reactors with recycle

In the hydrolytic polymerization of ?-caprolactam, the ring opening of the monomer is much slower than the polyaddition reaction. Hence, the mixing of aminocaproic acid to the feed results in a faster conversion of the monomer. Industrially, this fact is exploited by using a recycle stream. An isothermal plug flow reactor (PFR) with a recycle is simulated in this study, using two techniques: the method of successive substitutions and Wegstein's method. It is found that, under certain operating conditions, the use of a recycle stream gives higher monomer conversions and lower cyclic dimer concentrations than either a PFR or a homogeneous continuous-flow stirred-tank reactor (HCSTR), with the degree of polymerization almost the same as that obtained in an HCSTR, and thus offers a considerable advantage. However, when a recycle reactor is coupled with a subsequent flashing operation and a finishing reactor, these advantages are considerably reduced.     

Multiobjective optimization of an industrial nylon-6 semibatch reactor system using genetic algorithm

Multiobjective Pareto optimal solutions for three different grades of nylon-6 produced in an industrial semibatch reactor are obtained by using the adapted Nondominated Sorting Genetic Algorithm (adapted NSGA). The two objective functions minimized are the total reaction time and the concentration of undesirable cyclic dimer in the product, while simultaneously attaining desired values of the monomer conversion and the number average chain length. The control variables used are the fractional valve opening f(t) and the jacket fluid temperature T_J. The study shows a marked improvement over current industrial operation. It is found that the optimal values of the cyclic dimer concentration in the product are worse (higher) when the reactor-control valve system is studied than when the reactor is considered alone. This is because the control valve leads to additional constraints. The technique used is quite general and can be used to study other reactor systems as well. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 729–739, 1999     

Anionic polymerization of styrene: The search for an industrial process

Anionic polymerizations were carried out in the laboratory using a CSTR reactor design and conditions typical of current commercial mass polystyrene plants. Polystyrene having excellent color and polydispersity was produced. Polymer quality, styrene conversion, and molecular weight control were all linked to use of polymerization feed of consistently high purity and polymerization in the 90–110°C temperature range. The results of this study clearly show that high quality polystyrene can be made utilizing anionic polymerization chemistry in existing well mixed mass polystyrene reactors of the CSTR design. The key to the successful practice of this technology is the ability to produce consistently high purity polymerization feed.     

Modeling and optimization of the cyclic steady state operation of adsorptive reactors

Adsorptive reactors(AR),in which an adsorptive functionality is incorporated into the catalytic reactors,offer enhanced performance over their conventional counterparts due to the effective manipulation of concentration and temperature profiles.The operation of these attractive reactors is,however,inherently unsteady state,complicating the design and operation of such sorption-enhanced processes.In order to capture,comprehend and capitalize upon the rich dynamic texture of adsorptive reactors,it is necessary to employ cyclic steady state algorithms describing the entire reaction-adsorption/desorption cycle.The stability of this cyclic steady state is of great importance for the design and operation of adsorptive reactors.In this paper,the cyclic steady state of previously proposed novel adsorptive reactor designs has been calculated and then optimized to give maximum space–time yields.The results obtained revealed unambiguously that an improvement potential of up to multifold level could be attained under the optimized cyclic steady state conditions.This additional improvement resulted from the reduction of the regeneration time well below the reaction-adsorption time,which means,in turn,more space–time yield.     

Optimization of a tubular nylon 6 reactor with radial gradients

Optimal jacket-fluid temperature profiles for tubular Nylon 6 reactors (in the presence of radial gradients of temperature and concentration) have been obtained using an algorithm based on the continuous minimum principle developed for a distributed parameter system. A gradient search technique has been devised and implemented for obtaining these optimal profiles. The optimal temperature profiles are found to be at the maximum permissible temperature, T_max, at the beginning of the reactor and then slowly decrease to the minimum permissible temperature, T_min, near the end of the reactor. The effect of varying several parameters is also studied. The desired value of the chain length and the reaction time are found to be the parameters which effect the optimal profiles most significantly.     

Dynamics of a cascade of two continuous stirred tank polymerization reactors with a binary initiator mixture

The dynamic behavior of two continuous stirred tank reactors in series has been investigated for free radical solution polymerization of styrene with a binary mixture of two initiators having different thermal decomposition activities. For a wide range of initiator feed composition, both reactors exhibit quite complex nonlinear steady state and transient behavior. When the reactor residence time is used as a bifurcation parameter, the second reactor can have up to five steady states. For certain range of reactor operating conditions, bifurcations to various types of periodic solutions have been observed, such as Hopf bifurcation, isolas, period doubling, period-doubling cascade, and homoclinics. The effects of other reactor variables, such as total initiator concentration, coolant temperature, and reactor volume ratio on the reactor dynamics, are illustrated to show the complex dynamic behavior of the two-reactor system catalyzed by a mixture of t-butyl perbenzoate and benzoyl peroxide.     

Algorithm for computation of molecular weight distribution and its moments in reversible step-growth polymerization in batch reactors

The differential equations governing the molecular weight distribution (MWD) in step-growth polymerization are coupled and nonlinear and a large number of them must be solved simultaneously to keep the truncation error low. In this work, these equations have been decoupled so that they can be solved sequentially. The solution of these is independent of the truncation error and there is considerable saving of computation time. To demonstrate the efficiency of the algorithm, the formation of polyethylene terephthalate (PET) in batch reactors with ethylene glycol evaporating has been analyzed. The feed to the reactor is taken as polymer with its oligomers present according to the Flory's distribution. The effect of pressure and temperature of the reactor on the progress of polymerization has been modelled and evaluated. The amount of ethylene glycol distilled, the concentrations of the first five oligomers Q₁ to Q₅, the number average chain length, and the polydispersity index of the polymer have been determined. It is shown that the reduced pressure and increased temperature reduce the concentration of the condensation product in the reaction mass, thus pushing the polymerization in the forward direction. Lastly the CPU time on Dec 1090 using this algorithm is only 0.40 s compared to about 10 min for similar computations using other existing methods.     

Molecular weight distribution of polyethylene terephthalate in homogeneous,continuous-flow-stirred tank reactors

Poly(ethylene terephthalate) (PET) formation in homogeneous, continuous-flow-stirred tank reactors (HCSTRs) operating at steady state has been simulated. The feed to the reactor is assumed to consist of the monomer bis-(hydroxyethyl) terephthalate and monofunctional compound (MF₁) cetyl alcohol. The overall polymerization is assumed to consist of the polycondensation, reaction with monofunctional compounds, redistribution, and cyclization reactions. At a given time, the reaction mass consists of polyester molecules (P_n), polyester molecules with an ending of molecules of monofunctional compound (MF_n), and cyclic polymers (C_n). A mass balance for each of these species in the reactor gives rise to a set of algebraic equations to be solved simultaneously. The MWD calculations show that the redistribution reaction plays a major role and cannot be ignored, This result is in contrast lo the observation for semi-batch reactors, for which redistribution becomes important when the cyclization reaction is included. For the same residence times of semi-batch and HCSTRs, the latter gives considerably lower-number average molecular weight, N_av, and polydispersity index, ρ. However, for the same conversions, the ρ for CSTR is higher. The concentration of the monofurctional compound, [MF₁]₀, in the feed and the reactor temperature both influence ρ, but the effect is small within the range studied.     

Experimental study and model simulation of a two-stage continuous polymerization process for polystyrene

Free radical solution polymerization of styrene in two stage polymerization process has been studied using a binary mixture of symmetrical bifunctional initiators. The continuous reactor system was composed of two reactor units; a prepolymerization reactor (e.g. stirred tank reactors) and a filled tubular reactor packed with static mixers. When the stirred tank reactor was used as a prepolymerizer, a feed stream to the filled tubular reactor was more viscous than the monomer/solvent mixture. It was of interest to investigate how the performance of the filled tubular reactor has been investigated by the feed of viscous prepolymer solution. A dynamic model of the continuous two stage polymerization process was presented by experimental data and model simulation. A reasonably good agreement between the model and the experimental data was obtained without using any adjustable parameters. The experimental results of the two stage polymerization were compared with the results without prepolymerization reactor. It was found that the addition of a prepolymerization reactor has almost no effect on the performance of the filled tubular reactor.     

Optimization of the polycondensation step of polyethylene terephthalate formation in semibatch reactors

The polycondensation stage of polyethylene terephthalate (PET) formation is assumed to include side reactions leading to the formation of diethylene glycol, vinyl end groups, and acid end groups, in addition to the usual polymerization of bis (2-hydroxyethyl) terephthalate (BHET) in semi-batch reactors. A, flexible objective function has been proposed with temperature and pressure as control variables. Computations from the first variation technique show that the pressure should be reduced to the lowest limit under all possible conditions. Consequently, optimal temperature profiles in batch reactors are obtained for various lower limits of reactor pressures using the combination of first and second variation techniques. For the first variation technique, the vector iteration method of computation was used, and the near optimal profile so obtained was used as the initial guess for the second variation technique. The result of optimization shows that the lower limit of pressure and weighting parameters appearing in the objective function have profound effects on the optimum profiles. For higher pressures, it is shown that a high temperature must be used initially; but must be lowered later to minimize the formation of side products. However, for lower pressures, the temperature must be increased from a low value initially; but for large polymerization times, the temperature must be further reduced to minimize the formation of side products. It is thus seen that the optimum temperature profile for low pressures exhibits a broad maximum.     

我国镍系顺丁橡胶聚合过程的工程分析及其改进——Ⅱ.管式组合反应器聚合工艺

在对我国镍系顺丁橡胶现行釜式丁二烯聚合工艺进行动力学分析和工程分析的基础上,提出了三级管式组合反应器聚合工艺的技术改造方案,并对此作了可行性论证。该方案分别选择环管反应器和带刮刀直管反应器作为引发聚合反应器和第二、三级主聚合反应器。经初步设计核算认为,管式聚合工艺过程具有动力学反应学制特性、反应器具有热稳态操作特性。     

Dynamics and stability of ethylene polymerization in multizone circulating reactors

Multizone circulating bed reactors (MZCR) have the exclusive characteristics of producing polymers of different molecular weights in a single particle. Traditional fluidized bed reactors, on the other hand, can produce only one kind of molecular weight with relatively narrow distribution. A dynamic model for the MZCR is used to illustrate the basic dynamic behavior of the new reactor design used for polyethylene production. The model is used to study the copolymerization of ethylene with butene. Several parameter sensitivity analyses are performed to show the computer-simulated time responses for reactor temperature, number-average molecular weight, weight-average molecular weight, catalyst feed rate and the monomer/comonomer concentration along the reactor length. At certain operating conditions dynamic instability is observed and the results for the effect of cooling water temperature, catalyst feed rate, monomer and comonomer initial feed concentration on the reactor temperature and polymer molecular weight reveal that the system is very sensitive to disturbances in the heat exchanger coolant temperature. Also, at some operating conditions, the reactor temperature oscillates above the polymer melting temperature. Temperature runaway above polymer softening point is a serious problem which may cause polymer melting and hence reactor shutdown. The oscillatory behavior of the reactor temperature necessitates a suitable temperature control scheme to be installed.     

Multiplicity of the steady state in fluidized bed reactors—VIII. Partial oxidation of o-xylene

A model is derived for the case of a fluidized bed reactor in which partial oxidation of o-xylene occurs. The use of fluidized beds instead of fixed bed reactors allows for higher feed concentrations and lower feed temperatures. However, multiple steady states arise and it is shown that the maximum yield is obtained when the reactor is operated at the unstable middle steady state. However, for maximum productivity, the reactor must be operated at a lower temperature than that corresponding to maximum yield. This is due to the pathological dependence of the middle steady state on feed temperature and concentration.     

Simulation of continuous solid‐phase polymerization of nylon 6,6. III. Simplified model

Solid‐phase polymerization (SPP) reactors are used to increase the degree of polymerization (DP) during nylon 6,6 production. In previous articles, a reactor model with partial differential equations (PDEs) in time and two spatial dimensions was developed to describe dynamic changes in polymer property profiles (DP, temperature, and moisture content) over the height of the reactor and within the polymer particles. In the current article, a simplified model is developed by deriving appropriate expressions for heat‐ and mass‐transfer coefficients and performing a lumped heat‐ and mass‐transfer analysis. Using this approach, the radial dimension is removed from the PDEs, so that the effort required to solve the model equations is substantially reduced. Predictions of the complex and simplified models are compared through simulation of two different start‐up processes. Good agreement between simplified and complex models is obtained, indicating that the simplified model can be used in place of the complex model if the polymer properties profiles within individual particles are not of particular concern to the model user. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3701–3712, 2003