Optimization of nylon 6 reactors with end-point constraints

Optimal temperature profiles for nylon 6 polymerization in plug–flow reactors have been obtained with end-point constraints involving the degree of polymerization and the cyclic dimer concentration, using the most recent kinetic information. Computations suggest that the temperature at the feed end of the reactor must be maintained close to the highest permissible level (determined by the boiling point of the ?-caprolactam). The temperatures in this region control the degree of polymerization more than other variables. Thereafter, the temperature should be reduced. This second zone controls the undesirable cyclic dimer concentration. The effect of a systematic change of values of the various design variables is studied. The profiles obtained herein are qualitatively similar to those obtained by earlier workers using similar formulations. However, they differ significantly from the profiles obtained by us earlier, using different objective functions which are more relevant to the design of new reactors. Attempts have also been made to obtain a global optimal scheme to produce polymer of a desired degree of polymerization and cyclic dimer content, using as short a reactor as possible, and using the water content and the modifier concentration in the feed as the independent variables.     

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 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.     

Temperature Control of a Bench‐Scale Batch Polymerization Reactor for Polystyrene Production

Batch polymerization reactors commonly use optimal temperature control as the strategic operation parameter. This strategy allows for better operability and a more economic process. The main objective of the batch polymerization reactor control is to obtain acceptable product quality. Direct measurement of polymer quality is rarely achievable, which makes the online control of the reactor difficult. Temperature is the most controllable operational variable in the polymer reactor, which is seen to have a direct effect on the polymer properties. Temperature is chosen as the set point by using either the isothermal temperature or optimal temperature trajectory. Online control of the optimal temperature profile of a bench‐scale batch polymerization reactor was experimentally investigated in this study. The temperature trajectory was used as the target for controllers to follow. The time‐profile temperature was obtained with the objective of obtaining the desired conversion and number‐average chain length within the minimum time. Two advanced controls of fuzzy logic control and generic model control were applied to the polymer reactor. A comparison of the controllers reveals that both performed better than conventional controllers.     

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.     

Computation of near-optimal control policies for free-radical polymerization reactors

A polymer is characterized by the average degree of polymerization and the molecular weight distribution. Approximate optimization of temperature control, or catalyst feed rate control, or both are performed to attain not only the desired average degree of polymerization but also the desired molecular weight distribution. This near-optimal policy, which is a function of time only for a batch polymerization reactor, is first expressed by a polynomial, and the coefficients of the polynomial are estimated by a pattern search technique. This coefficient's estimation method coupled with a nonlinear search technique was found to be suitable for solving this type of our optimization problem involving complex chemical kinetics.     

Optimization of the polycondensation stage of poly(ethylene terephthalate) reactors

A general kinetic scheme for the polycondensation step of the PET formation has been used to establish the mole balance equations of various functional groups in batch reactors. An objective function has been defined which aims to attain a desired degree of polymerization in the shortest time, has a specified level of diethylene glycol group content, and minimizes the other side products. Using the control vector iteration procedure, an optimum temperature profile has been calculated. The computations suggest that a high temperature should be used initially which must be lowered as the time of reaction increases for limiting the formation of side products.     

Dynamic optimization of an industrial semi-batch nylon 6 reactor with end point constraints and stopping conditions

In this study, optimal vapor release rate (or pressure) histories have been generated for an industrial semi-batch nylon 6 reactor using Pontryagin's minimum principle. The batch time has been taken as the objective function, which is to be minimized. The pressure is constrained to lie between a lower and an upper limit. The temperature, a state variable, is also constrained to lie between 220°C and 270°C in order to ensure single-phase polymerization. Optimization has been carried out with a single end-point constraint (on monomer conversion) and a stopping condition (obtaining a product having a desired degree of polymerization, μ_n). Techniques have been developed to overcome the discontinuities present in the model, as well as to take care of state variable constraints. The effects of various physical and computational variables on the optimal pressure history and the corresponding batch time have been studied. It is found that the optimal batch time is almost 50% of the industrial value used currently. Interestingly, the optimal pressure history is quite similar qualitatively with the current practice though quantitatively there is a significant difference. Improvements in reactor operation along these lines have been reported. © 1996 John Wiley & Sons, Inc.     

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.     

TRACKING PERFORMANCE OF CONTROL METHODS

In this work, the optimal temperature control of a styrene solution polymerization reactor with two different control algorithms is considered. DMC and PFD control mefhods are used to accomplish the optimal temperature control of the polystyrene reactor. Reactor optimal temperature profiles at different initiator initiation concentrations were obtained by applying maximum principle to the mathematical model of the free radical batch polymerization reactor lo produce polystyrene with desired conversion and molecular weight in a minimum lime. The results obtained from the experimental implementation of DMC and PID controller for the control of optimal temperature path of the polymerization reactor were compared.     

TRACKING PERFORMANCE OF CONTROL METHODS

In this work, the optimal temperature control of a styrene solution polymerization reactor with two different control algorithms is considered. DMC and PFD control mefhods are used to accomplish the optimal temperature control of the polystyrene reactor. Reactor optimal temperature profiles at different initiator initiation concentrations were obtained by applying maximum principle to the mathematical model of the free radical batch polymerization reactor lo produce polystyrene with desired conversion and molecular weight in a minimum lime. The results obtained from the experimental implementation of DMC and PID controller for the control of optimal temperature path of the polymerization reactor were compared.     

Optimization of a batch polymerization reactor at the final stage of conversion. II. Molecular weight constraint

A mathematical model for the free radical batch solution polymerization of methyl methacrylate that takes depropagation into account was developed. This model was then used to derive optimal temperature and initiator concentration policies to reduce residual monomer concentration to desired levels, producing at the same time a polymer with the desired number average molecular weight. An objective function was formulated to take account of the cost of the initiator with respect to the cost of time of reaction. It was observed that when the cost of initiator increased, optimal initiator concentration decreased whereas optimal temperature increased. Finally temperature reached a limiting value above which polymer with desired number average molecular weight could not be produced. These results give insight into the factors that determine the policies that could be employed in optimizing the operation of a reactor.     

Application of experimental non-linear control based on generic algorithm to a polymerization reactor

The dynamics of free radical polymerization of styrene and on-line control of temperature in a cooling jacketed batch polymerization reactor is investigated. The benzoyl peroxide initiator is introduced into the reactor once at the beginning of the reaction to obtain the desired monomer conversion and the desired average chain length in a minimum reaction time. The optimal constant set temperature, which is generally realized in industrial applications, and the set profile are used as two different optimal operating conditions. The temperature control of the polymerization reactor is achieved experimentally and theoretically. The control of nonlinear systems has progressed considerably, and various nonlinear process model based control techniques have appeared in the literature. The problem is how to tune the controller in order to obtain comparable closed loop responses. Generic model control (GMC) is applied and the performance of the control results are compared with the previously published control results.     

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     

原位螯合制备含镁聚磷酸铵的工艺研究

采用一步投料法,将磷铵、尿素和硫酸镁充分混合后粉碎,再加入反应器中原位螯合制备含镁元素的水溶性聚磷酸铵（APP）肥料。研究镁添加量、尿素/磷铵物质的量比、反应温度、反应器搅拌转速对产品聚合度及聚合度分布的影响。结果表明：当镁添加量＜5%（质量分数）时,可以促进磷铵与尿素的聚合反应,提高产品聚合度;增加尿素比例、提高反应温度,可显著提高产品聚合度;随着反应器搅拌转速增加,含镁APP产品聚合度增加,而纯APP产品聚合度降低。各实验因素对APP聚合度的影响由大到小顺序为尿素/磷铵物质的量比、反应温度、搅拌转速、镁添加量。     

The optimal control of polymerisation reactors

Two separate but related problems are treated in this paper: (i) the optimal control policy for continuous stirred tank polymerization reactors; (ii) the optimal control program for batch polymerization reactors. The first problem concerns determining the temperature and initiator control policy which brings the reactor to the desired steady state while minimizing some objective functional (e.g. start-up time, cost of control action, etc.). The second problem is concerned with finding the best temperature and initiator program so that the product from the batch reactor has the best possible molecular weight distribution. Both free radical polymerization and linear condensation polymerization examples are considered with molecular weight distribution moments being used to characterize the polymer. Kinetic parameters typical of styrene are used for the free radical case, and realistic parameters are chosen for the condensation examples. The techniques used can be immediately carried over to other polymerization systems, and hopefully generalizations about the character of the optimal policies for such new systems can be made by considering the policies found for the systems studied. The results of the study demonstrate some of the potential gains possible through supervisory computer control of polymerization reactors.     

Development of Synthetic Ketonic Resin

In the present work, the self-polymerization reaction of cyclohexanone was studied to develop a synthetic resin. Synthetic resins are extensively used in paint industry to improve the adhesiveness of paints. Polymerization reactions were carried out in a high-pressure reactor. The results suggest that the self-polymerization of cyclohexanone mainly depends on alkali concentration, reaction temperature, and reaction time. As the ketone-to-alkali ratio decreases, the degree of polymerization increases, which leads to an increase in the hydroxyl value and softening point and a remarkable decrease in solubility. A good-quality solid resin could be obtained with a ketone-to-alkali ratio less than 5 in the temperature range between 130°C and 160°C and within the time duration of 12–22 h. These data may be useful to develop the desired quality of resin in the field of paint application.     

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     

Experimental validation of the optimal trajectory of initiator concentration in a batch MMA polymerization reactor

This article presents a method to determine the trajectory of initiator concentration that will produce polymer with desired number‐ and weight‐average molecular weights at a prespecified level of monomer conversion. The optimal control theory is applied to the mathematical model for a batch methymethacrylate (MMA) solution polymerization reactor system. By imposing the constraint that initiator concentration should decrease within the range of self‐consumption by the initiation reaction, one can obtain the initiator concentration trajectory that can be tracked by feeding the initiator alone. A control scheme is constructed with a cascade proportional‐integral‐derivative (PID) control algorithm for temperature control and a micropump is installed to manipulate the initiator feed rate. The experimental results show satisfactory tracking control performance despite the nonlinear features of the polymerization reactor system. Also, the monomer conversion and the average molecular weights measured are found to be in fairly good agreement with those of model prediction, respectively. In conclusion, the polymer having desired molecular weight distribution can be produced by operating the batch reactor with the initiator supplement policy calculated from the model. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1256–1266, 2000     

Analysis of tanks-in-series model with backflow for free-radical polymerization

Free-radical polymerization in a flow reactor represented by the tanks-in-series model with backflow was considered. Conversions and molecular weight distributions were computed as functions of the backflow parameter, and the results were compared with the conversion and molecular weight distribution from a CSTR and those from a plug-flow reactor. Backflow was found to be undesirable for the polymerization mechanism under investigation. Values of the degree of segregation for the tanks-in-series model were calculated by using Zwietering's approach as a function of backflow.