Parametric sensitivity in co-currently cooled tubular reactors

An intrinsic criterion was derived for parametric sensitivity and runaway in co-currently cooled tubular reactors. It is essentially based on the approach of Van Welsenaere and Froment (1970) developed for the constant wall temperature case and which makes use of fundamental properties of the trajectory in the temperature vs. partial pressure plane. The criterion limits the maximum allowable temperature on an objective basis and permits the calculation of the corresponding critical inlet values for the operating variables, like partial pressure of the reactant, temperature of the reactor fluid, temperature of the cooling medium, coolant flow rate, reactor throughput ... . In addition to the rigorous treatment, a simple extrapolation procedure is presented, which proves to be very useful and accurate, provided the conditions are not too severe.     

Parametric sensitivity of chain polymerization reactors exhibiting the trommsdorff effect

The recently developed mathematical technique for studying the parametric sensitivity of reactors is extended to include chain polymerization systems exhibiting the gel and glass effects, as well as physical property variations. The sensitivities of the two temperature maxima with respect to various parameters are computed. It is found that, for a sample system, poly(methyl methacrylate), all the sensitivities of the gel effect induced temperature peak attain their maxima at the same conditions—this leads to a generalized temperature sensitivity constraint applicable to reactor design or operation. This sensitivity boundary is associated with high conversions and high molecular weights. The analysis shows that the dimensionless propagation activation energy, ?_p, and the dimensionless initiation activation energy, ?_d, are the two most important parameters governing the system performance. Sensitivities of the gel effect-induced number average chain length peak with respect to various parameters are also obtained. Again, all of these chain length sensitivities show maxima at the same condition, leading to the concept of a generalized chain length sensitivity criterion of constraint. Most importantly, the temperature and chain length sensitivity boundaries are virtually identical.     

Parametric sensitivity in fixed-bed reactors

Parametric sensitivity in fixed-bed reactors has been analysed by previous workers using the quasihomogeneous model [i.e. for the kinetic regime only]. In the present paper a general treatment is proposed in which transport limitations are also considered. It is shown that the critical inlet partial pressure is strongly dependent on the transport processes. Based on the analysis presented, four regimes of fixed-bed reactor operation are postulated and conditions are stated to identify the regime in which a given system would operate. These conditions are applied to some industrially important reactions to show that the regimes represent realistic systems. Procedures are developed to obtain the critical inlet partial pressure for systems lying in the various postulated regimes. Illustrative examples are then solved to demonstrate the procedures developed in the text. The correctness of the procedures is established by comparing the values of the critical inlet partial pressure obtained from the present analysis with those obtained from numerical solution.     

Radial transport in tubular polymerization reactors

The importance of radial convective flows in tubular polymerization reactors is examined by analysing a model problem which contains many of the features of an actual tubular reactor. The transport equations for the model problem are simplified using lubrication theory, and a convergent finite-difference method is formulated to obtain solutions to the simplified equation set. The computed solutions show that significant errors can be introduced in the velocity and concentration fields if the radial convective term in the species continuity equation for the monomer is neglected when the ratio of polymer to monomer viscosities is sufficiently large. It is also shown that a fine finite-difference mesh is needed to obtain accurate solutions for high viscosity ratios.     

Parametric sensitivity in fixed-bed catalytic reactors

This paper introduces a criterion for runaway in fixed-bed catalytic reactors based on the behaviour of sensitivity coefficients along the reactor. The criterion can be used when the temperature variation in a co-current cooling medium is taken into account; and also, it is not restricted to simple kinetics. In addition, multiple reactions may be analysed. Some examples of industrial significance are studied and the results are compared with those obtained by other authors.     

Free-radical polymerization of methyl methacrylate in tubular reactors

Mathematical modeling and experimental studies of the freeradical polymerization of methylmethacrylate in tubular reactors have been performed to ascertain the operating constraints, reactor behavior, and product quality of this process. This paper focuses on reactions at a temperature below the glass transition of poly(methyl methacrylate). This class of experiments is here referred to as low-temperature runs, in contrast to above-Tg polymerization. Reactor temperature and conversion histories of these low-temperature experiments are successfully described by a rheokinetic model, incorporating both detailed considerations of velocity profile development in the reactor and conversion-dependent kinetics. The limitations of this process are discussed in light of the complex fluid flow and heat transfer problems encountered in the system.     

Scaleup factors of tubular emulsion polymerization reactors

This paper examines the important dimensionless numbers that control emulsion polymerization in a tubular reactor. It was found that the activation energy of polymerization was of major importance, while the role of monomer diffusion was not very significant. By selecting certain combinations of the dimensionless numbers, changes occurring during scaleup from a small tubular diameter to a larger diameter can be approximated.     

Parametric sensitivity of the ignition process to mass transfer in adiabatic tubular reactors with exothermic heterogeneous reactions

The alternative effects of reaction kinetics, mass, heat and momentum transport on mass conversion by chemical reactions are examined theoretically for a reacot tube with laminar flow. The reaction enthalpy is considered. A heterogeneous reaction between several gaseous components takes place at the inner surface of this reactor tube. Strongly exothermic reactions lead to self-acceleration of the reaction, unless reaction enthalpy is removed through the tube wall. Under certain conditions, there will be a sudden change from mass transfer controlled by the reaction to that controlled by diffusion. This phenomenon is known as ignition of the reaction. The effect of ignition and its sensitivity to reaction enthalpy, thermal conductivity and diffusivity of the fluid as well as activation energy of the first order heterogeneous wall reaction are investigated by a numerical solution of the transport equations. Axial conduction of heat and mass is neglected both in the fluid and in the tube wall. Non-stoichiometric wall reactions of first order, with temperature dependent reaction rates and equilibrium constants, are considered. The results are presented in graphical form, as plots of the local mass flux at the reacting wall as functions of the dimensionless tube length.     

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.     

Modeling of ethylene polymerization with difunctional initiators in tubular reactors

The severe thermodynamic conditions of the high‐pressure ethylene polymerization process hinder ethylene from going to full conversion. One remedy to improve the monomer conversion is to make effective use of difunctional peroxides. Multifunctional peroxides can accelerate the polymerization rate, produce branching, and modify the rheological properties of molten polymers. This article proposes a kinetic model based on a postulated reaction mechanism for ethylene polymerization initiated by difunctional initiators in a high‐pressure tubular reactor. Three peroxides suitable for ethylene polymerization were compared for their effectiveness. Compared to dioctanoyl peroxide, the two difunctional peroxides considered performed much better for the higher temperature regions of the reactor and gave ethylene conversions nearly twice as high for only half of the initial amount of dioctanoyl. They also generated low‐density polyethylene polymer with a broader molecular weight distribution and longer chain branching. These two important polymer characteristics can influence the end‐product rheological properties. Injecting fresh ethylene at different points along the reactor improved the conversion and produced more branched polymer. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

High pressure tubular reactors for ethylene polymerization optimization aspects

Optimal policies for operation of high pressure tubular reactors for ethylene polymerization are presented. The work is based on a previously developed model, allowing accurate representation of different configurations and operation conditions of industrial relevance. Several policies based on temperature and initiator concentration as control parameters are evaluated and compared.     

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.     

Bulk polymerization in tubular reactors I. Experimental observations on fouling

Conditions under which fouling (polymer deposition) occurs in tubular polymerization reactors were studied using bulk methyl methacrylate polymerizations at 70°. It was demonstrated that reactor orientation and flow direction have a significant effect on fouling behaviour. Natural convection becomes increasingly important as concentration gradients in the reactor increase. Using the optimum reactor configuration determined in the first part of the study, a feasible operating region for the reactor was established, thereby permitting selection of conditions which will prevent reactor fouling.     

非绝热式固定床反应器的参数敏感性及热失控临界参数

寻找安全有效的反应条件一直是绿色化工的重要研究内容之一。采用邻二甲苯氧化的反应动力学模型,分析了非绝热式固定床反应器的参数灵敏性和热失控行为,考察了非绝热式固定床反应器温度对冷却介质流量、进料温度和初始压力的敏感性。模拟计算结果表明,当反应进入敏感性区域后,反应器对冷却介质流量、进料温度和初始压力的改变极其敏感。采用系统散度判据（div>0）计算该反应的热失控临界操作参数,计算结果与文献中的判据进行了分析比较,得到类似的结果,但计算更简单。考虑冷却介质的影响,修正了div判据,得到更准确的热失控临界操作参数。研究结果表明,此判据能为反应器的设计及过程控制提供重要的参考依据。     

Use of neural networks for modeling of olefin polymerization in high pressure tubular reactors

Neural network computing is one of the fastest growing fields of artificial intelligence due to its ability to “learn” nonlinear relationships. This article presents the approach of back propagation neural networks for modeling of free radical polymerization in high pressure tubular reactors. Industrial data were used to train the network for prediction of the temperature profile along the reactor, as well as polymer properties such as density, melt flow index, and molecular weight averages. Comparisons were made between the neural network and mechanistic model predictions published in the literature. Results showed the promising capability of a neural network as an alternative approach to model polymeric systems. © 1994 John Wiley & Sons, Inc.     

Design of tubular reactors in recycle systems

The article presents an approach to design tubular reactors in recycle systems, based on non-linear analysis. A pseudo-homogeneous plug-flow reactor model is used. It is assumed that the separation unit delivers product and recycle streams with fixed composition. The stand-alone reactor has a unique stable steady state. The coupled reactor–separation–recycle system shows four types of conversion versus plant Damköhler number bifurcation diagrams. A feasible steady state exists only if the reactor volume exceeds a critical value. For isothermal reactor, the steady state is unique and stable. For non-isothermal reactor, one or two steady states are possible. In the second situation the low-conversion state is unstable. In some parameter regions, the unique state is unstable. The design should ensure state unicity and stability, which are favoured by large heat-transfer capacity, low coolant temperature and high reactor-inlet temperature. A case study demonstrates that these phenomena can be easily found in real plants.     

Optimal location of measurements in tubular reactors

The optimal location of temperature measurements along the length of a non-adiabatic tubular reactor in which a first-order exothermic reaction is occu     

Thermal stability of polymerization reactors

Temperature rises which occur in the early stages of polymerization in batch reactors are discussed. Comparisons between experimental results and a reactor model shows that realistic predictions of temperature rises can be made when the model allows for changes in density and specific heat of the reaction fluid. In the case of styrene polymerization, the neglect of density and specific heat changes leads to the prediction of large temperature increases, which are not found in practice. When allowance for these changes in physical properties is made, agreement between theoretical prediction and experimental results is good.