A dynamically distributed reactor model for identifying the flow fields in industrial loop propylene polymerization reactors

The use of distributed parameter model is becoming a common approach for simulating liquid–solid flow in loop polymerization reactors. However, there are still several issues with it. One of them is the absence of modeling of distributed pressure, as no thermodynamic state‐equation is incorporated into the model. In this work, inner pressure of the reactor was associated with temperature using a thermodynamic state‐equation for high‐pressure liquid. The thermodynamic state‐equation was solved together with a dynamically distributed reactor model based on the mass, energy, and momentum conservation as well as polymerization kinetics to predict the dynamic trajectories of component concentration, temperature, pressure, and bulk mass velocity in the reactor. Industrial steady‐state data were used for model validation. The application of the model was demonstrated by simulating the effect of recycle ratio on the above distributed reactor parameters. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

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.     

The bifurcation behavior of continuous free-radical solution loop polymerization reactors

The bifurcation behavior of continuous free-radical solution loop polymerization reactors is analyzed in this work. A mathematical model is developed in order to describe the impact of the recycling pump and other external reactor parts upon the process dynamics and stability. Stability analysis is performed using bifurcation theory and continuation methods. It is shown that under certain operational conditions as many as seven steady states are predicted for the loop polymerization reactor. Oscillatory behavior is observed for a wide range of process parameters and onset of oscillations is observed during the transition from operation without material recycling to operation with partial recirculation of the polymer solution. Besides, at certain constrained range of operation conditions, complex dynamics can be observed, including the onset of chaotic behavior. It is also shown that the thermal parameters of the reactor and recycling pump exert a profound effect upon the process stability. For this reason it is shown that oscillatory behavior is very unlikely to occur in actual industrial reactors.     

Liapunov functional method for analysis of nonadiabatic tubular reactors with axial mixing and recycle

Sufficient conditions for stability of steady state are derived through Liapunov's direct method for a class of distributed-parameter systems and applied to nonadiabatic tubular reactors with axial mixing and recycle (NATRAMAR), for which previously only numerical results have been reported. Several sufficient conditions are presented in terms of system parameters and steady state profiles, system parameters and the exit conditions, or system parameters only. The last conditions involving system parameters only are very convenient since they do not require any solution of differential equations and are particularly useful since they show the manner in which the operating conditions of the reactor affect the stability of steady state.     

Nonlinear control of competitive mixed‐culture bioreactors via specific cell adhesion

A nonlinear control strategy is developed for competitive mixed‐culture bioreactors in which two cell populations compete for a common growth limiting substrate. A stream is periodically removed from the reactor, and the two cell populations are separated using specific cell adhesion. The steady state corresponding to the desired population fraction is stabilized by discarding faster growing cells and recycling slower growing cells to the reactor. The recycle loop must be operated periodically to allow regeneration of the adhesion column after each separation. As a result, the manipulated input is chosen as the sampling interval during which material is removed from the reactor. The nonlinear controller is designed using a simplified dynamic model that assumes continuous separation of the cell populations. The controller is implemented by calculating the sampling interval that leads to the same amount of material being removed from the reactor as that computed from the continuous control law. A nonlinear, closed‐loop observer is used to generate one‐time‐delay‐ahead predictions of the measured cell concentrations and the unmeasured substrate concentration. The efficacy of the proposed control strategy is evaluated via simulation.     

Spectral properties and low‐dimensional description of loop and recycle reactors

The spectral properties of the discrete and continuous convection and convection‐diffusion operators with loop or recycle boundary condition are analyzed. It is shown that the spectral properties of these nonsymmetric operators are closely related to the theory of circulant (Toeplitz) matrices and the complex Fourier series, respectively. Although there may be many complex eigenvalues, the smallest eigenvalue is real and approaches zero as the loop circulation or recycle ratio increases. This property is used to simplify nonlinear diffusion‐convection‐reaction models of loop and recycle reactors to obtain two‐mode low‐dimensional averaged models that are accurate in the limit of large recycle ratio. Explicit expressions for the two mixing coefficients that relate the two concentration modes and their dependence on various inlet conditions are also derived. Finally, the application of the low‐dimensional models to determine the impact of macromixing on the conversion, yield, and selectivity for the case of nonlinear kinetics is illustrated. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3365–3377, 2013     

Die maximal durchmischte Zwillingsschlaufe. Ein erweitertes Schlaufenmodell für isotherme,homogene reaktionen

The total range of reactor performance, that is between the PFR and the whole reactor volume being a stagnant zone, may be represented by the three parameter twin loop model. The two basic assumptions made in the model—plug-flow with no longitudinal mixing in each loop, as well as immediate mixing of the two recycling streams and the inflow on the molecular scale (maximum mixedness)—are fairly well achieved in large-scale reactors. Consequently, such reactors are easy to calculate without scale-up problems. At constant mean residence time the three parameters—total recycle number, partial recycle number, ratio of recycle times—can be varied independently. Thus, the twin loop is rather adaptable and easy to control.     

The bifurcation behavior of tubular reactors

Methods for studying the bifurcation behavior of tubular reactors have been developed. This involves the application of static and Hopf bifurcation theory for PDE's and the very precise determination of steady state profiles. Practical computational methods for carrying out this analysis are discussed in some detail. For the special case of a first order, irreversible reaction in a tubular reactor with axial dispersion, the bifurcation behavior is classified and summarized in parameter space plots. In particular the influence of the Lewis and Peclet numbers is investigated. It is shown that oscillations due to interaction of dispersion and reaction effects should not exist in fixed bed reactors and moreover, should only occur in very short “empty” tubular reactors. The parameter study not only brings together previously published examples of multiple and periodic solutions but also reveals a hitherto undiscovered wealth of bifurcation structures. Sixteen of these structures, which come about by combinations of as many as four bifurcations to multiple steady states and four bifurcations to periodic solutions, are illustrated with numerical examples. Although the analysis is based on the pseudohomogeneous axial dispersion model, it can readily be applied to other reaction diffusion equations such as the general two phase models for fixed bed reactors.     

Transients in adiabatic tubular reactors. Axial dispersion models with well-mixed appended sections

Using boundary conditions more general than those due to Danckwerts, the authors recently showed that significant variations may be encountered in the global stability characteristics of an axially dispersed adiabatic tubular reactor. The numerical results presented in this communication demonstra that for a fixed initial state of the reactor, steady states very different from those predicted with Danckwerts conditions are reached depending on th initial state of the reactor appendages. The cases where the reactor is preceded or succeeded by well-mixed (non-reactive) sections are considered. The findings will be very useful in regulation of the dynamics of tubular reactors.     

A stochastic flow model for a tubular solution polymerization reactor

Residence time distributions were evaluated experimentally for three tubular solution polymerization reactors to analyze aspects of the fluid‐dynamic behavior of these reactors. The analysis of the available experimental data indicates that the flow characteristics of these reactors may be subject to stochastic perturbations. A stochastic flow model is then proposed by assuming that a viscous polymer layer is formed in the proximities of the reactor walls and that plugs of polymer material are released at random during the operations. This model is able to represent the available experimental data fairly well for three tubular reactors with different configurations. POLYM. ENG. SCI., 47:1839–1846, 2007. © 2007 Society of Plastics Engineers     

A Novel Radial‐Flow,Spherical‐Bed Reactor Concept for Methanol Synthesis in the Presence of Catalyst Deactivation

A radial‐flow, spherical‐bed reactor concept for methanol synthesis in the presence of catalyst deactivation, has been proposed. This reactor configuration visualizes the concentration and temperature distribution inside a radial‐flow packed bed with a novel design for improving reactor performance with lower pressure drop. The dynamic simulation of spherical multi‐stage reactors has been studied in the presence of long‐term catalyst deactivation. Model equations were solved by the orthogonal collocation method. The performance of the spherical multi‐stage reactors was compared with a conventional single‐type tubular reactor. The results show that for this case study and with similar reactor specifications and operating conditions, the two‐stage spherical reactor is better than other alternatives such as single‐stage spherical, three‐stage spherical and conventional tubular reactors. By increasing the number of stages of a spherical reactor, one increases the quality of production and decreases the quantity of production.     

3‐D Simulations of an Internal Airlift Loop Reactor using a Steady Two‐Fluid Model

Three‐dimensional (3‐D) simulations of an internal airlift loop reactor in a cylindrical reference frame are presented, which are based on a two‐fluid model with a revised k‐? turbulence model for two‐phase bubbly flow. A steady state formulation is used with the purpose of time saving for cases with superficial gas velocity values as high as 0.12 m/s. Special 3‐D treatment of the boundary conditions at the axis is undertaken to allow asymmetric gas‐liquid flow. The simulation results are compared to the experimental data on average gas holdup, average liquid velocity in the riser and the downcomer, and good agreement is observed. The turbulent dispersion in the present two‐fluid model has a strong effect on the gas holdup distribution and wall‐peaking behavior is predicted. The CFD code developed has the potential to be applied as a tool for scaling up loop reactors.     

Fast gas–liquid–solid reactions in monoliths: A case study of nitro-aromatic hydrogenation

Monolith catalyst supports are attractive as fixed bed reactors that, at the scale of the catalyst dimension, exhibit the mass transfer characteristics of slurry reactors. This paper presents a reactor design study for the single-pass conversion of dinitrotoluene in a loop configuration with an external heat exchanger. The advantage of such a loop system is the elimination of a solvent, which in turn allows more reaction heat to be recovered. The advantages of using a monolith are the low pressure drop at high recycle ratio, while maintaining good mass transfer characteristics. The modelling includes internal diffusion limitation, external mass transfer characteristics, heat effects, maldistribution and flow stability. The optimal design is found at the lowest hydrodynamic stable flow rates, where the mass transfer is fastest and the residence time in the column maximal.     

Qualitative and quantitative observations on the tubular reactor

The tubular reactor in the steady state is considered for a single chemical reaction. It is shown that almost all of the qualitative features of the temperature and concentration profiles may be deduced from the equations themselves without solving them. Extensive numerical calculations are also presented both for the finite and semi-infinite reactor. Comparisons are made with the lumped constant system. It is shown that the solution for the semi-infinite reactor is always unique and serves as a bounding solution for all finite reactors with the same parameters.     

Two‐phase model for continuous final‐stage melt polycondensation of poly(ethylene terephthalate). III. Modeling of multiple reactors with multiple reaction zones

A steady‐state two‐phase model has been developed for a continuous finishing stage of the melt polycondensation process that consists of two rotating‐disk reactors in series. Each reactor has multiple reaction zones with different types of rotating disks to establish plug flow profiles and to facilitate the removal of volatile reaction byproducts. The effect on reactor performance of varying the mass transfer parameter was found to be small for the reaction conditions used. The simulation results show that the use of two reactors offers increased flexibility in reactor operations to obtain the desired polymer properties. Although the proposed model has not been fully validated with experimental or plant data, it has illustrated that the complex multizone reactor system can be easily modeled by the two‐phase modeling technique and that added physical insights can be made through numerical model simulations. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 1088–1095, 2003     

新型连续乳液聚合反应器

介绍了4种主要连续乳液聚合反应器的研究新进展,包括连续搅拌釜式反应器、连续环管式反应器、脉冲填料塔式反应器及库爱特-泰勒旋流式反应器。提出了连续乳液聚合反应器的发展方向。     

Performance Enhancement by Unsteady‐State Reactor Operation: Theoretical Analysis for Two‐Sites Kinetic Model

Theoretical analysis of the reactor performance under unsteady‐state conditions was carried out. The reactions are described by two kinetic models, which involve the participation in catalytic reaction of two types of active sites. The kinetic model I assumes the blocking of one of the active sites by a reactant, and the kinetic model II suggests a transformation of active sites of one type into another under the influence of the reaction temperature. The unsteady‐state conditions on the catalyst surface are supposed to be created (i) by forced oscillations of temperature and concentration in the reactor inlet (periodic operation of reactor) and (ii) by catalyst circulation between two reactors in a dual‐reactor system (spatial regulation). The influence of various parameters like concentration of reactant, cycle split, length of period of forced oscillations, temperatures and the ratio of catalyst volumes in the dual‐reactor was investigated with respect to the yield of the desired product. It is shown that for both cases of unsteady‐state conditions (periodic reactor operation as well as in a dual‐reactor system), a mean reaction rate predicted by the kinetic model I was up to two times higher than the steady‐state value. The kinetic model II shows a 20 % increase of the selectivity towards the desired product.     

Multiple steady states in adiabatic tubular reactors with recycle

In this paper numerical and pseudo-analytical methods of determining the regions of MSS in adiabatic tubular reactors with recycle are presented. These methods are valid for the general case when not only R independent reactions occur but the feed flow rate in the reactor is also a function of the recycle ratio.     

Function space methods for analysis of nonadiabatic tubular reactors with axial mixing-I. Uniqueness criteria of the steady state and computation of the steady state profiles

Use is made of abstract function spaces to investigate the uniqueness of the steady state of nonadiabatic tubular reactors with axial mixing. For the study, the system differential equations are first transformed into integral equations. The properties of the integral operators are then investigated in the space of square integrable functions in order to obtain sufficient conditions for the uniqueness of solution of the system equations. A uniqueness criterion is obtained by use of the Contraction Mapping theorem, which permits one to compute the steady state profiles of reactor temperature and concentration by means of successive iteration with the transformed integral system equations. The computation involved here is quite simple compared to the numerical solution of the system differential equations with split boundary conditions. Numerical examples are given to investigate the effects of various system parameters on the steady state profiles of reactor temperature and concentration.