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.     

Liquid‐phase axial dispersion of turbulent gas–liquid co‐current flow through screen‐type static mixers

This article discusses the characteristics of turbulent gas–liquid flow through tubular reactors/contactors equipped with screen‐type static mixers from a macromixing perspective. The effect of changing the reactor configuration, and the operating conditions, were investigated by using four different screen geometries of varying mesh numbers. Residence time distribution experiments were conducted in the turbulent regime (4500 < Re < 29,000). Using a deconvolution technique, the RTD function was extracted to quantify the axial/longitudinal liquid‐phase dispersion coefficient. The findings highlight that axial dispersion increases with an increasing flow rate and/or gas‐phase volume fraction. However, regardless of the number and geometry of the mixing elements, reactor configuration, and/or operating conditions, the recorded liquid‐phase axial dispersion coefficients in the presence of screens was lower than that for an empty pipe. Furthermore, the geometry of the screen was found to directly affect the axial dispersion coefficient in the reactor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1390–1403, 2017     

A mathematical model for the dehydrogenation of methylcyclohexane in a packed bed reactor

A model for the dehydrogenation of methylcyclohexane in a tubular reactor over an industrial catalyst Pt-Sn/Al₂O₃ has been established. This model takes into account the axial dispersion at the inlet of the catalytic bed reactor as well as the heat transfer at the wall of the reactor. The heat transfer at the wall is satisfactorily represented by using a heat transfer coefficient correlation for which the parameters are obtained by fitting to the experimental data. The model provides a good representation of the radial and axial temperature profiles in the packed bed and can be also used to calculate the conversion.     

Static mixers for laminar flow reactors with low aspect ratios

Conventional static mixers typically require high length to diameter ratios to be effective. This paper considers static mixers design to increase first appearance times in short, fat reactors. Three types are considered: conical baffles and annular baffles for tubular reactors and axial baffles for reactors with a rectangular cross-section. Relatively simple designs allow production increases (or reactor volume decreases) on the order of 20–50%.     

Polymerisation of methyl methacrylate in a pilot-scale tubular reactor: modelling and experimental studies

A pilot-scale tubular reactor fitted with in-line static mixers is experimentally and theoretically evaluated for the polymerisation of methyl methacrylate (MMA). A non-isothermal and non-adiabatic axially dispersed plug-flow model is used to describe the flow characteristics of the reactor. The model is applied to the polymerisation of a concentrated MMA solution (up to 72% (v/v)). Key model parameters were attained through independent bench and pilot-scale experiments. Measured monomer conversions and polymer molecular weight were accurately predicted by model simulation. The presence of static mixers is shown to give near-ideal plug-flow operation for the experimental conditions of this study. Furthermore, an approximately four-fold increase in overall heat transfer coefficient is indicated due to the radial mixing incited by the mixers. Studies also demonstrated the importance of inhibitor kinetics on the dynamic and steady-state performance of the reactor.     

Optimal Homotopy-Based Approximate Solutions for Process Systems Represented by the Axial Dispersion Model

An efficient variant of the homotopy analysis method, namely the optimal homotopy analysis method (OHAM), has been presented for the solution of chemical process systems that are represented by the axial dispersion model. To show its efficiency OHAM has been successfully applied to one of the popular chemical engineering systems, i.e., axial dispersion model of a tubular chemical reactor sustaining nonlinear kinetics. The obtained optimal homotopy results have been shown to agree closely with the numerically obtained results. The usefulness of OHAM has further been illustrated by effectively capturing multiple solutions, which frequently arise in non-monotonic kinetics. Convergence of the so-obtained OHAM results has also been discussed. It is also worthwhile to mention that the presented methodology of OHAM, with slight modification, can easily be extended to other engineering systems not represented by the axial dispersion model.     

A STUDY OF THE HIGH PRESSURE POLYETHYLENE TUBULAR REACTOR

As an example of the free radical polymerization reactor we have conducted a theoretical study of the high pressure polyethylene tubular reactor with cooling from the jacket. The plug flow model including the axial dispersion is considered with as well as without the steady state assumption for the active intermediates. We observe that the axial dispersion has negligible effect on the reactor performance and that the steady slate assumption is quite reasonable. The performance of the reactor is characterized by the exit monomer conversion, the peak temperature and the number and weight average degrees of polymerization, and the effects of various operating conditions are extensively investigated. Finally, an optimal temperature policy that would maximize the exit monomer conversion is determined by means of the Maximum Principle.     

Design And Efficiency Of Ozone Contactors For Disinfection

One commercial contact chamber which is designed for ozone disinfection has been tested for the following : determination of residence time distribution (RTD), measurement of dissolved ozone concentrations in water, and measurement total plate counts. Disinfection is achieved but this type of reactor is not ideal, due to dispersion of the residence time distribution. As these bubble contactors do not behave like plug flow reactors, it is possible to improve the hydrodynamics of ozone contactors with the use of static mixers. Experiments with ozone static mixers have been conducted.     

Motionless mixers for the design of multitubular polymerization reactors

Experimental investigations of thermal bulk polymerization of styrene in pilot plants of different sizes have been performed. Each pilot plant is composed of a tubular recycle reactor, connected in series with a tubular reactor, both completely filled with Sulzer motionless mixers. Kinetic, reactor and viscosity models have been verified in a wide range of styrene conversions (up to 96%) temperatures (up to 210 °C) and polystyrene molar masses (up to 360 000). Scale-up studies were carried out which confirmed that multitubular reactors of special design can be applied for industrial polymerization process.     

Micromixing effects on a parallel reaction in flow reactors

Using the micromixing concepts of Danckwerts and Zwietering, the Peclet number Pe has been correlated mathematically to the degree of segregation J for the axial dispersion model. The results were applied to compare the micromixing effects on a model, mixed-order parallel reaction system in continuous flow reactors. Axial dispersion model, and Ng and Rippin's two-environment model were used to find the micromixing effects in tubular and stirred tank reactors, respectively. The performance of these reactors, with varying geometries, has been evaluated in terms of overall conversion, selectivity, and yield under identical operating and reaction conditions. The overall conversion increases in a tubular reactor with the increase in J, irrespective of the kinetic orders. However, in a stirred tank reactor, the conversion is found to be micromixing-sensitive, depending on the order of reaction. For m = 1 and n = 2 (case 1), the conversion is fairly insensitive to micromixing effects while it decreases for m = 0.5 and n = 1 (case 2) with increasing J. For the same extent of micromixing, a tubular reactor gives, in both cases, a higher conversion than a stirred tank reactor. The selectivity, in either case, decreases in both reactors with increasing segregation effects. However, in each case, the selectivity of a tubular reactor was fairly close to that of a stirred tank reactor at the same value of J. As far as the yield is concerned, both reactors achieve nearly the same value, without significant micromixing effects.     

Mixing characteristics in the torus reactor

The hydrodynamic characteristics of propeller-induced toroidal flow in a loop reactor were investigated by performing an RTD analysis. The experimental determination of circulation time allows the calculation of the mean axial velocity with respect to the rotational speed of the impeller. RTD measurements are interpreted with the aid of the dispersion plug flow model, and it is shown that axial dispersion is relatively weak in the torus reactor. The mixing time was also determined experimentally and related to the circulation time. A direct relationship between mixing time and axial dispersion coefficient has been established, leading to a correlation for the mixing time in a torus reactor.     

PRODUCTION OF ETHANOL WITH SACCHAROMYCES CEREVISIAE IN A CONTINUOUS REACTOR Note II: tests and modelling for a packed tubular reactor with immobilized yeasts

The biochemical production of ethanol has been studied in a packed tubular reactor with Saccharomyces Cerevisiae immobilized on wooden cubes.

The kinetics of the reaction was described in a previous paper. The experimental axial profiles for the substrate and product concentrations are compared with those calculated from a reactor model obtained by introducing the biochemical kinetic expression in the design equations. A good fit between the experimental and the calculated values could only be obtained by including a biological efficiency coefficient.

The reactor was kept in operation for 28 days to assess its technological reliability. It was found to be biologically stable. Its productivity was constant and comparable to that reported in the literature for similar reactors.     

AN UNSTEADY-STATE TUBULAR REACTOR WITH THREE-DIMENSIONAL DISPERSION

A tubular reactor model with dispersion in three spatial dimensions, namely in the radial, axial and angular directions, is considered; and its analytical solution for an arbitrary non-uniform initial concentration distribution and an arbitrary non-uniform time-varying feed is obtained. Some special cases are deduced and the relationships between the three-dimensional dispersion model and two or one dimensional dispersion models are elucidated.     

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.     

The unsteady-state solution for a finite dispersion-type catalytic packed-bed tubular reactor

The unsteady-state solution is obtained by an operator theory in functional analysis setting for a general finite catalytic packed-bed tubular reactor model with axial dispersion in the bed, mass transfer between the catalyst particles and the flowing phase, and intraparticle diffusion and surface reaction in the catalyst particles.     

Dynamic modelling of a gas phase catalytic fixed-bed reactor—I: Experimental apparatus and determination of reaction kinetics

A large scale fixed bed pilot reactor for performing dynamic experiments is described. The reactor system is especially designed to suppress secondary dispersion effects not characteristic for the packed bed itself.As a model reaction the reaction between oxygen (<1%) and hydrogen on a platinum catalyst supported by alumina has been used.Differential reactor experiments disclosed a hysteresis phenomenon in the catalyst activity. The catalyst is generally more active when going from high to low temperatures than vice versa.A global first order reaction rate expression with Arrhenius temperature dependency fits the fixed-bed reactor profiles well but the static gains badly. However by simultaneous estimation of frequency factor and activation energy in several axial segments a much better approximation to the static gains was obtained. This result indicates that the reaction kinetics is more complicated than first assumed. However for dynamic modelling the exact reaction mechanism is not needed.     

Tubular reactor design—I Two dimensional model

Conservation equations for a packed tubular reactor are modelled using a radially varying axial velocity, radial diffusivity and radial thermal conductivity. Radial diffusivity and thermal conductivity profiles are obtained from relations presented in this work. Instead of using a wall heat transfer coefficient, the model accounts for the higher resistance to heat flow near the reactor wall by using a lower value of the thermal conductivity. Axial diffusion is not included in the bulk of the bed, but its effect on the inlet temperature and conversion profiles are accounted for by considering axial diffusion in the pre-reaction zone.The two partial differential equations are converted into ordinary differential equations by using orthogonal collocation in the radial direction. The conventional orthogonal collocation method is modified by adding balance equations at the center of the tube, so as to improve the prediction of hot spot temperature.The model was applied to the sulfur dioxide reactor of Schuler et al. The results agreed quite well with the experimental data without the need for adjustment of parameters or constants.     

Comparative analysis of different static mixers performance by CFD technique: An innovative mixer

The flow and mixing behavior of two miscible liquids has been studied in an innovative static mixer by using CFD,with Reynolds numbers ranging from 20 to 160. The performance of the new mixer is compared with those of Kenics, SMX, and Komax static mixers. The pressure drop ratio(Z-factor), coefficient of variation(CoV), and extensional efficiency(α) features have been used to evaluate power consumption, distributive mixing, and dispersive mixing performances, respectively, in all mixers. The model is firstly validated based on experimental data measured for the pressure drop ratio and the coefficient of variation. CFD results are consistent with measured data and those obtained by available correlations in the literature. The new mixer shows a superior mixing performance compared to the other mixers.     

ISOTHERMAL AXIAL DISPERSION REACTORS IN COAL LIQUEFACTION HYDROPROCESSING

The purpose of this study is to provide a better understanding of reactors for hydroprocessing of liquid-solid mixtures, and to assist in the design and scale-up of large scale reactors from the information obtained from small scale experimental units. The paper describes a linear, isothermal, cocurrent upflow tubular reactor model with axial dispersion. The model is applied to coal liquefaction, assuming that the complex liquefaction kinetics can be represented by five lumped components-six first order reactions, and that the three phase (coal-solvent-gas) flow can be approximated by a two phase (slurry-gas)flow.     

ISOTHERMAL AXIAL DISPERSION REACTORS IN COAL LIQUEFACTION HYDROPROCESSING

The purpose of this study is to provide a better understanding of reactors for hydroprocessing of liquid-solid mixtures, and to assist in the design and scale-up of large scale reactors from the information obtained from small scale experimental units. The paper describes a linear, isothermal, cocurrent upflow tubular reactor model with axial dispersion. The model is applied to coal liquefaction, assuming that the complex liquefaction kinetics can be represented by five lumped components-six first order reactions, and that the three phase (coal-solvent-gas) flow can be approximated by a two phase (slurry-gas)flow.