Polymerization tubular reactor model

A theoretical polymerization tubular reactor model was used to study the effects of reactor operating parameters on conversion... 

For a practically useful tubular reactor model, the reacting (polymerizing) mixture is considered homogeneous and only axial dispersion is considered. At each specific position along the tube, perfect radial mixing and a uniform velocity profile are assumed. The tube, therefore, can be modeled as a one-dimensional tubular reactor. Also, instantaneous fluid dynamics are assumed because of the incompressibility of the liquid mixture (hence the calculation of the velocity profile is simplified). 

Temperature and free-radical concentration are important features that vary along the length of the plug-flow tubular reactor model of the polymerization of ethylene/ Stirred-tank reactor models of the anionic polymerization of styrene and of butadiene have been described and tested against experiments. Mathematical modelling of polymerization reactions receives some attention in the book by Froment and Bischoff. ... 

The computer model used for this analysis is based on a plug flow tubular reactor operating under restraints of the commonly accepted kinetic mechanism for polymerization reactions ( 5 ) ... 

Example 13.9 Illustrate temperature and molecular weight changes in a tubular reactor by constructing a simple model of styrene polymerization in a tube. 

Mathematical Modeling of Bulk and Solution Polymerization in a Tubular Reactor... 

Polymer production technology involves a diversity of products produced from even a single monomer. Polymerizations are carried out in a variety of reactor types batch, semi-batch and continuous flow stirred tank or tubular reactors. However, very few commercial or fundamental polymer or latex properties can be measured on-line. Therefore, if one aims to develop and apply control strategies to achieve desired polymer (or latex) property trajectories under such a variety of conditions, it is important to have a valid mechanistic model capable of predicting at least the major effects of the process variables. 

Tsai, K. and R. O. Fox (1993). PDF modeling of free-radical polymerization in an axisymmetric reactor. EES Report 254, Kansas State University, Manhattan, Kansas. (1994a). Modeling the effect of turbulent mixing on a series-parallel reaction in a tubular reactor. ICRES Report 9403, Kansas State University, Manhattan, Kansas. 

A complete analysis of the role of the radial distributions of all the parameters that determine the flow through a tubular reactor during polymerization is a very complicated, and it is doubtful whether general solutions can be found. However, solutions can be obtained for various situations for a system with known kinetic and rheological properties, because we will be searching for specific details rather than for a general physical picture of the process. It is also possible to carry out a general analysis at certain simplified models, which nevertheless include the principal rheokinetic effects. 

Now we shall discuss the method used to calculate the "cup"-averaged MWD-H, in which all portions of a polymerized liquid are mixed and averaged in a "cup" (vessel) positioned after the reactor. In this analysis, recourse was made to the so-called "suspension" model of a tubular reactor. According to this model, the reaction mass is regarded as an assemblage of immiscible microvolume batch reactors. Each of these microreactors moves along its own flow line. The most important point is that the duration of the reaction is different in each microreactor, as the residence time of each microvolume depends on its position at any given time, i.e., on its distance from the reactor axis. 

While vinyl acetate is normally polymerized in batch or continuous stirred tank reactors, continuous reactors offer the possibility of better heat transfer and more uniform quality. Tubular reactors have been used to produce polystyrene by a mass process (1, 2), and to produce emulsion polymers from styrene and styrene-butadiene (3 -6). The use of mixed emulsifiers to produce mono-disperse latexes has been applied to polyvinyl toluene (5). Dunn and Taylor have proposed that nucleation in seeded vinyl acetate emulsion is prevented by entrapment of oligomeric radicals by the seed particles (6j. Because of the solubility of vinyl acetate in water, Smith -Ewart kinetics (case 2) does not seem to apply, but the kinetic models developed by Ugelstad (7J and Friis (8 ) seem to be more appropriate. 

Polystyrene can be easily prepared by emulsion or suspension techniques. Harkins (1 ), Smith and Ewart(2) and Garden ( ) have described the mechanisms of emulsTon polymerization in batch reactors, and the results have been extended to a series of continuous stirred tank reactors (CSTR)( o Much information on continuous emulsion reactors Ts documented in the patent literature, with such innovations as use of a seed latex (5), use of pulsatile flow to reduce plugging of the tube ( ), and turbulent flow to reduce plugging (7 ). Feldon (8) discusses the tubular polymerization of SBR rubber wTth laminar flow (at Reynolds numbers of 660). There have been recent studies on continuous stirred tank reactors utilizing Smith-Ewart kinetics in a single CSTR ( ) as well as predictions of particle size distribution (10). Continuous tubular reactors have been examined for non-polymeric reactions (1 1 ) and polymeric reactions (12.1 31 The objective of this study was to develop a model for the continuous emulsion polymerization of styrene in a tubular reactor, and to verify the model with experimental data. 

The objective was to develop a model for continuous emulsion polymerization of styrene in tubular reactors which predicts the radial and axial profiles of temperature and concentration, and to verify the model using a 240 ft. long, 1/2 in. OD Stainless Steel Tubular reactor. The mathematical model (solved by numerical techniques on a digital computer and based on Smith-Ewart kinetics) accurately predicts the experimental conversion, except at low conversions. Hiqh soap level (1.0%) and low temperature (less than 70°C) permitted the reactor to perform without plugging, giving a uniform latex of 30% solids and up to 90% conversion, with a particle size of about 1000 K and a molecular weight of about 2 X 10 . 

PBE with both short and long branches are prepared from radical polymerization in the traditional high pressure process. These PE are called low density polyethylene (LDPE). A molecular model of a conformation of a typical LDPE is shown in Eig. 3.3. LDPE with different proportions of short and long branches are formed using autoclave or tubular reactors. There are many short branches with average... 

All these factors yield the following heat balance equation for the flow of a polymerizing liquid under specific geometric conditicms, particular, in a cylindrical tube (model of a tubular reactor) ... 

This nucleation/emulsifier utilization phenomena is one reason why batch kinetics and product characteristics are difficult to extrapolate from batch reactor to continuous stined-tank systems. A comparison of Equations (8.4) and (8.10) illustrates this in a quantitative manner for Smith-Ewart Case 2 kinetics. It should be noted that both formulation and operational variables (such as ) can influence nucleation and polymerization rates differently in the two reactor systems — even for the same kinetic model. One can change some aspects of this potential disadvantage of a CSTR by use of a small particle size seed in the feed stream or by placing a continuous tubular reactor upstream of the CSTR. These techniques can remove the nucleation phenomena tom the CSTR system which can then be used exclusively to grow the seed particles. 

Process models are also important components of reactor control schemes. Kiparissides et al. [17] and Penlidis et al. [16] have used reactor models for control simulation studies. Particle number and size characteristics are the most difficult latex properties to control. Particle nucleation can be very rapid and a strong function of the concentration of free emulsifier, electrolytes and various possible reagent impurities. Hence the control of particle number and the related particle surface areas can be a difficult problem. Even with on-line light scattering, chromatographic [18], surface tension and/or conversion measurements [19], control of nucleation in a CSTR system can be difficult. The use of a pre-made seed or an upstream tubular reactor can be utilized to avoid nucleation in the CSTR and thereby imjHOve particle number control as well as increase the number of particles formed [20-22]. Figures 8.6 and 8.7 illustrate open-loop CTSR systems for the emulsion polymerization of methyl methacrylate with and... 

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