The role of radial distributions

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. 

As a first approximation, the several authors assumed a fixed constant parabolic velocity profile.193,194 However, this approach is generally inadequate for a rheokinetic liquid because, first, real velocity profiles have a very different shape (as will be demonstrated below), and second, 

The intense heat dissipated by viscous flow near the walls of a tubular reactor leads to an increase in local temperature and acceleration of the chemical reaction, which also promotes an increase in temperature the local situation then propagates to the axis of the tubular reactor. This effect, which was discovered theoretically, may occur in practice in the flow of a highly viscous liquid with relatively weak dependence of viscosity on degree of conversion. However, it is questionable whether this approach could be applied to the flow of ethylene in a tubular reactor as was proposed in the original publication.199 In turbulent flow of a monomer, the near-wall zone is not physically distinct in a hydrodynamic sense, while for a laminar flow the growth of viscosity leads to a directly opposite tendency - a slowing-down of the flow near the walls. In addition, the nature of the viscosity-versus-conversion dependence rj(P) also influences the results of theoretical calculations. For example, although this factor was included in the calculations in Ref.,200 it did not affect the flow patterns because of the rather weak q(P) dependence for the system that was analyzed. 

The investigation by Lynn and Huff201 was the first one in which the true velocity profiles during polymerization in a tubular reactor were determined. The idea of the dependence of the hydrodynamic field on the varying rheokinetics during a chemical reaction is quite fruitful and has 

Second, if the flow rate is very high, we have breakthrough of the initial reactants that had insufficient time to react to reach any significant degree of conversion. Then we have a thin almost motionless near-wall layer of material with a high degree of conversion and a central fast stream of low viscosity material, which is close in chemical nature to the initial reactants, because the reaction time was too short. This situation is shown in the lower part of Fig. 4.25. 

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