Laminar flow reactors axial dispersion approximation

The molecule diffuses across the tube and samples many streamlines, some with high velocity and some with low velocity, during its stay in the reactor. It will travel with an average velocity near u and will emerge from the long reactor with a residence time close to F. The axial dispersion model is a reasonable approximation for overall dispersion in a long, laminar flow reactor. The appropriate value for D is known from theory ... 

We will now find the RDT for several models of tubular reactors. We noted previously that the perfect PFTR cannot in fact exist because, if flow in a tube is sufficiently fast for turbulence (Rco > 2100), then turbulent eddies cause considerable axial dispersion, while if flow is slow enough for laminar flow, then the parabolic flow profile causes considerable deviation from plug flow. We stated previously that we would ignore this contradiction, but now we will see how these effects alter the conversion from the plug-flow approximation. 

Equation 2 expresses whether radial diffusion, which in the case of laminar flow is due to molecular diffusion, is fast enough to outlevel radial concentration profiles. This approximation usually holds for monolithic reactors because of the rather small channel diameter. The corresponding axial dispersion coefficient can be calculated [1] from the following ... 

A tubular reactor with laminar flow has been mentioned as a good approximation to segregated flow. If the dispersion due to molecular diffusion is neglected, the approximation is exact. Since the flow is segregated and the velocity profile is known, the RTD can be calculated. It is instruc- tive to compare the calculated results with those for the ideal forms given in Fig. 6-5. The velocity in the axial direction for laminar flow is parabolic,... 

Solution Equation (6-22) gives the RTD, or (C/Co)step, for the laminar-flow tubular reactor. This equation, shown as a dashed line in Fig. 6-8, is in marked contrast to the dispersion curves. It is evident that introducing axial diffusion cannot account for the RTD given by segregated flow. The shape of the dashed curve is so different from those for the dispersion model that a value of DJuL cannot be chosen that will be even approximately correct. The effect on conversion of using a model which does not predict the correct RTD is illustrated in Sec. 6-7. 

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