Peclet number radial dispersion model

If one were to attempt to determine any communality in the discussion of models given in this chapter, about the best would be to say that the parameters invoked are derivatives of the model, as would be inferred from the titles of the previous sections. For example, there is the overall heat-transfer coefficient, h, that appears in the nonisothermal, one-dimensional axial dispersion model, which is not to be confused with the wall heat transfer coefficient, a y, that belongs to the radial dispersion model. Similarly, would the bed thermal conductivity be the same in an axial dispersion model as in a radial dispersion model What is the difference between a mass Peclet number and a thermal Peclet number and so on. In fact, let us take a moment... 

The main parameter in this model characterizing the quality of the flow is the axial dispersion coefficient. The term axial is used to distinguish mixing in the direction of flow from mixing in the radial direction. Then, based on this parameter, the particle Peclet number is introduced ... 

Axial dispersion is negligible. Whether this assumption is valid, can be seen from the Peclet number uJJD) for typical conditions = 1 m/sec, L = 0.5 m) and laminar flow, the Peclet number is larger than 1000, and even for turbulent flow it will be much larger than 10. In laminar flow, the radial flow profile within a subchannel will also result in deviation from plug flow. The effect of this deviation can be estimated by comparing the predictions from different mathematical models, one of which takes the flow profile into account and the other of which assumes plug flow. 

The Peclet number of radial dispersion was found to be between 8 and 15. as we have noted above. However, the axial Peclet number is about 2. which shows that the axial eddy diffusion coefficient is anywhere from four to seven times the radial coefficient Er. A very simple model gives some indication why this should be so. The flow through a packed bed has been described... 

Figure 31 shows the model analysis of the effects of radial gas dispersion coefficient on radial profiles of propylene concentration. The radial mass transfer has a significant effect on the conversion and yield. When the radial Peclet number decreases from 1400 to 200, the conversion of propylene increases by over 10%, and the yield of acrylonitrile increases by about 7%. Since the reaction is first order with respect to propylene, risers are operated under dilute conditions at Pe = 200, so the radial concentration distribution of propylene is uniform and radial mass transfer is not... 

This simply assumes that axial dispersion (D m. s ) is superimposed onto plug flow. Axial dispersion may be caused by a velocity profile in the radial direction or statistical dispersion in a packing or turbulent diffusion or by any physicochemical process which delayes some particles with respect to others. The model parameter is the axial PECLET number, Pe = uL/D, or its reciprocal, the dispersion number, D /uL. Depending on the boundary conditions assumed at the reactor inlet and outlet (which are different from those of the simple assumptions above), a lot of mathematical formulae can be found in the literature for the RTD [3]. This is often academic as in the range of usefulness of the model (small deviation from plug flow, say Pe > 20) all conditions lead to res-... 

Heat transfer coefficient for a one-dimensional model (ht) Wall coefficient for a two-dimensional model (/ ,) Radial Peclet number for mass dispersion ((Pe)r)... 

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