Flow regime axial dispersion

In practice, the process regime will often be less transparent than suggested by Table 1.4. As an example, a process may neither be diffusion nor reaction-rate limited, rather some intermediate regime may prevail. In addition, solid heat transfer, entrance flow or axial dispersion effects, which were neglected in the present study, may be superposed. In the analysis presented here only the leading-order effects were taken into account. As a result, the dependence of the characteristic quantities listed in Table 1.5 on the channel diameter will be more complex. For a detailed study of such more complex scenarios, computational fluid dynamics, to be discussed in Section 2.3, offers powerful tools and methods. However, the present analysis serves the purpose to differentiate the potential inherent in decreasing the characteristic dimensions of process equipment and to identify some cornerstones to be considered when attempting process intensification via size reduction. 

This model is referred to as the axial dispersed plug flow model or the longitudinal dispersed plug flow model. (Dg)j. ean be negleeted relative to (Dg)[ when the ratio of eolumn diameter to length is very small and the flow is in the turbulent regime. This model is widely used for ehemieal reaetors and other eontaeting deviees. 

Yerushalmi and Avidan (1985) suggest that the axial dispersion coefficient of solids in slugging and turbulent flow varies approximately linearly with the bed diameter, similar to Thiel and Potter (1978). The data are shown in Fig. 17 although May s results are probably in the bubbling fluidization regime rather than turbulent flow. 

Concerning the hydrodynamics and the dimensioning of the test reactor, some rules of thumb are a valuable aid for the experimentalist. It is important that the reactor is operated under plug-flow conditions in order to avoid axial dispersion and diffusion limitation phenomena. Again, it has to be made clear that in many cases testing of monolithic bodies such as metal gauzes, foam ceramics, or monoliths used for environmental catalysis, often needs to be performed in the laminar flow regime. 

The gas phase can be considered in a plug flow regime, and the axial dispersion can be calculated by the expression suggested by Mangartz and Pilhofer [39] ... 

Recommendations For a cylindrical packed bubble-column, the use of Eq. (7-23) for the calculation of axial dispersion coefficient in the liquid phase is recommended. The axial dispersion in the gas phase of large columns needs to be investigated. Future study on this subject should concentrate on the pulsed-flow regime and the hydrocarbon systems. 

Significant literature on the axiaj dispersion in gas and liquid phases for countercurrent-flow packed-bed columns have been reported. Trickle- and bubble-flow regimes have been considered. Unlike the holdup, there is quite a discrepancy in the results of various investigators. Almost all the RTD data are correlated by a single-parameter axial dispersion model. A summary of the reported axial dispersion studies in countercurrent flow through a packed bed is given in Table 8-1. 

In the homogeneous bubble flow regime, the gas phase is generally assumed to move in plug flow and the liquid phase axial mixing is characterized by the axial dispersion coefficient. The axial dispersion coefficient is dependent upon gas velocity and column diameter according to (26,41,42)... 

If the flow regime in the reactor has some mixing and/or dispersion and deviates slightly from plug flow conditions, then the mass balance can account for this with an axial dispersion model, a one-parameter model/ The material balance is shown below in Eq. (7). 

The dispersion in tubular reactors depends on the flow regime and is characterized by the Bodenstein number, the ratio of the axial diffusion time, tu,ax, in the reactor to the mean fluid residence time, x. 

For longer residence times, the axial convection inherent to the laminar flow regime starts to contribute more significantly to the dispersion process, especially when higher carrier stream flow rates are used, and a tendency of the sample zone towards a skewed Gaussian distribution due to the combined influences of convection and diffusion manifests itself in a more pronounced manner. 

Axial dispersion in packed beds, and Taylor dispersion of a tracer in a capillary tube, are described by the same form of the mass transfer equation. The Taylor dispersion problem, which was formulated in the early 1950s, corresponds to unsteady-state one-dimensional convection and two-dimensional diffusion of a tracer in a straight tube with circular cross section in the laminar flow regime. The microscopic form of the generalized mass transfer equation without chemical reaction is... 

---