Reactor dispersion number

A more precise appreciation of conditions in the reactor can be gained from the reactor dispersion number (see Sect. 3.3 of this chapter and Sect. 5.4 of Chap. 6). 

Using the chart given by Levenspiel [2], a value of Re = 4 x 10 corresponds to D ud 0.3 and thus the reactor dispersion number... 

With this value of the reactor dispersion number, the departure from true plug flow in the reactor will be very small. 

With the same aspect ratio as before, this corresponds to a Reynolds number of about lO" and flow will again be turbulent. The reactor dispersion number is 0.002, which again implies that the performance of the actual reactor will be very close to that calculated on the basis of the plug-flow assumption. 

For a particular reactor, the dispersion number can be determined by analysis of the response at the reactor outlet to the injection of a tracer at the inlet. The procedure is fully described in Chap. 6. Alternatively, use may be made of published correlations [2], which give the reactor dispersion number as a function of either the Reynolds number or the product of the Reynolds and Schmidt numbers. Once a value of the reactor dispersion number is available, it can be used in one of the following ways to determine reactor performance for particular cases. 

Figure 4.16. Concentration profiles in the tubular reactor for extreme and intermediate values of the dispersion number. 

The term Lu / D is known as the Peclet number, Pe, and its inverse as the dispersion number. The magnitude of the Peclet number defines the degree of axial mixing in the reactor. 

It may be that the extent of dispersion is to be determined from correlations rather than by direct experimental means. Suitable correlations based on large quantities of data exist for common reactor geometries, i.e. tubular reactors, both empty and packed, fluidised beds or bubble columns. Some of these are expressed in graphical form in, for instance, refs. 17, 21 and 26. Most forms of correlation give the intensity of dispersion D/ud as a function of Reynolds and/or Schmidt numbers if this intensity is multiplied by an aspect ratio, i.e. djL for a tubular reactor, then the dispersion number is obtained. 

Find the vessel dispersion number in a fixed-bed reactor packed with 0.625-cm catalyst pellets. For this purpose tracer experiments are run in equipment shown in Fig. E13.3. 

RTD studies were carried out by Jagadeesh and Satyanarayana (lEC/PDD 11 520, 1972) in a tubular reactor (L = 1.21 m, 35 mm ID). A squirt of NaCl solution (5 N) was rapidly injected at the reactor entrance, and mixing cup measurements were taken at the exit. From the following results calculate the vessel dispersion number also the fraction of reactor volume taken up by the baffles. 

Flow patterns in the reactor can vary greatly. To characterize backmixing, of the longitudinal dispersion number, D/uL, is often used,... 

The dimensionless group Del/uL is known as the dispersion number and is the parameter that measures the extent of axial dispersion. The degree to which axial dispersion influences the performance of a chemical reactor is determined by the value of the Peclet number (NPe). A high value of NPe corresponds to a slightly dispersed reactor. That is,... 

The various tanks are characterized by different dispersion numbers. If the overflow rate, which was set to 0.58 m/h for the investigations reported in Figure 3, is increased, then the absolute values of the dispersion number will also change, generally to larger values. Some reactors show a more noticeable effect than others (5). 

Reactor theory yields the basis for an evaluation of the meaning of the dispersion number very small values indicate that the flow regime increasingly... 

In a large-scale operation there is a continuum of particles and floes in the separation reactor. However, the concentrations of aggregates are not necessarily larger if mixing is neglected, which can occur in a first approximation to the observed dispersion numbers. This technical deviation seemed necessary from an analytical point of view and was considered acceptable. 

These suspensions were separated with varying efficacy in the tanks investigated. Tank C, for instance, a so-called upflow clarifier, has been identified as a reactor with a relatively stable flow structure. It showed little change in dispersion number when the hydraulic surface loading was increased, but very high values of removal efficiency over the whole range of chemical conditions investigated. 

For reactors in which the dispersion number varies significantly with changing hydraulic loading (i.e., less stable hydraulics) the effectiveness of the floe formation process is more significant than for other reactor types. 

The second-order differential equation is solved with a numerical differential equation solver. The dispersion number is estimated by first predicting the particle Peclet number, Pe, from the equation above. Then, the value of the reactor Peclet number, Pe, is predicted from the particle Peclet number Pe by multiplying by the ratio of the particle diameter, dp, to the reactor length, L. Pe is the only parameter required to solve the dispersion model equation. 

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