Applications and limitations of the dispersed plug-flow model

Applications and Limitations of the Dispersed Plug-Flow Model 

When DJuL is found to be large and the tracer response curve is skewed, as in Fig. 2.23b, but without a significant delay, a continuous stirred-tanks in series model (Section 2.3.2), may be found to be more appropriate. The tracer response curve will then resemble one of those in Fig. 2.8 or Fig. 2.9. The variance a2 of such a curve with a mean of tc is related to the number of tanks / by the expression a2 = t2/i (which can be shown for example by the Laplace transform method 7 from the equations set out in Section 2.3.2). Calculations of the mean and variance of an experimental curve can be used to determine either a dispersion coefficient Dl or a number of tanks i. Thus each of the models can be described as a one parameter model , the parameter being DL in the one case and i in the other. It should be noted that the value of i calculated in this way will not necessarily be integral but this can be accommodated in the more mathematically general form of the tanks-in-series model as described by Nauman and Buffham 7 . 

In conclusion the following example shows how a real stirred tank might be modelled0 6). 

As a model of a certain poorly agitated continuous stirred-tank reactor of total volume V, it is supposed that only a fraction w is well mixed, the remainder being a dead-water zone. Furthermore, a fraction / of the total volume flowrate v fed to the tank by-passes the well-mixed zone completely (Fig. 2.24a). 

Next consider mixing of this stream with the by-pass giving a final exit concentration Cex. 

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