Tube Flow Reactor With Axial Dispersion

The model for the tank cascade starts with one CSTR coupled with a second stage and so on. Alternatively, we shall begin with a PFR model which is extended by a dispersion term:

dT dx dx2

By using the Peclet number: w L

Dx the tracer balance can be written in dimensionless form:

For a flow reactor with sludge recycle: Pe=W(1+nR)L (6.80)

Dx must be introduced instead of Eq. (6.99). One initial and two boundary conditions are needed.

Several different types of boundary conditions exist (Wen and Fan 1975). We want to limit the discussion only to the type of boundary condition "closed, closed". Closed boundary means, that in both tubes at the left and right side of the reactor (see Fig. 6.7) are no concentration gradient because of the low section area compared with that inside the reactor.

These boundary conditions are:

The first analytical solution of Eq. (6.98) respectively Eq. (6.100) was published by Danckwerts 1955. We only want to present this solution in graphical form (Wen and Fan 1975):

Pe' = — = 0 Dx characterizes the limit for DxPwL, which agrees with the signal of a CSTR, In contrast to that, Pe'; e shows the signal of a ideal plug flow reactor without an axial mixture.

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