Further development of tracer injection theory

Some interesting and useful conclusions can be drawn from further examination of the response of a system to an input of tracer although the mathematical derivation of these conclusions 7 is too involved to be considered here. 

In the early days of the development of the dispersed plug-flow model, there was considerable controversy over the precise formulation of the boundary conditions 

The exact formulation of the inlet and outlet boundary conditions becomes important only if the dispersion number (DjuL) is large ( 0.01). Fortunately, when DjuL is small ( 0.01) and the C-curve approximates to a normal Gaussian distribution, differences in behaviour between open and closed types of boundary condition are not significant. Also, for small dispersion numbers DjuL it has been shown rather surprisingly that we do not need to have ideal pulse injection in order to obtain dispersion coefficients from C-curves. A tracer pulse of any arbitrary shape is introduced at any convenient point upstream and the concentration measured over a period of time at both inlet and outlet of a reaction vessel whose dispersion characteristics are to be determined, as in Fig. 2.18. The means 7in and fout and the variances and out for each of the C-curves are found. 

In order to investigate the dispersion characteristics of a reaction vessel, a non-reactive tracer is injected at a convenient location some way upstream from the inlet to the vessel. Subsequently, samples (taken over very short periods of time) are collected from two positions, one being the inlet pipe to the vessel, the other at the vessel outlet, with the following results  

Estimate (i) the mean residence time in the vessel and (ii) the value of the dispersion number for the vessel. 

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