Model for the overall residence time distribution

In the impinging stream contactor shown in Fig. 3.1 the particles pass through the four sub-spaccs in series described above, and the overall residence time distribution 

Note that, for the dynamic response, both t -dL and t rai are transfer lag time, also called pure lag time. For convenience, the total lag time, )a , is defined as 

According to the nature of residence time distribution, the following relationship should hold  

On the other hand, the first convolution integral in Eq. (3.22) can be found by Laplace transformation and its inversion, as 

Substituting Eqs. (3.25) and (3.27) into Eq. (3.19) and solving the resulting expression for the final yield 

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This is the model for the overall residence time distribution of the particles in the impinging stream contactor under consideration. The model contains several parameters related to equipment structure and operating conditions, i.e. the mean residence times in the four sub-spaces, 7ac, 7im, 7fai and cs. Among the four parameters, the mean residence time in the impingement zone, t m, and that in the collision-slipping region, fcs, are symmetrical parameters, which have the same influence on the overall residence time distribution. It can be seen from Eq. (3.27) or... 

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