Tracer imperfect pulse

Fig. 21. Two-station measurement the system is tested with an imperfect pulse of tracer.

The inlet concentration most often takes the form of either a perfect pitlse input (Dirac delta function), imperfect pulse injection (see Figure 13-4), or a step input-Just as the RTD function (/) can be determined directly from a pulse input, the cumulative distribution Fit) can be determined directly from a step input. We will now analyze a step input in the tracer concentration for a system with a constant volumetric flow rate. Consider a constant rate of tracer addition to a feed that is initiated at time t = 0. Before this time no tracer was added to the feed, Stated symbolically, we have... 

Imperfect pulse technique was applied [29,30] to study the residence time distribution in the gas phase. Helium was injected in the air stream at the entrance, and tracer concentration was determined at the exit stream. At zero solid mass flux (i.e., no flowing solids in the system), the Bodenstein number (Bog = Ugds/Dgs) was found to be close to the value of 2, so that the height of one Pall rings layer corresponds to a single ideally mixed unit [29,30]. 

What made Danckwert s theory very successful is that E(t) and the related distributions can be experimentally measured by means of tracers. In particular, E(t) appears as the response of the reactor to a unit-pulse injection. of tracer. The flow-system may thus be considered as a linear dynamic system (with respect to tracer concentration) and all the resources of Systems Dynamics can be used for identifying E(t) from tracer experiments. In particular, the response y(t) to an imperfect pulse injection is given by the convolution product... 

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