Pulse input tracer experiment

FIGURE 3-18 Dispersion of a continuous tracer injection in a sand column experiment. The behavior of a front of the tracer is shown in the next to last panel tracer concentration is presented as a function of distance at fixed times t0 and t1. A breakthrough curve, a plot of concentration as a function of time at a fixed point, is shown in the bottom panel. (Compare with Fig. 3-28, which shows breakthrough curves for pulse inputs.)... 

The curve fitting procedure used (7, has one other adjustable parameter, pulse input, or number of pore volumes for which the contaminant was fed. As column pore volume was known from independently measurements, pulse input was fixed rather than fit. That is, particle and bulk density of the packing were known from prior measurements, pore volume was determined for each column by weighing dry versus wet, and flow velocity was measured for each experiment. Further, fitted conservative-tracer breakthrough curves gave R = I, suggesting that pulse input and pore volume measurements were consistent. 

A second type of experiment often used in the determination of RTD is the response to a pulse input of tracer rather than a step function. Here a total quantity, Q, of the tracer is injected into the feed stream at a concentration of Q over a small time period At. Differing residence times of molecules in the system will lead to a dispersion of the pulse with typical response curves shown in the C-diagram of Figure 4.4, corresponding to those illustrated in Figure 4.3. The response of the C(t) curves of Figure 4.4 is just the derivative of the F t) curves in Figure 4.3. 

Since tracer experiments are used to obtain RTD functions, we wish to establish that the response to a pulse-tracer input is related to (r) or E(0). For this purpose, c(t) must be normalized appropriately. We call c(t), in arbitrary units, the nonnormalized response, and define a normalized response C(t) by... 

Two types of tracer experiments are commonly employed and they are the input of a pulse or a step function. Figure 8.2.1 illustrates the exit concentration curves and thus the shape of the (f)-curves (same shape as exit concentration curve) for an impulse input. Figure 8.2.2 shows the exit concentration for a step input of tracer. The (r)-curve for this case is related to the time derivative of the exit concentration. 

A non-intrusive method for RTD characterization has been claimed [17], which has been proven already for visualization of velocity fields in microchannels [18]. Aphoto-activated fluorescent dye dissolved in an aqueous solution is introduced continuously into a flow. A defined section of the inlet channel is exposed to a UV pulse to activate the tracer, which turns fluorescent Due to this inside start of the pulse experiment, artifacts from peripheral equipment can be eliminated. The method generates almost ideal input signals, which simplifies the numerical treatment of experimental data. The new approach was found to be superior to various traditional injection methods. The ideal shape of the stimulus signal was demonstrated for an analytically well-defined straight channel and compared with a signal derived from deconvolution of non-ideal input signals [19]. 

When a steady stream of fluid flows through a vessel, different elements of the fluid spend different times within it. The time spent by each fluid element can be identified by an inert tracer experiment, where a pulse or a step input of a tracer is injected into the flow stream, and the concentration of the pulse in the effluent is detected. As the reader may quickly infer, the tracer must leave the PFR undisturbed. On the other hand, a step pulse may give rise to an exponential distribution in a CSTR. In the beginning of this chapter, we already demonstrated that PFR behavior approaches that of a CSTR under infinite recycle. It follows that infinite CSTRs in series behave like a PFR. Thus, we conclude that any nonideal reactor can be represented as a combination of the PFR and MFR to a certain degree. First, let us show a representative pulse response curve for each of the ideal reactors in Figure 3.5. As seen in the figure, the response to a step input of tracer in a PFR is identical to the input function, whereas the response in a CSTR exhibits an exponential decay. The response curves as shown in Figure 3.5 are called washout functions. The input function of the inert tracer concentration [/] can be mathematically expressed as... 

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