Tracer input curve

Obtain the tracer response curve to a step input disturbance of tracer solution by setting k = 0. 

The tracer response curve of an impulse input to a reactor has the... 

The tracer response curve of impulse input to a reactor is a trapezoid with the given equations. For a second order reaction with kC0 = 2, find the... 

A reactor has a tracer response curve from an impulse input with the equation C = 0.5 cos(-nt/4) over the range 0 t 2. A reaction A= B=>C with k2 =... 

This additivity property of variances also allows us to treat any one-shot tracer input, no matter what its shape, and to extract from it the variance of the E curve of the vessel. So, on referring to Fig. 13.6, if we write for a one-shot input... 

FINDING THE VESSEL E CURVE USING A SLOPPY TRACER INPUT... 

C Curve—The Response to an Instantaneous Pulse Tracer Input... 

When we talk about tracers, we generally mean conservative tracers with no sources or sinks. This is opposed to gas tracers, with gas transfer to the atmosphere, and reactive tracers, with a reaction occurring. Tracer studies typically use a conservative tracer, input to the system in a highly unsteady manner, such as a pulse or a front. The pulse and front are typically a more stringent test of the model than a steady-state process with any variety of reactions. Thus, a model that properly simulates the output concentration curve of a pulse or front is assumed to be sufficient for most real conditions with reactions. 

In the vast majority of experimental studies, the backmixing characteristics of a flowing phase are examined using a -pulse tracer input. For the fixed-bed systems shown in Fig. 3-2, if a perfect pulse input is used, then, as shown by Levenspiel,5 6 the axial dispersion coefficient or the Peclet number can be obtained from the variance of the RTD curve. For example, for a closed system and large extent of dispersion, the variance, it, is related to the Peclet number by the equation... 

The function f(t) is straightforwardly related to the experimental tracer response curve for a slug input, the downstream concentration vs. time curve is proportional to the function f(t). Response curves for different modes of input theoretically convey equivalent information, although certain inputs are experimentally convenient to carry out. Thus, redoing tracer experiments for different inputs gives no added information about the flow. 

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. 

Tracer concentration for step test, (a) Tracer input concentration, (b) Tracer output concentration (C-curve). 

F(t) is a probability distribution which can be obtained directly from measurements of the system s response in the outflow to a step-up tracer input in the inflow. Consider that at time t = 0 we start introducing a red dye at the entrance of the vessel into a steady flow rate Q of white carrier fluid. The concentration of the red dye in the inlet flow is C. At the outlet we monitor the concentration of the red dye, C(t . If our system is closed, i.e. if every molecule of dye can have only one entry and exit from the system (which is equivalent to asserting that input and output occur by convection only), then QC(t)/QCQ is the residence time distribution of the dye. This is evident since all molecules of the dye appearing at the exit at time t must have entered into the system between time 0 and time t and hence have residence times less than t. Only if our red dye is a perfect tracer, i.e.. if it behaves identically to the white carrier fluid, then we have also obtained the residence time distribution for the carrier fluid and F(t) = C(t)/C. To prove that the tracer behaves ideally and that the F curve is obtained, the experiment should be repeated at different levels of C. The ratio C(t)/C at a given time should be invariant to C, i.e. the tracer response and tracer input must be linearly related. If this is not the case, then C(t)/CQ is only the step response for the tracer, which includes some nonlinear effects of tracer interactions in the system, and which does not represent the true residence time distribution for the system. 

One method of characterising the residence time distribution is by means of the E-curve or external-age distribution function. This defines the fraction of material in the reactor exit which has spent time between t and t -i- dt in the reactor. The response to a pulse input of tracer in the inlet flow to the reactor gives rise to an outlet response in the form of an E-curve. This is shown below in Fig. 3.20. 

Figure 3.20. E-curve response to pulse input of tracer.

Derive the F(t) curve for a CSTR by considering its response to a step change in the input tracer concentration. Let Wq and represent the weight fraction tracer in the feed before and... 

A test with an impulse input of tracer gave a parabolic response curve... 

The response curve to an impulse input of tracer is a triangle with the equations... 

The effluent curve of a vessel to which an impulse of tracer has been injected has a straight line portion and a semicircle. E(t) and F t) are to be found. The equations of the input are,... 

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