Input tracer signals

Figure 11.16 Modification of an input tracer signal on passing through three successive regions.

For ease of interpretation, it is important that the input tracer signal should be an ideal Dirac delta function. This is difficult to achieve manually, especially when distortion by peripheral equipment is taken into consideration. 

Because of the different paths taken by elements of a fluid to pass through a packed column, a residence-time distribution is generally obtained using a tracer signal at the bed input (salt, dyes), and by analysis of the output response [11]. A ical downstream signal is obtained, dependent on the kind of flow and mixing in the reactor (plug-flow reactor, mixed-flow reactor). The experimental distribution curve may be characterized in terms of mean and variance by ... 

Kinds oi Inputs Since a tracer material balance is represented by a linear differential equation, the response to anv one kind of input is derivable from some other known input, either analytically or numerically. Although in practice some arbitrary variation of input concentration with time may be employed, five mathematically simple input signals supply most needs. Impulse and step are defined in the Glossaiy (Table 23-3). Square pulse is changed at time a, kept constant for an interval, then reduced to the original value. Ramp is changed at a constant rate for a period of interest. A sinusoid is a signal that varies sinusoidally with time. Sinusoidal concentrations are not easy to achieve, but such variations of flow rate and temperature are treated in the vast literature of automatic control and may have potential in tracer studies. 

Solution This solution illustrates a possible definition of the delta function as the limit of an ordinary function. Disturb the reactor with a rectangular tracer pulse of duration At and height A/t so that A units of tracer are injected. The input signal is Cm = 0, t < 0 = A/Af, 0 < t < At ... 

The Piston Flow Reactor. Any input signal of an inert tracer is transmitted through a PFR without distortion but with a time delay of F seconds. When the input is a negative step change, the output will be a delayed negative step change. Thus, for a PFR,... 

Water is drawn from a lake, flows through a pump and passes down a long pipe in turbulent flow. A slug of tracer (not an ideal pulse input) enters the intake line at the lake, and is recorded downstream at two locations in the pipe L meters apart. The mean residence time of fluid between recording points is 100 sec, and variance of the two recorded signals is... 

The experimental technique used for finding this desired distribution of residence times of fluid in the vessel is a stimulus-response technique using tracer material in the flowing fluid. The stimulus or input signal is simply tracer introduced in a known manner into the fluid stream enter-... 

When the flow through a reactor or any other type of process vessel is non-ideal, experiments with non-reactive tracers can provide most valuable information on the nature of the flow. The injection of a tracer and the subsequent analysis of the exit stream is an example of the general stimulus-response methods described under Process Control in Chapter 7. In tracer experiments various input signals can be... 

Fio. 2.2. Tracer measurements types of input signals and output responses (a) Step input—F-curve (A) Pulse input—C-curve (c) Sinusoidal input... 

The observations described above indicate that, with good control, the concentration of the tracer particles in the out stream of the screw feeder can be determined to be a known function of time, and, furthermore, it is feasible to use such a known function as the input signal to the impinging stream equipment to be tested. In this way the experimental procedure can be greatly simplified. Of course, this scheme calls for corresponding mathematical relationship(s) for data interpretation. 

In order to protect the flow stability from turbulence caused by the input signal, the properties of the tracer used should be as close as possible to those of the process particles. In the investigation carried out by the author of this book the process particles are yellow millets while purplish-red rape seeds are used as the tracer, the properties of which are very similar those of the millets. The properties of the process and the tracer particles are listed in Table 3.1. The concentration of the tracer is represented in terms of mass fraction, and is measured by manually separating the tracer from the process particles according to the difference in color and weighing the amount of tracer. This is laborious and time-consuming work, but it can yield reliable data. 

Using the procedure described above, input a step change of the tracer to the hopper and then measure the response of the screw feeder to the step change as a known function of time, which is used as the input signal to the following impinging stream device for the measurement of RTD. 

The methods used in determining the RTD are an impulse signal and a step-change or a periodic input of the tracer. The following reviews these methods of injecting a tracer to analyze the RTD in flow systems. 

Inputs Although some arbitrary variation of input concentration with time may be employed, five mathematically simple tracer input signals meet most needs. These are impulse, step, square pulse (started at time a, kept constant for an interval, then reduced to the original value), ramp (increased at a constant rate for a period of interest), and sinusoidal. Sinusoidal inputs are difficult to generate experimentally. 

The extent of gas dispersion can usually be computed from experimentally measured gas residence time distribution. The dual probe detection method followed by least square regression of data in the time domain is effective in eliminating error introduced from the usual pulse technique which could not produce an ideal Delta function input (Wu, 1988). By this method, tracer is injected at a point in the fast bed, and tracer concentration is monitored downstream of the injection point by two sampling probes spaced a given distance apart, which are connected to two individual thermal conductivity cells. The response signal produced by the first probe is taken as the input to the second probe. The difference between the concentration-versus-time curves is used to describe gas mixing. 

The closed recirculation system shown below comprises of Z perfectly-mixed reactors of not the same volume. If a tracer is introduced in a form of a pulse input into the first reactor, the recorder will measure the tracer as it flows the first time, the second time, and so on. In fact, it measures a tracer which passed through Z reactors, 2Z reactors and so on, i.e. the superposition of all these signals. 

Let us first discuss the choice of input signals. The practical aspects of type of tracer for various situations is surveyed in Wen and Fan [2]. Also see Hougen [95] for an extensive discussion. The advantages and disadvantages of various types of signals are as follows. 

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]. 

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