Tracer response curves

Ross (R2) measured liquid-phase holdup and residence-time distribution by a tracer-pulse technique. Experiments were carried out for cocurrent flow in model columns of 2- and 4-in. diameter with air and water as fluid media, as well as in pilot-scale and industrial-scale reactors of 2-in. and 6.5-ft diameters used for the catalytic hydrogenation of petroleum fractions. The columns were packed with commercial cylindrical catalyst pellets of -in. diameter and length. The liquid holdup was from 40 to 50% of total bed volume for nominal liquid velocities from 8 to 200 ft/hr in the model reactors, from 26 to 32% of volume for nominal liquid velocities from 6 to 10.5 ft/hr in the pilot unit, and from 20 to 27 % for nominal liquid velocities from 27.9 to 68.6 ft/hr in the industrial unit. In that work, a few sets of results of residence-time distribution experiments are reported in graphical form, as tracer-response curves. 

The forms of actual tracer response curves may be used to formulate models of the actual mixing processes in the reactor. One has, however, to be careful since the tracer response curve does not give a unique solution. It does, for example, not allow one to distinguish between early and late mixing, which may be important when used in the estimation of conversion in a particular reactor-reaction system. 

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

Tracer response curve. Reprinted from M. J. Hopkins, A. J. Sheppard and P. Eisenklam, Chem. Eng. Sci., 24 (1131), 1969. Used with permission of Pergamon Press, Ltd. 

Determining Pe, from Tracer Data As noted in Section 19.4.2.2.1, values of PeL, the single parameter in the axial dispersion model, may be obtained from the characteristics of the pulse-tracer response curve, C(0) = E(6). 

The impulse tracer response curve of a pilot plant reactor has the shape of a trapezoid with the given equations. A first order reaction conducted in... 

A tracer response curve is made up of two quarter circles with the equat ions... 

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 tracer response curve in the shape of a trapezoid with a right angle has the given equations. Find the conversion of a second order reaction with kC0 = 1.25 under segregated flow conditions (a) with the directly evaluated RTD (b) with a Gamma RTD having the same Variance. 

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 =... 

For a tracer response curve with cr2(tr) = 0.2 compare segregated... 

In Sect. 4.1, we examine how to predict theoretically the form of a tracer response curve and find that a convolution integral is involved. The equivalent, but much more simple, calculation in the Laplace domain is then made and is shown to give identical results. 

We are now in the position of being able to predict the form of tracer response curves from systems for which we have theoretical descriptions. From these curves we can recover the system RTD the details of the processing method required to achieve this will depend on the forcing function in question and Sects. 3.2.1—3.2.5 have considered the most common of these. In addition, we have seen in Example 1 how raw experimental measurements can be processed to give E(f) or E(0) data in the absence of any theoretical model. In this section, we now see how to use theoretical or experimental RTD data to predict the conversion which will be expected when a reaction with known kinetics takes place under steady-state conditions in the system under consideration. 

From the measured pulse tracer response curves (see figure), find the fraction of gas, of flowing liquid, and of stagnant liquid in the gas-liquid contactor shown in Fig. E12.1. 

Figure 13.8 Tracer response curves for closed vessels and large deviations from plug flow.

As mentioned earlier, obtaining and interpreting the actual experimental flow pattern is usually impractical. Hence, the approach taken is to postulate a flow model which reasonably approximates real flow, and then use this flow model for predictive purposes. Naturally, if a flow model closely reflects a real situation, its predicted response curves will closely match the tracer-response curve of the real vessel this is one of the requirements in selecting a satisfactory model. 

In the preceding section we discussed the dispersion model which can account for small deviations from plug flow. It happens that a series of perfectly mixed tanks (backmix flow) will give tracer response curves that are somewhat similar in shape to those found from the dispersion model. Thus, either type of model could be used to correlate experimental tracer data. 

Using the completely stagnant interpretation of deadwater regions, Fig. 23 illustrates some simple combined models and their tracer-response curves. In these models Vh, Vp, and Va stand for the volume of backmix, plug flow, and deadwater regions. If V is the volume of vessel we then have... 

The two single-parameter models give RTD s which are somewhat different from each other, although at this low dispersion the differences are small. Neither of the two models fits the RTD obtained Irum the tracer response curve. 

Fig. 2.23. Types of tracer response curves showing indications that the dispersed plug-flow model is unlikely to be applicable, (a) two maxima (6) very skewed (c) long tail...

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