Tracer pulse

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. 

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 ... 

Figure 3.27. Tracer pulse response of a tanks-in-series system with and without dead zones.

The residence time distributions can be measured by applying tracer pulses and step changes as explained in Sec. 3.2.9. The response curves are best normalised such that the dimensionless time is... 

Solution of equation (10) which involves sedimentation in the presence of mixing and that of equation (11) which contains the sedimentation term only, are exponential in nature. The major conclusion which arises from this is that the logarithmic nature of the activity-depth profiles by itself is not a guarantee for undisturbed particle by particle sediment accumulation, as has often been assumed. The effects of mixing and sedimentation on the radionuclide distribution in the sediment column have to be resolved to obtain pertinent information on the sediment accumulation rates. (It is pertinent to mention here that recently Guinasso and Schink [65] have developed a detailed mathematical model to calculate the depth profiles of a non-radioactive transient tracer pulse deposited on the sediment surface. Their model is yet to be applied in detail for radionuclides. )... 

The E-curve is evaluated by measuring experimentally the outlet tracer concentration versus time curve from a tracer pulse input and applying the following defining equation... 

Evaluate the conversion for first-order reaction from a tracer pulse response curve using the method in example CSTRPULSE. Show that although the residence time distributions may be the same in the two cases, the overall chemical conversion is not, excepting for the case of first-order reaction. 

In studying residence time distribution in a tank-flow electrolyzer, a tracer injected into it is recovered in a mixing tank placed downstream. If both tanks are perfectly stirred, then with a tracer pulse, the mole balance for the tracer can be written as... 

A computational model will be developed for numerous water quality parameters in the Platte River, Nebraska. In many locations, this river splits into multiple channels that are joined back together downstream. One significant split is the Kearney Canal diversion, illustrated in Figure E6.7.1, where 20% of the flow splits off into a second river at the city of Overton, only to return 20 km downstream at the city of Kearney. A tracer pulse was put into the river at location x = 0 and time t = 0, upstream of the diversion. Downstream of the diversion s return, the pulse at location x = 25 km is given in Figure E6.7.2. Develop a model for this reach that contains equal size tanks-in-series for the main channel and a similar number of tanks-in-series with the addition of a possible plug flow for the side channel, as illustrated in Figure E6.7.3. 

Figure E6.7.2. Results of a tracer pulse in the Overton-Kearney reach of the Platte River.

The information provided in Figure E6.7.2 was computed with the tracer pulse curves applied to the following equations ... 

There are many real-life situations resulting in a tracer pulse or front with a long tail, where the pulse or front does not decay nearly as quickly as it rises. The fit of the tanks-in-series to the tracer pulse in Example 6.7 is typical of the trailing edge problem. These can be solved by employing a leaky dead-zone model. There are physical arrangements of transport problems where the need of a leaky dead zone seems apparent, such as a side embayment on a lake or river, or a stratified lake where a well-mixed reactor will be used to model the lake. These are illustrated in... 

Figure 6.8. Circumstances requiring a leaky dead zone for a model that has minimal bias in fitting a tracer pulse.

Figure 6.8. But, the need of a leaky dead zone is more ubiquitous than these examples imply. To develop a model with a fit, which does not have a strong bias at certain parts of a tracer pulse curve for any reactor or river, for example, a leaky dead zone is a better model.

The concept of a leaky dead zone is illustrated in Figure 6.9. A complete mix reactor is connected to a leaky dead zone through the inflow and outflow discharges to and from the dead zone, Qd. The dead zone is, in itself, a complete mix reactor, but it is not part of the main flow system with discharge Q. The independent parameters that can be ht to a tracer pulse or front are the volume of the primary complete mix reactor, Vi, the volume of the dead zone, Vd, and the discharge into and out of the dead zone, Qd. 

Table E6.10.1 Time response of the air-stripping tower output after a conservative tracer pulse input att = 0...

The plug flow with dispersion model results in a degradation to 3.4% of the inflow trichloroethylene concentration. This is significantly different than the plug flow model (1.0%). It is also a more accurate solution. Whether it is the tail of a tracer pulse or a reaction that approaches complete degradation, one needs to be careful about applying the plug flow model when low concentrations, relative to the inflow, are important. 

Figure 9.1. Gas tracer pulses for the James River (North Dakota) used to measure the reaeration coefficient. GC, gas chromatograph SFe, suiter hexafloride.

In Reprint C in Chapter 7, the behavior of a tracer pulse in a stream flowing through a packed bed and exchanging heat or matter with the particles is studied. It is shown that the diffusion in the particles makes a contribution to the apparent dispersion coefficient that is proportional to v2 fi/D. The constant of proportionality has one part that is a function of the kinematic wave speed fi, but otherwise only a factor that depends on the shape of the particle (see p. 145 and in equation (42) ignore all except the last term and even the suffixes of this e, being unsuitable as special notation, will be replaced by A. e is defined in the middle of p. 143 of Chapter 7). In this equation, we should not be surprised to find a term of the same form as the Taylor dispersion coefficient, for it is diffusion across streams of different speeds that causes the dispersion in that case just as it is the diffusion into stationary particles that causes the dispersion in this.7 What is surprising is that the isothermal diffusion and reaction equation should come up, for A is defined by... 

The exact formulation of the inlet and outlet boundary conditions becomes important only if the dispersion number (DjuL) is large (> 0.01). Fortunately, when DjuL is small (< 0.01) and the C-curve approximates to a normal Gaussian distribution, differences in behaviour between open and closed types of boundary condition are not significant. Also, for small dispersion numbers DjuL it has been shown rather surprisingly that we do not need to have ideal pulse injection in order to obtain dispersion coefficients from C-curves. A tracer pulse of any arbitrary shape is introduced at any convenient point upstream and the concentration measured over a period of time at both inlet and outlet of a reaction vessel whose dispersion characteristics are to be determined, as in Fig. 2.18. The means 7in and fout and the variances and out for each of the C-curves are found. 

Mobile fluid interaction with the stationary phase in SFC was investigated with mass spectrometric tracer pulse chromatography (96). Using capillary supercritical fluid chromatography, the effect of methanol as an additive was studied on the partition behavior of n-pentane into 5 % phenylmethylsilicone stationary phase. The results showed that the mobile fluid uptake by the stationary phase decreased with increasing temperature and pressure. Thus suggests that stationary phase swelling, may occur in SFC. 

Table 1 lists the characteristics of the measured RTD for five different conditions. The first one is shown in Figure 2. The evolution of this curve can be explained by equation (1), although the peaks are not ideal Dirac pulses, because the flow inside the reactor (i.e. the reactor tube (c) and the recirculation pipe (d) in Figure 1) is not of the ideal plug flow type. Therefore, the tracer pulse broadens and eventually spreads throughout the reactor. Nevertheless, the distance between two peaks is a reasonably accurate estimate of the circulation time r/(R+1) in the reactor, and from this the flow through the reactor can be calculated. The recycle ratio R is calculated from the mean residence time r and the circulation time r/(R+l). 

For the assessment of the extent of change of the phase ratio of a HPLC column system with temperature or another experimental condition, several different experimental approaches can be employed. Classical volumetric or gravimetric methods have proved to be unsuitable for the measurement of the values of the stationary phase volume Vs or mobile phase volume Vm, and thus the phase ratio ( = Vs/Vm). The tracer pulse method266,267 with isotopically labeled solutes as probes represents a convenient experimental procedure to determine Vs and V0, where V0 is the thermodynamic dead volume of the column packed with a defined chromatographic sorbent. The value of Vm can be the calculated in the usual manner from the expression Vm = Eo — Vs. In addition, the true value of Vm can be independently measured using an analyte that is not adsorbed to the sorbent and resides exclusively in the mobile phase. As a further independent measure, the extent of change of 4> with T can be assessed with weakly interacting neutral or... 

In a pulse input, an amount of tracer Nq is suddenly injected in one shot into the feedstreain entering the reactor in as short a time as possible. The outlet concentration is then measured as a function of time. Typical concentration-time curves at the inlet and outlet of an arbitrary reactor are shown in The c curve Figure 13-4. The effluent concentration-time curve is referred to as the C curve in RTD analysis. We shall analyze the injection of a tracer pulse for a single-input and single-output system in which only flow (i.e., no dispersion) carries the tracer imaterial across system boundaries. First, we choose an increment of time At sufficiently small that the concentration of tracer, C(t), exiting between time t and t + At is essentially constant. The mount of tracer material, Ah leaving Ihe reactor between time t and t At vs then... 

The RTD will be analyzed from a tracer pulse injected into the first reactor of three equally sized CSTRs in series. Using the definition of the RTD presented in Section 13.2. the fraction of material leaving the system of three reactors (i.e., leaving the third reactor) that has been in the system between time t and / + Ar is... 

To illustrate how dispersion affects the concentration profile in a tubular reactor we consider the injection of a perfect tracer pulse. Figure 14-3 shows how dispersion causes the pulse to broaden as it moves down the reactor and becomes less concentrated. 

Sloppy Tracer Inputs It is not alw s possible to inject a tracer pulse cleanly as an input to a system, owing to the fact that it takes a finite time to inject the tracer. When the injection does not approach a perfect pulse input (Figure 14-10), the differences in the variances between the input and output tracer measurements are used to calculate the Peclet number ... 

The problem now is to evaluate the parameters a and p using the RTD data. A mole balance on a tracer pulse injected at t = 0 for each of the tanks is... 

Analyte Competition on Polyimide Adsorbents Studied by Deuterated Tracer Pulse Chromatography... 

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