Tracer pulse method

The tracer pulse method was also used by Bliimel et al. [112] to determine the binary isotherms of the enantiomers of l-phenoxy-2-propanol on Chiralcel OD, by Lindholm et al. [113] to determine the binary isotherms of methyl-mandelate on Chiral AGP, and by Mihlbachler et al. [1] to determine those of the enantiomers of Troger s base on Chiralpak AD. In this last case, an imusual isotherm was obtained, illustrated in Figure 4.28. The adsorption of the more retained (+) enantiomer is not competitive the amoimt adsorbed by the chiral stationary phase at equilibrium with a constant concentration of the (+) enantiomer is independent of the concentration of the (-) enantiomer. On the other hand, the adsorption of the less retained enantiomer is cooperative the amoimt of this (-) enantiomer adsorbed by the CSP at equilibrium with a constant concentration of this enantiomer increases with increasing concentration of the (+) enantiomer. The isotherm data are best accounted for by an isotherm model derived assuming multilayer adsorption. 

A significant drawback of the tracer pulse methods remains that they require large volumes of rather concentrated solutions, hence large amounts of the chemicals studied, larger even than those needed in FA (since the measurements to make on the plateau concentrations last longer). These solutions are more difficult to re-... 

Arnell, R. and Fornstedt, T. (206) Validation of the tracer-pulse method for multicomponent liquid chromatography, a classical paradox revisited. Anal. 

Al-Ameeri, R.S., and Danner, R.P., Improved tracer-pulse method for measurement of gas adsorption equilibria, Chem. Eng. Commun., 26( 1), 11 -24 (1984). 

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. 

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... 

Two different implementations of these methods have been developed, the tracer pulse technique (or elution of an isotope on a plateau) and the concentration pulse technique (or elution on a plateau). They are very different in principle although they share much theoretical backgroimd. Only the second one has now any practical applications in liquid chromatography. 

The fundamentals of the phenomena involved in the pulse methods are discussed elsewhere in detail (Chapter 13). Suffice to say here that when a small sample of an n-component mixture is injected into a chromatographic system the mobile phase of which contains p additives, n + p peaks are formed and eluted, as illustrated in Figure 4.27. Although in pulse methods, tracers have the same isotherms as the components studied, their concentrations are different and, accordingly, the migration rates of the tracer peaks are different from the velocities of the component perturbations at the plateau concentrations. Thus, upon injection of one tracer (n = 1) in a the binary solution (p = 2) used as the mobile phase, we expect to see three peaks on the plateau of each component, as shown in Figure 4.27 in the case of a binary mixture, assuming that the two components... 

Figure 4.27 Illustration of the binary step and pulse method. Plateau concentrations 45mg/mL for component 1, 50 mg/mL for component 2. Amoimt of tracer injected 0.3 mg fp = 0.143 min mL/min. L = 25cm N= 2500 fcgi = 6.17 /Cq2 = 12.3 bi = 0.0267 62 = 0.05 to = 60 s. (a) Elution of an isotopic tracer of component 1 in a mobile phase containing components 1 and 2 chromatograms shown by detectors selective for components 1, 2, and the tracer, (b) Same as (a), but chromatograms shown by a nonselective detector (Total) and by a detector selective for 1, but having the same response for 1 and its isotopic tracer, (c) Same as (a), but with injection of an isotopic tracer of component 2. (d) Same as (b), but with injection of an isotopic tracer of 2. (e) Selective chromatograms obtained upon injection of a mixture of isotopic tracers of 1 and 2. (f) Chromatograms obtained with a nonselective detector (Total), and with detectors selective for 1 or 2.

The principle of this pulse method and its general equations are easily extended to the case of several components in a mixture. The method was used by Lindholm et al. [24] to determine the quaternary isotherms of the enantiomers of methyl- and ethyl-mandelate on the chiral phase Chiral AGP. One of the serious roadblocks encountered in the use of the pulse tracer method is that the amplitudes of most of the system peaks decrease rapidly when the plateau concentration increases. Since the signal noise increases in the same time, it becomes rapidly impossible to make any accurate measurements of the retention time of these peaks. On the basis of fundamental work by Tondeur et al. [114], the origin of this variation of the relative intensity of the system peaks was explained by Forss n et al. [47], who then derived an effective rule to determine the composition of a perturbation pulse that generates system peaks that are detected easily. The concentrations of the components in the injected perturbation pulse should... 

Measurement of the residence time distribution as the tracer passes through a system is another basic principle of tracer techniques. Typical applications are measurement of the transit time of a tracer pulse, a method applied in flow measurement, as well as measurement of a system response to a transient, a method that gives valuable information on a system, mainly industrial and environmental processes. 

The transit time method is based on measuring the residence time of a tracer pulse between two measuring points. The flow rate Q is... 

In the pulse method, the tracer is introduced momentarily (as a pulse) and the resulting response shows a maximum as illustrated in Figure 4.6a. If the tracer is introduced over a very short time interval—infinitesimally short—the pulse is called an impulse, and the mathematical treatment then becomes quite simple. The tracer can also be introduced by including several consecutive pulses of varying lengths in the system. In this case, we discuss a so-called pulse train. 

St-Pierre et al. (2007) developed a residence-time distribution method based on the injection and subsequent detection of a tracer substance. The time required for the tracer pulse to travel between the injection and detection points defines an average residence time. Because the reactant flow rate is known, the free volume of the cell can be determined. Measurements performed in the absence and the presence of liquid water allow determination of the volume occupied by liquid water. 

Measurements of the relationship between e and tracer method [119] and pulse methods [108] led to greatly divergent results. According to [119], adsorption of ethylene on platinum obeys the Langmuir isotherm. In the maximum adsorption region (0.2 -0.4 V), according to [108], the Qorg the values for ethylene and acetylene do not depend on their partial pressures. These differences are evidently due to different conditions for the preliminary treatment of the electrodes and assessment of their true surface areas. 

The technique just described requires the porous medium to be sealed in a cell, so It cannot be used with pellets of irregular shape or granular material. For such materials an alternative technique Introduced by Eberly [64] is attractive. In Eberly s method the porous pellets or granules are packed into a tube through which the carrier gas flows steadily. A sharp pulse of tracer gas is then injected at the entry to the tube, and Its transit time through the tube and spreading at the exit are observed. A "chromatographic" system of this sort is very attractive to the experimenter,... 

Via a passive scalar method [6] where or, denotes the volume fraction of the i-th phase, while T, represents the diffusivity coefiBcient of the tracer in the i-th phase. The transient form of the scalar transport equation was utilized to track the pulse of tracer through the computational domain. The exit age distribution was evaluated from the normalized concentration curve obtained via measurements at the reactor outlet at 1 second intervals. This was subsequently used to determine the mean residence time, tm and Peclet number, Pe [7]. 

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. 

A disadvantage of tracer methods is the frequent presence of exchange processes which are difficult to account for. This hampered Happel s work with 180 (30) and complicated the interpretation of the work of Conner and Bennett (34), who used pulses of tracers and a qualitative interpretation of their data on CO oxidation over NiO. 

We describe two approximate methods of determining the value of N in the TIS model from pulse-tracer experiments. One is based on the first moment or mean 0, and the other on the variance a as determined from the tracer data. 

The SFM is applied to a (single-stage) CSTR in Chapter 14, to a PFR in Chapter 15, and to an LFR in Chapter 16. In these cases, E(t) is known in exact analytical form. It is shown that the SFM gives equivalent results for a PFR and an LFR for any kinetics. For a CSTR, however, it gives an equivalent result only for first-order (i.e., linear) kinetics. This raises the question as to the usefulness of the SFM both for arbitrary kinetics and for arbitrary flow through a vessel. We first consider two methods of using equation 13.5-2 in conjunction with discrete experimental tracer data from a pulse input. 

Since all tracer entered the system at the same time, t = 0, the response gives the distribution or range of residence times the tracer has spent in the system. Thus, by definition, eqn. (8) is the RTD of the tracer because the tracer behaves identically to the process fluid, it is also the system RTD. This was depicted previously in Fig. 3. Furthermore, eqn. (8) is general in that it shows that the inverse of a system transfer function is equal to the RTD of that system. To create a pulse of tracer which approximates to a dirac delta function may be difficult to achieve in practice, but the simplicity of the test and ease of interpreting results is a strong incentive for using impulse response testing methods. 

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