Inert Tracer Experiments

Transient experiments with inert tracers are used to determine RTDs. In real systems, they will be actual experiments. In theoretical studies, the experiments are mathematical and are applied to a dynamic model of the system. 

Suppose that an inert tracer has been fed to a CSTR for an extended period of time, giving Cin = Cout = Co for t 0. At time t = 0, the tracer supply is suddenly stopped so that Cin = 0 for r 0. Equation 14.2 governs the transient response of the system. 

Tracer molecules originally in the system at time t = 0 gradually wash out. The exponential form of Equation 15.1 is specific to a CSTR, but the concept of washout applies to any flow system. Consider some time t 0 when the fraction of molecules remaining in the system is W t) = C(t)/Co. These molecules must necessarily have entered the reactor before time t = 0 since no tracer was fed after that time. Thus these molecules have residence times of t or longer. The residence time washout function is defined as 

W(t) = fraction of molecules leaving the system that experienced a residence time greater than t 

It is apparent that 1T(0) = 1 since all molecules must have a residence time of zero or longer and that W (oo) = 0 since all molecules will eventually leave the system. Also, the function W(t) will be nonincreasing. 

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The use of inert tracer experiments to measure residence time distributions can be extended to systems with multiple inlets and outlets, multiple phases within the reactor, and species-dependent residence times. This discussion ignores these complications, but see Suggestions for Further Reading. ... 

Thus, t can be found from inert tracer experiments. It can also be found from measurements of the system inventory and throughput since... 

Vanderborght, J., Vanclooster, M., Timmerman, A., Seuntjens, P., Mallants, D., Kim, D.J., Jacques, D., Hubrechts, L., Gonzalez, C., Feyen, J., Diels, J., and Deckers, J. Overview of inert tracer experiment in key belgian soil types relation between transport, and soil morphological and hydraulic properties. Water Resources Research 37[12], 2873-2888. 2001. 

When a steady stream of fluid flows through a vessel, different elements of the fluid spend different times within it. The time spent by each fluid element can be identified by an inert tracer experiment, where a pulse or a step input of a tracer is injected into the flow stream, and the concentration of the pulse in the effluent is detected. As the reader may quickly infer, the tracer must leave the PFR undisturbed. On the other hand, a step pulse may give rise to an exponential distribution in a CSTR. In the beginning of this chapter, we already demonstrated that PFR behavior approaches that of a CSTR under infinite recycle. It follows that infinite CSTRs in series behave like a PFR. Thus, we conclude that any nonideal reactor can be represented as a combination of the PFR and MFR to a certain degree. First, let us show a representative pulse response curve for each of the ideal reactors in Figure 3.5. As seen in the figure, the response to a step input of tracer in a PFR is identical to the input function, whereas the response in a CSTR exhibits an exponential decay. The response curves as shown in Figure 3.5 are called washout functions. The input function of the inert tracer concentration [/] can be mathematically expressed as... 

Thus t can be found from inert tracer experiments. It can also be found from measurements of the system inventory and throughput. Agreement of the t s calculated by these two methods provides a good check on experimental accuracy. Occasionally, eq. (1-1) is used to determine an unknown volume or an unknown density from inert tracer data. 

Adsorption process has been widely used in many chemical and related industries, such as the separation of hydrocarbon mixtures, the desulfurization of natural gas, and the removal of trace impurities in fine chemical production. Most of the adsorption researches in the past are focused on the experimental measurement of the breakthrough curve for studying the dynamics. The conventional model used for the adsorption process is based on one-dimensional or two-dimensional dispersion, in which the adsorbate flow is either simplified or computed by using computational fluid dynamics (CFD), and the distribution of adsorbate concentration is obtained by adding dispersion term to the adsorption equation with unknown turbulent mass dififusivity D(. Nevertheless, the usual way to find the D, is either by employing empirical correlation obtained from inert tracer experiment or by guessing a Schmidt number applied to the whole process. As stated in Chap. 3, such empirical method is unreliable and lacking theoretical basis. 

Finally, in connection with the comments of Dr. Gordon, we have looked at the reduction of chlorate by hexachloroiridate. The final products, of course, are hexachloroiridate and chloride. The reaction is stoichiometric. So far, no tracer experiments have been done to try to identify any of the unstable intermediates but both of the iridium species are well known to be substitution inert, and the reaction surely involves a one-electron reduction of chlorate. 

The state of mixing in a given reactor can be evaluated by RTD experiments by means of inert tracers, by temperature measurements, by flow visualization and, finally, by studying in the reactor under consideration the kinetics of an otherwise well-known reaction (because its mechanism has been carefully elucidated from experiments carried out in an ideal reactor, the batch reactor being generally chosen as a reference for this purpose). From these experimental results, a reactor model may be deduced. Very often, in the laboratory but also even in industrial practice, the real reactor is not far from ideal or can be modelled successfully by simple combinations of ideal reactors this last approach is of frequent use in chemical reaction engineering. But... 

The experiments with the inert tracer may only show that the time, necessary for the fluid in the reactor to be well mixed, is much smaller than the average residence time. When a chemical reaction takes place, an additional time-scale, the time constant of the chemical reaction, appears. This time characterizes the reaction rate and can be defined as the time in which the reaction proceeds to a certain conversion, say 50%. For many practical heterogeneous catalytic reactions, the reaction time is so short that reactants entering the reactor may be converted without being mixed, for example, during the first cycle. For such fast reactions, of course, the reactor cannot be considered as gradient-free, whatever the recirculation ratio is. 

The RTD for a given reactor and flow rate can be established from response-type experiments. In these experiments the concentration of an inert tracer is disturbed in the feed stream and its effect on the effluent stream is measured. The three most common perturbations are a step function, a pulse (square wave), and a sinusoidal wave. The relationships between the observed concentration-vs-time curves and the RTD are examined here for step functions and pulses. The analysis of sinusoidal perturbations is more complex but is available in the literature. ... 

Attack as a Nucleophile. Hydrolysis of esters or amides can occur through the nucleophilic attack of metal-bound hydroxide ions, as exemplified by N (49, 50). In most cases, however, this mechanism is not easily differentiated from the kinetically equivalent attack by hydroxide ion at the metal-bound carbonyl carbon (A) (38). In the case of substitutionaUy inert complexes of Co(lll), 0-tracer experiments revealed that both of the two mechanisms occur in the hydrolysis of the bound amino acid esters and amides (36, 49, 51, 52). At a pH 7-8, ionization of Co(III)-bound amide I (R = H) produced N in >90% of the total concentration, and N was hydrolyzed with a half-life of 100 min at 20°C (36). 

The balance contains just two adjustable hydrodynamic parameters, tl l and PeL. The Peclet number is estimated from the separate impulse experiments carried out with the inert tracer (NaCl), while the quantity Tl l is estimated from the kinetic experiments in order to ensure a correct description of the reactor dynamics. The flow pattern of the reactor is characterised by separate impulse experiments with an inert tracer component injecting the tracer at the reactor inlet and measuring in this case the conductivity response at the outlet of the reactor with a conductivity cell operated at atmospheric pressure. In order to get a proper conductivity response, water was employed as the liquid phase. The liquid and hydrogen flow rates should be the same as in the hydrogenation experiments and the liquid hold up was evaluated by weighing the reactor. Some results from the tracer experiments are given in Figure 8.12. 

NSSTK and SSITK experiments were performed with an atmospheric flow system using either a tubular quartz microreactor (70 mg of catalyst) or a catalytic DRIFT cell from Spectratech, allowing the gases to flow through a fixed bed of catalyst pellets (about 30 mg) and able to be heated up to 1173 K. The gas composition was continuously monitored at the reactor outlet by online mass spectrometer and the surface composition was investigated by a FT-BR. spectrometer (Nicolet 550) with one spectrum recorded per second In all cases, the catalyst was pre-treated with He at 1013 K for 40 min. The reacting feed was composed of 10 vol.% methane ( CHj, CHj or CD4) and 90 vol.% He with a total flow rate of 24 ml/min. The reaction was carried out at 1 atm and 1013 K. Ar was used as an inert tracer. 

You have designed the following tracer experiment to determine whether your continuous flow reactor for pilot-scale study is perfectly mixed, like an ideal CSTR. At time t = 0, you inject 100 g of an inert tracer into the 100 L reactor after establishing a feed flow rate of 25 L per min. Your technician measures the tracer concentration in the outlet stream for a few minutes and provides you with the following data ... 

Recently, HOgstrtJm and others studied the wet fallout of sulfate and the SO2 to sulfate transformation rate at an oil fired 1000 MW power plant in Sweden. This project comprised a number of wet fallout tests with not less than 100 sampling locations up to 60 km from the source. In their experiments, they made use of an inert tracer, SF5. They found that about 70 percent of the emitted amount was deposited within 80 - 120 km from the source. This confirmed the earlier results from 197. In the dispersion experiments, they found that on a day with close to 100 percent relative humidity, 70 percent of the sulfur from the power plant occurred as sulfate at a distance of 30 km from the source. On a much drier day, the corresponding figure was only 10 percent at 30 km. 

In principle, by matching the theoretical moments with the corresponding experimental moments, the adsorption and diffusion parameters can be extracted. To facilitate the reliability of the parameter extracted, we can make use of an inert tracer as well as an adsorbing tracer, and carry out experiments for both of them at different flow rates. 

Figure 8.9. (a) Breakthrough curve for three Br tracer experiments showing that the inert tracer breakthrough occurs at one pore volume.The dashed line shows the pattern expected for ideal plug flow and the deviation of concentration from this line is the result of dispersion and diffusion, (b) Breakthrough curve for the Zn + experiment showing that c/c occurs after 26 pore volumes have eluted. 

RTD methods are based on the concept of age distribution functions and make use of the experimentally measured or calculated residence time distribution of fluid elements in a reactor vessel (Figure 12.3-1, C and D). A Lagrangian perspective is taken and the age of a fluid element is defined as the time elapsed since it entered the reactor. In what follows, steady state operation of a vessel fed with a volumetric flow rate F is considered. A residence time distribution (RTD) experiment can be performed with inert tracers, such that at an instant of time all fluid elements entering a reactor or process vessel are marked. The injection of an impulse of tracer into the vessel at time zero can be mathematically represented by means of the Dirac delta function or perfect unit impulse function ... 

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