Tracer concentration measurement

The main sources of error which define the accuracy are counting statistics in tracer concentration measurements, the dispersion of the tracer cloud in the flare gas stream, and the stationarity of the flow during measurements. 

Fig. 19-11. Example of tracer concentration measurements along a sampling arc.

Explain carefully the dispersed plug-flow model for representing departure from ideal plug flow. What are the requirements and limitations of the tracer response technique for determining Dispersion Number from measurements of tracer concentration at only one location in the system Discuss the advantages of using two locations for tracer concentration measurements. 

The nature of the tracer dictates the detection system. For the liquid phase, quite often the tracers (e.g., NaCl, H2S04, etc.) are such that the detection probe is directly inserted into the reactor and continuous monitoring of the concentration at any fixed position is obtained by means of an electrical conductivity cell and a recorder. In this case, no external sampling of liquid is necessary. If the tracer concentration measurement requires an analytical procedure such as titration, etc., sampling of the liquid is required. For the solid phase, a magnetic tracer is sometimes used. The concentration of a solid-phase tracer can also be measured by a capacitance probe if the tracer material has a different dielectric constant than the solid phase. In general, however, for solid and sometimes gas phases, some suitable radioactive tracer is convenient to use. The detection systems for a radioactive tracer (which include scintillation counters, a recorder, etc.) can be expensive. Some of the tracers for the gas, liquid, and solid phases reported in the literature are summarized in Table 3-1. 

The observed temperature dependence of the absorption cross section of 3-pentanone and the corresponding fluorescence intensity offers the possibility for a new type of temperature measurements.This technique gives access to 2D-temperature distributions between 300 and 1000 K relevant for precombustion conditions that could hardly be assessed with other laser spectroscopic techniques developed for combustion thermometry. By calculating temperatures from the ratio of simultaneously acquired intensity distributions, the measurement is independent on local tracer concentrations. Measurements in inhomogeneously mixed environments are therefore feasible. 

The RTD for a reactor is to be determined by tracer-concentration measurements. With a constant-density isothermal system, the following effluent concentration data are obtained in response to a pulse of tracer added to the feed ... 

Experimental data on exit-age or residence-time distributions most often take the form of discrete values of tracer concentration measured at successive time intervals after introduction of the tracer. Thus, the integrals involved can be replaced by summations in the analysis of actual data. We will illustrate the procedure for the analysis of a pulse-response experiment. Available are tracer concentrations in the effluent, C t) and corresponding times, and from these data we would like to determine the exit-age distribution, or E 0)d6, the distribution in terms of the residencetime variable 6. First determine E t) from C t) versus t by... 

Figure 1.1 Scheme for the determination of flow velocity distributions from tomographic tracer concentration measurements. 

Tracer techniques are commonly used to determine the gas dispersion coefficients in fluidized bed reactors. The tracer concentration measured at the outlet in response to a pulse or step input of the tracer at the inlet can be used to calculate the dispersion coefficient based on the dispersion models in a form similar to Eq. (11), i.e.,... 

Swab samples showed approximately 16% loss in screen factor from the wellhead and 15% loss in viscosity (Table 4). Polymer and tracer concentration measurements and, gel permeation chromatography analysis showed that the loss in properties was due to degradation of the polymer and not to dilution. 

In the case, where all 3 phases are present, the detector measurements reveal the amounts of tracers in each phase and the position of the boundaries between the phases The cross section area of each phase is calculated fi-om the latter. From this the tracer concentrations and hence the volume flows of the 3 phases are calculated. 

Measurements have been made in a static laboratory set-up. A simulation model for generating supplementary data has been developed and verified. A statistical data treatment method has been applied to estimate tracer concentration from detector measurements. Accuracy in parameter estimation in the range of 5-10% has been obtained. 

Aircraft can take vertical temperature soundings and can measure air pollutant and tracer concentrations and turbulence intensity. Airborne lidar can measure plume heights, and integrating nephelometers can determine particle size distributions. 

If the tracer concentration is X measured at each sampling position that has its position at y, on a scale along the arc (either in degrees or in meters), estimates of the mean posiHon of the plume at ground level and the variance of the groundlevel concentration distribution are given by ... 

In a time period from t = 0 to t = 6t seconds, a quantity m (g) of a tracer is introduced at the system inlet, and the tracer concentration C(t) (g/1) is measured in the exit from the system. Subject to the above conditions, the residence time density function from the measured tracer response is ... 

Total area under tracer concentration (or a quantity proportional to it) curve versus time as measured at the outlet... 

Glaser and Lichtenstein (G3) measured the liquid residence-time distribution for cocurrent downward flow of gas and liquid in columns of -in., 2-in., and 1-ft diameter packed with porous or nonporous -pg-in. or -in. cylindrical packings. The fluid media were an aqueous calcium chloride solution and air in one series of experiments and kerosene and hydrogen in another. Pulses of radioactive tracer (carbon-12, phosphorous-32, or rubi-dium-86) were injected outside the column, and the effluent concentration measured by Geiger counter. Axial dispersion was characterized by variability (defined as the standard deviation of residence time divided by the average residence time), and corrections for end effects were included in the analysis. The experiments indicate no effect of bed diameter upon variability. For a packed bed of porous particles, variability was found to consist of three components (1) Variability due to bulk flow through the bed... 

Development in recent years of fast-response instruments able to measure rapid fluctuations of the wind velocity (V ) and of fhe tracer concentration (c ), has made it possible to calculate the turbulent flux directly from the correlation expression in Equation (41), without having to resort to uncertain assumptions about eddy diffusivities. For example, Grelle and Lindroth (1996) used this eddy-correlation technique to calculate the vertical flux of CO2 above a foresf canopy in Sweden. Since the mean vertical velocity w) has to vanish above such a flat surface, the only contribution to the vertical flux of CO2 comes from the eddy-correlation term c w ). In order to capture the contributions from all important eddies, both the anemometer and the CO2 instrument must be able to resolve fluctuations on time scales down to about 0.1 s. 

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

Impulse Response and the Differential Distribution. Suppose a small amount of tracer is instantaneously injected at time 1 = 0 into the inlet of a reactor. All the tracer molecules enter together but leave at varying times. The tracer concentration at the outlet is measured and integrated with respect to time. The integral will be finite and proportional to the total quantity of tracer that was injected. The concentration measurement at the reactor outlet is normalized by this integral to obtain the impulse response function. ... 

A tracer is injected into the reactor and its concentration is measured at a certain location. The observed tracer concentration will oscillate whereby the amplitude of the oscillations. A, decreases with time, finally approaching the asymptote determined by the averaged concentration over the mixing zone. This relationship can be presented as ... 

The time variations of the effluent tracer concentration in response to step and pulse inputs and the frequency-response diagram all contain essentially the same information. In principle, any one can be mathematically transformed into the other two. However, since it is easier experimentally to effect a change in input tracer concentration that approximates a step change or an impulse function, and since the measurements associated with sinusoidal variations are much more time consuming and require special equipment, the latter are used much less often in simple reactor studies. Even in the first two cases, one can obtain good experimental results only if the average residence time in the system is relatively long. 

Capsules were equilibrated with a tracer solution overnight. A capsule pellet (0.2-0.5 ml) was then placed in 5 ml test buffer (PBS or RPMI-1640 medium, Gib-co/BRL, New York, NY) on a shaker and a 0.2-ml aliquot was immediately sampled by a screen-protected pipette with further samples being taken over the next 700 s. The tracer quantity was assayed using the methods described below. A final sample was taken after the capsules has been in contact with the buffer for several hours (equilibrated tracer quantity) and the increment to the tracer concentration at each time was calculated. From the progress of tracer to equilibrium on a semilog plot a slope denoted as the zero -order rate flux constant was obtained and has been used as a measure of capsule permeability. [3H] -Glucose (580 daltons),insulin (6.2 kDa), and ovalbumin (45 kDa) have been used as tracers. Radioactivity was measured by means of a Packard 2000CA Liquid Scintillation Counter (Packard Instruments,... 

The convolution integral and the Exponential Piston Flow Model (EPM) were used to relate measured tracer concentrations to historical tracer input. The tritium input function is based on tritium concentrations measured monthly since the 1960s near Wellington, New Zealand. CFC and SF6 input functions are based on measured and reconstructed data from southern hemisphere sites. The EPM was applied consistently in this study because statistical justification for selection of some other response function requires a substantial record of time-series tracer data which is not yet available for the majority of NGMP sites, and for those NGMP sites with the required time-series data, the EPM and other response functions yield similar results for groundwater age. 

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... 

Potentiometric measurements give log(3/ values which are correct to within 10% but the relative accuracy is difficult to assess due to the successive, repetitive nature of the experiments. Probably the most significant source of error, as we have stated, is the variation of pH with time. At tracer concentrations the enthalpy AH0 can be determined only by the temperature differential method. However, the temperature differential method is not as precise as the calorimetric one. The enthalpy of formation for each complex is computed with the assumption that ACp is constant over the temperature range and that the range of error corresponds to 10%. 

Lozano, A., B. Yip, and R. K. Hanson. 1992. Acetone A tracer for concentration measurements in gaseous flows by planar laser-induced fluorescence. Experiments Fluids 13 369-76. 

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