Dispersion tracer data

Equations 19.4-56 and -58 provide two methods of estimating Pe, for small dispersion from tracer data. ... 

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). 

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. 

There are no direct correlations of the variance (or the corresponding parameter n) in terms of the geometry and operating conditions of a vessel. For this reason the RTD is not yet a design tool, but it does have value as a diagnostic tool for the performance of existing equipment on which tracer tests can be made. RTDs obtained from tracer tests or perhaps estimated from dispersion coefficient data or correlations sometimes are applicable to the prediction of the limits between which a chemical conversion can take place in the vessel. 

Hanna, S.R., Britter, R., and Franzese, P. (2003) A baseline urban dispersion model evaluated with Salt Lake City and Los Angeles tracer data, Atmos. Environ 37, 5069-5082. 

Interpretation of tracer data by means of residence time theory, in the extremes of complete and minimum segregation, has been reviewed and extended to treat transient response under reacting conditions. While residence time theory was initially developed for industrial application to nonideal steady state reactors, its transient extension seems especially well suited for describing segments of natural flows which are too complex to interpret using simpler models, such as dispersion. 

Calculate and X from sloppy tracer data. [2nd Ed. P14-6 j Use RTD data from Oak Ridge National Laboraioty to calculate the conversion from the tanks[Pg.1004]

CFCs, and Kr were studied in a sandy, unconfined aquifer on the Delmarva Peninsula in the eastern USA by Ekwurzel et al. (1994). H and H+ He depth-profiles show peak-shaped curves that correspond to the time series of H concentration precipitation, smoothed by dispersion (Fig. 18a). The peak occuring at a depth of about 8m below the water table therefore most likely reflects the H peak in precipitation that occurred in 1963 (Fig. 6). The H- He ages show a linear increase with depth, reaching a maximum of about 32 years. The H- He ages are also supported by CFC-11, CFC-12, and Kr tracer data (Fig. 18b). The latter tracers are used here as dyes and their concentrations are converted into residence times by using the known history of the atmospheric concentrations and their solubility in water. From the vertical H- He age profile at well nest 4 at the Delmarva site, the vertical flow velocity can be... 

Interpreting radioactive tracer data is complicated by the flow structure, injection pulse and detector geometry. Detection dispersion arises from collimator geometry... 

Dunn et al. (D7) measured axial dispersion in the gas phase in the system referred to in Section V,A,4, using helium as tracer. The data were correlated reasonably well by the random-walk model, and reproducibility was good, characterized by a mean deviation of 10%. The degree of axial mixing increases with both gas flow rate (from 300 to 1100 lb/ft2-hr) and liquid flow rate (from 0 to 11,000 lb/ft2-hr), the following empirical correlations being proposed ... 

In Figure 2.9.8(b), the mean traveling time of a neutral tracer across the percolation duster is plotted versus the Pedet number [43]. Two regimes can be identified, namely isotropic dispersion (Pe C 1) and mechanical dispersion (Pe > 1) with a crossover dose toPe 1. In the latter case, the data can be represented by a power law... 

PS-08.13. DISPERSED AND SEGREGATED Impulse tracer response data... 

Figure 5.6 The quasi-hard sphere diffusion data of Ottewill and Williams14 as a function of volume fraction. The long (DL) and short (Ds) time tracer diffusion coefficients are shown (symbols). The dotted line is representative of the relative fluidity of a hard sphere dispersion...

The aim of dispersion models is the prediction of atmospheric dilution of pollutants in order to prevent or avoid nuisance. Established dispersion models, designed for the large scale of industrial air pollution have to be modified to the small scale of agricultural pollutions. An experimental setup is described to measure atmospheric dilution of tracer gas under agricultural conditions. The experimental results deliver the data base to identify the parameters of the models, For undisturbed airflow modified Gaussian models are applicable. For the consideration of obstacles more sophisticated models are necessary,... 

The published guideline VDI 3881 /2—4/ describes, how to measure odour emissions for application in dispersion models. Results obtained by this method have to be completed with physical data like flow rates etc. As olfactometric odour threshold determination is rather expensive, it is supplemented with tracer gas emissions, easy to quantify. In the mobile tracer gas emission source, fig, 2, up to 50 kg propane per hour are diluted with up to 1000 m2 3 air per hour. This blend is blown into the open atmosphere. The dilution device, including the fan, can be seperated from the trailer and mounted at any place, e.g. 

To obtain multiple sets of experimental dispersion data, in each experiment 50 samples of tracer-polluted ambient air downwind in the plume of the propane emission source are taken by 10 sample units, distributed in the field, see fig. 3, Each unit carries five glass cylinders, filled with... 

As has been discussed, the usual method of finding the dispersion coefficients is to inject a tracer of some sort into the system. The tracer concentration is then measured downstream, and the dispersion coefficients may be found from an analysis of the concentration data. For these tracer experiments there are no chemical reactions, and so r = 0. Also the source term is given by... 

Packed Beds. Data on liquid systems using a steady point source of tracer and measurement of a concentration profile have been obtained by Bernard and Wilhelm (B6), Jacques and Vermeulen (Jl), Latinen (L4), and Prausnitz (P9). Blackwell (B16) used the method of sampling from an annular region with the use of Eq. (62). Hartman et al. (H6) used a bed of ion-exchange resin through which a solution of one kind of ion flowed and another was steadily injected at a point source. After steady state conditions were attained, the flows were stopped and the total amount of injected ion determined. The radial dispersion coefficients can be determined from this information without having to measure detailed concentration profiles. 

The data were plotted, as shown in Fig. 11, using the effective diameter of Eq. (50) as the characteristic length. For fully turbulent flow, the liquid and gas data join, although the two types of systems differ at lower Reynolds numbers. Rough estimates of radial dispersion coefficients from a random-walk theory to be discussed later also agree with the experimental data. There is not as much scatter in the data as there was with the axial data. This is probably partly due to the fact that a steady flow of tracer is quite easy to obtain experimentally, and so there were no gross injection difficulties as were present with the inputs used for axial dispersion coefficient measurement. In addition, end-effect errors are much smaller for radial measurements (B14). Thus, more experimentation needs to be done mainly in the range of low flow rates. 

The samples were analyzed for trace metals and sulfate as well as for three fractions of particulate organic matter (POM) using sequential extraction with cyclohexane (CYC), dichloromethane (DCM) and acetone (ACE). Factor analysis was used to identify the principal types of emission sources and select source tracers. Using the selected source tracers, models were developed of the form POM = a(V) + b(Pb) + - - -, where a and b are regression coefficients determined from ambient data adjusted to constant dispersion conditions. The models for CYC and ACE together, which constitute 90% of the POM, indicate that 40% (3.0 pg/m ) of the mass was associated with oil-burning, 19% (1.4 pg/m ) was from automotive and related sources and 15% (1.1 pg/m ) was associated with soil-like particles. 

The above example demonstrates that treatment of the basic data by different numerical methods can produce distinctly different results. The discrepancy between the results in this case is, in part, due to the inadequacy of the data provided the data points are too few in number and their precision is poor. A lesson to be drawn from this example is that tracer experiments set up with the intention of measuring dispersion coefficients accurately need to be very carefully designed. As an alternative to the pulse injection method considered here, it is possible to introduce the tracer as a continuous sinusoidal concentration wave (Fig. 2.2c), the amplitude and frequency of which can be adjusted. Also there is a variety of different ways of numerically treating the data from either pulse or sinusoidal injection so that more weight is given to the most accurate and reliable of the data points. There has been extensive research to determine the best experimental method to adopt in particular circumstances 7 " . 

In support of the WVDP, eight column tests were conducted at the University at Buffalo using WVDP groundwater spiked with nonradioactive Sr2+, over four durations 10, 20, 40, and 60 days. A single Kdof 2045 mL/g was calibrated from data from one of the 60-day columns, then used to successively predict the results for the other columns (Figure 5, 10-day data omitted for brevity). The importance of the specified boundary condition was highlighted by comparing results from various calibration schemes. For example, specification of a constant-concentration entrance boundary led to similar model fits but estimated Kd values that were 50% lower. Even when the recommended third-type BC was applied, efforts to simultaneously calibrate both the sorption and dispersion coefficient yielded similar fits for several combinations of parameters. Specification of the dispersion coefficient to a value obtained from an independent tracer test was necessary to obtain a robust estimate of the sorption coefficient. 

At a close level of scrutiny, real systems behave differently than predicted by the axial dispersion model but the model is useful for many purposes. Values for Pe can be determined experimentally using transient experiments with nonreac-tive tracers. See Chapter 15. A correlation for D that combines experimental and theoretical results is shown in Figure 9.6. The dimensionless number, udt/D, depends on the Reynolds number and on molecular diffusivity as measured by the Schmidt number, Sc = yu/(p a), but the dependence on Sc is weak for Re > 5000. As indicated in Figure 9.6, data for gases will lie near the top of the range and data for liquids will lie near the bottom. For high Re, udt/D = 5 is a reasonable choice. 

A one-dimensional search optimization technique, such as the Fibonacci search, is employed to minimize Equation 8-113. A computer program (PROG81) was developed to estimate the equivalent number of ideal tanks N for the given effluent tracer response versus time data. Additionally, the program calculates the mean residence time, variance, dimensionless variance, dispersion number, and the Peclet number. 

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