Tracer, dispersion 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. 

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. 

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. 

Direct estimates of diapycnal exchange coefficients have been made by Kullenberg (1977) from dispersion measurements of injected dye tracer in the thermoline and halocline of the Arkona Basin and the Bornholm Basin in the Baltic Sea. 

Transverse dispersivity has been less studied, but it is smaller than the longitudinal dispersivity. Measurements from tracer studies indicate that the transverse horizontal dispersivity is about 10% of the longitudinal dispersivity in the bedding plane, and the transverse vertical dispersivity is about 1% (Gelhar, 1997). Klenk and Grathwohl (2002) found that the transverse vertical dispersivity was determined mostly by diffusion. 

The accuracy of the radioactive tracer velocity measurement was within 1.5%. Detector separation was measured to 0.02%, and the count rate peak locations were within 0.5% of the reading. The averaging of 15 particle velocity measurements reduced the typical velocity dispersion of 5.8% to 1.5%. 

Radial and axial dispersion measurements in risers were first reported by van Zoonen [71]. With hydrogen gas as a tracer he found that radial dispersion coefficients ranged between 2.5 and 36 cmVs and axial gas dispersion coefficients were between 4,500 and 14,400 cmVs. 

Figure 9.4 Column for two-phase dispersion measurements. To emphasize the tracer spread outside the column, most of the long column has been omitted in this graph. (A) The 10 pi injection loop (B) a thin needle is located inside the T-connector and reducing coimector, (C) the needle is inserted into the bed of particles (D) the gas-liquid separatory (E) detail of the separator, including the relevant liquid volume (F) a short tube connects the separator to the flow cell. (Source Marquez et al. [20]. Reproduced with permission of John Wiley Sons.)...

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.,... 

Until recently, numerical tools and resources were also underdeveloped relative to the magnitude of the striation measurement problem Poincare sections and tracer dispersion simulations were the primary techniques used to characterize mixing. To reconstruct striation patterns successfully by computational methods, it is necessary to track continuous material lines (i.e., dye blobs) injected in chaotic flows. The difficulty of such a numerical experiment is hidden in one word of the previous sentence continuous. The feasibility of tracking material lines or surfaces numerically was explored by Franjione and Ottino, (Franjione and Ottino, 1987). These authors estimations of time and disk space demands... 

The experimental findings of gas flow patterns in fluidized beds (in the interpretation of which it is impossible to separate the effects of the emulsion and the bubble phases) indicate that the overall flow pattern lies between plug flow and complete mixing. Yoshida and Kunii [51] showed that experimental measurements of tracer dispersion may be adequately interpreted in terms of the bubbling bed model through the use of the exchange coefficients between the emulsion and the bubble phases. 

Axial Dispersion and the Peclet Number Peclet numbers are measures or deviation from phig flow. They may be calculated from residence time distributions found by tracer tests. Their values in trickle beds are fA to Ve, those of flow of liquid alone at the same Reynolds numbers. A correlation by Michell and Furzer (Chem. Eng. /., 4, 53 [1972]) is... 

Gryning, S. E., and Lyck, E., "Comparison between Dispersion Calculation Methods Based on In-Situ Meteorological Measurements and Results from Elevated- Source Tracer Experiments in an Urban Area." National Agency of Environmental Protection, Air Pollution Laboratory, MST Luft - A40. Riso National Laboratory, Denmark, 1980. 

For a tracer release that can be considered to be at ground level, approximate the vertical dispersion cr at the downwind distance where measurements indicate that the concentra-... 

The distribution of tracer molecule residence times in the reactor is the result of molecular diffusion and turbulent mixing if tlie Reynolds number exceeds a critical value. Additionally, a non-uniform velocity profile causes different portions of the tracer to move at different rates, and this results in a spreading of the measured response at the reactor outlet. The dispersion coefficient D (m /sec) represents this result in the tracer cloud. Therefore, a large D indicates a rapid spreading of the tracer curve, a small D indicates slow spreading, and D = 0 means no spreading (hence, plug flow). 

For a large amount of dispersion or small value of Np, the pulse response is broad, and it passes the measurement point slowly enough for changes to occur in the shape of the tracer curve. This gives a non-symmetrical E-curve. 

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 ... 

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... 

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 = but the dependence on Sc is weak for... 

Washout experiments can be used to measure the residence time distribution in continuous-flow systems. A good step change must be made at the reactor inlet. The concentration of tracer molecules leaving the system must be accurately measured at the outlet. If the tracer has a background concentration, it is subtracted from the experimental measurements. The flow properties of the tracer molecules must be similar to those of the reactant molecules. It is usually possible to meet these requirements in practice. The major theoretical requirement is that the inlet and outlet streams have unidirectional flows so that molecules that once enter the system stay in until they exit, never to return. Systems with unidirectional inlet and outlet streams are closed in the sense of the axial dispersion model i.e., Di = D ut = 0- See Sections 9.3.1 and 15.2.2. Most systems of chemical engineering importance are closed to a reasonable approximation. 

Given k fit) for nny reactor, you automatically have an expression for the fraction unreacted for a first-order reaction with rate constant k. Alternatively, given ttoutik), you also know the Laplace transform of the differential distribution of residence time (e.g., k[f(t)] = exp(—t/t) for a PER). This fact resolves what was long a mystery in chemical engineering science. What is f i) for an open system governed by the axial dispersion model Chapter 9 shows that the conversion in an open system is identical to that of a closed system. Thus, the residence time distributions must be the same. It cannot be directly measured in an open system because time spent outside the system boundaries does not count as residence but does affect the tracer measurements. 

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