Tracer concentration-time profile

Hence the axial dispersion is quantified by fitting the above equations to experimental tracer concentration-time profile. Some of the experimental techniques applied to characterize an MSR are listed in Table 15.2. The following points should be borne in mind in coimection with the RTD for an MSR ... 

Quantitative values on the drugs/tracers radioactivity concentration-time profile in different organs or sub-regions of organs are determined. 

Occasionally, various methods for evaluating tracer data and for estimating the mixing parameter in the TIS model lead to different estimates for t and N In these cases, the accuracy of t and N must be verified by comparing the concentration-versus-time profiles predicted from the model with the experimental data. In general, the predicted profile can be determined by numerically integrating N simultaneous ordinary differential equations of the form ... 

The Gaussian plume illustrated in Figure 6 represents the cross-section of a time-averaged, tracer concentration. That is, if time-series concentration measurements taken at a number of points across the plume were separately averaged over their duration, then one would expect to obtain a Gaussian profile. However, at any one time the instantaneous concentration profile would look very different. Figure 12, a typical instantaneous concentration cross-section, shows the small-scale concentration fluctuations resulting from the interaction of coherent structures... 

The mixing behavior inside the test chamber can easily be checked hy the tracer gas method , in which an inert tracer gas (e.g. SFg) is continuously added to the inlet air stream of the test chamber by means of the mass flow control. After a certain period of time the tracer gas supply is cut off. At the exit of the chamber the concentration of tracer gas is determined continuously. The mixing should be checked inside the gas chamber including a sample to be tested. Figure 2.1-3 shows a typical concentra-tion/time profile for this test set-up. Should the measured values of the increasing or decreasing tracer gas concentration differ more than 10% from the theoretical curve, the mixing of the chamber atmosphere is unsatisfactory. This happens, e.g., in the case of a technical ventilation problem, when the air inlet and the air outlet of the test chamber are short-circuited . 

The tracer is injected at the inlet at the reference time 0 = 0. C,(0) and C(0) are the tracer concentrations, at the inlet and the outlet, respectively. In an ideal PFR, there is complete mixing in the radial direction and no mixing in the axial direction. So, the tracer material injected at the inlet, at time 0 = 0, spreads uniformly in the radial direction (due to complete mixing) and all the tracer elements move at the same velocity in the axial direction (no axial mixing and flat velocity profile). Thus, all the fluid eluents have the same residence time, which is equal to the mean residence time Q = V/q. Thus, C(0) is the same as Cj(0) shifted along the time axis by 0. 

The bed was first operated at the preselected conditions at a steady state then about 455 kg of the coarse crushed-acrylic particles, similar to that used as the bed material but of sizes larger than 6-mesh, were injected into the bed as fast as possible to serve as the tracer particles. Solids samples were then continuously collected from five different sampling locations at 30-second intervals for the first 18 minutes and at 60-second intervals thereafter. The samples were then sieved and analyzed for coarse tracer particle concentration. Typical tracer particle concentration profiles vs. time at each sampling location are presented in Figs. 38-42 for set point 3. 

In the ideal plug flow reactor, the flow traverses through the reactor hke a plug, with a uniform velocity profile and no diffusion in the longitudinal direction, as illustrated in Figure 6.2. A nonreactive tracer would travel through the reactor and leave with the same concentration versus time curve, except later. The mass transport equation is... 

This approach is based on the premise that Al can be used as a tracer for bottom sediment material and that the concentration of Al in resus-pendable surface sediment is fairly uniform basinwide. Detailed profiles of size-fractionated particulate aluminum concentrations spaced closely in time over the unstratified period show vertical concentration profiles at nearly uniform levels, indicating that a pseudosteady state had been achieved. The mean areal pool of Al during this period was designated as the net resuspended pool (80-90% settles from the water column by September), and the quantity of surface sediment required to supply this pool was calculated. 

During this 4-day study, the vertical H202 concentration profiles would not have been predicted from low-resolution vertical temperature profiles. H202 may be useful as an in situ tracer for mixing on short time scales (i.e., less than 24 h), and the development of on-line continuous analytical instrumentation for use in humic waters would be helpful. 

Fig. 2.14. Response of the dispersed plug-flow model to a pulse input of tracer. Three snapshot concentration profiles at different times tx, t2, h are shown. The inset shows the C-curve derived from measurements at a fixed position, z = L. If axial dispersion occurs to only a small extent (small DJuL) the C-curve is almost symmetrical...

Powerful methods for the determination of diffusion coefficients relate to the use of tracers, typically radioactive isotopes. A diffusion profile and/or time dependence of the isotope concentration near a gas/solid, liq-uid/solid, or solid/solid interface, can be analyzed using an appropriate solution of - Fick s laws for given boundary conditions [i-iii]. These methods require, however, complex analytic equipment. Also, the calculation of self-diffusion coefficients from the tracer diffusion coefficients makes it necessary to postulate the so-called correlation factors, accounting for nonrandom migration of isotope particles. The correlation factors are known for a limited number of lattices, whilst their calculation requires exact knowledge on the microscopic diffusion mechanisms. 

The proportionality of t] to Q/D in both cases and the absence of any dependence on the cross section area of the channel are easy to understand. First, the molecules which are initially near the tube walls reach the surface by diffusion in a short time they are also carried by the laminar flow only a small distance. The layers near the surface are soon depleted, and the resulting steady shape of the concentration profile of the tracer over the radius no longer depends on that profile at the inlet of the channel. Then the probability of deposition per unit length gets constant and only one exponential term must characterize the density profile of the deposit. Second, the respective mean deposition length must be proportional to the flow velocity multiplied by the time of diffusion across the tube section For circular... 

In the isothermal chromatography (IC) experiments, one usually measures elution curves - the time-dependent relative concentration of each of the analytes in carrier gas at the column exit. In principle, one could also fix the internal chromatogram (e.g., by rapid cooling of the column well below the working temperature) actually, it is impractical except for the compounds of similar volatility. In the ther-mochromatographic (TC) separations of mixtures of differently volatile tracers, given a proper stationary temperature profile, each of the components finally comes to practical rest somewhere within the column. The temperature gradient g may... 

The close relationship of the P()4V profile to other features in the water column led Tugrul et al. (37) to propose using PO/ (which is relatively easy to measure) as a tracer for the first appearance of sulfide (which is a more difficult measurement) and the presence of a suboxic zone. Buesseler et al. (18) took this idea one step further and suggested that the PO/ minima in historical data sets suggest that a suboxic zone existed at that time. This hypothesis is difficult to evaluate, because it is most likely that formation of oxidized particulate forms of Fe and Mn do not give an indication of whether or not oxygen concentrations were within the suboxic range. 

Figure 7.14 Retention times of the plateau and tracer peaks. Experimental chromatograms showing the perturbation peak and the tracer peak recorded over a series of concentration plateaus. The lines are plots versus the plateau concentration of the retention times of the plateau perturbations (fat solid line) and of the tracer peaks (dashed line). The fat solid line is also the elution profile of a large rectangular pulse (with an initial condition = 0) given by Eq. 7.4. That of the dashed line is Eq. 7.10. Reproduced with permission from ]. Samuelsson et at, Anal. Ckem., 76 (2004) 953 (Fig. 6). 2004 American Chemical Society.

Figure 19.6 (a) Comparison of depth profiles obtained for 8 and 80 min of tracer deposition. The general shape of the profiles is similar. Increasing the evaporation time by a factor of ten leads to an increase in the metal concentration by one order of... 

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... 

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