Tracer, steady-state concentration profil

In the present research, we use a dispersion-type model. Techniques for estimating dispersion coefficients are classed as non-steady or steady state. Steady-state methods usually incorporate the continuous addition of a fixed tracer concentration into the liquid stream followed by the measurement of the steady-state concentration profile along the column length. 

Figure 5-3 shows the effect of the dispersion coefficient on the tracer distribution in a soil column. Of course, the figure shows a 10-fold increase in dispersion coefficient quickly dampens out fluctuations in the concentration distribution curve leading to a near steady-state concentration profile for x > 200 cm. By con-... 

As a point of note, the axial dispersion coefficient can also be obtained from the steady-state concentration-versus-distance profile of the tracer. This method, among others, has been used by Watson and McNeese, 09 Shestopalov et al.,97 Kato et al.,49 Imafulcu et al.,47 and Deckwer et al.32 The two-dimensional axial dispersion models for the evaluation of RTD are considered by Schugerl94 and Tanoka and Inoue.103... 

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. 

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. 

One of the first applications of ocean radiocarbon data was as a constraint on the vertical diffusivity, upwelling, and oxygen consumption rates in the deep waters below the main thermocline. As illustrated in Figure 2, the oxygen and radiocarbon concentrations in the North Pacific show a minimum at mid-depth and then increase toward the ocean seabed. This reflects particle remineralization in the water column and the inflow and gradual upwelling of more recently ventilated bottom waters from the Southern Ocean. Mathematically, the vertical profiles for radiocarbon, oxygen (O2), and a conservative tracer salinity (5) can be posed as steady-state, 1-D balances ... 

A radial gas dispersion coefficient can be obtained from the steady-state tracer method by fitting measured radial profiles of tracer concentration downstream of the injection point to a two-dimensional... 

Typically, there are two ways to inject tracers, steady tracer injection and unsteady tracer injection. It has been verified that both methods lead to the same results (Deckwer et al., 1974). For the steady injection method, a tracer is injected at the exit or some other convenient point, and the axial concentration profile is measured upward of the liquid bulk flow. The dispersion coefficients are then evaluated from this profile. With the unsteady injection method, a variable flow of tracer is injected, usually at the contactor inlet, and samples are normally taken at the exit. Electrolyte, dye, and heat are normally applied as the tracer for both methods, and each of them yields identical dispersion coefficients. Based on the assumptions that the velocities and holdups of individual phases are uniform in the radial and axial directions, and the axial and radial dispersion coefficients, E and E, are constant throughout the fluidized bed, the two-dimensional unsteady-state dispersion model is expressed by... 

Vail et al. [68] used a steady state technique involving steady injection of aqueous NaCl solution at a given level of the column, to monitor the axial mixing of the liquid. The fluidized bed contained air, water and 0.87 mm spheres with a density of 2700 kg/m. The concentration profiles of tracer measured below the injection point provided information about axial dispersion coefficients and the characteristic mixing length (ratio of the axial dispersion with respect to the fluid velocity). It was observed that the presence of solids and the increase of the gas and liquid velocities were all factors promoting axial mixing of the liquid phase. 

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