Nonadsorbing tracers

As mentioned in Section 11.3, fluidized-bed reactors are difficult to scale. One approach is to build a cold-flow model of the process. This is a unit in which the solids are fluidized to simulate the proposed plant, but at ambient temperature and with plain air as the fluidizing gas. The objective is to determine the gas and solid flow patterns. Experiments using both adsorbed and nonadsorbed tracers can be used in this determination. The nonadsorbed tracer determines the gas-phase residence time using the methods of Chapter 15. The adsorbed tracer also measures time spent on the solid surface, from which the contact time distribution can be estimated. See Section 15.4.2. 

For a short pulse input of a nonadsorbable tracer and a catalyst characterized by a unidisperse pore structure, the following relationships are obtained for the first moment and second central moment of the effluent curve of the bed [24] ... 

System assumptions that should be valid for such applications include fluid flow in the porous media is isotropic and adsorption is fast, reversible, and linear (cf. Freeze and Cherry 1979). Given these constraints, the comparative transport of a conserved (nonadsorbed) tracer, such as Br , and an adsorbed or retarded species, such as Am, can be described as shown in Fig. 10.29. A comparison of migration distances of the two species after time t, is made at concentrations where C(measured)/Co(initial) = 0.5 for the conserved and adsorbed species. The migration distance X of the conserved species after time r is a measure of the average groundwater velocity (U), or X = vt. Similarly, the migration distance of the adsorbed species (X,) i related to its velocity of movement (v ) by Xf = vj. The retardation factor (/tj for the adsorbed species is then given by... 

The striking difference in salinity between the Ekoflsk formation water and the injected seawater is S04 , which is abundant in the seawater but almost zero in the formation water. The preceding wettability modification mechanism is also supported by the fact that 864 has strong affinity onto the chalk surfaces. Figure 3.9 compares 864 affinity with that of the nonadsorbing tracer 8CN toward the chalk surface at different temperatures. 804 retarded more and more relative to 8CN as the temperatures increased, and a large increase in adsorption occurred between 100 and 130°C (8trand et al., 2006). 

A core-flood for adsorption determination consists of injecting a measured volume of surfactant solution containing a nonadsorbing tracer into a brine-saturated core and collecting effluent fractions at the core outlet. Chemical analysis of the effluent samples allows the calculation of an adsorption level based on material balance considerations and also results in a set of effluent profiles for the surfactant and the tracer. In addition to the material balance, adsorption is evaluated by matching experimental effluent concentrations from the core-floods with a convection—dispersion—adsorption numerical model. The model parameters then allow calculation of a complete adsorption isotherm. 

As pointed out in Table 6.5, the HETP plot is useful to analyze peak widths measured for tracers and solutes. With nonadsorbable tracers the theoretical HETP plot would be a straight horizontal line (C = 0) allowing to determine A and, thereby, Dax/Mim- To fit within the simplified framework presented here, for every solute only the slope C needs to be determined and keff can be subsequently evaluated. Basically, A can also be derived from these plots, but in practice different axis intercepts A might be observed for solutes and tracers. Because of the frequently limited precision in determining second moments and the application of the linearized HETP plot, the accuracy of the derived parameters is rather limited and the values for A and C and keff) can be seen as initial guesses ... 

To calculate the void fraction (Equation 2.6) and the (total) porosity (Equation 2.8) pulses of a nonpenetrating tracer (Tl) and of a nonadsorbable tracer (T2), which penetrates into the pore system (to marker), respectively, are injected. When the resulting measured elution profiles are evaluated by means of moment analysis (Section 6.5.3.1 Figure 6.11), the retention time (it has to be corrected by the dead... 

Mireur and Bischoff [6] correlated data on k[ and versus easily accessible parameters like uju f and d,/Lf the results are shovra in Figs. 13.4-3 and 4. The curve RTD data was obtained from residence time distribution experiments. These are performed with a nonadsorbable tracer like helium. The reaction experiments leading to the curve conversion data obviously involves adsorbable species. This may explain the difference between the two curves. The correlation is not meant to be d nitive since it does not account for the effect of the particle-size distribution pointed out by de Groot [2], by van Swaay and Zuiderweg [23], and by de Vries et al. [24]. The particle-size distribution is known to affect the quality of fluidization. De Vries et al. found that = Lfki/u, varies linearly as a flinction of the percentage of fines firom 4 at 7 percent fines to about 1.S at 30 percent fines. Also, Ro = is markedly affected by this variable. Nevertheless... 

Gas backmixing is obtained from steady state tracer injection tests in which tracer is injected continuously from one location and its concentration is monitored upstream of the injection point. A one-dimensional vertical dispersion process with a nonadsorbing tracer can be represented by... 

For an inert (nonadsorbable) tracer, the first moment becomes... 

Starting with a CSTR system containing porous catalysts and assuming that experiments are carried out with a nonadsorbable tracer at constant temperature we get ... 

This demonstrates that successful scaleup must duplicate conditions on the microscopic (single catalyst particle) level which results in the same H(kt) upon scaleup, and on the macroscale (flow pattern) which results in the same E (t). Therefore, nonadsorbing tracers provide very useful information with respect to the macroscopic aspect of scaleup. The limiting case of the above... 

Thus the p.d.f for nonadsorbing tracers can be used directly to estimate the p.d.f. of sojourn times on the catalyst surface if the partition coefficient, K, for the reactant is known and adsorption-desorption is fast. 

When we deal with beds of porous catalyst particles we often assume that we have plug flow for a long pilot scale reactor. We cannot find a tracer that does not diffuse into the particles and hence even the curve for a nonadsorbing tracer is not a... 

In the above discussion the behavior of nonlinear reaction schemes was not considered. Conventional approaches to reactor modeling based on ideal reactor models are suggested and tracer studies with nonadsorbing tracers should be conducted to determine whether the assumptions of ideal flow patterns are satisfied. Adsorbing tracers can be used to assess catalyst contacting through the use of the central volume principle. 

Detailed equations are presented elsewhere (118-120). A nonadsorbing tracer can then be used to determine the holdup of the liquid, 1, while gas holdup is obtained by difference 2 = 1 - i An absorbing tracer can then be used to evaluate K and A from the zeroth and first moment, or A directly from the zeroth moment if K is known. Examples of the use of various moments in determination of system parameters are presented by Mills et. al. (118) and Ramachandran and Smith (119,120). 

In an often quoted study Overcashier et. al. (156) used inert nonadsorbing tracers and showed that the use of horizontal baffles in the bed allows one to approach the plug flow RTD for the gas. 

Nauman and Collinge (159,160) expanded upon the concept of contact time distributions introduced by Orcutt et. al. (157) and showed how to obtain it by use of an adsorbing and a nonadsorbing tracer or of a pair of adsorbing tracers with different adsorption rate constants. The tracers must adsorb linearly and reversibly. 

The unsteady-state material balance on a nonreactive, nonadsorbing tracer that obeys the Dispersion model is... 

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