Plug flow reactor tracer response curves

Because of the different paths taken by elements of a fluid to pass through a packed column, a residence-time distribution is generally obtained using a tracer signal at the bed input (salt, dyes), and by analysis of the output response [11]. A ical downstream signal is obtained, dependent on the kind of flow and mixing in the reactor (plug-flow reactor, mixed-flow reactor). The experimental distribution curve may be characterized in terms of mean and variance by ... 

In the previous section, we learned that not all fluid elements spend exactly the same time in a reactor, excqit for the special case of an ideal, plug-flow reactor. Residence tune distribution functions provide a quantitative way to describe how much time a flowing fluid spends in a reactor. Residence time distribution functions can be obtained from tracer response curves. 

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). 

Fortunately, it is not always necessary to recover the system RTD curve from the impulse response, so the complications alluded to above are often of theoretical rather than practical concern. In addition, the dispersion model is most appropriately used to describe small extents of dispersion, i.e. minor deviations from plug flow. In this case, particularly if the inlet pipe is of small diameter compared with the reactor itself, the vessel can be satisfactorily assumed to possess closed boundaries [62]. An impulse of tracer will enter the system and broaden as it passes along the reactor so that the observed response at the outlet will be an RTD and will be a symmetrical pulse, the width of which is a function of DjuL alone. 

An RTD, however, does not represent the mixing behavior in a vessel uniquely, because several arrangements of the internals of a vessel may give the same tracer response, for example, any series arrangements of reactor elements such as plug flow or complete mixing. This is a consequence of the fact that tracer behavior is represented by linear differential equations. The lack of uniqueness limits direct application of tracer studies to first-order reactions with constant specific rates. For other reactions, the tracer curve may determine the upper and lower limits of reactor performance. When this range is not too broad, the result can be useful. Tracer data also may be taken at several representative positions in the vessel in order to develop a realistic model of the reactor. 

To predict the response curve to an ideal pulse tracer injection at the entrance of the tubular reactor, the boundary conditions at both ends have to be known. Suppose the flow is undisturbed as it passes the inlet and the outlet boundaries of the reactor. This situation is depicted in Figure 3.11a and called an open/open system to dispersion. In contrary to this situation, ideal plug flow D = 0) is considered outside of the boundaries as illustrated in Figure 3.11b. A sudden change of the axial dispersion occurs at the inlet and the outlet of the reactor. This situation corresponds to a closed/closed system. In addition to these situations, vessels open for dispersion at only one site can be discussed. 

The RTD in the tubular reactor was determined experimentally with water as fluid and Brilliant Blue dye as tracer. The tracer was introduced at the reactor inlet in the form of a step function. The concentration of the dye was measured with an UV-vis spectrometer and the response curve is given as f-curve. As the experimental f-curve shown in Figure 3.29 is very steep, a low axial dispersion can be expected. Therefore, RTD will be described with the dispersion model supposing small deviation from plug flow (Equation 3.50). The f-curve valid for small dispersion Bo > 100) can be obtained by integrating the RTD given by (0) (Equation 3.50). 

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