RTDs for

Numerical solutions of the maximum mixedness and segregated flow equations for the Erlang model have been obtained by Novosad and Thyn (Coll Czech. Chem. Comm., 31,3,710-3,720 [1966]). A few comparisons are made in Fig. 23-14. In some ranges of the parameters n or fte ihe differences in conversion or reaclor sizes for the same conversions are substantial. On the basis of only an RTD for the flow pattern, perhaps only an average of the two calculated extreme performances is justifiable. 

RTDs) for 6 sets of copper conductor cables (2 cores for each set)... 

It is desired to compare the residence time distributions (RTD) for these cases. 

Fig. 5.1.9 (a) MR measured propagators and es the velocity distribution narrows due to the (b) corresponding calculated RTDs for flow in a dispersion mechanisms of the porous media model packed bed reactor composed of 241- this effect is observed in the RTDs as a pm monodisperse beads in a 5-mm id circular narrowing of the time window during which column for observation times A ranging from spins will reside relative to the mean residence 20 to 300 ms. As the observation time increas- time as the conduit length is increased. 

With temperature, we can use a thermocouple, which typically has a resolution on the order of 0.05 mV/°C. (We could always use a RTD for better resolution and response time.) That is too small a change in output for most 12-bit analog-digital converters, so we must have an amplifier to boost the signal. This is something we do in a lab, but commercially, we should find off-the-... 

Both E and F are RTD functions. Although not apparent here, each corresponds to a different way of experimentally investigating RTD for arbitrary flow (Chapter 19 see also problem 13-1), and hence each is important. 

Consider the steady flow of fluid at a volumetric rate q through a stirred tank as a closed vessel, containing a volume V of fluid, as illustrated in Figure 13.4. We assume the flow is ideal in the form of BMF at constant density, and that no chemical reaction occurs. We wish to derive an expression for E(t) describing the residence-time distribution (RTD) for this situation. 

Some multiple-vessel configurations and consequences for design and performance are discussed previously in Section 14.4 (CSTRs in series) and in Section 15.4 (PFRs in series and in parallel). Here, we consider some additional configurations, and the residence-time distribution (RTD) for multiple-vessel configurations. 

For CSTRs in parallel with the feed split as for optimal performance, the fact that two (or more) reactors behave the same as one CSTR of the same total volume means that the RTD is also the same in each case. Here, we consider the RTD for CSTRs in series, as in a multistage CSTR (Section 14.4). In the following example, the RTD is obtained for two tanks in series. The general case of N tanks in series is considered in Chapter... 

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

Compare conversions in CSTRs and in segregated flow with Erlang or Gaussian RTDs, for second order reactions. 

Figure 8.12 Experimental and numerical determination of the RTD for a sheet of dye positioned across the channel in the feed and perpendicular to the flight. The screw was operated in extrusion mode...

In a final RTD experiment, a sheet of dye was frozen as before and positioned in the feed channel perpendicular to the flight tip. The sheet positioned the dye evenly across the entire cross section. After the dye thawed, the extruder was operated at five rpm in extrusion mode. The experimental and numerical RTDs for this experiment are shown in Fig. 8.12, and they show the characteristic residence-time distribution for a single-screw extruder. The long peak indicates that most of the dye exits at one time. The shallow decay function indicates wall effects pulling the fluid back up the channel of the extruder, while the extended tail describes dye trapped in the Moffat eddies that greatly impede the down-channel movement of the dye at the flight corners. Moffat eddies will be discussed more next. Due to the physical limitations of the process, sampling was stopped before the tail had completely decreased to zero concentration. 

These RTDs for the perfect PFTR and CSTR are shown in Figure 8-3. 

Fig. 8.20. Experimental dimensionless RTD for a finned monolith (IFM) of 75 cm length. (From Ref. [10].)...

Fig. 8.21. Experimental dimensionless RTD for a continuous monolith of 100 cm length (RC, full line) and stacked monoliths (50 cpsi/25 cpsi, length 100 cm, dotted I i ne).

Fig. 8.22. Experimental dimensionless RTD for katapak-S packing (from Ref. [22]) far below loading point (dashed line) at loading point (dotted line) beyond loading point (full line).

Table 1 lists the characteristics of the measured RTD for five different conditions. The first one is shown in Figure 2. The evolution of this curve can be explained by equation (1), although the peaks are not ideal Dirac pulses, because the flow inside the reactor (i.e. the reactor tube (c) and the recirculation pipe (d) in Figure 1) is not of the ideal plug flow type. Therefore, the tracer pulse broadens and eventually spreads throughout the reactor. Nevertheless, the distance between two peaks is a reasonably accurate estimate of the circulation time r/(R+1) in the reactor, and from this the flow through the reactor can be calculated. The recycle ratio R is calculated from the mean residence time r and the circulation time r/(R+l). 

RTD for both phases in droplet-size distribution are important for scale-up purposes—backmixing is a problem for scale-up... 

The RTD for a flowing fluid is normally obtained by the so-called stimulus-response technique. This technique involves the injection of a tracer at the inlet stream or at some point within a reactor and the observation of the corresponding response at the exit stream or at some other downstream point within the reactor. A suitable flow model can then be selected by matching the experimental RTD curve with that obtained from the mathematical model. This approach implies that a transient analysis of reactor and flow model behavior is necessary. 

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