Characteristics of the RTD

Sometimes E t) is called the exit-age distribution function. If we regard the age of an atom as the time it has resided in the reaction environment, then E t) concerns the age distribution of the effluent stream. It is tbe most used of the distribution functions connected with reactor analysis because it characterizes ttie lengths of time various atoms spend at reaction conditions. 

---

Table 1 Characteristics of the RTD-functions in the recycle electrobalance reactor.

This is a Hory distribution or most probable distribution and much broader (D>1) than the Poisson distribution (D=l) resulting from batch polymerization. The increase in molecular weight polydispersity is due to the fact that the chains are living, and so are directly impacted by the RTD. Recall that the polydispersity of the RTD for a CSTR is 2. For long residence time, approaches 1 and D becomes 2. Thus, the number chain length distribution (NCLD) takes on the breadth characteristics of the RTD, due to the living nature of the polymer chains. For comparison, one should recall that the lifetime of a free radical is 1-10 s. This is insignificant in comparison with the RTD and so that RTD has little to no effect on D in free radical polymerization. 

An RTD curve, for instance, can be represented in algebraic form in more than one way and for different purposes. The characteristic bell shape of many RTDs is evident in the real examples of Figure 5.4. Such shapes invite comparison with some well-known statistical distributions and representation of the RTD by their equations. Or a realistic mechanism may be postulated, such as a network of reactor elements and a type of flow pattern, and the parameters of that mechanism evaluated from a measured RTD. 

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). 

Methods for evaluating the axial dispersion coefficient from RTD data As mentioned earlier, the one-parameter axial-dispersion model is widely used to correlate RTD data. The nature of the RTD depends upon the nature of the tracer input and the nature of the. flow, characteristics. For the RTD shown in Fig. 3-4 o), the axial dispersion coefficients for the liquid and solid phases can be obtained by fitting the equation... 

In the vast majority of experimental studies, the backmixing characteristics of a flowing phase are examined using a -pulse tracer input. For the fixed-bed systems shown in Fig. 3-2, if a perfect pulse input is used, then, as shown by Levenspiel,5 6 the axial dispersion coefficient or the Peclet number can be obtained from the variance of the RTD curve. For example, for a closed system and large extent of dispersion, the variance, it, is related to the Peclet number by the equation... 

The model requires two arbitrary parameters, /, the fraction of liquid which is stagnant, and K, the mass-transfer coefficient between flowing and stagnant liquid, to describe the extent of liquid backmixing. The relationship between / and K and the characteristics of the experimental RTD curve have been developed by many workers.28,29 / may be calculated from the expression... 

In general, an unsteady-state operation is obtained as a result of catalyst aging. The reactor is, of course, not very useful for gathering the kinetic data when the catalyst decays rapidly. Multiple taps can be employed to give multiple conversion and selectivity points for each experimental run. As shown in Chaps. 6 through 8, the RTD characteristics of the gas and liquid phases depend on the orientation of the gas and liquid flows (e.g., both cocurrent downwards, both cocurrent upwards, etc.). 

It should be noted that the RTD character of a whole recycle reactor system, quantified with BOt j, depends not only on the recycle ratio r, but also on BOint, the internal RTD characteristic of the reactor (Moser, 1985a). 

Vertical wind profile and turbulence were measured using three Gill bivane anemometers installed at a tower 600 m upwind of the release point. The data from these sensors were not transferred from LLNL to WRI. On this same tower, five levels of platinum RTD sensors at heights of 1, 2, 4, 8, and 16 m were installed to measure the ambient temperature and temperature lapse rate. Eighteen (18) stations using two-axis cup-and-vane anemometers (Met-One) mounted 2 m above the ground were used to determine the characteristics of the wind field before, during and after each release. 

A major advantage of these normalized RTD curves is that conveying characteristics of different extruders can be directly compared. From comparison of Figs. 11.21-11.23 it is clear that the conveying characteristics of the single screw extruder are quite positive compared to the two twin screw extruders. This is partially due to the plug flow of the solid bed in the single screw extruder. The solid bed in a twin screw... 

Residence time distribution (RTD) is a classical tool in the prediction of the comportment of a chemical reactor provided that the reaction kinetics and mass transfer characteristics of the system are known, the reactor performance can be calculated by combining kinetic and mass transfer models to an appropriate residence time distribution model. RTDs can be determined experimentally, as described in classical textbooks of chemical reaction engineering (e.g. Levenspiel 1999). RTD experiments are typically carried out as pulse or step-response experiments. The technique is principally elegant, but it requires the access to the real reactor system. In large-scale production, experimental RTD studies are not always possible or allowed. Furthermore, a predictive tool is needed, as the design of a new reactor is considered. 

Frequently used macro-PDFs are the so-called Internal Age Distribution, /(a), and related Residence Time Distribution (RTD), E 6), which are closely related to the macro-PDF of the velocity, (v). The characteristics and practical use of the RTD are discussed in more detail in the next sub-sections. RTD methods are commonly based on the response of the reactor to a tracer impulse or step given at the reactor inlet. This implies statistically non-stationary calculations, for which (12.6.1-1) can be extended to... 

An experimentally measured RTD of a steady state flow reactor reflects the spatial characteristics of the macro-flow and -mixing in the reactor, including eventual effects of micro-flow and -mixing phenomena on the macro-flow and -mixing. Hence, inspection of experimental RTD can be used to infer certain properties of the flow pattern. Local information on the macro- or micro-flow and mixing behavior inside the reactor can, however, not be revealed, due to the length scale over which RTD are defined (see (12.6.1-2)) and measurements are... 

RTD is a classical tool in predicting the comportment of a chemical reactor provided that the reaction kinetics and mass transfer characteristics of the system are known, reactor... 

The exit concentration data shown in Table P4.8 were obtained from a tracer experiment studying the mixing characteristics of a continuous flow reactor. Calculate the RTT> function, cumulative distribution function, mean residence time, and the variance of the RTD function of this reactor. 

The RTD is a distinctive characteristic of mixing behavior. In Fig. 7-2>e, the CSTR has an RTD that varies as the negative exponential of the time and the PFR is represented by a vertical line at = 1. Multistage units and many packed beds have beU-shaped RTDs, like that of... 

---