Residence time plug flow reactor

A reasonable assumption for the fluidized-bed reactor is that the fluid is partially mixed, whereas the solid is fully mixed. If we assume that the fluid is in plug flow, the residence time distribution of the solids will be given by exp(-t). As for the fixed-bed reactor, we shall first consider exponential decay. Therefore, the average rate constant to be used in solving Equation 12.46 is... 

In most of the attractive examples of intensified process equipment (e.g. in-line mixers, spinning disc reactors, rotating packed-beds, micro-reactors, etc.) the fluid residence time is measured in seconds. Therefore, a process designer should consider the use of these devices, provided that the reactions are (or can be made to be) completed in this time frame. If this is not the case, then the fluid intensity should be detuned to match the relatively relaxed kinetic environment. In this event, with a continuous process, a simple tubular reactor with very modest flow velocities could provide adequate plug flow and residence times up to several hours. In the case of a number of biological processes, as an alternative example, substantial intensification can be achieved using a continuous oscillatory baffled reactor (COBR, see Chapter 5), where residence times may be at best minutes and could extend to hours. 

In a continuous reactor with pure plug flow, the residence time x should he >... 

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. 

Fig. 8. Combined flow reactor models (a) parallel flow reactors with longitudinal diffusion (diffusivities can differ), (b) internal recycle—cross-flow reactor (the recycle can be in either direction), comprising two countercurrent plug-flow reactors with intercormecting distributed flows, (c) plug-flow and weU-mixed reactors in series, and (d) 2ero-interniixing model, in which plug-flow reactors are parallel and a distribution of residence times dupHcates that...

One quantitative measure of reactor efficiency at a conversion level x is the ratio of the mean residence time or the reactor volume in a plug flow reactor to that of the reactor in question,... 

Space time ST is equal to the residence time in a plug flow reactor only if the volumetric flowrate remains constant throughout the reactor. The residence time depends on the change in the flowrate through the reactor, as well as V/u. The change in u depends on the variation in temperature, pressure, and the number of moles. The concept of SV with conversions in the design of a plug flow reactor is discussed later in this chapter. 

Fig ure 5-36. Residence time in CFSTR and plug flow reactors from versus C q plot. 

An ideal plug flow reactor, for example, has no spread in residence time because the fluid flows like a plug through the reactor (Westerterp etal., 1995). For an ideal continuously stirred reactor, however, the RTD function becomes a decaying exponential function with a wide spread of possible residence times for the fluid elements. 

Figure 1. Typical reactor temperature profile for continuous addition polymerization a plug-flow tubular reactor. Kinetic parameters for the initiator 1 = 10 ppm Ea = 32.921 kcal/mol In = 26.492 In sec f = 0.5. Reactor parameter [(4hT r)/ (DpCp)] = 5148.2. [(Cp) = heat capacity of the reaction mixture (p) = density of the reaction mixture (h) = overall heat-transfer coefficient (Tf) = reactor jacket temperature (r) = reactor residence time (D) = reactor diameter].

If the process is carried out in a stirred batch reactor (SBR) or in a plug-flow reactor (PFR) the final product will always be the mixture of both products, i.e. the selectivity will be less than one. Contrary to this, the selectivity in a continuous stirred-tank reactor (CSTR) can approach one. A selectivity equal to one, however, can only be achieved in an infinite time. In order to reach a high selectivity the mean residence time must be very long, and, consequently, the productivity of the reactor will be very low. A compromise must be made between selectivity and productivity. This is always a choice based upon economics. 

The above equations also apply to a plug flow reactor, where 0 is the dimensionless residence time, which varies with distance. 

Two template examples based on a capillary geometry are the plug flow ideal reactor and the non-ideal Poiseuille flow reactor [3]. Because in the plug flow reactor there is a single velocity, v0, with a velocity probability distribution P(v) = v0 16 (v - Vo) the residence time distribution for capillary of length L is the normalized delta function RTD(t) = T 1S(t-1), where x = I/v0. The non-ideal reactor with the para-... 

It should be noted that the analysis for an ideal-batch reactor is the same as that for a plug-flow reactor (compare Equations 5.43 and 5.61). All fluid elements have the same residence time in both cases. Thus... 

Alternatively, the residence time in the plug-flow reactor could be calculated from the batch equations given in Table 5.10. This... 

As with continuous processes, the heart of a batch chemical process is its reactor. Idealized reactor models were considered in Chapter 5. In an ideal-batch reactor, all fluid elements have the same residence time. There is thus an analogy between ideal-batch reactors and plug-flow reactors. There are four major factors that effect batch reactor performance ... 

For plug flow reactors all fluid elements take the same length of time to travel from the reactor inlet to the reactor outlet. This time is the mean residence time 7. 

This equation is the basic relation for the mean residence time in a plug flow reactor with arbitrary reaction kinetics. Note that this expression differs from that for the space time (equation 8.2.9) by the inclusion of the term (1 + SAfA) and that this term appears inside the integral sign. The two quantities become identical only when 5a is zero (i.e., the fluid density is constant). The differences between the two characteristic times may be quite substantial, as we will see in Illustration 8.5. Of the two quantities, the reactor... 

ILLUSTRATION 8.5 DETERMINATION OF MEAN RESIDENCE TIME IN A PLUG FLOW REACTOR UNDER ISOTHERMAL OPERATING CONDITIONS—VARIABLE DENSITY CASE... 

For isothermal operation at 500 °C and 5 atrp, it was shown that the space time required to achieve 90% conversion was 29.9 sec. Compare this value with the mean residence time of the material in the plug flow reactor. 

Unlike the situation in a plug flow reactor, the various fluid elements mix with one another in a CSTR. In the limit of perfect mixing, a tracer molecule that enters at the reactor inlet has equal probability of being anywhere in the vessel after an infinitesimally small time increment. Thus all fluid elements in the reactor have equal probability of leaving in the next time increment. Consequently there will be a broad distribution of residence times for various tracer molecules. The character of the distribution is discussed in Section 11.1. Because some of the... 

Except for the case of an ideal plug flow reactor, different fluid elements will take different lengths of time to flow through a chemical reactor. In order to be able to predict the behavior of a given piece of equipment as a chemical reactor, one must be able to determine how long different fluid elements remain in the reactor. One does this by measuring the response of the effluent stream to changes in the concentration of inert species in the feed stream—the so-called stimulus-response technique. In this section we will discuss the analytical form in which the distribution of residence times is cast, derive relationships of this type for various reactor models, and illustrate how experimental data are treated in order to determine the distribution function. 

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

Note that in this case the right side of equation 11.1.68 is zero for t = 0 and unity for t = 00. Figure 11.9 contains several F(t) curves for various values of n. As n increases, the spread in residence time decreases. In the limit, as n approaches infinity the F(t) curve approaches that for an ideal plug flow reactor. If the residence time distribution function given by 11.1.69 is differentiated, one obtains an... 

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

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