Plug flow element

Plug flow element. Such an element depicted in Fig.4-3 is characterized by the following transition probabilities for a pulse input introduced at 

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Reaction takes place only within the plug flow element of the recycle reactor, and the gross product stream from this element is divided into two portions one becomes the net product and the second is mixed with fresh feed. The mixture of the fresh feed and recycle stream is then fed to the plug flow element. By varying the relative quantities of the net product and recycle streams, one is able to obtain widely varying performance characteristics. At... 

The basic design equation for a plug flow reactor (equation 8.2.7) may be used to describe the steady-state conversion achieved in the plug flow element of the recycle reactor ... 

First, a mechanism is assumed whether completely mixed, plug flow, laminar, with dispersion, with bypass or recycle or dead space, steady or unsteady, ana so on. Then, for a differential element of space and/or time the elements of a conservation law. 

Consider the elemental volume S6l at length 1 of the plug flow. Applying the general energy balanee in differential form gives... 

During plug flow, all material passes through the vessel without any mixing, and eaeh fluid element stays in the vessel for exaetly the same length of time. Eor a step input, the front or interfaee between the traeer and non-traeer fluids traverses down the vessel and exits at the other end in a time equal to the mean residenee time f. Therefore, the E(6) eurve is a step funetion and is expressed as... 

The laminar veloeity profile in Figure 8-2la is approximated by a series of annuli, within eaeh of whieh the veloeity is eonstant as illustrated in Figure 8-21b. Eaeh annulus is eonsidered to be a plug flow tubular reaetor having its own spaee veloeity. The veloeities of the fluid elements at different radii are given by the parabolie veloeity profile for fully developed laminar flow. The veloeity is expressed as... 

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. 

Sakata [180] evaluates the degree of mixing of the liquid as it flows across a tray and its effect on the tray efficiency, Figure 8-30. For plug flow the liquid flows across the tray with no mixing, while for partial or spot mixing as it flow s over the tray, an improved tray efficiency can be expected. For a completely mixed tray liquid, the point efficiency for a small element of the tray, Eog> tray efficiency, E V, are equal. 

A system has been constructed which allows combined studies of reaction kinetics and catalyst surface properties. Key elements of the system are a computer-controlled pilot plant with a plug flow reactor coupled In series to a minireactor which Is connected, via a high vacuum sample transfer system, to a surface analysis Instrument equipped with XFS, AES, SAM, and SIMS. When Interesting kinetic data are observed, the reaction Is stopped and the test sample Is transferred from the mlnlreactor to the surface analysis chamber. Unique features and problem areas of this new approach will be discussed. The power of the system will be Illustrated with a study of surface chemical changes of a Cu0/Zn0/Al203 catalyst during activation and methanol synthesis. Metallic Cu was Identified by XFS as the only Cu surface site during methanol synthesis. 

The importance of the linear arrangement of mixer/funnel/tubular reactor is shown when processing in a set-up with a curved flow element (0.3 m long bent Teflon tube of 0.3 mm inner diameter) in between the funnel and tubular reactor [78]. If a straight tube of equal dimensions as given above is used, plugging occius after 30 s. Hence even short curved flow passages are detrimental for micro-chan-nel-based amidation studies. 

Consider a small element of volume, AV, of an ideal plug-flow tubular reactor, as shown in Fig. 4.6. 

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... 

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 ... 

There will be velocity gradients in the radial direction so all fluid elements will not have the same residence time in the reactor. Under turbulent flow conditions in reactors with large length to diameter ratios, any disparities between observed values and model predictions arising from this factor should be small. For short reactors and/or laminar flow conditions the disparities can be appreciable. Some of the techniques used in the analysis of isothermal tubular reactors that deviate from plug flow are treated in Chapter 11. 

Consider the segment of tubular reactor shown in Figure 8.3. Since the fluid composition varies with longitudinal position, we must write our material balance for a reactant species over a different element of reactor (dVR). Moreover, since plug flow reactors are operated at steady state except during start-up and shut-down procedures, the relations of major interest are those in which the accumulation term is missing from equation 8.0.1. Thus... 

Schematic representation of differential volume element of plug flow reactor.

It should be emphasized that for ideal tubular reactors, it is the total volume per unit of feed that determines the conversion level achieved. The ratio of the length of the tube to its diameter is irrelevant, provided that plug flow is maintained and that one uses the same flow rates and pressure-temperature profiles expressed in terms of reactor volume elements. 

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. 

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. 

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