Real plug flow reactor

Model 5 The Real Plug Flow Reactor CPFR WITH Dispersion... 

An ideal plug flow reactor has a fixed residence time Any fluid (plug) that enters the reactor at time t will exit the reactor at time t + x, where x is the residence time of the reactor. The residence time distribution function is therefore a dirac delta function at x. A real plug flow reactor has a residence time distribution that is a narrow pulse around the mean residence time distribution. 

Choose the right type of reactor for testing There are quite a number of different reactors. The above-mentioned plug flow reactor and the continuously stirred tank reactor are usually preferred for research laboratory use, but other set-ups may also be of interest for simulating real industrial conditions. 

The responses of this system to ideal step and pulse inputs are shown in Figure 11.3. Because the flow patterns in real tubular reactors will always involve some axial mixing and boundary layer flow near the walls of the vessels, they will distort the response curves for the ideal plug flow reactor. Consequently, the responses of a real tubular reactor to these inputs may look like those shown in Figure 11.3. 

Response of ideal plug flow reactor and real tubular reactor to step and impulse inputs. 

Comparison of real and plug flow reactors for the first-order reaction A -4 products, assuming negligible expansion = 0). (Adapted from Chemical Reaction Engineering, Second Edition, by O. Levenspiel. Copyright 1972. Reprinted by permission of John Wiley and Sons, Inc.)... 

Comparison of real and plug flow reactors for the second-order reactions... 

Find the fraction of reactant unconverted in the real reactor and compare this with the fraction unconverted in a plug flow reactor of the same size. 

Figure 13.19 Comparison of real and plug flow reactors for the first-order A products, assuming negligible expansion from Levenspiel and Bischoff (1959, 1961).

Equation 20 with Eq. 5.17 compares the performance of real reactors which are close to plug flow with plug flow reactors. Thus the size ratio needed for identical conversion is given by... 

In real tubular (or column) reactors there is, usually, a back-mixing effect which influences the performance of the ideal plug-flow reactor. This axial dispersion is higher for fluidized-bed reactors than for packed-bed reactors, although comparatively lower than for continuous-feed stirred-tank reactors, where the mixing is complete. 

The modeling of real immobilized-enzyme column reactors, mainly the fluidized-bed type, has been described (Emeiy and Cardoso, 1978 Allen, Charles and Coughlin, 1979 Kobayashi and Moo-Young, 1971) by mathematical models based on the dispersion concept (Levenspiel, 1972), by incorporation of an additional term to account for back-mixing in the ideal plug-flow reactor. This term describes the non-ideal effects in terms of a dispersion coefficient. 

The RTD in a system is a measure of the degree to which fluid elements mix. In an ideal plug flow reactor, there is no mixing, while in a perfect mixer, the elements of different ages are uniformly mixed. A real process fluid is neither a macrofluid nor a microfluid, but tends toward one or the other of these extremes. Fluid mixing in a vessel, as reviewed in Chapter 7, is a complex process and can be analyzed on both macroscopic and microscopic scales. In a non-ideal system, there are irregularities that account for the fluid mixing of different... 

The fluidized-bed reactor involves a rapid movement of the solid catalytic particles throughout the bed so that the operation can come close to one of uniform temperature throughout the reactor. The actual flow pattern for the operation of a fluidized bed is very complex and is between that for the ideal back-mix reactor and the ideal plug-flow reactor so that special methods for design may be required to approximate the real situation. 

This chapter discusses four methods of gas phase ceramic powder synthesis by flames, fiunaces, lasers, and plasmas. In each case, the reaction thermodynamics and kinetics are similar, but the reactor design is different. To account for the particle size distribution produced in a gas phase synthesis reactor, the population balance must account for nudeation, atomistic growth (also called vapor condensation) and particle—particle segregation. These gas phase reactors are real life examples of idealized plug flow reactors that are modeled by the dispersion model for plve flow. To obtain narrow size distribution ceramic powders by gas phase synthesis, dispersion must be minimized because it leads to a broadening of the particle size distribution. Finally the gas must be quickly quenched or cooled to freeze the ceramic particles, which are often liquid at the reaction temperature, and thus prevent further aggregation. 

A criterion for an acceptably small deviation from an ideal plug-flow reactor has been proposed by Gierman [12], based on the argument that the temperatures required for a given conversion in the real reactor and the ideal plug-flow reactor should not differ by more than 1 C, which is approximately the attainable accuracy of temperature definition in practice. This criterion is given by the expression... 

Show that to achieve the same conversion, the relationship between the volume of a plug-flow reactor Vp and volume of a real reactor V in which dispersion occurs is... 

The two extremes of the state of mixedness arc represented by the plug flow reactor (PFR, no mixing) and by the perfectly stirred reactor (PSR, perfectly mixed). The reactant flow in the PFR is neither macro nor micro mixed, whereas in the PSR mixing occurs down to the molecular level, thus both macro and micro mixing take place (see Figure 6). A variety of real flows can be characterised by series, parallel or loop connections of PFR and PSR. Additionally there exist other models such as the dispersion model (dispersed plug flow) which allows to model mixing conditions between the two extremes of PFR and PSR. 

Most large reactors do not fit the foregoing criteria, but in many cases the deviations from ideal reactors are small, and the equations for ideal reactors can be used for approximate design calculations and sometimes for determining optimum reaction conditions. In this chapter, ideal stirred-tank reactors are considered first and then plug-flow reactors are discussed. The effects of heat transfer, mass transfer, and partial mixing in real reactors are treated in later chapters. 

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