Reactors plug flow with dispersion

Plug Flow with Dispersion - Plug flow with dispersion is a concept that is often used to describe one-dimensional flow systems. It is somewhat more flexible in computational models because the mixing within the system is not dependent on reactor size, as with complete mix tanks in series. Plug flow with dispersion will be described in the second half of this chapter because special techniques are needed for the analysis. 

A similar spatial mean velocity (bulk mean velocity) is used for the plug flow reactor model. Thus, plug flow with dispersion is a natural match, where the mixing that truly occurs in any reactor or environmental flow is modeled as dispersion. This is the model that will be applied to utilize dispersion as a mixing model. 

The response of a plug flow with dispersion model to a pulse input, equation (6.42), is given in Figure 6.13 for various values of the Peclet number, Pe = UL/Dl. Equation (6.41) will be applied to the analysis of a pulse with dispersion in a reactor in Example 6.10. 

EXAMPLE 6.10 Air-Stripping tower with first-order degradation, modeled as plugfiow, plug flow with dispersion, and mixed tanks-in-series reactors... 

The assumption that Cou = 1 in equation (6.43) is really only accurate when Pe > 10. The only way to apply this tracer curve to the plug flow with dispersion model while Cou 1 would be to route each portion of the tracer curve through the reactor. With Pe = 9.4, this solution will be close, although stiU an approximation. 

Rivers are close to the perfect environmental flow for describing the flow as plug flow with dispersion. The flow is confined in the transverse and vertical directions, such that a cross-sectional mean velocity and concentration can be easily defined. In addition, there is less variation in rivers than there is, for example, in estuaries or reactors - both of which are also described by the plug flow with dispersion model. For that reason, the numerous tracer tests that have been made in rivers are useful to characterize longitudinal dispersion coefficient for use in untested river reaches. A sampling of the dispersion coefficients at various river reaches that were... 

Simpler optimization problems exist in which the process models represent flow through a single pipe, flow in parallel pipes, compressors, heat exchangers, and so on. Other flow optimization problems occur in chemical reactors, for which various types of process models have been proposed for the flow behavior, including well-mixed tanks, tanks with dead space and bypassing, plug flow vessels, dispersion models, and so on. This subject is treated in Chapter 14. 

The next thing we note about chromatography is that it is equivalent to tracer injection into a PFTR. Whereas in Chapter 8 we used tracer injection to determine the residence time distribution in a reactor, here we have nearly plug flow (with the pulse spread somewhat by dispersion), but adsorption from the fluid phase onto the solid reduces the flow velocity and increases the residence time to be much longer than x. ... 

Plug Flow Reactor with Dispersion. The residence time is still 15 min. The plug flow with a dispersion model gives equation (6.43) ... 

Plug Flow With a significant amount of axial dispersion, Equation (3), describing the normal bed temperature profile, must be modified to account for this dispersion. The effect of this modification is that the ultimate vertical asymptote in temperature is moved forward in the extended bed. Dispersion enhances the tendency of a reactor to run away. However, with the type of dispersion that occurs in a trickle bed, by variations in velocity from point to point, the profile retains its vertical asymptote. The solution of Equation (3) plus dispersion is almost identical with Equation (5), but with a different value of SD. Since SD drops out in the ultimate stability criterion, axial dispersion cannot be of any particular significance in the development of local hot spots. It affects the global stability of the normal part of the reactor, but it has little influence on the way disturbances grow, relative to the normal regions. 

Figure 3-11 A mixing model for the trickle-bed reactor which comprises an axially dispersed plug flow with mass exchange with stagnant areas.106...

The H-Oil reactor (Fig. 21) is rather unique and is called an ebullated bed catalytic reactor. A recycle pump, located either internally or externally, circulates the reactor fluids down through a central downcomer and then upward through a distributor plate and into the ebullated catalyst bed. The reactor is usually well insulated and operated adiabatically. Frequently, the reactor-mixing pattern is defined as backmixed, but this is not strictly true. A better description of the flow pattern is dispersed plug flow with recycle. Thus, the reactor equations for the axial dispersion model are modified appropriately to account for recycle conditions. 

In an ideal fixed-bed reactor, plug flow of gas is assumed. This is, however, not a good assumption for reactive solids, because the bed properties vary with position, mainly due to changing pellet properties (and dimensions in most cases), and hence the use of nonideal models is often necessary. The dispersion model, with all its limitations, is still the most practical one. The equations involved are cumbersome, but their asymptotic solutions are simple, particularly for systems... 

The reactor is in plug flow with negligible axial and infinite radial dispersion. 

The reactor is assumed to be adiabatic with plug flow. Axial dispersion can be ignored. Any effect of limitations of mass or heat transfer inside the catalyst pellet is lumped into the rate constants given in Table 1. The catalyst activity is assumed to be constant. Use the conversion of ethylbenzene or water in the set of continuity equations. Use the Ergun equation to describe the pressure drop. 

In Chapter 2, the design of the so-called ideal reactors was discussed. The reactor ideahty was based on defined hydrodynamic behavior. We had assumedtwo flow patterns plug flow (piston type) where axial dispersion is excluded and completely mixed flow achieved in ideal stirred tank reactors. These flow patterns are often used for reactor design because the mass and heat balances are relatively simple to treat. But real equipment often deviates from that of the ideal flow pattern. In tubular reactors radial velocity and concentration profiles may develop in laminar flow. In turbulent flow, velocity fluctuations can lead to an axial dispersion. In catalytic packed bed reactors, irregular flow with the formation of channels may occur while stagnant fluid zones (dead zones) may develop in other parts of the reactor. Incompletely mixed zones and thus inhomogeneity can also be observed in CSTR, especially in the cases of viscous media. 

Other models to characterize residence time distributions are based on fitting the measured distribution to models for a plug flow with axial dispersion or for series of continuously ideally stirred tank reactors in series. For the first model the Peclet number is the characteristic parameter, for the second model the number of ideally stirred tank reactors needed to fit the residence time distribution typifies the distribution. However, these models should be used with care because they assume a standard distribution in residence times. Most distributions in extruders show a distinct scewness, which could lead to erroneous results at very short and very long residence times. The only exception is the co-kneader the high amount of back mixing in this type of machine leads to a nearly perfect normal distribution. 

Note that this equation has no physical significance It is only for first order reactions that these two models pr ict the same conversion for the same mean residence time. There is, however, an important physical difference between the two models in the cascade model there is no bacl xing from reactor number N to reactor number N-1, whereas in the model for plug flow with axial dispersion there is only one discontinuity, that is at the reactor entrance. 

This simply assumes that axial dispersion (D m. s ) is superimposed onto plug flow. Axial dispersion may be caused by a velocity profile in the radial direction or statistical dispersion in a packing or turbulent diffusion or by any physicochemical process which delayes some particles with respect to others. The model parameter is the axial PECLET number, Pe = uL/D, or its reciprocal, the dispersion number, D /uL. Depending on the boundary conditions assumed at the reactor inlet and outlet (which are different from those of the simple assumptions above), a lot of mathematical formulae can be found in the literature for the RTD [3]. This is often academic as in the range of usefulness of the model (small deviation from plug flow, say Pe > 20) all conditions lead to res-... 

A one-dimensional isothermal plug-flow model is used because the inner diameter of the reactor is 4 mm. Although the apparent gas flow rate is small, axial dispersion can be neglected because the catalj st is closely compacted and the concentration profile is placid. With the assumption of Langmuir adsorption, the reactor model can be formulated as. 

A pilot scale UASB reactor was simulated by the dispersed plug flow model with Monod kinetic parameters for the hypothetical influent composition for the three VPA ccmiponents. As a result, the COD removal efflciency for the propionic acid is smallest because its decomposition rate is cptite slow compared with other substrate components their COD removal eflSciencies are in order as, acetic acid 0.765 > butyric acid 0.705 > propionic acid 0.138. And the estimated value of the total COD removal efficiency is 0.561. This means that flie inclusion of large amount of propionic acid will lead to a significant reduction in the total VFA removal efficiency. 

Figure 7.4c shows an in-line static mixer. Dispersion is usually promoted by repeatedly changing the direction of flow locally within the mixing device as the liquids are pumped through. This will give a good approximation to plug-flow in both phases in cocurrent flow. As with gas-liquid reactors, static mixers are particularly suitable when a short residence time is required. 

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