Plug flow performance equation

For each run in a differential reactor the plug flow performance equation becomes... 

To find the amount of catalyst needed without using an analytic expression for the rate concentration relationship requires graphical integration of the plug flow performance equation, or... 

Table 4.10.3 gives the conversion in a batch reactor, a PFR, and a CSTR for different values of 8v for the example of Do = 1. The data indicate that, in contrast to a batch reactor, Xa decreases for a reaction with increasing volume both in a CSTR and in a PFR, which is in general true for a reaction order >0 [see Levenspiel (1996, 1999)]. For a reaction with decreasing volume rate, this is reversed. In both flow reactors (PFR, CSTR), the residence time changes compared to a constant volume reaction, while in a batch reactor the reaction time does not. Thus for reactions with changing volume, the batch and the plug flow performance equations are different. 

In some cases it is possible to perform experiments at conversions low enough to allow neglect of the effect of conversion on the rate. In other words the rate is constant throughout the plug flow reactor. Equation (7.159) can then be integrated to ... 

A model of a reaction process is a set of data and equations that is believed to represent the performance of a specific vessel configuration (mixed, plug flow, laminar, dispersed, and so on). The equations include the stoichiometric relations, rate equations, heat and material balances, and auxihaiy relations such as those of mass transfer, pressure variation, contac ting efficiency, residence time distribution, and so on. The data describe physical and thermodynamic properties and, in the ultimate analysis, economic factors. 

Another view is given in Figure 3.1.2 (Berty 1979), to understand the inner workings of recycle reactors. Here the recycle reactor is represented as an ideal, isothermal, plug-flow, tubular reactor with external recycle. This view justifies the frequently used name loop reactor. As is customary for the calculation of performance for tubular reactors, the rate equations are integrated from initial to final conditions within the inner balance limit. This calculation represents an implicit problem since the initial conditions depend on the result because of the recycle stream. Therefore, repeated trial and error calculations are needed for recycle... 

Three basic fluid contacting patterns describe the majority of gas-liquid mixing operations. These are (1) mixed gas/mixed liquid - a stirred tank with continuous in and out gas and liquid flow (2) mixed gas/batch mixed liquid - a stirred tank with continuous in and out gas flow only (3) concurrent plug flow of gas and liquid - an inline mixer with continuous in and out flow. For these cases the material balance/rate expressions and resulting performance equations can be formalized as ... 

By comparing the design equations of batch, CFSTR, and plug flow reactors, it is possible to establish their performances. Consider a single stage CFSTR. 

Davis et al. [9] have performed studies on the bateh hydration of ethylene oxide. Their work determined the value of the produet distribution eonstant K. This value is used in Equation 5-378 to determine the expeeted performanee in a plug flow reaetor. This value is also used in Equation 5-394 to illustrate the poor performanee that would be obtained with eomplete baekmixing. 

The equation for conversion in laminar flow is developed in problem P4.08.01 which also compares the performance with that in plug flow when the rate equation is first or second order. The residual concentration is higher (the conversion is lower) with laminar flow. A similar result is found in problem P4.08.09 which is for straight line radial variation or n = co. Numerical magnitudes of the variation of concentration over a cross section are found in problem P4.08.07. Other problems point out the errors in... 

Conversions by all models, Equations (3), (4), (5) and (6) are all about the same. The large value of n from the variance indicates that the performance does approximate plug flow. 

Figure 5.6 Graphical representation of the performance equations for plug flow reactors.

For systems of constant density (constant-volume batch and constant-density plug flow) the performance equations are identical, r for plug flow is equivalent to t for the batch reactor, and the equations can be used interchangeably. 

For systems of changing density there is no direct correspondence between the batch and the plug flow equations and the correct equation must be used for each particular situation. In this case the performance equations cannot be used interchangeably. 

Equations 1 and 2 are displayed in graphical form in Fig. 6.1 to provide a quick comparison of the performance of plug flow with mixed flow reactors. For... 

This recycle ratio can be made to vary from zero to infinity. Reflection suggests that as the recycle ratio is raised the behavior shifts from plug flow R = 0) to mixed flow (R = oo). Thus, recycling provides a means for obtaining various degrees of backmixing with a plug flow reactor. Let us develop the performance equation for the recycle reactor. 

Batch or Plug Flow Reactors. Integration gives the performance equations for this system... 

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... 

Batch-Solids, Plug Constant Flow of Fluid. For plug flow the performance equation combined with the rate of Eq. lAa becomes... 

Table 21.1 Performance equations for plug flow G/batch S, with the simple first...

The performance equations for this rate form and mixed flow are analogous to those for plug flow, shown in Table 21.1,... 

Now let us return to our batch (or plug flow) reactor. Applying its performance equation we find... 

These kinetics are displayed in Fig. 30.5. The performance equation for plug flow is quite messy however, for mixed flow the performance equation can be obtained directly. Thus in general, for Cqq 0 and Crq 0 we have... 

The viability of one particular use of a membrane reactor for partial oxidation reactions has been studied through mathematical modeling. The partial oxidation of methane has been used as a model selective oxidation reaction, where the intermediate product is much more reactive than the reactant. Kinetic data for V205/Si02 catalysts for methane partial oxidation are available in the literature and have been used in the modeling. Values have been selected for the other key parameters which appear in the dimensionless form of the reactor design equations based upon the physical properties of commercially available membrane materials. This parametric study has identified which parameters are most important, and what the values of these parameters must be to realize a performance enhancement over a plug-flow reactor. 

The space velocity for a given conversion is often used as a ready measure of the performance of a reactor. The use of equation 1.25 to calculate reaction time, as if for a batch reactor, is not to be recommended as normal practice it can be equated to VJv only if there is no change in volume. Further, the method of using reaction time is a blind alley in the sense that it has to be abandoned when the theory of tubular reactors is extended to take into account longitudinal and radial dispersion and other departures from the plug flow hypothesis which are important in the design of catalytic tubular reactors (Chapter 3, Section 3.6.1)... 

If axial dispersion were an important effect, the reactor performance would tend to fall below that of a plug flow reactor. In this event an extra term must be added to equation 3.87 to account for the net dispersion occurring within the element of bed. This subject is considered later. 

Thus, since FA0 = i>0- CA0, the performance equation of the ideal plug flow reactor can be written as... 

The recycling reactor behaves similarly to the plug flow reactor, with one major difference, that the conversion range in the reactor is narrower than in the true plug flow reactor (Figure 8.10). This reactor type is also named the differential reactor. The performance equation is [1, 2, 6, 7]... 

Equation 5-307 is the design performance equation for a plug flow reactor at constant density. Figure 5-30 shows the profiles of these equations. 

---