Plug Flow Criterion

Using the methodology of Mears [19], the effect of axial dispersion on the performance of a tubular reactor can be ignored if the constraint given in Eq. (14) is satisfied  

For example, consider the short residence time case presented earlier (7 s residence time, 1-m long channel with 0.007-inch diameter). For a first order reaction with = 0.05 and an inlet concentration of 100 mol m, about 30% conversion would be achieved. The right-hand side of the dimensionless inequality above, assuming a molecular diffusivity of 1.16 X 10 m s is 0.007. Thus, the plug flow criterion is easily satisfied. For rate constants lower than the value in this example, the above criterion is even more readily satisfied. Thus, the channel dimensions used in this example will enable a plug flow mass balance to be the basis for all reaction rate parameter calculations, simplifying the data analysis. 

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Aside from the requirement of a sharp residence time distribution, the ideal fixed-bed reactor should also allow all parts of the catalyst bed to fully participate in the overall conversion, i.e., all catalyst particles must be contacted by the reactant fluid. With a single fluid phase, this condition is generally met when the plug flow criterion is obeyed since in this case there is a uniform flow through the bed. However, in two... 

For ideal plug flow, the direction of flow is inconsequential. The difference in behavior between the two directions of flow is therefore due entirely to the dispersion effect. For example, for the ammonia reactor, which satisfies the plug-flow criterion given by Equation (11.126), the change of direction makes no difference. 

Plug flow is approached at low values of the dispersion coefficient or hi values or Peclet number. A criterion developed by Mears (Chem. Eng. Sci., 26, 1361 [1971]) is that conversion will be within 5 percent of that predicted by phig flow when... 

Partial oxidation of methane in the membrane reactor configuration shown in Figure 1 will not lead to higher yields of desired products than a plug flow reactor unless the diffusivity of the intermediate product, formaldehyde, is approximately four times that of methane. Presently available membranes that can withstand partial oxidation temperatures do not satisfy this criterion. 

Taking into account that the ratio Z/dp is 5000, we can assume that the plug-flow condition is assured for both phases. Here, we can use the criterion of Mears (eq. (3.421)) ... 

At this point, it is also important to check the plug-flow assumption, as the models assume plug flow for liquid. The correlation of Michell-Furzer (eq. (3.417)) for the liquid is used and the results are shown in Table 5.17. The minimum values of Z/Jp are evaluated by using the Mears criterion (eq. (3.421)). 

Hydraulic parameters and Mears criterion for plug flow... 

The next parameter of importance is the Peclet number of the liquid and the gas phase. For the specified Reynolds number, the Peclet number for the liquid phase using the Michell-Furzer correlation (eq. (3.417)) is 0.74. The minimum value of Z/dp for ethanol conversion between 0.1 and 0.9, evaluated using the Mears criterion (eq. (3.421)), is 2.84 and 62.11 respectively, much lower than the value used in the example, which is about 2500. Thus, the operation can be assumed to follow the plug-flow model. 

In our case the right hand parameter of this criterion is about 373, which means that we can use the plug-flow model. 

The Pe is given in Fig. 3.4-13 as a function of ReSc. As is seen, Pe is not far from unity. Assuming that plug-flow is attained for N-100 mixers, the Eqn. (3.4-82) provides a value for the necessary ratio, L dp. This should be around 200. This is about the same criterion as for... 

For a sufficiently close approach to an ideal plug flow reactor, N or Pe should exceed a certain value which depends on the degree of conversion and reaction order. Gierman [20] refined the criterion of Mears [21] and arrived at eq. 9, which can also be used for monoliths. In the latter case the axial dispersion coefficient should be replaced by the smaller molecular diffusivity, thus relaxing the criterion for monolithic elements as compared to packed beds ... 

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. 

Mears23 presented a criterion for the minimum L/dp required to hold the isothermal reactor length within 5 percent of that needed for plug flow. He suggested that, if... 

Allowable Spread in Residence Time. Other ways of stating the requirement of equal residence time of all parts of the reactant is that the flow through the reactor should approach plug flow or that the residence time distribution (RTD) should be equivalent to that in a large number of mixers in series. An often used rule of thumb is that this requirement is met when the equivalent number of mixers (N ) exceeds a certain value, say 5. However, this criterion is at best a semi-quantitative one, since the minimum value of is dependent upon the accepted deviation from the ideal reactor, and on the degree of conversion and the reaction order. 

Figure 1 shows the minimum Pe number and equivalent number of mixers for a first and second order reaction as a function of conversion depth according to Equation 1. It clearly follows that a fixed number of mixers (e.g, 5 or 10) as a criterion for an acceptable deviation from an ideal plug flow reactor is a gross oversimplification which can be misleading. 

The simplicity and general utility of the Madon-Boudart criterion make it one of the most important experimental tests to confirm that kinetic data are free from artifacts. It can be used for heterogeneous catalytic reactions carried out in batch, continuous stirred tank, and tubular plug flow reactors. 

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... 

The plug-flow assumption can be misleading a simple and approximate criterion for plug flow is not generally satisfied ... 

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