The tubular reactor with plug flow

In analysing the behaviour of a tubular reactor, the simplest assumption to make is that plug flow occurs. In plug flow, there is negligible diffusion relative to bulk flow and, over any cross-section normal to the fluid motion, the mass flow rate and fluid properties are uniform. This situation is quite closely approached in many industrial reactors and it means that 

In a packed bed, the transition between laminar and turbulent flow occurs in the region of Rep 40 Rep is the Reynolds number based on the equivalent particle 

In any real situation, reactants only flow through the reactor because there is a difference in pressure between the inlet and the outlet. Methods for calculating the pressure drop in pipes and packed beds have been outlined in Chap. 1. Often, the pressure drop is negligible compared with the total pressure and it is usual to assume that a tubular reactor with plug flow operates at constant pressure. 

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In Sect. 3.2, the development of the design equation for the tubular reactor with plug flow was based on the assumption that velocity and concentration gradients do not exist in the direction perpendiculeir to fluid flow. In industrial tubular reactors, turbulent flow is usually desirable since it is accompanied by effective heat and mass transfer and when turbulent flow takes place, the deviation from true plug flow is not great. However, especially in dealing with liquids of high viscosity, it may not be possible to achieve turbulent flow with a reasonable pressure drop and laminar flow must then be tolerated. 

Finally, it should be added that the phenomenon of parametric sensitivity, dealt with in this section, is essentially different from the instability encountered in Chapter 10. The tubular reactor with plug flow without recycle as considered here is intrinsically stable in the strict sense (except if kinetic instability would occur). On removal of the perturbation, the reactor will return to its original state. The hysteresis phenomenon encountered in Chapter 10 is not possible in the present case all intermediate steady states are possible. 

The approach to the design of non-isothermal tubular reactors with plug flow parallels that already outlined for batch reactors (see Sect. 2.4.)... 

As i the term in brackets above tends to exp (vit/V) for t < V/v), and F becomes zero(7>. Thus, for an infinite number of tanks the fraction of tracer that has escaped is zero for all times less than the residence time V/v. This is exactly the same as for the case of an ideal tubular reactor with plug flow. 

Beyne and Froment [1993] simulated a tubular reactor with plug flow and diffiisional limitations inside the catalyst for the process discussed already in Section 3. The main reaction is of the type A B and coke is formed through a polymerization mechanism from a site covered by coke... 

De Pauw and Froment [1975] studied n.Cj isomerization on a Pt/alumina catalyst in an isothermal tubular reactor with plug flow, yielding n.Cj-conversion, x, versus W/F °-data. Therefore, the following objective function was chosen for the parameter estimation ... 

The reaction is carried out in an isothermal tubular reactor with plug flow. Accordingly, when the rate equation for the disappearance of A is substituted into the integrated continuity equation for Ai,... 

The experimental study of Froment et al. (loc. cit) was carried out in a tubular reactor with plug flow. Tlie data were obtained as follows total conversion of propane versus a measure of the residence time, lyfF cH.fe conversion of propane into propylene versus 1V(Kcjh,)o reactor volume reduced to... 

This is the energy equation for a single-phase tubular reactor with plug flow. Note that Eq. 7.1d-4 is coupled with the continuity equation, mainly by the reaction term, but also through the heat capacity term on the left-hand side. The latter is sometimes written in terms of a specific heat that is averaged with respect to temperature and composition, that is, Yj = "c,. 

The process A B C is canied out in a tubular reactor with plug flow. Both reactions are of first order. The feed consists of pure A. Given the following data... 

Calculate the effect of recycle on the conversion in tubular reactors with plug flow. NONIDEAL FLOW PATTERNS AND POPULATION BALANCE MODELS 655... 

The Continuity, Energy, and Momentum Equations Kinetic Studies Using a Tubular Reactor with Plug Flow... 

The thermal cracking of propane was studied at atmospheric pressure and 800°C in a tubular reactor with plug flow and operated in the integral mode. The... 

At 25 °C the reaction is first-order in each reactant with a rate constant of 9.92 m3/ kmole-ksec. A feed stream containing equimolal quantities of B and C (0.1 kmole/m3) is to be processed at a rate of 0.1111 m3/ksec. A tubular reactor (assume plug flow) with an effective volume of 2.20 m3 is to be employed in the processing operation. 

Figure 8-6 Plots of the ratio of conversions in a tubular reactor with laminar flow to that in a perfect PFTR for first- md second-order kinetics. The lower pmd shows the percent loss in conversion from l nin flow comp ed to plug flow.

The other two methods are subject to both these errors, since both the form ofi the RTD and the extent of micromixing are assumed. Their advantage is that they permit analytical solution for the conversion. In the axial-dispersion model the reactor is represented by allowing for axial diffusion in an otherwise ideal tubular-flow reactor. In this case the RTD for the actual reactor is used to calculate the best axial dififusivity for the model (Sec. 6-5), and this diffusivity is then employed to predict the conversion (Sec. 6-9). This is a good approximation for most tubular reactors with turbulent flow, since the deviations from plug-flow performance are small. In the third model the reactor is represented by a series of ideal stirred tanks of equal volume. Response data from the actual reactor are used to determine the number of tanks in series (Sec. 6-6). Then the conversion can be evaluated by the method for multiple stirred tanks in series (Sec. 6-10). 

For reactors with known mixing characteristics the response curve and the RTD can be predicted no experiments are necessary. As an illustration let us deyelop the RTD for the plug-flow reactor, a single ideal stirred-tank reactor, and a tubular reactor with laminar flow. 

This equation indicates that the conversion in the tubular reactor with dispersion will always be less than that in the plug flow reactor (Q dispersion > plug). For the case where one Axes the effluent composition instead of the reactor size, equations (11.2.13) and (11.2.14) can be manipulated to show that for small Vi/uL at the same conversion,... 

The derivation of the rather complicated Eq. (4.10.29) is given in other textbooks (Westerterp, van Swaaij, and Beenackers, 1998 Levenspiel, 1996, 1999). Note that Eq. (4.10.29) is only valid for Newtonian fluids. The case of non-Newtonian fluids may also be important, such as, for example, in polymerization reactors, and is treated in the literature (Wen and Fan, 1975). Table 4.10.1 gives selected values of the exponential integral in Eq. (4.10.29). Figure 4.10.17 compares the conversion reached in a plug flow reactor with that in a tubular reactor with laminar flow. 

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