Plug flow tube reactor model

For a plug flow tube reactor model, it is assumed that... 

The plug flow tube reactor model can be used to describe the liquid-phase reactions in a microreactor by using miscible and partially miscible liquids. 

Using a developed plug-flow membrane reactor model with the catalyst packed on the tube side, Mohan and Govind [1986] studied cyclohexane dehydrogenation. They concluded that, for a fixed length of the membrane reactor, the maximum conversion occurs at an optimum ratio of the permeation rate to the reaction rate. This effect will be discussed in more detail in Chapter 11. They also found that, as expected, a membrane with a highly permselective membrane for the product(s) over the reactant(s) results in a high conversion. 

In models for continuous ideal reactors, the continuously stirred tank reactor, CSTR, and the plug flow tube reactor, PFTR, are distinguished. Both are shown schematically in Figure 4-2. Both are characterized by a simultaneous input feed of educts and solvents on one side and a removal of the reaction mixture on the other side with a constant reaction rate. As a consequence, the reaction volume remains constant in both reactors throughout the reaction period. 

A tube reactor, in which turbulent flow characteristics prevail, the radial velocity profile, is flattened so that, as a good approximation, it can be assumed to be flat. Function (f) becomes extremely narrow and infinitely high at the residence time of the fluid. This function is called a Dirac S function. The residence time functions (0) and T(0) for the plug flow and backmix models are presented in Figure 4.15. In this figure, the differences between these extreme flow models are dramatically emphasized. 

McCullough et al heated NO/Ar mixtures to temperatures in the range 1750-2100 K in an alumina flow tube reactor and monitored the fractional decomposition of NO as a function of flow rate (residence time) in the reactor using a commercial chemiluminescent analyzer. Experiments at low temperatures were also performed but the data were excluded because of the influence of surface reactions. The high-temperature central section of the reactor was packed with small pieces of alumina to promote uniform flow, and pulsed tracer experiments were conducted to determine deviations from plug flow. A detailed kinetic and flow model was used, with some simplifications to reduce computing time, to calculate the fractional removal of NO versus flow rate. A... 

Both the mass-transfer approach as well as the diffusion approach are required to describe the influence of mass transport on the overall polycondensation rate in industrial reactors. For the modelling of continuous stirred tank reactors, the mass-transfer concept can be applied successfully. For the modelling of finishers used for polycondensation at medium to high melt viscosities, the diffusion approach is necessary to describe the mass transport of EG and water in the polymer film on the surface area of the stirrer. Those tube-type reactors, which operate close to plug-flow conditions, allow the mass-transfer model to be applied successfully to describe the mass transport of volatile compounds from the polymer bulk at the bottom of the reactor to the high-vacuum gas phase. 

The solution procedure to this equation is the same as described for the temporal isothermal species equations described above. In addition, the associated temperature sensitivity equation can be simply obtained by taking the derivative of Eq. (2.87) with respect to each of the input parameters to the model. The governing equations for similar types of homogeneous reaction systems can be developed for constant volume systems, and stirred and plug flow reactors as described in Chapters 3 and 4 and elsewhere [31-37], The solution to homogeneous systems described by Eq. (2.81) and Eq. (2.87) are often used to study reaction mechanisms in the absence of mass diffusion. These equations (or very similar ones) can approximate the chemical kinetics in flow reactor and shock tube experiments, which are frequently used for developing hydrocarbon combustion reaction mechanisms. 

The solution of Eq. (173) poses a rather formidable task in general. Thus the dispersed plug-flow model has not been as extensively studied as the axial-dispersed plug-flow model. Actually, if there are no initial radial gradients in C, the radial terms will be identically zero, and Eq. (173) will reduce to the simpler Eq. (167). Thus for a simple isothermal reactor, the dispersed plug flow model is not useful. Its greatest use is for either nonisothermal reactions with radial temperature gradients or tube wall catalysed reactions. Of course, if the reactants were not introduced uniformly across a plane the model could be used, but this would not be a common practice. Paneth and Herzfeld (P2) have used this model for a first order wall catalysed reaction. The boundary conditions used were the same as those discussed for tracer measurements for radial dispersion coefficients in Section II,C,3,b, except that at the wall. 

We will now find the RDT for several models of tubular reactors. We noted previously that the perfect PFTR cannot in fact exist because, if flow in a tube is sufficiently fast for turbulence (Rco > 2100), then turbulent eddies cause considerable axial dispersion, while if flow is slow enough for laminar flow, then the parabolic flow profile causes considerable deviation from plug flow. We stated previously that we would ignore this contradiction, but now we will see how these effects alter the conversion from the plug-flow approximation. 

Thirty years later, Gerhard Damkohler (1937) in his historic paper, summarized various reactor models and formulated the two-dimensional CDR model for tubular reactors in complete generality, allowing for finite mixing both in the radial and axial directions. In this paper, Damkohler used the flux-type boundary condition at the inlet and also replaced the assumption of plug flow with parabolic velocity profile, which is typical of laminar flow in tubes. 

Dispersion In tubes, and particularly in packed beds, the flow pattern is disturbed by eddies Amose effect is taken into account by a dispersion coefficient in Pick s diffusion law. A PFR has a dispersion coefficient of 0 and a CSTR of . Some rough correlations of the Peclet number uL/D in terms of Reynolds and Schmidt numbers are Eqs. (23-47) to (23-49). There is also a relation between the Peclet number and the value of n of the RTD equation, Eq. (7-111). The dispersion model is sometimes said to be an adequate representation of a reactor with a small deviation from plug flow, without specifying the magnitude of small. As a point of superiority to the RTD model, the dispersion model does have the empirical correlations that have been cited and can therefore be used for design purposes within the limits of those correlations. 

Figure 10.2 Schematic diagram of a plug-flow macroscopic model for a packed-bed membrane shell-and-tube reactor...

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