Longitudinal catalytic reactor

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Figure 1-13 Longitudinal catalytic packed-bed reactor. [From Cropley, American Institute of Chemical Engineeis, 86(2), 34 (1990). Reproduced with permission of the American Institute of Chemical Engineeis, Copyright 1990AIChE. AH rights reserved]...

Fig. 3-4 Deviations from ideal tubular-flow performance (a) longitudinal mixing due to vortices and turbulence, (b) laminar-flow (poor radial mixing), (c) bypassing in fixed-bed catalytic reactor...

A section of a fixed-bed catalytic reactor is shown in Fig. 13-4. Consider a small volume element of radius r, width Ar, and height Ar, through which reaction mixture flows isothermally. Suppose that radial and longitudinal diffusion can be expressed by Pick s law, with and Dj as effective diffusivities, based on the total (void and nonvoid) area perpendicular to the direction of diffusion. We want to write a mass balance for a reactant over the volume element. With radial and longitudinal diffusion and longitudinal convection taken into account, the input term is... 

This expression still includes the effect of longitudinal dispersion. It is identical to Eq. (6-41), except that the rate for a homogeneous reaction has been replaced with the global rate XpPs per unit volume for a heterogeneous catal)dic reaction. In Sec. 6-9 Eq. (6-41) was solved analytically for first-order kinetics to give Eq. (6-45). Hence that result can be adapted for fixed-bed catalytic reactors. The first-order global rate would be... 

Moving- and fluidized-bed catalytic reactors Longitudinal Backmixing Distillation column... 

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)... 

Figure 9 Longitudinal section view of the catalytic membrane reactor according to the patent and a section taken along line A-A. (From Ref. 108.)...

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