Adiabatic reactor, with axial diffusion

Two-dimensional models have been developed for non adiabatic reactors with pronounced heat effects and when radial diffusion cannot be considered infinite. In one-dimensional models the radial heat and mass transfer rates are considered infinite and thus the radial concentration and temperature profiles are flat. It therefore predicts uniform temperature and concentrations in the radial direction at every axial position along the length of the reactor. On the other hand two-dimensional models predict the detailed temperature and concentration patterns in the reactor (Froment, 1972 Karanth and Hughes, 1974 Froment and Bischoff, 1979). 

The flow patterns, composition profiles, and temperature profiles in a real tubular reactor can often be quite complex. Temperature and composition gradients can exist in both the axial and radial dimensions. Flow can be laminar or turbulent. Axial diffusion and conduction can occur. All of these potential complexities are eliminated when the plug flow assumption is made. A plug flow tubular reactor (PFR) assumes that the process fluid moves with a uniform velocity profile over the entire cross-sectional area of the reactor and no radial gradients exist. This assumption is fairly reasonable for adiabatic reactors. But for nonadiabatic reactors, radial temperature gradients are inherent features. If tube diameters are kept small, the plug flow assumption in more correct. Nevertheless the PFR can be used for many systems, and this idealized tubular reactor will be assumed in the examples considered in this book. We also assume that there is no axial conduction or diffusion. 

A maximum reactor temperature of 500 K is used in this study. This maximum temperature occurs at the exit of the adiabatic reactor under steady-state conditions. Plug flow is assumed with no radial gradients in concentrations or temperatures and no axial diffusion or conduction. 

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