Safe Normal Operation of the Cooled PFTR

The radial overheating towards the middle of the tube depends in its extent mainly on the diameter of the tube. In order to be able to assess this overheating, some assumptions have to be made. The transport mechanism by which the chemically produced heat is led towards the wall determines how pronounced a temperature profile 

Cs is a parameter which characterizes the properties of the solid bed and which is best determined experimentally. If such experimental results are not available, Cs can be estimated with the help of a rough approximation, which correlates this parameter with the mean particle diameter and the pipe diameter. 

Safety engineering now focuses its interest in the most critical spot of the pipe, which corresponds to the site of highest overheating. For this spot a heat balance describing the radial profile can be formulated using cylindrical coordinates. 

Two proximations allow the solution of this balance. First, the dependency of the reaction rate on temperature shall follow the approximation already used in the discussion of the heat explosion theory. The second step neglects the development of radial concentration profiles. 

This second approximation is somewhat problematic as it turns out to be part of an indirect procedure. Its justification is finally given by the safety criterion to be deduced. The application of the latter excludes operating conditions, for which the approximation is invalid. However, this procedure is the only one known so far and which has proven valid in practice. 

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