A tubular reactor consists of a cylindrical pipe and is normally operated at steady state. We consider the flow here to be highly turbulent and the flow field may be modeled by that of plug flow. That is, there is no radial variation in concentration and the reactor is referred to as a plug-flow reactor.

General mole balance for PFR:

rearranging gives:

taking the limit as  , we obtain:

multiply both sides by -1, we get:

where by stoichometry

by substitution

This can be rewritten :

This equation deals with volume where we have been given catalyst weight. To solve this problem we can divide the equation by the catalyst bulk density and arrive at:

When the reaction rate is divided by the catalyst density it becomes the reaction rate with respect to catalyst and is designated with a prime :

So :

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