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.

Starting with the differential PFR eqn:

multiply both sides by -1, we get:

from the definition of conversion we have :

substituting for F_A in the derivative::

since F_A0 is a constant, it's derivative will be zero, and it can be removed from the derivative of F_A0X:

so that finally: