In an ideal plug flow reactor (PFR) the fluid particles leave in the same order they arrived, not mixing with those in front and behind. Therefore, the particles entering at time t will exit at time t + T, all spending a time T inside the reactor. The residence time distribution will be then a Dirac delta function delayed by T:
The mean is T and the variance is zero.
The RTD of a real reactor deviates from that of an ideal reactor, depending on the hydrodynamics within the vessel. A non-zero variance indicates that there is some dispersion along the path of the fluid, which may be attributed to turbulence, a non-uniform velocity profile, or diffusion. If the mean of the distribution is earlier than the expected time T it indicates that there is stagnant fluid within the vessel. If the RTD curve shows more than one main peak it may indicate channeling, parallel paths to the exit, or strong internal circulation.
In PFRs, reactants enter the reactor at one end and react as they move down the reactor. Consequently, the reaction rate is dependent on the concentrations which vary along the reactor requiring the inverse of the reaction rate to be integrated over the fractional conversion.