residence time distribution function is therefore a Dirac delta function at . A real plug flow reactor has a residence time distribution that is a narrow pulse around the mean residence time distribution. A typical plug flow reactor could be a tube packed with some solid material (frequently a catalyst). Typically these types of reactors are called packed bed reactors or PBR's. Sometimes the tube will be a tube in a shell and tube heat exchanger. When a plug flow model can not be applied, the dispersion model is usually employed. Residence-time distribution The residence-time distribution (RTD) of a reactor is a characteristic of the mixing that occurs in the chemical reactor. There is no axial mixing in a plug-flow reactor, and this omission is reflected in the RTD which is exhibited by this class of reactors. Real plug flow reactors do not satisfy the idealized flow patterns, back mix flow or plug flow deviation from ideal behavior can be due to channeling of fluid through the vessel, recycling of fluid within the vessel or due to the presence of stagnant region or dead zone of fluid in the vessel. Real plug flow reactors with non-ideal behavior have also been modelled. To predict the exact behavior of a vessel as a chemical reactor, RTD or stimulus response technique is used. The tracer technique, the most widely used method for the study of axial dispersion, is usually used in the form of: Pulse input Step input Cyclic input Random input The RTD is determined experimentally by injecting an inert chemical, molecule, or atom, called a tracer, into the reactor at some time t = 0 and then measuring the tracer concentration, C, in the effluent stream as a function of time. The RTD curve of fluid leaving a vessel is called the E-Curve. This curve is normalized in such a way that the area under it is unity: (1) The mean age of the exit stream or mean residence time is: (2) When a tracer is injected into a reactor at a location more than two or three particle diameters downstream from the entrance and measured some distance upstream from the exit, the system can be described by the dispersion model with combinations of open or close boundary conditions. For such a system where there is no discontinuity in type of flow at the point of tracer injection or at the