## Residence Time Distribution - Flow Reactors

The study of fluid mixing processes is important so that the
required level of mixedness can be delivered from a chemical reactor,
consequently leading to reduced production costs and on time delivery.

For ideal plug flow within a vessel all fluid elements will spend the same
amount of time in the system. Non ideal flow through a container will have a
distribution of residence times. The figure below represents the distribution of
fluid ages that might be found at the exit stream of an imperfectly mixed tank.

The Residence Time Distribution (RTD) function E(t) is defined in such a way that E(t)dt is the fraction of fluid at the outlet that has spent a time between t and t+dt in the reactor. Since all of the fluid must have spent some time in the reactor, the integral of E(t)dt between t = 0 and t =
infinity, must be equal to 1.0. The fraction of fluid that is older than time t1
is given by the equation below.

## Tracer Tests

Tracer tests involve the injection of a conservative material at the inlet
stream to a container. The concentration of material is then measured at the
outlet stream and is logged with time. The most commonly used tracer test is
that of the the pulse input.

The pulse input involves the injection of a pulse of trace over a very short period of time, known as the Dirac delta function:

The pulse input involves the injection of a pulse of trace over a very short period of time, known as the Dirac delta function:

where ta is a specified value of time, and

The concentration at the outlet is then measured with time until it has fallen to zero. If the concentration values at the outlet are then divided by the area under the concentration-time curve, the normalised response is obtained known as the C-Curve.

Ideal flow distribution regimes such as Perfectly Mixed and Plug Flow may be modellized and fitted to Residence Time Distribution curves.