Residence time distribution

The residence time distribution (RTD) of a chemical reactor is a probability distribution function that describes the amount of time a fluid element could spend inside the reactor. Chemical engineers use the RTD to characterize the mixing and flow within reactors and to compare the behavior of real reactors to their ideal models. This is useful, not only for troubleshooting existing reactors, but in estimating the yield of a given reaction and designing future reactors.

The concept was first proposed by MacMullin and Weber in 1935, but was not used extensively until P.V. Danckwerts analyzed a number of important RTDs in 1953.

The theory of residence time distributions generally begins with three assumptions:

The incompressibility assumption is not required, but compressible flows are more difficult to work with and less common in chemical processes. A further level of complexity is required for multi-phase reactors, where a separate RTD will describe the flow of each phase, for example bubbling air through a liquid.

The distribution of residence times is represented by an exit age distribution, ${\displaystyle E(t)}$. The function ${\displaystyle E(t)}$ has the units of time⁻¹ and is defined such that

The fraction of the fluid that spends a given duration, ${\displaystyle t}$ inside the reactor is given by the value of ${\displaystyle E(t)dt}$.

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