Residence time

The residence time of a fluid parcel is the total time that the parcel has spent inside a control volume (e.g.: a chemical reactor, a lake, a human body). The residence time of a set of parcels is quantified in terms of the frequency distribution of the residence time in the set, which is known as residence time distribution (RTD), or in terms of its average, known as mean residence time. Residence time plays an important role in chemistry and especially in environmental science and pharmacology. Under the name lead time or waiting time it plays a central role respectively in supply chain management and queueing theory, where the material that flows is usually discrete instead of continuous. The concept of residence time originated in models of chemical reactors. The first such model was an axial dispersion model by Irving Langmuir in 1908. This received little attention for 45 years; other models were developed such as the plug flow reactor model and the continuous stirred-tank reactor, and the concept of a washout function (representing the response to a sudden change in the input) was introduced. Then, in 1953, Peter Danckwerts resurrected the axial dispersion model and formulated the modern concept of residence time. The time that a particle of fluid has been in a control volume (e.g. a reservoir) is known as its age. In general, each particle has a different age. The frequency of occurrence of the age in the set of all the particles that are located inside the control volume at time is quantified by means of the (internal) age distribution . At the moment a particle leaves the control volume, its age is the total time that the particle has spent inside the control volume, which is known as its residence time. The frequency of occurrence of the age in the set of all the particles that are leaving the control volume at time is quantified by means of the residence time distribution, also known as exit age distribution .