What is "residence time"

n. (context hydrology English) The average time a particular molecule of water will remain in a body of water.

n. the period of time spent in a particular place

Residence time, also known as removal time, is the average amount of time spent in a control volume by the particles of a fluid. Since there're more than one way of averaging the time spent by particles inside the volume, there're also more than one definition of residence time. In case the flow is stationary and respects continuity, the definition most usually adopted is:

$$\text{continuity and stationarity} \implies \tau:=\frac{m}{f}$$
where

• τ is the residence time,
• m is the quantity of material contained in the system (the mass, in case of fluid dynamics),
• f is the flow (the mass flow rate, in case of fluid dynamics).

Residence time play an important role in environmental engineering and chemistry. In these fields, not only the (mean) residence time is of interest, but also the whole residence time distribution. Nevertheless, the simple definition just introduced can be employed to quantify the residence times of specific compounds in a mixture only under the hypothesis that no chemical reaction takes place (otherwise continuity wouldn't be satisfied) and that the compounds concentrations are uniform.

Beyond fluid dynamics and chemistry, the definition(s) of residence time can be applied to any flow network, where the flows of generic "resources" is modeled (e.g.: people, cars, money, products). Most notably, the over-mentioned definition of residence time is extended to stationary random processes by averaging on time ( fluid limit), obtaining the so-called Little's Law, which is a prominent relation in queueing theory and supply chain management. In the context of queueing theory, the residence time is addressed as waiting time, while in the context of supply chain management it is most often addressed as lead time.

In statistics, the residence time is the average amount of time it takes for a random process to reach a certain boundary value, usually a boundary far from the mean.

Residence time may refer to:

• Residence time distribution, a probability distribution function that describes the amount of time a fluid element could spend inside a chemical reactor
• Residence time (fluid dynamics), the average amount of time that a particle spends in a particular system
  • Residence time of lake water, the time that water spends in a particular lake
• Residence time (statistics), the average amount of time it takes for a random process to reach a certain boundary value