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# Residence time

Residence time is a broadly useful concept that expresses how fast something moves through a system in equilibrium. It is the average time a substance spends within a specified region of space, such as a reservoir. For example, the residence time of water stored in deep groundwater, as part of the water cycle, is about 10,000 years. A common method for determining residence times is to calculate how long it would take for a region of space to become filled with a substance.

In chemical oceanography, residence time (t) of each element expresses how long it takes to add an amount of the element to the ocean that is equal to the amount of the element in the ocean at steady state:

t = Mean Concentration in Ocean × Ocean Volume / Input per year

where the ocean volume is (1.37×1021 L). The input sum all inputs to the ocean. For many elements, the major input is from rivers and the input per year is the Mean River Concentration × Continental Runoff Rate (3.6×1016 L/yr). If the concentration of an element is not changing, then the Input and Output of an element must be equal. The residence time can then be calculated using the estimated output, if that is known.

In the designing of chemical reactors, the residence time is regarded as the average time for the processing of the feed in one reactor volume measured at specified conditions.It is also known as space time and is denoted by τ.

It is related to the volume and the volumetric flow rate v in the mathematical relation $\tau = \frac{V}{v}$.

The τ is also related to space velocity s, which is the number of reactor volumes of feed treated per unit time at specified conditions.

Residence time not only relates to hydraulic residence time but bacterial residence time as well. It has a symbol Г (tow). It is the inverse of the eigen value derived form the mass balance method.

Both space time and space velocity are adequate performance measures for the mixed flow reactor and the plug flow reactor.