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Residence time is the average amount of time that a particle spends in a particular system.

=Introduction=

Residence time is a widely used term that is mostly seen in science, technological and medical disciplines. The base definition is the amount of time that a particle spends in a particular system. Every discipline that uses residence time in some way adapts the definition in order to make it more specific to the application to which it is referring. The base definition for residence time also has a universal mathematical equation that can be added to and adapted for different disciplines. This is as follows:


 * $$\frac{The~capacity~of~a~system~to~hold~a~substance}{The~rate~of~flow~of~the~substance~into~the~system}$$

The generic variable form of this equation is as follows:


 * $$\tau = \frac{V}{q}$$

where $$\tau$$ is used as the variable for residence time, V is the capacity of the system, and q is the flow for the system.

Residence time begins from the moment that a particle of a particular substance enters the system and ends the moment that the same particle of that substance leaves the system. The system in question is arbitrary and can be defined as needed according to the application. If a large amount of a substance enters a system, the longer it will take for the substance to leave the system, resulting in a longer residence time. This is assuming that the inflow and outflow for the system are kept constant. By this same logic, the smaller the amount of a substance in a particular system, the shorter the residence time will be.

Inflow and outflow will also have an effect on the residence time of a system. If the inflow and outflow are increased, the residence time of the system will be shorter. However, if the inflow and the outflow of a system are decreased, the residence time will be longer. This is assuming that the concentration of the substance in the system and the size of the system remain constant, and assuming steady-state [1] conditions.

If the size of the system is changed, the residence time of the system will be change as well. The larger the system, then larger the residence time, assuming the inflow and outflow rates are held constant. The smaller the system, the shorter the residence time will be, again assuming steady state conditions.

=Assumptions=

When using the residence time equation, a variety of assumptions are made to reduce the complexity of the system being modeled. These assumptions include, but are not limited to: steady state inflow and outflow (link), constant volume, constant temperature, and uniform distribution of the substance throughout the volume of the system. It is also assumed that chemical degradation does not occur in the system in question and that particles do not attach to surfaces that would hinder their flow. If chemical degradation (chemical decomposition) were to occur in a system, the substance that originally entered the system may react with other existing compounds in the system, causing the residence time to be significantly shorter since the substance would be chemically broken down and effectively be removed from the system before it was able to naturally flow out of the system.

=Applications= Depending on the complexity of the system being modeled and the application for which it is being used, the residence time equation can be altered significantly or even used as a factor.

Engineering
Residence time is widely used across all engineering disciplines, including chemical engineering, biological systems engineering, biomedical engineering, environmental engineering and geological engineering. The residence time formula is adapted for each of these disciplines depending on the system, the complexity, and the substance involved.

In environmental engineering, residence time applies to water treatment and wastewater treatment in the amount of time that water is spends in a batch reactor, plug flow reactor, completely mixed flow reactor (CMFR), and/or flocculation tanks. Batch reactors, plug flow reactors, and CMFR’s are used in wastewater treatment plants as a means of treating wastewater. Flocculation tanks are part of drinking water treatment facilities where the chemically treated water needs enough time to form flocs [2] before reaching the sedimentation basin. These processes are dependent on an adapted version of residence time. In this situation, the important parameter is how long a concentration of fluid needs to remain in the system for in order to be adequately treated.


 * $$C=C_{o}*\exp^{(-k*\tau)}$$


 * C=Concentration
 * C0=Initial Concentration
 * k= reaction rate constant
 * $$\tau$$= batch reactor residence time

Here the residence time is being used to determine the changing concentration of a contaminant in a system. This residence time is based on the inflow, outflow, volume, initial concentration of contaminant, the added chemical for treatment, and the rate at which the reactions take place. This is useful for a flash mixer in a water treatment facility to determine if too little or too much a particular chemical is initially being introduced into the system.

Environmental
In environmental terms, the residence time definition is adapted to fit with ground water, the atmosphere, glaciers, lakes, streams, and oceans. Ground water residence time applications are useful for determining the amount of time it will take for a pollutant to reach and contaminate a ground water drinking water source and at what concentration it will arrive. This can also work to the opposite effect to determine how long until a ground water source becomes uncontaminated via inflow, outflow, and volume. The residence time of lakes and streams is important as well to determine the concentration of pollutants in a lake and how this may affect the local population and marine life. Hydro-science, the study of water, discusses the water budget in terms of residence time. The amount of time that water spends in each different stage of life (glacier, atmosphere, ocean, lake, stream, river), is used to show the relation of all of the water on the earth and how it relates in its different forms.

Pharmaceutical
For the medical field, residence time often refers to the amount of time that a pharmaceutical spend in the body. This is dependent on an individual’s body size, the rate at which the pharmaceutical will move through and react within the person’s body, and the amount of the pharmaceutical administered. The Mean Residence Time (MRT) in Pharmaceuticals deviates from the previous equations as it is based on a statistical derivation. This still runs off a steady-state volume assumption but then uses the area under a distribution curve to find the average drug dose clearance time. The distribution is comprised of numerical data derived from either urinary or plasma data collected. Each drug will have a different residence time based on its chemical composition and technique of administration. Some of these drug molecules will remain in the system for a very short time while others may remain for a lifetime. Since individual molecules are hard to trace, groups of molecules are tracked and the distribution of these is plotted to find a mean residence time. The equation for this distribution comes from the following equation:


 * MRT = $$\frac{\displaystyle \sum_{i=1}^m t_i*n_i}{N}$$


 * $$m$$=total number of groups
 * $$t_i$$=the average time in the body
 * $$n_i$$=number of molecules in the ith group
 * $$N$$=total number of molecules introduced into the system

=Footnotes= [1] Steady-state refers to a system in which the given parameter is held constant over time

[2] Flocs are colloidal particles that have combined with a coagulant in order to form large enough particles that will eventually settle out in the next phase of water treatment.

=References=
 * Davis, M, & Masten, S. (2004). Principles of environmental engineering and science. New York, New York: McGraw Hill. —Preceding unsigned comment added by Stephaniedar (talk • contribs) 15:20, 9 March 2010 (UTC)


 * Leckner, Bo, & Ghirelli, Federico. (2004). Transport equation for local residence time of a fluid. Science Direct, 59(3), 513 - 523.


 * Montgomery, C, & Reichard, J. (2007). Environmental geology. United States: McGraw Hill.
 * (Intext Citations: (Montgomery, & Reichard, 2007))


 * Rowland, M, & Tozer, T. (1995). Clinical pharmacokinetics. Philadelphia, PA: Lippincott Williams & 	Wilkins


 * Wolf, David, & Resnik, William. (1963). Residence time distribution in real systems. Industrial & Engineering Chemistry :Fundamentals, 2(4), 1
 * (Intext Citation: Wolf, & Resnik, 1963)