The continuous stirred-tank reactor (CSTR) is also known as vat- or backmix reactor and is a common ideal reactor type. A CSTR often refers to a model used to estimate the key unit operation variables when using a continuous agitated-tank reactor to reach a specified output and the mathematical model works for all fluids: liquids, gases, and slurries.

The behavior of a CSTR is often approximated or modeled by that of a Continuous Ideally Stirred-Tank Reactor (CISTR) with all calculations performed with CISTRs assuming perfect mixing. The assumption taken is that if the residence time is 5-10 times the mixing time, the approximation is valid for engineering purposes. The CISTR model is often used to simplify engineering calculations and can be used to describe research reactors while in practice it can only be approached in industrial size reactors.

Integral mass balance on number of moles Ni of species i in a reactor of volume V is done and is as follows:

Accumulation in reactor = in - out + generation

dNi/dt = Fio – Fi + Vviri

where Fio is the molar flow rate inlet of species i, Fi the molar flow rate outlet, and vi is stoichiometric co-efficient. The reaction rate, r, is generally dependent on the reactant concentration and the rate constant (k) and can be figured by using the Arrhenius equation. In most of the cases,s the temperature increases so does the rate at which the reaction occurs. The average amount of time a discrete quantity of reagent spends inside the tank is residence time.

To model systems that do not obey the assumptions of constant temperature and a single reaction, additional dependent variables must be considered and if the system is considered to be in unsteady-state, a differential equation or a system of coupled differential equations must be solved.

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