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Concept
Continuous stirred-tank reactor
Summary
The continuous stirred-tank reactor (CSTR), also known as vat- or backmix reactor, mixed flow reactor (MFR), or a continuous-flow stirred-tank reactor (CFSTR), is a common model for a chemical reactor in chemical engineering and environmental engineering. 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. The mathematical model works for all fluids: liquids, gases, and slurries.
The behavior of a CSTR is often approximated or modeled by that of an ideal CSTR, which assumes perfect mixing. In a perfectly mixed reactor, reagent is instantaneously and uniformly mixed throughout the reactor upon entry. Consequently, the output composition is identical to composition of the material inside the reactor, which is a function of residence time and reaction rate. The CSTR is the ideal limit of complete mixing in reactor design, which is the complete opposite of a plug flow reactor (PFR). In practice, no reactors behave ideally but instead fall somewhere in between the mixing limits of an ideal CSTR and PFR.
A continuous fluid flow containing non-conservative chemical reactant A enters an ideal CSTR of volume V.
Assumptions:
perfect or ideal mixing
steady state , where NA is the number of moles of species A
closed boundaries
constant fluid density (valid for most liquids; valid for gases only if there is no net change in the number of moles or drastic temperature change)
nth-order reaction (r = kCAn), where k is the reaction rate constant, CA is the concentration of species A, and n is the order of the reaction
isothermal conditions, or constant temperature (k is constant)
single, irreversible reaction (νA = −1)
All reactant A is converted to products via chemical reaction
NA = CA V
Integral mass balance on number of moles NA of species A in a reactor of volume V:
where,
FAo is the molar flow rate inlet of species A
FA is the molar flow rate outlet of species A
vA is the stoichiometric coefficient
rA is the reaction rate
Applying the assumptions of steady state and νA = −1, Equation 2 simplifies to:
The molar flow rates of species A can then be rewritten in terms of the concentration of A and the fluid flow rate (Q):
Equation 4 can then be rearranged to isolate rA and simplified:
where,
is the theoretical residence time ()
CAo is the inlet concentration of species A
CA is the reactor/outlet concentration of species A
Residence time is the total amount of time a discrete quantity of reagent spends inside the reactor.
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