CSTR Model
Continuous Stirred-Tank Reactor Model · Also known as: ideal mixed reactor, back-mix reactor, CSTR
The CSTR (Continuous Stirred-Tank Reactor) model describes the behavior of an ideal mixed reactor where fresh feed is continuously added, products are withdrawn, and contents are kept uniform by vigorous stirring. This fundamental model, formalized by Octave Levenspiel in the 1960s, is widely used to design and scale batch and continuous processes. Despite its simplicity, it captures essential dynamics of industrial reactors and is the baseline for process control and optimization.
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When to use it
Use the CSTR model for preliminary design of batch and continuous reactors, especially when conversion and residence time are the key variables. It is ideal for fast reactions and applications requiring rapid mixing (e.g., exothermic reactions, homogeneous catalysis). Avoid when mixing is slow or when spatial gradients (temperature, concentration) are important.
Strengths & limitations
- Simple to analyze; analytical solutions exist for many kinetic schemes
- Physically transparent; residence time and conversion are directly related
- Conservative estimate of reactor performance (lower conversion than PFR for same residence time)
- Widely used in industry; correlations and design methods are established
- Assumes perfect mixing; real reactors have dead zones and short-circuiting
- Does not capture spatial temperature gradients; assumes isothermal or well-controlled temperature
- Lower conversion than plug-flow reactors at same residence time (mixing penalty)
- Not suitable for reactions with long induction periods or complex kinetics
Frequently asked
Why is CSTR conversion lower than PFR at the same residence time?
In a CSTR, all reactants at any instant experience the outlet concentration (low conversion), so the average reaction rate is lower. In a PFR, reactants experience a concentration gradient from high (inlet) to low (outlet), so the average rate is higher.
How many CSTRs in series approximate a PFR?
As the number of ideal CSTRs in series increases, the cascade behavior approaches PFR. Typically, 5-10 CSTRs in series gives a reasonable approximation, but infinity is required for perfect plug-flow.
What is residence time and how is it measured?
Residence time τ = V / v₀ is the average time a molecule spends in the reactor. It is measured by tracer injection and analyzing outlet concentration versus time (residence time distribution, RTD).
Sources
- Levenspiel, O. (1999). Chemical Reaction Engineering (3rd ed.). John Wiley & Sons. ISBN: 978-0-471-25424-9
- Fogler, H. S. (2016). Elements of Chemical Reaction Engineering (5th ed.). Pearson. ISBN: 978-0-13-388928-8
- Bailey, J. E., & Ollis, D. F. (2004). Biochemical Engineering Fundamentals (2nd ed.). McGraw-Hill. ISBN: 978-0-07-303443-8
How to cite this page
ScholarGate. (2026, June 3). Continuous Stirred-Tank Reactor Model. ScholarGate. https://scholargate.app/en/applied-physics/cstr-model
Which method?
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