PFR Model
Also known as: ideal tubular reactor, plug-flow model, PFR
The PFR (Plug Flow Reactor) model describes the behavior of a tubular reactor in which fluid elements move through as distinct plugs with no axial mixing. Fluid at the inlet is freshly unreacted; as it travels downstream, reactions progress. This idealized model, formalized by Octave Levenspiel alongside CSTR theory, is the opposite extreme: while CSTRs are fully mixed, PFRs have no axial mixing. In practice, PFRs achieve higher conversion than CSTRs for the same residence time and are widely used in the chemical and petroleum industries.
Key highlights
- Higher conversion than CSTR at same residence time (no back-mixing penalty)
- Differential equations are well-studied; many analytical solutions exist
- Ideal baseline for comparing real reactor performance
- Can model temperature and concentration profiles explicitly (non-isothermal PFR)
Intuition
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How it works
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When to use it
Use the PFR model for design of tubular reactors, pipe reactors, and packed-bed reactors. It provides the upper bound on conversion for a given residence time. Apply when axial mixing is negligible (high flow velocity, adequate pipe diameter) and when high conversion or selectivity is desired. Avoid in recirculating reactors or when radial mixing is critical (e.g., heterogeneous catalysis with local hot spots).
Strengths & limitations
- Higher conversion than CSTR at same residence time (no back-mixing penalty)
- Differential equations are well-studied; many analytical solutions exist
- Ideal baseline for comparing real reactor performance
- Can model temperature and concentration profiles explicitly (non-isothermal PFR)
- Assumes no axial mixing; real pipes have diffusion and turbulent mixing
- Does not account for radial concentration or temperature gradients
- Requires integration of differential equations; complex kinetics need numerical methods
- Residence time distribution is uniform; deviations from ideal behavior require dispersion models
Common pitfalls
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Applications
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Frequently asked
When should I use PFR vs. CSTR?
Use PFR when high conversion is needed and mixing is not critical (tubular geometry). Use CSTR when rapid mixing is important (exothermic, viscous, multiphase). For most cases, PFR gives the most economical design.
What is axial dispersion and why does it matter?
In real reactors, turbulent eddies cause some mixing backward along the flow direction (axial dispersion). This reduces conversion relative to ideal PFR. Dispersion models account for this by adding a diffusion term.
How do I model a non-isothermal PFR?
Add an energy balance equation: dT/dz = (Q + ΔH_rxn) / (ρ c_p v₀). This couples temperature and conversion changes. Often requires numerical integration.
Sources
- 1.Levenspiel, O. (1999). Chemical Reaction Engineering (3rd ed.). John Wiley & Sons.ISBN 978-0-471-25424-9
- 2.Fogler, H. S. (2016). Elements of Chemical Reaction Engineering (5th ed.). Pearson.ISBN 978-0-13-388928-8
- 3.Schmidt, L. D. (2005). The Engineering of Chemical Reactions (2nd ed.). Oxford University Press.ISBN 978-0-195-10490-0
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Cite this page
ScholarGate. (2026, June 3). PFR Model. ScholarGate. https://scholargate.app/applied-physics/pfr-model