##  [Plug Flow Reactor](/plug-flow-reactor-0) 

 Definition

An idealised tubular reactor model in which fluid elements move in piston‑like (plug) flow with negligible axial mixing, so concentration and temperature vary only along the flow direction and each fluid element experiences a residence time equal to the reactor length divided by linear velocity; performance is governed by differential mass and energy balances along the axial coordinate.

 

 

 

 

 

 





## Principle

Principle

Negligible axial dispersion means each fluid element retains its identity along the tube, so conversion is calculated by integrating local reaction rates over residence time; for many reaction orders this yields higher single‑pass conversion per unit volume than a single CSTR of equal volume.

 

 

 

 

 





## Demonstration

Demonstration

Illustrative derivation → For a first‑order reaction A → products with rate r = k·C_A in a PFR, the differential mass balance dC_A/dt = −k·C_A along residence time t integrates to C_A = C_A0·exp(−k·τ), giving conversion dependent on τ = V/Q and an exponential decay profile (Consequence for design comparisons).

 

 

 

 

## Misapplication

Misapplication

Treating a tubular reactor with backmixing or significant axial dispersion as ideal plug flow. The semantic error is neglecting dispersion and residence time distribution; the predicted conversion and selectivity will deviate when dispersion is non‑negligible.

 

 

 

 

 





## Consequence

Consequence

When PFR assumptions hold, reactors achieve higher conversions per unit volume for certain kinetics and allow strong axial temperature and concentration control; when invalid, hotspots, lower conversion, or unintended by‑product formation may occur, requiring internals or different reactor selection.

 

 

 

 

## Reversal

Reversal

With significant axial dispersion, low Peclet number, or strong radial gradients, the PFR model fails and alternatives (axial dispersion model, series of CSTRs) better represent reality; for non‑ideal flow, PFR predictions overestimate conversion.

 

 

 

 

 





## Boundary

Boundary

Applies to tubular reactors, packed tubes, and annular flow regimes where axial mixing is small relative to convective transport (high Peclet number). Excludes stirred tanks, highly backmixed tubular systems, and reactors dominated by interphase transport limitations without axial homogeneity.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Conversion per volume versus control of temperature and selectivity: PFRs can maximise conversion for favorable kinetics but may present axial hotspots and narrower thermal control, whereas backmixed designs (CSTRs or series) smooth profiles at possible cost to conversion efficiency.

 

 

 

 

 





## Synthesis

Synthesis

PFR is the appropriate idealisation when convective transport dominates axial dispersion: it concentrates reaction progress along the flow path and yields different conversion–selectivity trade‑offs than well‑mixed reactors, so model selection must match hydrodynamic character and kinetic sensitivity.