Reactor Residence-Time Distribution Lab

Reactor Model

Tanks in series N 4

Flow rate Q (m³/s) 0.50

Live Readouts

τ = V/Q (theoretical)

2.00 s

In vessel

Measured mean t̄

— s

Exited (samples)

Exit-Age Distribution E(t)

histogram = measured— theoretical

How it works

Volume V is held fixed at 1.0 m³. The flow rate Q sets the mean residence time τ = V/Q. A steady stream of tracer particles enters the vessel; each particle's age (time from entry to exit) is recorded into a running histogram — exactly the pulse-tracer test real plants use to diagnose non-ideal mixing.

CSTR (1 well-mixed tank):
  E(t) = (1/τ) e^(−t/τ)         Var = τ²

PFR (plug flow, no mixing):
  E(t) = δ(t − τ)               Var = 0

N tanks-in-series (Erlang):
  E(t) = (1/τ)·(N^N/(N−1)!)·(t/τ)^(N−1)·e^(−Nt/τ)
  Var = τ²/N

CSTR — each particle undergoes a memoryless random walk; every instant it has probability dt/τ of leaving, since the outlet stream always has the same composition as the perfectly-mixed tank.
PFR — every particle moves through the tube at the same velocity L/τ with zero back-mixing, so every particle exits at exactly t = τ (a spike, not a spread).
N-Series — N ideal CSTRs of volume V/N chained together. As N grows the Erlang curve narrows and approaches the PFR spike — this is the standard model engineers fit to real reactors that mix imperfectly between the two ideals.

Real-world relevance: RTD (residence-time distribution) analysis is a core chemical-engineering diagnostic — it reveals dead zones, bypassing, and short-circuiting in real reactors, and the tanks-in-series parameter N is routinely fitted to plant tracer data to characterize non-ideal flow.

Tracer particle Vessel boundary

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