This is a 2D process-flow-diagram twin of the 3D residence-time lab: instead of a camera orbiting a 3D vessel, the reactor is drawn as a schematic pipe-and-tank network on a flat canvas — the same layout a chemical engineer would sketch on paper. Volume V is fixed at 1.0 m³, so flow rate Q sets the mean residence time τ = V/Q. Tracer particles enter continuously; each particle's age (time from entry to exit) is recorded both into a running histogram and into the strip chart below, which plots every individual exit as a dot — the raw tracer-pulse data a plant would record, before it is binned.
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 2D random walk inside the tank disc; every instant it has probability dt/τ of leaving, since the outlet always carries the same composition as the perfectly-mixed tank.
- PFR — every particle advances along the pipe at the same speed 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 sum of N exponential(τ/N) sojourn times narrows toward the PFR spike (Erlang → delta), which is exactly why this measured variance falls as τ²/N.
Drag the main diagram to pan, scroll/pinch to zoom. Real-world relevance: RTD analysis is a core chemical-engineering diagnostic — it reveals dead zones, bypassing and short-circuiting in real reactors, and N is routinely fitted to plant tracer data to characterize non-ideal flow.