Dissolved Oxygen Sag Curve: River Pollution Simulator

Pollution Source

Organic load L₀ (BOD) 18 mg/L

Deoxygenation rate k_d 0.30 /day

Reaeration rate k_r (turbulence) 0.45 /day

Flow velocity v 8 km/day

Downstream Readouts

Critical distance x_c

— km

Minimum DO

— mg/L

Hypoxic stretch (DO < 4 mg/L)

— km

How it works

This is the Streeter–Phelps oxygen-sag model, the classic equation environmental engineers use to predict how dissolved oxygen (DO) responds to an organic pollution discharge in a river:

D(t) = (kd·L0)/(kr−kd) · (e^(−kd·t) − e^(−kr·t)) + D0·e^(−kr·t)
DO(t) = DOsat − D(t)          x = v·t

Two competing processes set the shape of the curve:

Deoxygenation (k_d) — bacteria consuming the organic load (BOD) use up dissolved oxygen as they respire, pulling DO down.
Reaeration (k_r) — turbulence and surface exchange with the atmosphere resupply oxygen, pulling DO back up. Riffles and rapids raise k_r; slow, deep, still water lowers it.

Near the outfall, deoxygenation dominates and DO falls. Once most of the BOD is consumed, reaeration wins and DO recovers. The lowest point of the resulting "sag" — the critical deficit — is where fish kills are most likely if DO drops below roughly 4 mg/L (stressed) or 2 mg/L (lethal to most fish). The critical point is found analytically:

tc = 1/(kr−kd) · ln[ (kr/kd)·(1 − D0(kr−kd)/(kd·L0)) ]
Dc = (kd/kr)·L0·e^(−kd·tc)

The particles drifting downstream represent parcels of river water; their color follows the same DO value as the glowing ribbon beneath them — green (healthy, >6 mg/L), amber (stressed, 4–6 mg/L), red (hypoxic, <4 mg/L). DO saturation is fixed at 9.2 mg/L (fresh water, ~20°C) and the initial mixing deficit D0 at 1.0 mg/L.

Healthy DO (>6 mg/L) Stressed (4–6 mg/L) Hypoxic (<4 mg/L)

O₂

low

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