River Water Quality: Pollution Mixing & Self-Purification

Pollution Sources

Industrial discharge 40%

Agricultural runoff 30%

River Conditions

Base flow (dilution) 20 m³/s

Self-purification rate 50%

Downstream Monitoring Station

WQI 0 — —

Turbidity

0 NTU

Nitrate

0 mg/L

Flow at outlet

0 m³/s

Fish population

How it works

The river is modelled along its length x as a plug-flow reach. At a point-source outfall, the pollutant mixes by mass balance:

C_mix = (Q·C_up + Qe·Ce) / (Q + Qe)
Q_down = Q + Qe

A diffuse source (farmland runoff) adds a steady loading L over a stretch of river instead of mixing at one point:

dC/dx = L/Q   (inside the runoff zone)

Between sources, the river self-purifies: sediment settles and microbes break down nutrients, both roughly first-order in distance:

dC/dx = -k·C  →  C(x) = C₀·e^(-k·(x-x₀))

Turbidity settles faster than nitrate degrades, so the two decay constants differ. A composite Water Quality Index blends both normalised sub-indices:

WQI = 50·(1 - turb/150) + 50·(1 - nitrate/20)
90-100 Excellent · 70-89 Good · 50-69 Fair · 25-49 Poor · 0-24 Very poor

Industrial discharge / Agricultural runoff — the two pollution sources; raise them and watch the plume darken downstream.
Base flow — a bigger river dilutes the same pollutant load far more, exactly like Q in the mixing equation above.
Self-purification rate — stands in for aeration, temperature and microbial activity (the decay constant k); push it up and the river recovers faster.
The fish school thins and the algae patch grows whenever nitrate-rich, low-oxygen conditions develop — a simplified stand-in for real eutrophication stress on aquatic life.

Clean water Turbid / polluted Algae bloom

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Environmental Water Quality Simulation