Self-purification of rivers; sag curve

Self-purification of a river

Self-purification is the natural process by which a polluted stream recovers its original quality by physical, chemical and biological actions, without human help. When sewage enters a river, the oxygen in the water is used for decomposition, but atmospheric oxygen and photosynthesis restore it as the stream flows downstream.

Process

1. Dilution by river water reduces concentration of pollutants.
2. Sedimentation of the suspended matter.
3. Oxidation of organic matter by aerobic bacteria (deoxygenation): $\text{organic matter}+O_2\to CO_2+H_2O+\dots$
4. Reaeration (reoxygenation) from the atmosphere through the surface, aided by turbulence, and oxygen from aquatic plants (photosynthesis).
5. Sunlight kills bacteria; reduction by anaerobic decomposition of the deposited sludge; and predation by protozoa.

Oxygen sag curve and zones of pollution

The DO is used by bacteria (deoxygenation) at a rate $K_1L_t$ and replaced from air (reaeration) at a rate $K_2D_t$. The net result is the oxygen sag curve:

$$D_t=\frac{K_1L_0}{K_2-K_1}\left(10^{-K_1t}-10^{-K_2t}\right)+D_010^{-K_2t}$$

 DO
 sat |----.                          ______ recovery
     |     '.                      .'
     |       '.                  .'
     |         '.    Dc        .'
 min |           '.___v_____.-'
     |  Degradation | Active |Recovery| Clean
     |    zone      |decomp. | zone   | water
     +---------------------------------------> distance/time
   outfall          critical point

Zones

1. Zone of degradation (just downstream of the outfall): water turns turbid and grey, DO falls to about 40% of saturation, aerobic bacteria and fungi grow, and fish may disappear.
2. Zone of active decomposition: DO falls to a minimum (zero in a heavily polluted stream, then anaerobic with black colour, bubbles of gas and bad smell). The critical point (maximum deficit $D_c$) is at the lowest DO.
3. Zone of recovery: reaeration exceeds the deoxygenation; DO rises, water clears, fish return, and nitrates form.
4. Zone of clear water: the river is restored to its original state with DO near saturation, and with the BOD satisfied.

The critical time is $t_c=\dfrac{1}{K_2-K_1}\log_{10}\left[\dfrac{K_2}{K_1}\left(1-\dfrac{(f-1)D_0}{L_0}\right)\right]$, where $f=K_2/K_1$.

Factors affecting self-purification

• Dilution (river flow): more flow dilutes the waste and supplies more oxygen.
• Temperature: speeds up decomposition but lowers the oxygen solubility.
• Sunlight: kills bacteria and helps algae release oxygen.
• Velocity and turbulence: increase reaeration.
• Nature and amount of pollutant, and the initial DO of the river.
• Sedimentation and the presence of algae and other aquatic life.