Streeter–Phelps Equation and DO Sag Curve in a River

The Streeter–Phelps equation determined the relation between the dissolved oxygen concentration and the biological oxygen demand over time (Streeter and Phelps 1925). The concentration of DO in a river is an indicator of general health of the river. All rivers have some capacity for self‐purification. As long as the discharge of oxygen demanding wastes is well within the self‐purification capacity, the DO level will remain high, and a diverse population of plants and animals, including game fish, can be found. As the amount of the waste increases, the self‐purification capacity can be exceeded, causing detrimental changes in plant and animal life. The stream loses its capacity to cleanse itself, and the DO level decreases. When the DO drops below about 4–5 mg/l, most game fish will have been driven out. If the DO is further reduced to or below 2 mg/l (critical point) (Figure 4.10), fish and other animals are killed or driven out, and extremely noxious conditions result. The water becomes foul‐smelling as organic waste and dead animal life decompose under anaerobic conditions (i.e. without oxygen).

One of the major tools of water quality management in rivers is increasing the capacity of a stream to absorb a waste load (also discussed in Section 4.8.1 in river TMDL and WLA). This is done by determining the profile of DO concentrations downstream from a waste discharge. This profile is called the DO sag curve (Figure 4.10) because the DO concentration dips as oxygen‐demanding materials are oxidized and then rises again further downstream as the oxygen is replenished from the atmosphere and photosynthesis processes.

Mixing of Wastewater in Rivers: Mass‐Balance Approach

When two streams or rivers merge or wastewater is discharged to a stream, it is possible to determine the BOD and DO after mixing assuming steady‐state conditions and instantaneous mixing (Jolánkai 1997). The two streams are considered as dilutions of each other; thus, the initial BOD and DO will be

(4.11)

and

(4.12)

where

• L _a is the initial concentration of ultimate BOD after mixing, g/m³ (mg/l)
• L _w is the ultimate BOD of the wastewater g/m³ (mg/l)
• L _r is the ultimate BOD of the river, g/m³ (mg/l)
• DO_w is the dissolved oxygen content in the wastewater g/m³ (mg/l)
• DO_r is the dissolved oxygen content in the river g/m³
• Q _w is the flow rate of wastewater m³/s
• Q _r is the flow rate of the river m³/s

EXAMPLE 4.8

A food‐processing plant in the town of Zella in Washington discharges 17 300 m³/day of treated wastewater into a nearby Salmon Creek. The treated wastewater has a BOD₅ of 12 mg/l, and the Salmon Creek has a flow rate of 0.43 m³/s. The DO of the wastewater is 1.0 mg/l and the DO in the Salmon Creek is 6.5 mg/l. Compute the DO after complete mixing.

SOLUTION

The DO after mixing is given by Eq. (4.12). To use this equation we must convert the wastewater flow rate to compatible units, that is, to cubic meter per second.