# Streeter Phelps Equation

Streeter Phelps Equation

Streeter-Phelps Model – DO sag curve

Many equations and computer programs are available today to describe the quality of water in streams, rivers and lakes

The most prevalent is the Streeter Phelps equation.

Addition of wastewater (BOD) typically causes a slow decrease in O2, followed by a gradual increase close to the dissolved oxygen saturation concentration (DOsat)

DO sag curve gives us the characteristic response in oxygen levels as a result of discharging oxygen-demanding wastes to a river or stream.

DO sag curve has 3 phases:

1. deoxygenation rate > reaeration rate

- DO levels fall

2. deoxygenation rate = reaeration rate

- Critical point

3. deoxygenation rate < reaeration rate

- DO levels increase, eventually reaching saturation

The critical point location and the DO level at this point are of principal interest because this is where water quality conditions are at their worst. Design calculations are based on this location.

Streeter-Phelps Model

Assumptions of the Model

stream is an ideal plug flow reactor

the only reactions of interest are BOD exertion and transfer of oxygen from air to water across air-water interface

Mass Balance for the Model

Not a Steady-state situation

rate O2 accumulation = rate O2 in – rate O2 out + O2 produced – O2 consumed

rate O2 accumulation = rate O2 in – 0 + 0 – rate O2 consumed

Both re-aeration and deoxygenation are 1st order rxns

rate of deoxygenation = -k1Lt

k1= deoxygenation constant, function of waste type and temperature

rate of re-aeration = k2D

D = deficit in DO or difference between saturation and current DO

k2 = re-aeration constant

Where

T = temperature of water, ºC

H= average depth of flow, m

u = mean stream velocity, m/s

Oxygen Deficit

D = DOsat – DOact

DO deficit = saturation DO – DO actual in the water

Deoxygenation rate is equivalent to BOD of waste

ro = -k1 Lt or dL/dt = -k1Lt

Lt = Loe-k1t

Lo = ultimate BOD of the wastewater and stream water mixture

In terms of the deficit with time

Source: Lectures notes from

Introduction to Wastewater Treatment

Lesson 8