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