Dissolved Oxygen Analysis Modeling

Introduction

Let us consider the case of a single input of wastewater discharge into a stream/river from the wastewater treatment plant (WWTP) or the publicly owned treatment work (POTW). We will use a plug flow model for this point source input.

Terms to understand

• Dissolved Oxygen (DO)
• Biochemical Oxygen Demand (BOD)
• Ultimate BOD (UBOD)
• Henry's Law for dissolution of oxygen into stream
• Mass Transfer Coefficient (KLa)
• DO deficit (D)
• Initial DO deficit (Do)
• Effect of temperature on reaction rate constants

• Effect of mixing on DO concentration, BOD concentration etc
Theory and Background
• Dissolved Oxygen (DO)
• Biochemical Oxygen Demand (BOD)
• Ultimate BOD (UBOD)
• Henry's Law for dissolution of oxygen into stream
• Mass Transfer Coefficient (KLa)
• DO deficit (D)
• Initial DO deficit (Do)
• Effect of temperature on reaction rate constants
• Effect of mixing on DO concentration, BOD concentration etc
• Figure 1. Stream and Waste Discharge Chracteristics

Assumptions
• Steady flow (no variation with time)
• Wastes are distributed uniformly across the stream
• No dispersion along the stream path (no mixing in downstream direction)
• The decay rate for the waste may be represented by a first order reaction
• There is only one entry point for the waste
• Effects of algae and bottom sludge are ignored
• Consider a section of the stream  and conduct a mass balance on DO in that section. DO Sink is the BOD utilized by bacteria and DO Source is the reaeration from atmosphere.

Figure 2. Mass Balance on DO in a section  of the stream

Continuity equation involving DO in a segment volume V can be written as:

(DO inflow + DO source) - (DO outflow + DO sink) = change in storage of DO in the segment

where:

where:

D = D 0 at X = 0
t = travel time = X / U
Critical Deficit Point

The DO deficit reaches a maximum at the location Xc given by critical time tc*.
At that point,

Model Example

• Single Point Source