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

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