Illinois Administrative Code › Title 35 - ENVIRONMENTAL PROTECTION › Part 373 - THIRD STAGE TREATMENT LAGOON EXEMPTIONS › Subpart C - STREAM INFORMATION › Appendix B - Modified Streeter-Phelps Equation

Current through Register Vol. 48, No. 28, July 12, 2024
The Modified Streeter-Phelps Equation mathematically defines
				  the relationship between carbonaceous oxygen demand, nitrogenous oxygen demand,
				  natural stream reaeration and the dissolved oxygen deficit as a function of
				  time:
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Definition and discussion of terms:
a) D = Dissolved oxygen deficit; units = mg/l;
				  defined as the difference between the dissolved oxygen concentration at
				  saturation and the actual instantaneous dissolved oxygen concentration at time
				  t, i.e.,
D = D.O.sat -
				  D.O.actual. From this relation, the stream dissolved
				  oxygen concentration can be computed for various times-of-travel (t's)
				  downstream and plotted on a graph of t vs.
				  D.O.actual.
b) Kc = carbonaceous decay
				  constant; units = 1/day; this constant describes the rate at which carbonaceous
				  BOD is utilized in a stream. Its value may be determined experimentally for a
				  specific effluent and a specific stream. The actual value of
				  Kc depends essentially upon the origin and strength of
				  the wastewater, the type of treatment that wastewater has undergone, as well as
				  various stream characteristics.
The following guidelines may be used for selection
				  of a Kc value for various applications:
1) Effluents containing up to and including 10
				  mg/l BOD5: 0.10
2) Effluents containing between 10 and 30 mg/l
				  BOD5: 0.30
3) Virtually all effluents may be tested using an
				  appropriate experimental procedure for a more precise determination of
				  Kc.
c) Lac = ultimate
				  carbonaceous demand; units = mg/l; this term may be calculated once the
				  BOD5 and Kc are known by use of
				  the following equation:
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In this equation, Ef is the
				  treatment works effluent BOD5.
d) K2 = stream reaeration
				  constant; units = 1/day; this constant describes the rate at which atmospheric
				  oxygen diffuses into the water of a flowing stream. Its value depends upon the
				  hydraulic and geometric properties of the stream in question. Many
				  investigators have developed equations to predict K2.
				  The equation given below has been shown to yield results which best fit the
				  field observations of many researchers over a wide variety of stream
				  types:
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In this equation, "H" is average depth of flow in
				  feet, "V" is stream average velocity in feet per second, and "S" is the
				  dimensionless parameter, stream slope, ft./ft. Velocity and average depth of
				  flow may not be estimated but must be field measured at the 7-day 10-year low
				  flow stream condition or computed from field measurements of stream geometry
				  (cross sections and slopes using ordinary principles of open-channel
				  hydraulics). Significant changes in stream geometry will change average
				  velocity and average depth of flow. K2 must be computed
				  for each stream segment as defined in Appendix C.
e) e = the Naperian logarithm base, dimensionless;
				  e = 2.71828....
f) t = time; units = days.
g) Kn = nitrogenous decay
				  constant; units = 1/day; this constant describes the rate at which nitrogenous
				  BOD is utilized in a stream. Its value may be determined experimentally for a
				  specific effluent and a specific stream. Previous experimental work has
				  established a range of typical values for Kn of 0.25 to
				  0.37 per day with an average of 0.29 per day. It should be noted that the
				  higher values of Kn yield generally more conservative
				  results when applied to the Streeter-Phelps Equation.
h) Lan = ultimate
				  nitrogenous demand; units = mg/l; this term may be calculated, once the initial
				  ammonia nitrogen concentration is established, by use of the following
				  formula:
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i) t0 = nitrogenous lag
				  time; units = days; when a waste contains both carbonaceous and nitrogenous
				  oxygen demand, there is usually a time lag before the onset of nitrogenous
				  oxygen demand. The time lag may typically vary from 0-10 days with its actual
				  value dependent upon the complex chemical characteristics of the waste as well
				  as various stream characteristics. The value of t0 may
				  be experimentally determined where effluent or stream field measurements are
				  practicable. In the case of well nitrified effluents, the value of
				  t0 may generally be considered to be less than 1 day.
				  Note that for t less than t0 the nitrogenous term,
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does not enter into the calculation of D.
j) Da = initial dissolved
				  oxygen deficit; units = mg/l. Determined by subtracting assumed effluent
				  dissolved oxygen concentration of 6.0 mg/l from dissolved oxygen saturation
				  value at the expected maximum stream temperature.
Temperature Adjustments
KC, K2,
				  Kn and Lac are temperature
				  dependent quantities. The values calculated in accordance with the above are 20
				  degree Celsius values. Since the saturation D.O. decreases with increasing
				  temperature, it will be necessary to adjust the parameters
				  KC, K2, Kn
				  and Lac to reflect the expected maximum stream
				  temperature condition. In the equations listed below, T is the expected maximum
				  stream temperature in degrees Celsius.
a) Kc(T) =
				  Kc x 1.047(T-20)
b) K2(T) =
				  K2 x 1.024(T-20)
c) Kn(T) =
				  Kn x 1.047(T-20)
d) Lac(T) =
				  Lac (0.02 T + 0.6 )
Since the time of the year at which the 7-day
				  10-year low flow occurs typically varies from stream to stream, it is not
				  possible to prescribe a uniform maximum temperature adjustment throughout the
				  state. The maximum temperature should be ascertained from field measurements in
				  the stream at the time of year at which 7-day 10-year low flow is expected to
				  occur. IEPA ambient water quality monitoring network data are available for
				  making such determination. This data may be obtained by contacting the Division
				  of Water Pollution Control.