The do sag curve and the streeter phelps equation

The do sag curve and the streeter phelps equation

1. The DO Sag Curve and the Streeter-Phelps Equation Submitted to- Dr . Anju Malik Submitted By- Keshav Roll no. 07 M.Sc. (F)

2. Dissolved oxygen The amount of gaseous oxygen dissolved in water . Oxygen enters the water by direct absorption of from the atmosphere by rapid movement or as waste product of photosynthesis.

3. BALANCE ORGANIC MATTER (C, N) DECAY SEDIMENT DEMAND RESPIRATION ATMOSPHERIC DIFFUSION PHOTOSYNTHESIS TRIBUTARIES TRIBUTARIES SOURCES SINKS

4. SHINK

5. One of the earliest mathematical water quality models was developed by for the Ohio River by H.S.Streeter and E.B. Phelps in 1925. Hence the model is referred to as the Streeter-Phelps model. The Streeter-Phelps equation accurately models the amount of DO in a stream after wastewater is discharge into it. The DO sag curve represents how the DO concentration in a volume of water changes over time or distance after organic material is introduced. This curve is calculated by the Streeter-Phelps equation The plot of the DO as a function of time is called the DO sag curve. This changing concentration of DO in a river after the introduction of organic material is called the DO sag curve .

6. The oxygen sag curve The deoxygenation caused by microbial decompostion of waste and oxygenation by reaeration Rate of deoxygenation = kd = the deoxygenation rate constant (per day) Lt = the BOD remaining t(days) after the wastes enter the river So , rate of deoxygenation = ---------(1)

7. Rate of Reaeration = kr = reaeration constant (per time) D = dissolved oxygen deficit (D = DOs – DO) DOs = saturated value of dissolved oxygen , DO = actual dissolved oxygen . From (1) &(2) : - Rate of increase of the deficit =rate of deoxygenation – rate of reaeration ------------(2) -------- -- (3)

8. Which has solution : we can write the equation for the DO as :- from equ . (4) :- Equation (5) is classic streeter phelps oxygen sag model first described in 1925. When :- k r = k d from equ . -------(4) D = ( k d L t + D ) e- k d t ----------(6) If the stream has a constant cross sectional area &traveling u , then time & distance downstream related by ----------(4) ----------(5)

9. x = ut where x = distance downstream u = stream speed t = time From equ . (4) ----------(7)

10. The Streeter-Phelps equation: D = dissolved oxygen deficit (DO saturation minus the actual level of DO) (mg /L) D0 = dissolved oxygen deficit at x = 0 (mg /L) ka = first-order reaeration rate coefficient (d-1) x = distance (m) u = average velocity (m /s) kd = first-order deoxygenation rate constant (d-1) L0 = CBOD (mg /L)

11. CONT …

12. MECHANISM The model is based on the assumption that dissolved oxygen concentration is dependent on two independent processes: decomposition of organic matter and reaeration . Both processes are described as first order reactions . The model is based on plug flow hydraulics.

13. CONT ……………

14. Limitations of the DO Sag Equation Steady state -- Streams aren't steady state. Flows, velocities, geometries, and temperatures all vary with time . Plug flow -- Streams aren't really plug flow.  Algae -- The model doesn't include algae which are a very important source of oxygen Benthic organisms -- The model assumes that all the oxygen demand is from suspended organisms