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The following approach can be used to estimate oxygen requirements

Ro = (1 - b * Yg ) * Rs  + b * d * X ,     mg O2/L-hr          
           
 where: 

Rs = rate of COD conversion, mg COD/L-hr (usually COD load * removal efficiency), 
Ro = rate of oxygen uptake, mg/L-hr,
X = microorganism concentration, mgVSS/L
Yg = biomass yield coefficient, mass VSS/mg COD removed (usually 0.3 kg VSS/kg COD removed)
b         = 1.42
d = endogenous decay rate (usually 0.1/day)

     So for 42 mg COD/L-hr maximum COD loading rate ( = 1 g COD/L-d) and an assumed 2,000 mg/L VSS in the mixed liquor and an endogenous decay rate of 0.00417/hr (= 0.1/day), the oxygen uptake rate would be:

Ro = (1 - 1.42*0.3) * (42 * 90%) + 1.42 * 0.00417 * 2000 mg/L = 34 mg O2/L/hr 

     The aeration equipment would have to equal or exceed this rate to insure positive DO in the aeration basin. Of course, you will need to make sure you calculate the loading rates correctly in the zone of interest. For example, for plug flow type processes, the COD loading rate would be that in the first section of the basin. 

     Most manufacturers and equipment vendors have readily available software for preliminary designs and will generally assist you with proper equipment/unit selection including recommended/minimum/maximum depth, oxygen dispersion diameter, complete mix diameter and so on.

     We can't go much higher in MLVSS than about 2,000 mg/L and still get good oxygen transfer in the aeration basins. 

MIXING

     Adequate contact must be provided between organic wastewater constituents and the microorganisms.  Mechanical aerator manufacturers often provide sizing charts or layout guidelines including recommended water depth, oxygen dispersion diameter and complete mix diameter estimates, the following being sample formulas for low-speed, floating surface mechanical aerators:
Mixing diameter (feet)                  =  2 x ((  646 x H.P.)/DEPTH)^0.5
Oxygen dispersion diameter (feet) = 2 x ((6490 x H.P.)/DEPTH)^0.5

     One surface aerator manufacturer's rule of thumb suggests that the HP/mg power density required for mixing with up-draft, direct-drive aerators is up to 1 HP/1,000 ft3 or about 133 HP/mg.

     Complete mix (CM) systems are designed to insure thorough content mixing and maintain biological solids in suspension. Typical power levels hover about 100 HP/mg. 

     Partial mix (PM) systems only aim to insure uniform dissolved oxygen throughout the reactor and mixing is partial, allowing a portion of solids and particulate BOD/other to settle and anaerobically decompose at the bottom of the basin. Power levels are maintained as per perceived/desired mixing/treatment objectives along the lines of 8 HP to 30 HP/mg

ACTUAL IN-WASTE/FIELD OXYGEN TRANSFER RATES

Rightly or wrongly, AOR/SOR ratios of about 0.7 are frequently used for quoting or budgeting direct-drive, mechanical surface aerators.  However, until alpha, beta, theta, elevation and required residual D.O. are known the 0.7 factor is nothing but a glorified guess. It should be obvious you don't want this type of guessing especially in the light of present day availability of highly qualified treatability assessments. 

It's illustrative to see how each aerator manufacturer decides to showcase their units. The following argumentation was proffered by a manufacturer of both surface aerators and submersible aerator blower combinations:

"Based on a flow rate of 1200 m3/day and a BOD of 1043 mg/l and TKN of 11 mg/l we calculate that the AOR will be 4385 lbO2/day. Using a correction factor to SOR = 8570 lbO2/day = 357 lbO2/hour. 

With our surface floating mechanical aerators at a transfer efficiency of 2.5 lb/Hp/hour you will need 142.8 BHp. Due to the shallow basin [swd=3.5m] we recommend three (3) 50 Hp (37.3 kW) aerators of stainless steel float design. 

If you can change your basin size to 16.5m square by 6.1m liquid depth then we would recommend one (1) 30 Hp submersible aerator mixer supplied air from one (1) 75 Hp blower with accessories. Total energy draw will be 30HP for the submersible aerator mixer and 64HP for the blower for a total of about 94 Hp (70 kW).

The submersible aerator mixer can either be hydraulic driven or electric driven at the same cost. The submersible aerator mixer and blower combination should save over 40 Kw of energy costs and this should more than pay for the capital cost difference in less than two years." 

Floating Mechanical Mixer

Mixing Do's and Don'ts

Clean water ratings and figures are nice but actual,  inwaste performance is what counts.

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