Alpha (α) & Beta (β) factors In Aeration Systems For Wastewater Treatment.

In the context of aeration systems in wastewater treatment, Alpha Factor (α) and Beta Factor (β)  relate to the performance of oxygen transfer from air (or pure oxygen) to the wastewater, particularly when comparing clean water conditions (like in lab tests) to real, often contaminated or mixed liquor conditions in actual wastewater treatment systems.

Beta (β) Factor:

Definition: The beta factor (β) represents the reduction in oxygen transfer efficiency due to the presence of dissolved substances in the wastewater (like surfactants, oils, or other contaminants), compared to clean water.

Formula:

β= C*wastewater / C*cleanwater

• C* is the saturation concentration of oxygen.

• The beta factor typically ranges between 0.85 and 0.95 for municipal wastewater, but can be lower in industrial wastewater.

Implication: If β = 0.90, it means the oxygen saturation concentration in wastewater is only 90% of that in clean water, indicating reduced transfer capacity due to contamination.

Alpha Factor:

Definition: The alpha factor (α) quantifies the ratio of the oxygen transfer rate (OTR) in actual wastewater to that in clean water under the same aeration conditions.

Formula:

α=OTRwastewater​​ / OTRcleanwater​

Typical Range: Ranges from 0.3 to 0.8, depending on the type of wastewater, temperature, and presence of surfactants or particulates.

Significance: If α = 0.6, it means the aeration system transfers only 60% as much oxygen in wastewater as it does in clean water.

Summary of Key Factors:

Factor	Symbol	Represents	Typical Range
Alpha	α	Oxygen transfer efficiency in wastewater vs. clean water	0.3 – 0.8
Beta	β	Reduction in O₂ saturation due to contaminants	0.85 – 0.95

Application in Design:

These correction factors are applied when calculating the Standard Oxygen Transfer Efficiency (SOTE) or Standard Aeration Efficiency (SAE) for real-world conditions, which significantly affects the energy efficiency and sizing of aeration systems.