Oxygen is a necessary nutrient. In suspended-growth processes, such as the activated sludge process, air must be literally forced into the liquid. The air, thus, dissolved provides the necessary oxygen nutrient for the microorganism stabilizing the wastewater.

The basic process for oxygen mass transfer from air to water is absorption. Call the equilibrium concentration of oxygen in water at a particular temperature and pressure as [Cos]. This equilibrium concentration is also called the saturation concentration of the dissolved oxygen (DO) and this corresponds to [ x* ]. Let the concentration in the water at any given moment be [C ]; this corresponds to x. The driving force for mass transfer is then [Cos] - [C ]. The rate at which the concentration of oxygen will increase is (d[C]/dt). In aeration, Kxa is normally written as KLa. Thus,

9.5.1 Equipment Specification

The rating of aeration equipment is reported at standard conditions defined as 20°C, one atmosphere pressure, and 0 mg/L of dissolved oxygen concentration in tap water (or distilled water). Under these conditions, Equation (9.8) becomes

(KLa)20 = the KLa at standard conditions and [Cos,20,sp] = the saturation DO at 20°C and standard pressure. This equation is the standard oxygen rate (SOR). Equipment is specified in terms of SOR. Testing is not normally done at standard conditions, so (KLa)20 must be obtained from the KLa obtained at the condition of testing using the Arrhenius temperature relation,

where 6 is the temperature correction factor, and T is the temperature in degrees Celsius at testing conditions. This equation assumes that the effect of pressure on KLa is negligible. In wastewater treatment, the value of 6 is usually taken as 1.024.

The ability of aeration equipment to transfer oxygen at field conditions is, using Equation (9.8),

where (KLa)w and [Cos,w] are the KLa and the [Cos] of the wastewater at field conditions, respectively. This equation represents the actual oxygenation rate (AOR). (KLa)w may also be expressed in terms of its value at 20°C, (KLa)w,20, by the Arrhenius temperature relation

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