Most of the biomass occurs as floes or aggregates, and the concentration of biomass is referred to as mixed liquid suspended solids (MLSS, ~1500 to 3500 mg/L). Sludge loading (kg BOD/m ³/day, ~0.4 to 1.2) is the ratio of biodegradable organic material to active biomass (Forster, 1990).

(4-47)

(4-48)

For high rate, conventional, and extended aeration systems, the OLR varies between 0.5 and 5, 0.25 and 0.45, and 0.05 and 0.2, respectively.

(4-49)

Minimum sludge age compatible with nitrification (t ^*)

(4-50)

Daily carbonaceous oxygen requirement (kg/day)

(4-51)

Air requirement for extended aeration

(4-52)

Air requirement for extended aeration and burning only carbonaceous material at 20 C

(4-53)

The mass balance equation for biomass production in a completely stirred, tank-activated sludge reactor is (see Fig. 4-2):

(4-54)

Figure 4-2: Activated sludge process.

Biomass production rate

(4-55)

When the biomass amount in the inflow and outflow liquid streams is negligible, then X _o and X _e = 0. Equation (4-54) becomes

(4-56)

Mass balance equation for substrate utilization

(4-57)

Substrate consumption rate

(4-58)

Since degradation is taking place only in the aeration tank,

(4-59)

Substituting Eqs. (4-58) and (4-59) into Eq. (4-57)

(4-60)

Cell residence time (sludge age)

(4-61)

or

(4-62)

Hydraulic residence time

(4-63)

Combining Eqs. (4-56) and (4-60), i.e., cell and substrate utilization balances,

(4-64)

Substituting Eqs. (4-61) and (4-63) into (4-64) gives an equation for the amount of biomass in the exit stream of the activated sludge plant.

(4-65)

Volumetric loading rate