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Y =

bacterial yield

U =

specific utilization rate, l/day

kd =

bacterial decay rate, l/day

Si =

influent BOD (after primary settling), mg/l

Se =

effluent BOD (soluble), mg/l

6c =

SRT, days

6 =

LRT in the aeration basin, days

The parameter 9c defines the average residence time of microorganisms in the system.

A mass balance of system BOD under steady-state conditions yields the following equation:

(Si - S„)/0 = kXSe/(Ks + Se) = MmXSe/Y(Ks + Se) 7.25(6) where:

k = maximum utilization rate, l/day K = half-velocity constant, mg/l pm = maximum growth rate, l/day

Equation 7.25(6) assumes that a hyperbolic (Monod or Michaelis-Menten) relationship exists between k (or p^) and the mixed-liquor BOD concentration (S) (see Figure 7.25.9). From Equations 7.25(4) to 7.25(6) the following equations can be written:

FIG. 7.25.9 Plot showing the effects of the substrate (BOD) concentration (S) on growth rate (p). Subscript m indicates the maximum value.

where Yo = observed bacterial yield. The F/M ratio is a widely used term in the analysis and design of the activated-sludge process and is calculated as follows:

where E = BOD removal efficiency, %.

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