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am, maximum growth rate at indicated temperature (T); Ks, half-saturation coefficient for the energy source; Kdo, half-saturation coefficient for dissolved oxygen; Y, yield (COD basis); b, decay coefficient. bSubstrate used as energy source. COD, chemical oxygen demand (see Section 13.1.3).

^Note that yields can be greater than 1.0, since during growth the organism incorporates oxygen and nutrients as well as the benzene or toluene carbon and hydrogen.

Based on International Association on Water's Activated Sludge Model No. 1 (ASM1); ASM1 lumps ammonium oxidation with nitrite oxidation. A typical value for the decay coefficient for autotrophs was not available.

am, maximum growth rate at indicated temperature (T); Ks, half-saturation coefficient for the energy source; Kdo, half-saturation coefficient for dissolved oxygen; Y, yield (COD basis); b, decay coefficient. bSubstrate used as energy source. COD, chemical oxygen demand (see Section 13.1.3).

^Note that yields can be greater than 1.0, since during growth the organism incorporates oxygen and nutrients as well as the benzene or toluene carbon and hydrogen.

Based on International Association on Water's Activated Sludge Model No. 1 (ASM1); ASM1 lumps ammonium oxidation with nitrite oxidation. A typical value for the decay coefficient for autotrophs was not available.

m=m^=10day x 5r20=10y=8.00day-1

Note that the growth rate is over 95% of the maximum with 100 mg/L of substrate, and is still 80% of the maximum when the substrate concentration is 20 mg/L.

Stationary Phase Once the substrate is sufficiently depleted, growth nearly stops (m ~ 0). This plateau in biomass concentration is referred to as the stationary phase. Actually, the cells may still be growing slowly, but this is counterbalanced by the loss in mass through decay (the next phase).

Decay Phase If a person stops eating, he or she gradually loses weight. This is also true of microorganisms. Their mass decreases, or decay occurs, if substrate is unavailable. The cell continues to carry on some metabolic processes, and if there are no external sources of energy, it must utilize internal ones. This is called endogenous metabolism. It will at first be based on storage materials but will then progress to include nonessential cell components, and eventually, essential ones. (The need to regenerate these components can be one cause of a lag phase when organisms from an old culture are transferred to fresh medium.) At some point, sufficient damage may be done so that the cell cannot recover and is thus no longer viable.

Energy is also used for cell maintenance during growth. Thus, the observed or net specific growth rate (mn) actually represents a higher true growth rate combined with some decay. Decay is often modeled as a first-order reaction with respect to biomass, with the decay coefficient constant for a given system. In the past, the symbol kd was often used for this coefficient, but now b is more common, so that mn = m - b (11.10)

Like growth rate, the decay coefficient has units of inverse time. Although it can vary considerably, in many wastewater treatment and other systems the decay coefficient may have a value of around 0.05 day-1. This means that about 5% of the biomass will decay away each day. [Actually, the amount that decays in 1 day is (1 - e(—1 day)(0-05day-1)) x 100% = 4.88%. This is less than 5% because as the amount of biomass present decreases, so does the amount that decays.]

Specialized resting stages, such as spores or cysts, can be formed by some microorganisms. By greatly slowing down cell metabolism, they decrease decay rates, sometimes very dramatically.

Overall Equation The growth equation (11.3) can now be rewritten incorporating Monod kinetics [equation (11.6)] and decay [equation (11.10)]:

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