For the activated-sludge unit shown in Fig. 16.7, the...

For the activated-sludge unit shown in Fig. 16.7, the specific growth rate of cells is given by $$ \mu_{\mathrm{net}}=\frac{\mu_{m} S}{K_{s}+S}-k_{d} $$ The following parameter values are known: $F=5001 / \mathrm{h}, \alpha=0.4, \gamma=0.1, X_{e}=0, V=15001$, $K_{s}=10 \mathrm{mg} / \mathrm{l}, \mu_{m}=1 \mathrm{~h}^{-1}, k_{d}=0.05 \mathrm{~h}^{-1}, S_{0}=1000 \mathrm{mg} / \mathrm{l}, Y_{X / S}^{M}=0.5 \mathrm{~g} \mathrm{dw} / \mathrm{g}$ substrate. a. Calculate the substrate concentration $(S)$ in the reactor at steady state. b. Calculate the cell concentration(s) in the reactor. c. Calculate $X_{r}$ and $S_{r}$ in the recycle stream.

For the activated-sludge unit shown in Fig. 16.7, the specific growth rate of cells is given by
$$
\mu_{\mathrm{net}}=\frac{\mu_{m} S}{K_{s}+S}-k_{d}
$$
The following parameter values are known: $F=5001 / \mathrm{h}, \alpha=0.4, \gamma=0.1, X_{e}=0, V=15001$, $K_{s}=10 \mathrm{mg} / \mathrm{l}, \mu_{m}=1 \mathrm{~h}^{-1}, k_{d}=0.05 \mathrm{~h}^{-1}, S_{0}=1000 \mathrm{mg} / \mathrm{l}, Y_{X / S}^{M}=0.5 \mathrm{~g} \mathrm{dw} / \mathrm{g}$ substrate.
a. Calculate the substrate concentration $(S)$ in the reactor at steady state.
b. Calculate the cell concentration(s) in the reactor.
c. Calculate $X_{r}$ and $S_{r}$ in the recycle stream.

Key Concepts

Activated Sludge Process

This process is a fundamental wastewater treatment method that employs a mixed microbial community to degrade organic pollutants in aerated tanks. It involves the mixing of wastewater with activated sludge, where microorganisms metabolize substrates, and often incorporates a recycle stream to maintain a sufficient biomass concentration.

Monod Kinetics

Monod kinetics is a model used to describe microbial growth, where the specific growth rate is expressed as a function of substrate concentration. The model uses a maximum specific growth rate and a half-saturation constant to capture how growth levels off at high substrate concentrations, thus reflecting saturation effects.

Steady-State Conditions

In the context of reactor systems, steady-state conditions refer to the point at which the concentrations of substrate and biomass remain constant over time. This occurs when the rates of microbial growth, substrate consumption, and flow (inflow and outflow) are in perfect balance.

Specific Growth Rate

This is the rate at which the microbial biomass increases per unit of biomass present, typically expressed in per time units. In many models, it is modified to account for both growth (linked to substrate concentration) and decay or endogenous metabolism.

Yield Coefficient

The yield coefficient quantifies how efficiently microorganisms convert substrate into biomass. It provides a ratio that relates the amount of substrate consumed to the mass of biomass produced, playing a critical role in process design and analysis.

Recycle Stream

The recycle stream is an integral part of many activated sludge systems. By returning a portion of the treated mixed liquor back to the biological reactor, it helps maintain a high concentration of active biomass, thereby improving treatment efficiency and stability.

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