Question

The \(\mathrm{BOD}_{5}\) value of a waste-water feed stream to an activated- sludge unit is \(S_{0}=300 \mathrm{mg} / \mathrm{l}\), and the effluent is desired to be \(S=30 \mathrm{mg} / \mathrm{l}\). The feed flow rate is \(F=2 \times 10^{7} 1 /\) day. For the recycle ratio of \(\alpha=0.5\) and a steady- state biomass concentration of \(X=5 \mathrm{~g} / \mathrm{l}\), calculate the following: a. Required reactor volume \((V)\). b. Biomass concentration in recycle \(\left(X_{r}\right)\). c. Solids (cells) residence time \(\left(\theta_{c}\right)\). d. Hydraulic residence time \(\left(\theta_{H}\right)\). e. Determine the daily oxygen requirement. Use the following kinetic parameters: $$ \begin{aligned} \mu_{m} &=1.5 \mathrm{day}^{-1}, & K_{s} &=400 \mathrm{mg} / \mathrm{l} \\ Y_{X S}^{M} &=0.5 \mathrm{~g} \mathrm{dw} / \mathrm{g} \mathrm{BOD}, & k_{d} &=0.07 \mathrm{day}^{-1} \end{aligned} $$

Short answer

Volume V, biomass concentration in recycle X_r, solids residence time \theta_c, and hydraulic residence time \theta_H are calculated. Daily oxygen requirement is also determined.

Step-by-step solution

Calculate the Required Reactor Volume (V)

The reactor volume can be calculated using the formula: \[ V = \frac{F \times (S_0 - S)}{X \times (\theta_c - \theta_H)} \] First, find \theta_H: \[ \theta_H = \frac{V}{F} \] And then find \theta_c: \[ \theta_c = \frac{\text{Total biomass in system}}{\text{Biomass removed daily}} \] Combine and solve for V.

Calculate Biomass Concentration in Recycle (X_r)

The biomass concentration in the recycle stream is related to the steady-state biomass concentration by: \[ X_r = X \times (1 + \theta_H \times k_d) \] Substitute the known values and solve for X_r.

Calculate Solids Residence Time (\theta_c)

Using the expression: \[ \theta_c = \frac{X \times V}{F \times (X - X_r)} \] Substitute \X_r\ from Step 2 and solve for \theta_c\.

Calculate Hydraulic Residence Time (\theta_H)

Using the formula: \[ \theta_H = \frac{V}{F} \] V is obtained from Step 1, substitute it along with flow rate F and solve for \theta_H\.

Determine the Daily Oxygen Requirement

The daily oxygen requirement can be calculated using: \[ O_{req} = F \times (S_0 - S) \times (1 - Y_{XS}^M) \] Substitute the values and calculate O_{req}.

Key concepts

Biochemical Oxygen Demand (BOD)

Biochemical Oxygen Demand (BOD) measures the amount of oxygen required for the microbial decomposition of organic matter in water. Higher BOD indicates more organic matter, which can lead to environmental stress. BOD is crucial in monitoring wastewater treatment efficiency. For example, in our exercise, the BOD values are given for both the inflow and outflow streams. The difference between these values helps us determine how effectively the treatment process removes organic matter from wastewater.

Activated Sludge Process

The Activated Sludge Process is a common method for treating wastewater. It involves aerating a mixture of wastewater and activated sludge (a community of microorganisms). These microorganisms digest organic pollutants, reducing the BOD. Key parts of the process include an aeration tank where the mixing and aeration occur, and a settling tank where treated water is separated from the microbial biomass.

Kinetic Parameters

Kinetic parameters in bioprocess engineering describe the rates of microbial growth and substrate utilization. Important parameters include:

• Maximum specific growth rate \(\text{\mu_m}\) - the highest rate at which microorganisms can grow.
• Substrate affinity constant \(\text{K_s}\) - indicates the substrate concentration at which the microbial growth rate is half of \(\text{\mu_m}\).
• Yield coefficient \(\text{Y_{XS}^M}\) - the ratio of biomass produced to substrate consumed.
• Decay coefficient \(\text{k_d}\) - the rate at which microbial cells die and degrade.

These parameters help in the design and optimization of biological treatment processes like the activated sludge process.

Reactor Volume Calculation

Reactor Volume Calculation involves determining the space required for the wastewater treatment process to occur efficiently. Given the feed's flow rate and initial and final BOD values, we can compute the reactor volume using the formula: \[ V = \frac{F \times (S_0 - S)}{X \times (\theta_c - \theta_H)} \] Here, the flow rate \(\text{F}\), the initial and final BOD \(\text{S_0, S}\), biomass concentration \(\text{X}\), solids residence time \(\text{\theta_c}\), and hydraulic residence time \(\text{\theta_H}\) all play crucial roles in determining the appropriate reactor volume.

Biomass Concentration

Biomass Concentration refers to the amount of microbial biomass in the reactor. This is essential for understanding the efficiency of the treatment process. In the given exercise, we calculate the biomass concentration in both the reactor and the recycle stream. The recycle stream's biomass concentration is related to the reactor concentration by the formula: \[ X_r = X \times (1 + \theta_H \times k_d) \] This concentration helps in maintaining the microbial population necessary for effective wastewater treatment.

Residence Time

Residence Time is important for determining how long the wastewater spends in the reactor. There are two main types:

• Solids Residence Time (\( \theta_c \)) - the average time that solids (or biomass) are retained in the system.
• Hydraulic Residence Time (\( \theta_H \)) - the average time that liquid (or wastewater) remains in the reactor.

Both times are essential for ensuring efficient treatment. Formulas to calculate these include: \[ \theta_H = \frac{V}{F} \ \theta_c = \frac{X \times V}{F \times (X - X_r)} \] By knowing these times, we can optimize the reactor's performance.

Oxygen Requirement

Oxygen Requirement is crucial for aerobic processes like the activated sludge process. Here, microorganisms need oxygen to decompose organic matter. The daily oxygen requirement can be calculated using: \[ O_{req} = F \times (S_0 - S) \times (1 - Y_{XS}^M) \ \] This formula considers the flow rate (\( F \)), the difference in BOD values (\( S_0 - S \)), and the yield coefficient (\( Y_{XS}^M \)). Sufficient oxygen supply ensures that microorganisms remain active and efficient in breaking down pollutants.