Endogenous Respiration Rate Constant Given Volume Of Aeration Tank Calculator

Formula Used:

\[ K_e = \frac{\left(\frac{Y \times Q_s \times (Q_i - Q_o) \times \theta_c}{V \times X} - 1\right)}{\theta_c} \]

Maximum Yield Coefficient (Y):

(dimensionless)

Sewage Discharge (Qs):

m³/s

Influent BOD (Qi):

kg/m³

Effluent BOD (Qo):

kg/m³

Sludge Age (θc):

seconds

Volume of Tank (V):

m³

MLSS (X):

kg/m³

Endogenous Respiration Rate Constant (Ke):

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1. What is Endogenous Respiration Rate Constant?

The Endogenous Respiration Rate Constant (Ke) is used for designing a complete-mix activated-sludge system. It represents the rate at which microorganisms consume their own cellular mass when external substrate is limited.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ K_e = \frac{\left(\frac{Y \times Q_s \times (Q_i - Q_o) \times \theta_c}{V \times X} - 1\right)}{\theta_c} \]

Where:

\( Y \) — Maximum Yield Coefficient (dimensionless)
\( Q_s \) — Sewage Discharge (m³/s)
\( Q_i \) — Influent BOD (kg/m³)
\( Q_o \) — Effluent BOD (kg/m³)
\( \theta_c \) — Sludge Age (seconds)
\( V \) — Volume of Tank (m³)
\( X \) — MLSS (kg/m³)

Explanation: The formula calculates the endogenous respiration rate constant based on system parameters and biological process characteristics.

3. Importance of Ke Calculation

Details: Accurate Ke estimation is crucial for designing efficient activated-sludge systems, predicting biomass decay rates, and optimizing wastewater treatment plant operations.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure values are positive and within reasonable ranges for wastewater treatment systems.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Ke values?
A: Ke values typically range from 0.02 to 0.10 per day (0.00000023 to 0.00000116 per second) for most activated sludge systems.

Q2: How does temperature affect Ke?
A: Ke increases with temperature, typically following an Arrhenius relationship with temperature coefficients around 1.04-1.08 per °C.

Q3: What factors influence the Maximum Yield Coefficient?
A: Y depends on substrate type, microbial community, temperature, and other environmental conditions, typically ranging from 0.4 to 0.8 mg cells/mg substrate.

Q4: Why is sludge age important in this calculation?
A: Sludge age determines the average residence time of microorganisms in the system, directly affecting endogenous respiration rates.

Q5: Are there limitations to this equation?
A: The equation assumes steady-state conditions and may not accurately represent systems with significant dynamic changes or unusual microbial populations.