Endogenous Respiration Rate Constant Given Mass Of Wasted Activated Sludge Calculator

Formula Used:

\[ K_e = \frac{(Y \times Q_s \times (Q_i - Q_o)) - M_{ws}}{X' \times V} \]

Maximum Yield Coefficient (Y):

(unitless)

Sewage Discharge (Qs):

m³/s

Influent BOD (Qi):

kg/m³

Effluent BOD (Qo):

kg/m³

Mass of Wasted Activated Sludge (Mws):

Mixed Liquor Suspended Solids (X'):

kg/m³

Volume of Tank (V):

m³

Endogenous Respiration Rate Constant (Ke):

Unit Converter ▲

Unit Converter ▼

From:	To:

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 under endogenous respiration conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ K_e = \frac{(Y \times Q_s \times (Q_i - Q_o)) - M_{ws}}{X' \times V} \]

Where:

\( K_e \) — Endogenous Respiration Rate Constant (1/s)
\( Y \) — Maximum Yield Coefficient (unitless)
\( Q_s \) — Sewage Discharge (m³/s)
\( Q_i \) — Influent BOD (kg/m³)
\( Q_o \) — Effluent BOD (kg/m³)
\( M_{ws} \) — Mass of Wasted Activated Sludge (kg)
\( X' \) — Mixed Liquor Suspended Solids (kg/m³)
\( V \) — Volume of Tank (m³)

Explanation: This formula calculates the endogenous respiration rate constant by considering the organic matter removal, sludge production, and system volume.

3. Importance of Ke Calculation

Details: Accurate calculation of Ke is crucial for designing and optimizing activated sludge systems, predicting sludge production, and maintaining proper treatment efficiency in wastewater treatment plants.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure that influent BOD is greater than effluent BOD for meaningful results. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Ke values?
A: Ke values typically range from 0.04 to 0.10 per day (0.000000463 to 0.000001157 per second) for most activated sludge systems.

Q2: How does temperature affect Ke?
A: Ke increases with temperature, typically following the Arrhenius relationship with a temperature coefficient (θ) of about 1.04-1.08.

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

Q4: When is this calculation most important?
A: This calculation is critical during the design phase of wastewater treatment plants and for optimizing existing activated sludge processes.

Q5: Are there limitations to this equation?
A: The equation assumes steady-state conditions and may need adjustment for systems with significant variations in loading or temperature.