Volume of Reactor Calculator

Reactor Volume Formula:

\[ V = \frac{θ_c \times Y \times Q_a \times (S_o - S)}{X_a \times (1 + (θ_c \times k_d))} \]

Mean Cell Residence Time:

days

Maximum Yield Coefficient:

Average Daily Influent Flow Rate:

m³/day

Influent Substrate Concentration:

mg/L

Effluent Substrate Concentration:

mg/L

MLVSS:

mg/L

Endogenous Decay Coefficient:

1/day

Reactor Volume (m³):

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1. What is a Volume of Reactor Calculator?

Definition: This calculator estimates the required volume of a biological reactor for wastewater treatment based on key process parameters.

Purpose: It helps environmental engineers and wastewater treatment professionals design and optimize biological treatment systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{θ_c \times Y \times Q_a \times (S_o - S)}{X_a \times (1 + (θ_c \times k_d))} \]

Where:

\( V \) — Reactor Volume (m³)
\( θ_c \) — Mean Cell Residence Time (days)
\( Y \) — Maximum Yield Coefficient (dimensionless)
\( Q_a \) — Average Daily Influent Flow Rate (m³/day)
\( S_o \) — Influent Substrate Concentration (mg/L)
\( S \) — Effluent Substrate Concentration (mg/L)
\( X_a \) — MLVSS (Mixed Liquor Volatile Suspended Solids) (mg/L)
\( k_d \) — Endogenous Decay Coefficient (1/day)

Explanation: The formula calculates the reactor volume needed to achieve the desired treatment efficiency based on microbial growth kinetics.

3. Importance of Reactor Volume Calculation

Details: Proper reactor sizing ensures effective organic matter removal, meets effluent quality standards, and optimizes operational costs.

4. Using the Calculator

Tips: Enter all required parameters. Typical values are provided as defaults where applicable. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is Mean Cell Residence Time (θc)?
A: Also called sludge age, it's the average time microorganisms remain in the system, typically 5-15 days for conventional activated sludge.

Q2: What's a typical Maximum Yield Coefficient (Y)?
A: For domestic wastewater, Y typically ranges from 0.4 to 0.8 mg biomass/mg substrate.

Q3: How do I determine MLVSS (Xa)?
A: MLVSS is determined through lab analysis of the mixed liquor, typically 2000-4000 mg/L for activated sludge systems.

Q4: What affects the Endogenous Decay Coefficient (kd)?
A: Temperature, microbial community, and wastewater characteristics affect kd, typically 0.04-0.075 1/day at 20°C.

Q5: Why is (So-S) important?
A: This represents the substrate concentration difference that drives biological treatment - the organic matter to be removed.