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Volume of Reactor Formula

GoVolume of Reactor given Hydraulic Retention Time Formula

GoVolume of Reactor given Wasting Rate from Return Line Formula

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Reactor Volume refers to the physical volume of a reactor used in chemical processes. Check FAQs

V = \frac{θ c \cdot Y \cdot Q a \cdot (S o - S)}{X a \cdot (1 + (θ c \cdot k d))}

V - Reactor Volume?θ_c - Mean Cell Residence Time?Y - Maximum Yield Coefficient?Q_a - Average Daily Influent Flow Rate?S_o - Influent Substrate Concentration?S - Effluent Substrate Concentration?X_a - MLVSS?k_d - Endogenous Decay Coefficient?

Volume of Reactor Example

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Here is how the Volume of Reactor equation looks like with Values.

Here is how the Volume of Reactor equation looks like with Units.

Here is how the Volume of Reactor equation looks like.

1075.2 = \frac{7 \cdot 0.5 \cdot 1.2 \cdot (25 - 15)}{2500 \cdot (1 + (7 \cdot 0.05))}

1075.2m³ = \frac{7d \cdot 0.5 \cdot 1.2m³/d \cdot (25mg/L - 15mg/L)}{2500mg/L \cdot (1 + (7d \cdot 0.05d⁻¹))}

1075.2 = \frac{7 \cdot 0.5 \cdot 1.2 \cdot (25 - 15)}{2500 \cdot (1 + (7 \cdot 0.05))}

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Volume of Reactor Solution

Follow our step by step solution on how to calculate Volume of Reactor?

FIRST Step Consider the formula

V = \frac{θ c \cdot Y \cdot Q a \cdot (S o - S)}{X a \cdot (1 + (θ c \cdot k d))}

Next Step Substitute values of Variables

∴

V = \frac{7d \cdot 0.5 \cdot 1.2m³/d \cdot (25mg/L - 15mg/L)}{2500mg/L \cdot (1 + (7d \cdot 0.05d⁻¹))}

Next Step Convert Units

∴

V = \frac{604800s \cdot 0.5 \cdot 1.2m³/d \cdot (25mg/L - 15mg/L)}{2500mg/L \cdot (1 + (604800s \cdot 5.8E-7s⁻¹))}

Next Step Prepare to Evaluate

∴

V = \frac{604800 \cdot 0.5 \cdot 1.2 \cdot (25 - 15)}{2500 \cdot (1 + (604800 \cdot 5.8E-7))}

LAST Step Evaluate

∴

V = 1075.2m³

Volume of Reactor Formula Elements

Variables

Reactor Volume

Reactor Volume refers to the physical volume of a reactor used in chemical processes.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Reactor Volume

Mean Cell Residence Time

Mean Cell Residence Time is the average time that the sludge remains in the reactor.

Symbol: θ_c

Measurement: TimeUnit: d

Note: Value should be between 5 to 15.

Formulas to find Mean Cell Residence Time

Maximum Yield Coefficient

Maximum Yield Coefficient refers to the maximum mg of cells produced per mg organic matter removed.

Symbol: Y

Measurement: NAUnit: Unitless

Note: Value should be between 0.4 to 0.8.

Formulas to find Maximum Yield Coefficient

Average Daily Influent Flow Rate

Average Daily Influent Flow Rate is the total discharge that comes in the reactor.

Symbol: Q_a

Measurement: Volumetric Flow RateUnit: m³/d

Note: Value should be greater than 0.

Formulas to find Average Daily Influent Flow Rate

Influent Substrate Concentration

Influent Substrate Concentration refers to the concentration of organic matter or nutrients in the raw wastewater entering a treatment plant.

Symbol: S_o

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Influent Substrate Concentration

Effluent Substrate Concentration

Effluent Substrate Concentration refers to the concentration of organic matter or nutrients present in the treated wastewater (effluent) that is discharged from a wastewater treatment plant.

Symbol: S

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Effluent Substrate Concentration

MLVSS

MLVSS refers to the amount of active microbial biomass, which is crucial for the biological degradation of organic pollutants.

Symbol: X_a

Measurement: DensityUnit: mg/L

Note: Value should be between 1000 to 6500.

Formulas to find MLVSS

Endogenous Decay Coefficient

Endogenous Decay Coefficient refers to the rate at which microorganisms in the biomass consume their own cell mass in the absence of an external food source.

Symbol: k_d

Measurement: First Order Reaction Rate ConstantUnit: d⁻¹

Note: Value should be between 0.025 to 0.075.

Formulas to find Endogenous Decay Coefficient

Other Formulas to find Reactor Volume

Go Volume of Reactor given Hydraulic Retention Time

V = θ \cdot Q a

Go Volume of Reactor given Wasting Rate from Return Line

V = θ c \cdot \frac{(Q w' \cdot X r) + (Q e \cdot X e)}{X}

How to Evaluate Volume of Reactor?

Volume of Reactor evaluator uses Reactor Volume = (Mean Cell Residence Time*Maximum Yield Coefficient*Average Daily Influent Flow Rate*(Influent Substrate Concentration-Effluent Substrate Concentration))/(MLVSS*(1+(Mean Cell Residence Time*Endogenous Decay Coefficient))) to evaluate the Reactor Volume, The Volume of reactor is the total capacity of the reactor to take the influent sludge. It is calculated in cubic meters per sec. Reactor Volume is denoted by V symbol.

How to evaluate Volume of Reactor using this online evaluator? To use this online evaluator for Volume of Reactor, enter Mean Cell Residence Time (θ_c), Maximum Yield Coefficient (Y), Average Daily Influent Flow Rate (Q_a), Influent Substrate Concentration (S_o), Effluent Substrate Concentration (S), MLVSS (X_a) & Endogenous Decay Coefficient (k_d) and hit the calculate button.

FAQs on Volume of Reactor

What is the formula to find Volume of Reactor?

The formula of Volume of Reactor is expressed as Reactor Volume = (Mean Cell Residence Time*Maximum Yield Coefficient*Average Daily Influent Flow Rate*(Influent Substrate Concentration-Effluent Substrate Concentration))/(MLVSS*(1+(Mean Cell Residence Time*Endogenous Decay Coefficient))). Here is an example- 1075.2 = (604800*0.5*1.38888888888889E-05*(0.025-0.015))/(2.5*(1+(604800*5.78703703703704E-07))).

How to calculate Volume of Reactor?

With Mean Cell Residence Time (θ_c), Maximum Yield Coefficient (Y), Average Daily Influent Flow Rate (Q_a), Influent Substrate Concentration (S_o), Effluent Substrate Concentration (S), MLVSS (X_a) & Endogenous Decay Coefficient (k_d) we can find Volume of Reactor using the formula - Reactor Volume = (Mean Cell Residence Time*Maximum Yield Coefficient*Average Daily Influent Flow Rate*(Influent Substrate Concentration-Effluent Substrate Concentration))/(MLVSS*(1+(Mean Cell Residence Time*Endogenous Decay Coefficient))).

What are the other ways to Calculate Reactor Volume?

Here are the different ways to Calculate Reactor Volume-

Reactor Volume=Hydraulic Retention Time*Average Daily Influent Flow Rate
Reactor Volume=Mean Cell Residence Time*((WAS Pumping Rate from Return Line*Sludge Concentration in Return Line)+(Effluent Flow Rate*Solid Concentration in Effluent))/MLSS
Reactor Volume=Mean Cell Residence Time*WAS Pumping Rate from Return Line*Sludge Concentration in Return Line/MLSS

Can the Volume of Reactor be negative?

No, the Volume of Reactor, measured in Volume cannot be negative.

Which unit is used to measure Volume of Reactor?

Volume of Reactor is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Reactor can be measured.

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: Unit

Volume of Reactor Formula

​GoVolume of Reactor given Hydraulic Retention Time Formula

​GoVolume of Reactor given Wasting Rate from Return Line Formula

Volume of Reactor Example

Volume of Reactor Solution

Volume of Reactor Formula Elements

Other Formulas to find Reactor Volume

How to Evaluate Volume of Reactor?

FAQs on Volume of Reactor

Variable Name

GoVolume of Reactor given Hydraulic Retention Time Formula

GoVolume of Reactor given Wasting Rate from Return Line Formula