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Mean Cell Residence Time given Reactor Volume Formula

GoMean Cell Residence Time given Observed Cell Yield Formula

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

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

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

Mean Cell Residence Time given Reactor Volume Example

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Here is how the Mean Cell Residence Time given Reactor Volume equation looks like with Values.

Here is how the Mean Cell Residence Time given Reactor Volume equation looks like with Units.

Here is how the Mean Cell Residence Time given Reactor Volume equation looks like.

6.3549 = \frac{1000 \cdot 2500}{1.2 \cdot 0.5 \cdot (25 - 15) - (1000 \cdot 2500 \cdot 0.05)}

6.3549d = \frac{1000m³ \cdot 2500mg/L}{1.2m³/d \cdot 0.5 \cdot (25mg/L - 15mg/L) - (1000m³ \cdot 2500mg/L \cdot 0.05d⁻¹)}

6.3549 = \frac{1000 \cdot 2500}{1.2 \cdot 0.5 \cdot (25 - 15) - (1000 \cdot 2500 \cdot 0.05)}

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Mean Cell Residence Time given Reactor Volume Solution

Follow our step by step solution on how to calculate Mean Cell Residence Time given Reactor Volume?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ c = \frac{1000m³ \cdot 2500mg/L}{1.2m³/d \cdot 0.5 \cdot (25mg/L - 15mg/L) - (1000m³ \cdot 2500mg/L \cdot 0.05d⁻¹)}

Next Step Convert Units

∴

θ c = \frac{1000m³ \cdot 2.5kg/m³}{1.2m³/d \cdot 0.5 \cdot (0.025kg/m³ - 0.015kg/m³) - (1000m³ \cdot 2.5kg/m³ \cdot 5.8E-7s⁻¹)}

Next Step Prepare to Evaluate

∴

θ c = \frac{1000 \cdot 2.5}{1.2 \cdot 0.5 \cdot (0.025 - 0.015) - (1000 \cdot 2.5 \cdot 5.8E-7)}

Next Step Evaluate

∴

θ c = 549059.481443823s

Next Step Convert to Output's Unit

∴

θ c = 6.35485510930351d

LAST Step Rounding Answer

∴

θ c = 6.3549d

Mean Cell Residence Time given Reactor Volume Formula Elements

Variables

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

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

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

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

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

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

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 Mean Cell Residence Time

Go Mean Cell Residence Time given Observed Cell Yield

θ c = \frac{Y obs - Y}{k d}

How to Evaluate Mean Cell Residence Time given Reactor Volume?

Mean Cell Residence Time given Reactor Volume evaluator uses Mean Cell Residence Time = (Reactor Volume*MLVSS)/(Average Daily Influent Flow Rate*Maximum Yield Coefficient*(Influent Substrate Concentration-Effluent Substrate Concentration)-(Reactor Volume*MLVSS*Endogenous Decay Coefficient)) to evaluate the Mean Cell Residence Time, Mean Cell Residence Time given Reactor Volume is the average time that the sludge remains in the reactor (sludge age). For a complete-mix activated sludge process ranges from 5 to 15 days. Mean Cell Residence Time is denoted by θ_c symbol.

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

FAQs on Mean Cell Residence Time given Reactor Volume

What is the formula to find Mean Cell Residence Time given Reactor Volume?

The formula of Mean Cell Residence Time given Reactor Volume is expressed as Mean Cell Residence Time = (Reactor Volume*MLVSS)/(Average Daily Influent Flow Rate*Maximum Yield Coefficient*(Influent Substrate Concentration-Effluent Substrate Concentration)-(Reactor Volume*MLVSS*Endogenous Decay Coefficient)). Here is an example- 7.4E-5 = (1000*2.5)/(1.38888888888889E-05*0.5*(0.025-0.015)-(1000*2.5*5.78703703703704E-07)).

How to calculate Mean Cell Residence Time given Reactor Volume?

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

What are the other ways to Calculate Mean Cell Residence Time?

Here are the different ways to Calculate Mean Cell Residence Time-

Mean Cell Residence Time=(Observed Cell Yield-Maximum Yield Coefficient)/Endogenous Decay Coefficient

Can the Mean Cell Residence Time given Reactor Volume be negative?

No, the Mean Cell Residence Time given Reactor Volume, measured in Time cannot be negative.

Which unit is used to measure Mean Cell Residence Time given Reactor Volume?

Mean Cell Residence Time given Reactor Volume is usually measured using the Day[d] for Time. Second[d], Millisecond[d], Microsecond[d] are the few other units in which Mean Cell Residence Time given Reactor Volume can be measured.

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Mean Cell Residence Time given Reactor Volume Formula

​GoMean Cell Residence Time given Observed Cell Yield Formula

Mean Cell Residence Time given Reactor Volume Example

Mean Cell Residence Time given Reactor Volume Solution

Mean Cell Residence Time given Reactor Volume Formula Elements

Other Formulas to find Mean Cell Residence Time

How to Evaluate Mean Cell Residence Time given Reactor Volume?

FAQs on Mean Cell Residence Time given Reactor Volume

Variable Name

GoMean Cell Residence Time given Observed Cell Yield Formula