Mean Cell Residence Time given Reactor Volume Calculator

✖Reactor Volume refers to the physical volume of a reactor used in chemical processes.ⓘ Reactor Volume [V]			+10% -10%
✖MLVSS refers to the amount of active microbial biomass, which is crucial for the biological degradation of organic pollutants.ⓘ MLVSS [X_a]			+10% -10%
✖Average Daily Influent Flow Rate is the total discharge that comes in the reactor.ⓘ Average Daily Influent Flow Rate [Q_a]			+10% -10%
✖Maximum Yield Coefficient refers to the maximum mg of cells produced per mg organic matter removed.ⓘ Maximum Yield Coefficient [Y]			+10% -10%
✖Influent Substrate Concentration refers to the concentration of organic matter or nutrients in the raw wastewater entering a treatment plant.ⓘ Influent Substrate Concentration [S_o]			+10% -10%
✖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.ⓘ Effluent Substrate Concentration [S]			+10% -10%
✖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.ⓘ Endogenous Decay Coefficient [k_d]			+10% -10%

✖Mean Cell Residence Time is the average time that the sludge remains in the reactor.ⓘ Mean Cell Residence Time given Reactor Volume [θ_c]

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Mean Cell Residence Time given Reactor Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
θ_c = (V*X_a)/(Q_a*Y*(S_o-S)-(V*X_a*k_d))
This formula uses 8 Variables

Variables Used

Mean Cell Residence Time - (Measured in Second) - Mean Cell Residence Time is the average time that the sludge remains in the reactor.
Reactor Volume - (Measured in Cubic Meter) - Reactor Volume refers to the physical volume of a reactor used in chemical processes.
MLVSS - (Measured in Kilogram per Cubic Meter) - MLVSS refers to the amount of active microbial biomass, which is crucial for the biological degradation of organic pollutants.
Average Daily Influent Flow Rate - (Measured in Cubic Meter per Day) - Average Daily Influent Flow Rate is the total discharge that comes in the reactor.
Maximum Yield Coefficient - Maximum Yield Coefficient refers to the maximum mg of cells produced per mg organic matter removed.
Influent Substrate Concentration - (Measured in Kilogram per Cubic Meter) - Influent Substrate Concentration refers to the concentration of organic matter or nutrients in the raw wastewater entering a treatment plant.
Effluent Substrate Concentration - (Measured in Kilogram per Cubic Meter) - 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.
Endogenous Decay Coefficient - (Measured in 1 Per Second) - 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.

STEP 1: Convert Input(s) to Base Unit

Reactor Volume: 1000 Cubic Meter --> 1000 Cubic Meter No Conversion Required
MLVSS: 2500 Milligram per Liter --> 2.5 Kilogram per Cubic Meter (Check conversion here)
Average Daily Influent Flow Rate: 1.2 Cubic Meter per Day --> 1.2 Cubic Meter per Day No Conversion Required
Maximum Yield Coefficient: 0.5 --> No Conversion Required
Influent Substrate Concentration: 25 Milligram per Liter --> 0.025 Kilogram per Cubic Meter (Check conversion here)
Effluent Substrate Concentration: 15 Milligram per Liter --> 0.015 Kilogram per Cubic Meter (Check conversion here)
Endogenous Decay Coefficient: 0.05 1 Per Day --> 5.78703703703704E-07 1 Per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_c = (V*X_a)/(Q_a*Y*(S_o-S)-(V*X_a*k_d)) --> (1000*2.5)/(1.2*0.5*(0.025-0.015)-(1000*2.5*5.78703703703704E-07))

Evaluating ... ...

θ_c = 549059.481443823

STEP 3: Convert Result to Output's Unit

549059.481443823 Second -->6.35485510930351 Day (Check conversion here)

FINAL ANSWER

6.35485510930351 ≈ 6.354855 Day <-- Mean Cell Residence Time

(Calculation completed in 00.021 seconds)

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< Mean Cell Residential Time Calculators

Mean Cell Residence Time given Reactor Volume

LaTeX Go 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))

Mean Cell Residence Time given Observed Cell Yield

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

Mean Cell Residence Time given Reactor Volume Formula

LaTeX Go

What is Volume of Reactor?

Volume of Reactor is the total capacity of the reactor which is allowed in it as influent sludge. It is calculated in cubic meters.

What is a Sludge Reactor?

Sludge Reactor refers to a multi-chamber reactor unit that makes use of highly concentrated microorganisms to degrade organics and remove nutrients from wastewater to produce a high-quality effluent.

How to Calculate Mean Cell Residence Time given Reactor Volume?

Mean Cell Residence Time given Reactor Volume calculator 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 calculate 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 calculate Mean Cell Residence Time given Reactor Volume using this online calculator? To use this online calculator 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. Here is how the Mean Cell Residence Time given Reactor Volume calculation can be explained with given input values -> 7.4E-5 = (1000*2.5)/(1.38888888888889E-05*0.5*(0.025-0.015)-(1000*2.5*5.78703703703704E-07)).

FAQ

What is Mean Cell Residence Time given Reactor Volume?

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 and is represented as θ_c = (V*X_a)/(Q_a*Y*(S_o-S)-(V*X_a*k_d)) or 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)). Reactor Volume refers to the physical volume of a reactor used in chemical processes, MLVSS refers to the amount of active microbial biomass, which is crucial for the biological degradation of organic pollutants, Average Daily Influent Flow Rate is the total discharge that comes in the reactor, Maximum Yield Coefficient refers to the maximum mg of cells produced per mg organic matter removed, Influent Substrate Concentration refers to the concentration of organic matter or nutrients in the raw wastewater entering a treatment plant, 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 & 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.

How to calculate Mean Cell Residence Time given Reactor Volume?

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 is calculated using 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 calculate Mean Cell Residence Time given Reactor Volume, you need 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). With our tool, you need to enter the respective value for Reactor Volume, MLVSS, Average Daily Influent Flow Rate, Maximum Yield Coefficient, Influent Substrate Concentration, Effluent Substrate Concentration & Endogenous Decay Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Mean Cell Residence Time?

In this formula, Mean Cell Residence Time uses Reactor Volume, MLVSS, Average Daily Influent Flow Rate, Maximum Yield Coefficient, Influent Substrate Concentration, Effluent Substrate Concentration & Endogenous Decay Coefficient. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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