Mean Cell Residence Time given Quantity of Volatile Solids Calculator

✖Endogenous coefficient is used for designing a complete-mix activated-sludge system.ⓘ Endogenous coefficient [k_d]			+10% -10%
✖Yield coefficient is defined as ratio of VSS to BOD.ⓘ Yield coefficient [Y]			+10% -10%
✖BOD in means the amount of dissolved oxygen enter anaerobic digester.ⓘ BOD in [BOD_in]			+10% -10%
✖BOD out means the amount of dissolved oxygen exits anaerobic digester.ⓘ BOD out [BOD_out]			+10% -10%
✖Volatile solids produced is defined in terms of mass flow rate.ⓘ Volatile Solids produced [P_x]			+10% -10%

✖Mean Cell Residence Time is the average time that the sludge remains in the reactor.ⓘ Mean Cell Residence Time given Quantity of Volatile Solids [θ_c]

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Formula

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Mean Cell Residence Time given Quantity of Volatile Solids

Formula

`"θ"_{"c"} = (1/"k"_{"d"})-("Y"*("BOD"_{"in"}-"BOD"_{"out"})/("P"_{"x"}*"k"_{"d"}))`

Example

`"-125d"=(1/"0.05d⁻¹")-("5"*("150kg/d"-"5kg/d")/("100kg/d"*"0.05d⁻¹"))`

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-125 : Output for this calculator is usually positive! Please check the input.

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Mean Cell Residence Time given Quantity of Volatile Solids Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean Cell Residence Time = (1/Endogenous coefficient)-(Yield coefficient*(BOD in-BOD out)/(Volatile Solids produced*Endogenous coefficient))
θ_c = (1/k_d)-(Y*(BOD_in-BOD_out)/(P_x*k_d))
This formula uses 6 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.
Endogenous coefficient - (Measured in 1 Per Second) - Endogenous coefficient is used for designing a complete-mix activated-sludge system.
Yield coefficient - Yield coefficient is defined as ratio of VSS to BOD.
BOD in - (Measured in Kilogram per Second) - BOD in means the amount of dissolved oxygen enter anaerobic digester.
BOD out - (Measured in Kilogram per Second) - BOD out means the amount of dissolved oxygen exits anaerobic digester.
Volatile Solids produced - (Measured in Kilogram per Second) - Volatile solids produced is defined in terms of mass flow rate.

STEP 1: Convert Input(s) to Base Unit

Endogenous coefficient: 0.05 1 Per Day --> 5.78703703703704E-07 1 Per Second (Check conversion here)
Yield coefficient: 5 --> No Conversion Required
BOD in: 150 Kilogram per Day --> 0.00173611111111111 Kilogram per Second (Check conversion here)
BOD out: 5 Kilogram per Day --> 5.78703703703704E-05 Kilogram per Second (Check conversion here)
Volatile Solids produced: 100 Kilogram per Day --> 0.00115740740740741 Kilogram per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_c = (1/k_d)-(Y*(BOD_in-BOD_out)/(P_x*k_d)) --> (1/5.78703703703704E-07)-(5*(0.00173611111111111-5.78703703703704E-05)/(0.00115740740740741*5.78703703703704E-07))

Evaluating ... ...

θ_c = -10800000

STEP 3: Convert Result to Output's Unit

-10800000 Second -->-124.999999999999 Day (Check conversion here)

FINAL ANSWER

-124.999999999999 ≈ -125 Day <-- Mean Cell Residence Time

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Environmental Engineering » Design of an Anaerobic Digester » Mean Cell Residence Time given Quantity of Volatile Solids

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 20 Design of an Anaerobic Digester Calculators

Endogenous Coefficient given Quantity of Volatile Solids

Go Endogenous coefficient = (1/Mean Cell Residence Time)-(Yield coefficient*(BOD in-BOD out)/(Volatile Solids produced*Mean Cell Residence Time))

Mean Cell Residence Time given Quantity of Volatile Solids

Go Mean Cell Residence Time = (1/Endogenous coefficient)-(Yield coefficient*(BOD in-BOD out)/(Volatile Solids produced*Endogenous coefficient))

Yield Coefficient given Quantity of Volatile Solids

Go Yield coefficient = (Volatile Solids produced*(1-Mean Cell Residence Time*Endogenous coefficient))/(BOD in-BOD out)

Quantity of Volatile Solids Produced Each Day

Go Volatile Solids produced = (Yield coefficient*(BOD in-BOD out))/(1-Endogenous coefficient*Mean Cell Residence Time)

BOD Out given Quantity of Volatile Solids

Go BOD out = BOD in-(Volatile Solids produced/Yield coefficient)*(1-Endogenous coefficient*Mean Cell Residence Time)

BOD in given Quantity of Volatile Solids

Go BOD in = (Volatile Solids produced/Yield coefficient)*(1-Endogenous coefficient*Mean Cell Residence Time)+BOD out

Volatile Solids produced given Percent Stabilization

Go Volatile Solids produced = (1/1.42)*(BOD in-BOD out-((Percent stabilization*BOD in)/100))

BOD Out given Percent Stabilization

Go BOD out = (BOD in*100-142*Volatile Solids produced-Percent stabilization*BOD in)/100

Percent Stabilization

Go Percent stabilization = ((BOD in-BOD out-1.42*Volatile Solids produced)/BOD in)*100

BOD in given Percent Stabilization

Go BOD in = (BOD out*100+142*Volatile Solids produced)/(100-Percent stabilization)

Volatile Solids produced given Volume of Methane Gas produced

Go Volatile Solids produced = (1/1.42)*(BOD in-BOD out-(Volume of methane/5.62))

BOD Out given Volume of Methane Gas Produced

Go BOD out = (BOD in-(Volume of methane/5.62)-(1.42*Volatile Solids produced))

BOD in given Volume of Methane Gas Produced

Go BOD in = (Volume of methane/5.62)+BOD out+(1.42*Volatile Solids produced)

Volume of Methane Gas Produced at Standard Conditions

Go Volume of methane = 5.62*(BOD in-BOD out-1.42*Volatile Solids produced)

Influent Sludge Flow Rate given Volume Required for Anaerobic Digester

Go Influent Sludge Flow Rate = (Volume/Hydraulic retention time)

Hydraulic Retention Time given Volume Required for Anaerobic Digester

Go Hydraulic Retention Time = (Volume/Influent Sludge Flow Rate)

Volume Required for Anaerobic Digester

Go Volume = (Hydraulic retention time*Influent Sludge Flow Rate)

Volumetric Flow Rate given Volumetric Loading in Anaerobic Digester

Go Volumetric Flow Rate = (BOD per day/Volumetric loading)

BOD Per Day given Volumetric Loading in Anaerobic Digester

Go BOD per day = (Volumetric loading*Volumetric Flow Rate)

Volumetric Loading in Anaerobic Digester

Go Volumetric loading = (BOD per day/Volumetric Flow Rate)

Mean Cell Residence Time given Quantity of Volatile Solids Formula

Mean Cell Residence Time = (1/Endogenous coefficient)-(Yield coefficient*(BOD in-BOD out)/(Volatile Solids produced*Endogenous coefficient))
θ_c = (1/k_d)-(Y*(BOD_in-BOD_out)/(P_x*k_d))

What is mean cell residence time ?

The mean cell residence time or MCRT is the amount of time, in days, that solids or bacteria are maintained in the activated sludge system. The MCRT is known also as the solids retention time (SRT).

How to Calculate Mean Cell Residence Time given Quantity of Volatile Solids?

Mean Cell Residence Time given Quantity of Volatile Solids calculator uses Mean Cell Residence Time = (1/Endogenous coefficient)-(Yield coefficient*(BOD in-BOD out)/(Volatile Solids produced*Endogenous coefficient)) to calculate the Mean Cell Residence Time, The Mean Cell Residence Time given Quantity of Volatile Solids is the amount of time, in days, that solids or bacteria are maintained in the activated sludge system. Mean Cell Residence Time is denoted by θ_c symbol.

How to calculate Mean Cell Residence Time given Quantity of Volatile Solids using this online calculator? To use this online calculator for Mean Cell Residence Time given Quantity of Volatile Solids, enter Endogenous coefficient (k_d), Yield coefficient (Y), BOD in (BOD_in), BOD out (BOD_out) & Volatile Solids produced (P_x) and hit the calculate button. Here is how the Mean Cell Residence Time given Quantity of Volatile Solids calculation can be explained with given input values -> 5.8E-5 = (1/5.78703703703704E-07)-(5*(0.00173611111111111-5.78703703703704E-05)/(0.00115740740740741*5.78703703703704E-07)).

FAQ

What is Mean Cell Residence Time given Quantity of Volatile Solids?

The Mean Cell Residence Time given Quantity of Volatile Solids is the amount of time, in days, that solids or bacteria are maintained in the activated sludge system and is represented as θ_c = (1/k_d)-(Y*(BOD_in-BOD_out)/(P_x*k_d)) or Mean Cell Residence Time = (1/Endogenous coefficient)-(Yield coefficient*(BOD in-BOD out)/(Volatile Solids produced*Endogenous coefficient)). Endogenous coefficient is used for designing a complete-mix activated-sludge system, Yield coefficient is defined as ratio of VSS to BOD, BOD in means the amount of dissolved oxygen enter anaerobic digester, BOD out means the amount of dissolved oxygen exits anaerobic digester & Volatile solids produced is defined in terms of mass flow rate.

How to calculate Mean Cell Residence Time given Quantity of Volatile Solids?

The Mean Cell Residence Time given Quantity of Volatile Solids is the amount of time, in days, that solids or bacteria are maintained in the activated sludge system is calculated using Mean Cell Residence Time = (1/Endogenous coefficient)-(Yield coefficient*(BOD in-BOD out)/(Volatile Solids produced*Endogenous coefficient)). To calculate Mean Cell Residence Time given Quantity of Volatile Solids, you need Endogenous coefficient (k_d), Yield coefficient (Y), BOD in (BOD_in), BOD out (BOD_out) & Volatile Solids produced (P_x). With our tool, you need to enter the respective value for Endogenous coefficient, Yield coefficient, BOD in, BOD out & Volatile Solids produced and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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