Volume of Aerobic Digester Calculator

✖Influent average flow rate to the digester is the discharge going to the digester.ⓘ Influent average flow rate [Q_i]			+10% -10%
✖Influent suspended solids refers to small solid particles which remain in suspension in water as a colloid.ⓘ Influent suspended solids [X_i]			+10% -10%
✖Digester total suspended solids is the dry-weight of suspended particles, that are not dissolved, in a sample of water.ⓘ Digester total suspended solids [X]			+10% -10%
✖Reaction rate constant quantifies the rate and direction of a chemical reaction.ⓘ Reaction rate constant [K_d]			+10% -10%
✖Volatile fraction of digester suspended solids.ⓘ Volatile fraction [P_v]			+10% -10%
✖Solids retention time is the time the solid fraction of the wastewater spends in a treatment unit.ⓘ Solids retention time [θ]			+10% -10%

✖The Volume of Aerobic Digester is the capacity of the digester.ⓘ Volume of Aerobic Digester [V_ad]

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Formula

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Volume of Aerobic Digester

Formula

`"V"_{"ad"} = ("Q"_{"i"}*"X"_{"i"})/("X"*(("K"_{"d"}*"P"_{"v"})+"θ"))`

Example

`"2.9E^-5m³"=("5m³/s"*"5mg/L")/("5mg/L"*(("0.05d⁻¹"*"0.5")+"2d"))`

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Volume of Aerobic Digester Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Aerobic Digester = (Influent average flow rate*Influent suspended solids)/(Digester total suspended solids*((Reaction rate constant*Volatile fraction)+Solids retention time))
V_ad = (Q_i*X_i)/(X*((K_d*P_v)+θ))
This formula uses 7 Variables

Variables Used

Volume of Aerobic Digester - (Measured in Cubic Meter) - The Volume of Aerobic Digester is the capacity of the digester.
Influent average flow rate - (Measured in Cubic Meter per Second) - Influent average flow rate to the digester is the discharge going to the digester.
Influent suspended solids - (Measured in Kilogram per Cubic Meter) - Influent suspended solids refers to small solid particles which remain in suspension in water as a colloid.
Digester total suspended solids - (Measured in Kilogram per Cubic Meter) - Digester total suspended solids is the dry-weight of suspended particles, that are not dissolved, in a sample of water.
Reaction rate constant - (Measured in 1 Per Second) - Reaction rate constant quantifies the rate and direction of a chemical reaction.
Volatile fraction - Volatile fraction of digester suspended solids.
Solids retention time - (Measured in Second) - Solids retention time is the time the solid fraction of the wastewater spends in a treatment unit.

STEP 1: Convert Input(s) to Base Unit

Influent average flow rate: 5 Cubic Meter per Second --> 5 Cubic Meter per Second No Conversion Required
Influent suspended solids: 5 Milligram per Liter --> 0.005 Kilogram per Cubic Meter (Check conversion here)
Digester total suspended solids: 5 Milligram per Liter --> 0.005 Kilogram per Cubic Meter (Check conversion here)
Reaction rate constant: 0.05 1 Per Day --> 5.78703703703704E-07 1 Per Second (Check conversion here)
Volatile fraction: 0.5 --> No Conversion Required
Solids retention time: 2 Day --> 172800 Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_ad = (Q_i*X_i)/(X*((K_d*P_v)+θ)) --> (5*0.005)/(0.005*((5.78703703703704E-07*0.5)+172800))

Evaluating ... ...

V_ad = 2.89351851851367E-05

STEP 3: Convert Result to Output's Unit

2.89351851851367E-05 Cubic Meter --> No Conversion Required

FINAL ANSWER

2.89351851851367E-05 ≈ 2.9E-5 Cubic Meter <-- Volume of Aerobic Digester

(Calculation completed in 00.004 seconds)

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Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2200+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 15 Design of an Aerobic Digester Calculators

Solids Retention Time given Volume of Aerobic Digester

Go Solids retention time = ((Influent average flow rate*Influent suspended solids)/(Volume of Aerobic Digester*Digester total suspended solids)-(Reaction rate constant*Volatile fraction))

Volume of Aerobic Digester

Go Volume of Aerobic Digester = (Influent average flow rate*Influent suspended solids)/(Digester total suspended solids*((Reaction rate constant*Volatile fraction)+Solids retention time))

Digester Total Suspended Solids given Volume of Aerobic Digester

Go Digester total suspended solids = (Influent average flow rate*Influent suspended solids)/(Volume of Aerobic Digester*(Reaction rate constant*Volatile fraction+Solids retention time))

Specific Gravity of Digested Sludge given Volume of Digested Sludge

Go Specific Gravity of Sludge = (Weight of sludge)/(Water Density*Sludge Volume*Percent Solids)

Density of Water given Volume of Digested Sludge

Go Water Density = (Weight of sludge)/(Sludge Volume*Specific Gravity of Sludge*Percent Solids)

Percent Solids given Volume of Digested Sludge

Go Percent Solids = (Weight of sludge)/(Sludge Volume*Water Density*Specific Gravity of Sludge)

Volume of Digested Sludge

Go Sludge Volume = (Weight of sludge)/(Water Density*Specific Gravity of Sludge*Percent Solids)

Weight of Sludge given Volume of Digested Sludge

Go Weight of sludge = (Water Density*Sludge Volume*Specific Gravity of Sludge*Percent Solids)

Initial Weight of Oxygen given Weight of Oxygen Required

Go Weight of initial oxygen = (Weight of oxygen*Volatile suspended solid weight)/(Volume of suspended solid*2.3)

VSS as Mass Flow Rate given Weight of Oxygen Required

Go Volume of suspended solid = (Weight of oxygen*Volatile suspended solid weight)/(2.3*Weight of initial oxygen)

Weight of VSS given Weight of Oxygen Required

Go Volatile suspended solid weight = (Volume of suspended solid*2.3*Weight of initial oxygen)/Weight of oxygen

Weight of Oxygen Required to Destroy VSS

Go Weight of oxygen = (Volume of suspended solid*2.3*Weight of initial oxygen)/Volatile suspended solid weight

Volume of Air Required at Standard Conditions

Go Volume of Air = (Weight of oxygen)/(Density of Air*0.232)

Density of Air given Volume of Air Required

Go Density of Air = (Weight of oxygen)/(Volume of Air*0.232)

Weight of Oxygen given Volume of Air

Go Weight of oxygen = (Volume of Air*Density of Air*0.232)

Volume of Aerobic Digester Formula

What is aerobic digestion ?

Aerobic digestion is a process in sewage treatment designed to reduce the volume of sewage sludge and make it suitable for subsequent use. More recently, technology has been developed that allows the treatment and reduction of other organic waste, such as food, cardboard and horticultural waste.

How to Calculate Volume of Aerobic Digester?

Volume of Aerobic Digester calculator uses Volume of Aerobic Digester = (Influent average flow rate*Influent suspended solids)/(Digester total suspended solids*((Reaction rate constant*Volatile fraction)+Solids retention time)) to calculate the Volume of Aerobic Digester, The Volume of Aerobic Digester calculates the volume of aerobic digester when we have prior information of other parameters related with aerobic digester. Volume of Aerobic Digester is denoted by V_ad symbol.

How to calculate Volume of Aerobic Digester using this online calculator? To use this online calculator for Volume of Aerobic Digester, enter Influent average flow rate (Q_i), Influent suspended solids (X_i), Digester total suspended solids (X), Reaction rate constant (K_d), Volatile fraction (P_v) & Solids retention time (θ) and hit the calculate button. Here is how the Volume of Aerobic Digester calculation can be explained with given input values -> 2.9E-5 = (5*0.005)/(0.005*((5.78703703703704E-07*0.5)+172800)).

FAQ

What is Volume of Aerobic Digester?

The Volume of Aerobic Digester calculates the volume of aerobic digester when we have prior information of other parameters related with aerobic digester and is represented as V_ad = (Q_i*X_i)/(X*((K_d*P_v)+θ)) or Volume of Aerobic Digester = (Influent average flow rate*Influent suspended solids)/(Digester total suspended solids*((Reaction rate constant*Volatile fraction)+Solids retention time)). Influent average flow rate to the digester is the discharge going to the digester, Influent suspended solids refers to small solid particles which remain in suspension in water as a colloid, Digester total suspended solids is the dry-weight of suspended particles, that are not dissolved, in a sample of water, Reaction rate constant quantifies the rate and direction of a chemical reaction, Volatile fraction of digester suspended solids & Solids retention time is the time the solid fraction of the wastewater spends in a treatment unit.

How to calculate Volume of Aerobic Digester?

The Volume of Aerobic Digester calculates the volume of aerobic digester when we have prior information of other parameters related with aerobic digester is calculated using Volume of Aerobic Digester = (Influent average flow rate*Influent suspended solids)/(Digester total suspended solids*((Reaction rate constant*Volatile fraction)+Solids retention time)). To calculate Volume of Aerobic Digester, you need Influent average flow rate (Q_i), Influent suspended solids (X_i), Digester total suspended solids (X), Reaction rate constant (K_d), Volatile fraction (P_v) & Solids retention time (θ). With our tool, you need to enter the respective value for Influent average flow rate, Influent suspended solids, Digester total suspended solids, Reaction rate constant, Volatile fraction & Solids retention time 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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