Volume of Reactor Calculator

✖Mean Cell Residence Time is the average time that the sludge remains in the reactor.ⓘ Mean Cell Residence Time [θ_c]			+10% -10%
✖Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed.ⓘ Maximum Yield Coefficient [Y]			+10% -10%
✖Average daily influent flow rate is the total discharge that comes in the reactor.ⓘ Average daily influent flow rate [Q]			+10% -10%
✖Influent Substrate Concentration is the concentration of BOD that is present in the influent.ⓘ Influent Substrate Concentration [S_o]			+10% -10%
✖Effluent substrate concentration is the concentration of the BOD present in the effluent.ⓘ Effluent substrate concentration [S]			+10% -10%
✖MLVSS is the concentration of microorganisms in the reactor.ⓘ MLVSS [X_a]			+10% -10%
✖Endogenous decay coefficient is a coefficient representing the decrease of cell mass in the MLVSS.ⓘ Endogenous decay coefficient [k_d]			+10% -10%

✖The Reactor Volume gives us the capacity of the reactor.ⓘ Volume of Reactor [V]

⎘ Copy

👎

Formula

✖

Volume of Reactor

Formula

`"V" = ("θ"_{"c"}*"Y"*"Q"*("S"_{"o"}-"S"))/("X"_{"a"}*(1+("θ"_{"c"}*"k"_{"d"})))`

Example

`"1075.2m³"=("7d"*"0.5"*"1.2m³/d"*("25mg/L"-"15mg/L"))/("2500mg/L"*(1+("7d"*"0.050d⁻¹")))`

Calculator

LaTeX

Reset

👍

Download Environmental Engineering Formula PDF

Volume of Reactor Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
V = (θ_c*Y*Q*(S_o-S))/(X_a*(1+(θ_c*k_d)))
This formula uses 8 Variables

Variables Used

Reactor Volume - (Measured in Cubic Meter) - The Reactor Volume gives us the capacity of the reactor.
Mean Cell Residence Time - (Measured in Second) - Mean Cell Residence Time is the average time that the sludge remains in the reactor.
Maximum Yield Coefficient - Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed.
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.
Influent Substrate Concentration - (Measured in Milligram per Liter) - Influent Substrate Concentration is the concentration of BOD that is present in the influent.
Effluent substrate concentration - (Measured in Milligram per Liter) - Effluent substrate concentration is the concentration of the BOD present in the effluent.
MLVSS - (Measured in Milligram per Liter) - MLVSS is the concentration of microorganisms in the reactor.
Endogenous decay coefficient - (Measured in 1 Per Second) - Endogenous decay coefficient is a coefficient representing the decrease of cell mass in the MLVSS.

STEP 1: Convert Input(s) to Base Unit

Mean Cell Residence Time: 7 Day --> 604800 Second (Check conversion here)
Maximum Yield Coefficient: 0.5 --> No Conversion Required
Average daily influent flow rate: 1.2 Cubic Meter per Day --> 1.2 Cubic Meter per Day No Conversion Required
Influent Substrate Concentration: 25 Milligram per Liter --> 25 Milligram per Liter No Conversion Required
Effluent substrate concentration: 15 Milligram per Liter --> 15 Milligram per Liter No Conversion Required
MLVSS: 2500 Milligram per Liter --> 2500 Milligram per Liter No Conversion Required
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

V = (θ_c*Y*Q*(S_o-S))/(X_a*(1+(θ_c*k_d))) --> (604800*0.5*1.2*(25-15))/(2500*(1+(604800*5.78703703703704E-07)))

Evaluating ... ...

V = 1075.2

STEP 3: Convert Result to Output's Unit

1075.2 Cubic Meter --> No Conversion Required

FINAL ANSWER

1075.2 Cubic Meter <-- Reactor Volume

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Environmental Engineering » Design of a complete mix activated sludge reactor » Volume of Reactor » Volume of Reactor

Credits

Created by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has created this Calculator and 500+ more calculators!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Calculator and 1700+ more calculators!

< 5 Volume of Reactor Calculators

Volume of Reactor

Go 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)))

Volume of Reactor given Wasting Rate from Return Line

Go 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

Volume of Reactor using Wasting Rate from Return Line when Concentration of Solid in Effluent is Low

Go Reactor Volume = Mean Cell Residence Time*WAS Pumping Rate from Return Line*Sludge Concentration in Return Line/MLSS

Volume of Reactor given Hydraulic Retention Time

Go Reactor Volume = Hydraulic retention time*Average daily influent flow rate

Volume of Reactor given WAS Pumping Rate from Aeration Tank

Go Reactor Volume = Mean Cell Residence Time*WAS Pumping Rate from Reactor

Volume of Reactor Formula

What is volume?

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic meter.

What is a sludge reactor?

It 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 Volume of Reactor?

Volume of Reactor calculator 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 calculate 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 calculate Volume of Reactor using this online calculator? To use this online calculator for Volume of Reactor, enter Mean Cell Residence Time (θ_c), Maximum Yield Coefficient (Y), Average daily influent flow rate (Q), Influent Substrate Concentration (S_o), Effluent substrate concentration (S), MLVSS (X_a) & Endogenous decay coefficient (k_d) and hit the calculate button. Here is how the Volume of Reactor calculation can be explained with given input values -> 1382.4 = (604800*0.5*1.38888888888889E-05*(0.025-0.015))/(2.5*(1+(604800*5.78703703703704E-07))).

FAQ

What is Volume of Reactor?

The Volume of reactor is the total capacity of the reactor to take the influent sludge. It is calculated in cubic meters per sec and is represented as V = (θ_c*Y*Q*(S_o-S))/(X_a*(1+(θ_c*k_d))) or 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))). Mean Cell Residence Time is the average time that the sludge remains in the reactor, Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed, Average daily influent flow rate is the total discharge that comes in the reactor, Influent Substrate Concentration is the concentration of BOD that is present in the influent, Effluent substrate concentration is the concentration of the BOD present in the effluent, MLVSS is the concentration of microorganisms in the reactor & Endogenous decay coefficient is a coefficient representing the decrease of cell mass in the MLVSS.

How to calculate Volume of Reactor?

The Volume of reactor is the total capacity of the reactor to take the influent sludge. It is calculated in cubic meters per sec is calculated using 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 calculate Volume of Reactor, you need Mean Cell Residence Time (θ_c), Maximum Yield Coefficient (Y), Average daily influent flow rate (Q), Influent Substrate Concentration (S_o), Effluent substrate concentration (S), MLVSS (X_a) & Endogenous decay coefficient (k_d). With our tool, you need to enter the respective value for Mean Cell Residence Time, Maximum Yield Coefficient, Average daily influent flow rate, Influent Substrate Concentration, Effluent substrate concentration, MLVSS & 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 Reactor Volume?

In this formula, Reactor Volume uses Mean Cell Residence Time, Maximum Yield Coefficient, Average daily influent flow rate, Influent Substrate Concentration, Effluent substrate concentration, MLVSS & Endogenous decay coefficient. We can use 4 other way(s) to calculate the same, which is/are as follows -

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
Reactor Volume = Mean Cell Residence Time*WAS Pumping Rate from Reactor

Home

FREE PDFs

🔍 Search