Influent Substrate Concentration given Volume of Reactor Calculator

✖The Reactor Volume gives us the capacity of the reactor.ⓘ Reactor Volume [V]			+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%
✖Mean Cell Residence Time is the average time that the sludge remains in the reactor.ⓘ Mean Cell Residence Time [θ_c]			+10% -10%
✖Average daily influent flow rate is the total discharge that comes in the reactor.ⓘ Average daily influent flow rate [Q]			+10% -10%
✖Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed.ⓘ Maximum Yield Coefficient [Y]			+10% -10%
✖Effluent substrate concentration is the concentration of the BOD present in the effluent.ⓘ Effluent substrate concentration [S]			+10% -10%

✖Influent Substrate Concentration is the concentration of BOD that is present in the influent.ⓘ Influent Substrate Concentration given Volume of Reactor [S_o]

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Formula

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Influent Substrate Concentration given Volume of Reactor

Formula

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

Example

`"803586.4mg/L"=(("1000m³"*"2500mg/L"*(1+("0.050d⁻¹"*"7d")))/("7d"*"1.2m³/d"*"0.5"))+"15mg/L"`

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Influent Substrate Concentration given Volume of Reactor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Influent Substrate Concentration = ((Reactor Volume*MLVSS*(1+(Endogenous decay coefficient*Mean Cell Residence Time)))/(Mean Cell Residence Time*Average daily influent flow rate*Maximum Yield Coefficient))+Effluent substrate concentration
S_o = ((V*X_a*(1+(k_d*θ_c)))/(θ_c*Q*Y))+S
This formula uses 8 Variables

Variables Used

Influent Substrate Concentration - (Measured in Kilogram per Cubic Meter) - Influent Substrate Concentration is the concentration of BOD that is present in the influent.
Reactor Volume - (Measured in Cubic Meter) - The Reactor Volume gives us the capacity of the reactor.
MLVSS - (Measured in Kilogram per Cubic Meter) - 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.
Mean Cell Residence Time - (Measured in Second) - Mean Cell Residence Time is the average time that the sludge remains in the reactor.
Average daily influent flow rate - (Measured in Cubic Meter per Second) - Average daily influent flow rate is the total discharge that comes in the reactor.
Maximum Yield Coefficient - Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed.
Effluent substrate concentration - (Measured in Kilogram per Cubic Meter) - Effluent substrate concentration is the concentration of the BOD present in the effluent.

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)
Endogenous decay coefficient: 0.05 1 Per Day --> 5.78703703703704E-07 1 Per Second (Check conversion here)
Mean Cell Residence Time: 7 Day --> 604800 Second (Check conversion here)
Average daily influent flow rate: 1.2 Cubic Meter per Day --> 1.38888888888889E-05 Cubic Meter per Second (Check conversion here)
Maximum Yield Coefficient: 0.5 --> No Conversion Required
Effluent substrate concentration: 15 Milligram per Liter --> 0.015 Kilogram per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_o = ((V*X_a*(1+(k_d*θ_c)))/(θ_c*Q*Y))+S --> ((1000*2.5*(1+(5.78703703703704E-07*604800)))/(604800*1.38888888888889E-05*0.5))+0.015

Evaluating ... ...

S_o = 803.586428571428

STEP 3: Convert Result to Output's Unit

803.586428571428 Kilogram per Cubic Meter -->803586.428571428 Milligram per Liter (Check conversion here)

FINAL ANSWER

803586.428571428 ≈ 803586.4 Milligram per Liter <-- Influent Substrate Concentration

(Calculation completed in 00.020 seconds)

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Created by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 5 Influent Substrate Concentration Calculators

Influent Substrate Concentration given Volume of Reactor

Go Influent Substrate Concentration = ((Reactor Volume*MLVSS*(1+(Endogenous decay coefficient*Mean Cell Residence Time)))/(Mean Cell Residence Time*Average daily influent flow rate*Maximum Yield Coefficient))+Effluent substrate concentration

Influent Substrate Concentration given Theoretical Oxygen Requirement

Go Influent Substrate Concentration = (Theoretical Oxygen Requirement+(1.42*Net waste activated sludge))*(BOD conversion factor/(8.34*Average daily influent flow rate))+Effluent substrate concentration

Influent Substrate Concentration given Net Waste Activated Sludge

Go Influent Substrate Concentration = (Net waste activated sludge/(8.34*Observed Cell Yield*Average daily influent flow rate))+Effluent substrate concentration

Influent Substrate Concentration given Organic Loading

Go Influent Substrate Concentration = Organic loading*Reactor Volume/Influent average flow rate

Influent Substrate Concentration for Organic Loading using Hydraulic Retention Time

Go Influent Substrate Concentration = Organic loading*Retention Time

Influent Substrate Concentration given Volume of Reactor Formula

What is volume of reactor?

The volume of the reactor is the total capacity of the reactor which is allowed in the reactor. It is calculated in cubic meters.

How is sludge treated?

Many sludges are treated using a variety of digestion techniques, the purpose of which is to reduce the amount of organic matter and the number of disease-causing microorganisms present in the solids. The most common treatment options include anaerobic digestion, aerobic digestion, and composting.

How to Calculate Influent Substrate Concentration given Volume of Reactor?

Influent Substrate Concentration given Volume of Reactor calculator uses Influent Substrate Concentration = ((Reactor Volume*MLVSS*(1+(Endogenous decay coefficient*Mean Cell Residence Time)))/(Mean Cell Residence Time*Average daily influent flow rate*Maximum Yield Coefficient))+Effluent substrate concentration to calculate the Influent Substrate Concentration, Influent Substrate Concentration given Volume of Reactor is the total BOD concentration in the incoming sludge. Influent Substrate Concentration is denoted by S_o symbol.

How to calculate Influent Substrate Concentration given Volume of Reactor using this online calculator? To use this online calculator for Influent Substrate Concentration given Volume of Reactor, enter Reactor Volume (V), MLVSS (X_a), Endogenous decay coefficient (k_d), Mean Cell Residence Time (θ_c), Average daily influent flow rate (Q), Maximum Yield Coefficient (Y) & Effluent substrate concentration (S) and hit the calculate button. Here is how the Influent Substrate Concentration given Volume of Reactor calculation can be explained with given input values -> 6.3E+8 = ((1000*2.5*(1+(5.78703703703704E-07*604800)))/(604800*1.38888888888889E-05*0.5))+0.015.

FAQ

What is Influent Substrate Concentration given Volume of Reactor?

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

How to calculate Influent Substrate Concentration given Volume of Reactor?

Influent Substrate Concentration given Volume of Reactor is the total BOD concentration in the incoming sludge is calculated using Influent Substrate Concentration = ((Reactor Volume*MLVSS*(1+(Endogenous decay coefficient*Mean Cell Residence Time)))/(Mean Cell Residence Time*Average daily influent flow rate*Maximum Yield Coefficient))+Effluent substrate concentration. To calculate Influent Substrate Concentration given Volume of Reactor, you need Reactor Volume (V), MLVSS (X_a), Endogenous decay coefficient (k_d), Mean Cell Residence Time (θ_c), Average daily influent flow rate (Q), Maximum Yield Coefficient (Y) & Effluent substrate concentration (S). With our tool, you need to enter the respective value for Reactor Volume, MLVSS, Endogenous decay coefficient, Mean Cell Residence Time, Average daily influent flow rate, Maximum Yield Coefficient & Effluent substrate concentration 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 Influent Substrate Concentration?

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

Influent Substrate Concentration = (Net waste activated sludge/(8.34*Observed Cell Yield*Average daily influent flow rate))+Effluent substrate concentration
Influent Substrate Concentration = (Theoretical Oxygen Requirement+(1.42*Net waste activated sludge))*(BOD conversion factor/(8.34*Average daily influent flow rate))+Effluent substrate concentration
Influent Substrate Concentration = Organic loading*Reactor Volume/Influent average flow rate
Influent Substrate Concentration = Organic loading*Retention Time

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