# Wastewater Calculator

Created by Jack Bowater
Reviewed by Purnima Singh, PhD and Adena Benn
Based on research by
Michael H. Gerardi Settleability Problems and Loss of Solids in the Activated Sludge Process.; John Wiley & Sons, Inc.; 2002
Last updated: Jan 18, 2024

This wastewater calculator allows you to construct a working model of an activated sludge plant. It follows the sewage from the primary clarifier, through the aeration tank, and out through the secondary clarifier, calculating important measures along the way. This tool is actually made of seven different calculators:

• BOD calculator;
• COD calculator;
• F/M ratio calculator;
• HRT calculator;
• MCRT calculator;
• Sludge age calculator; and
• SVI calculator.

Read the article below to learn what each of the parts of a wastewater treatment plant does and how to calculate each of these measures.

## Schematic of a wastewater treatment plant

A sewage plant is a series of different operations that all interconnect to form a unified whole. Depending on the area's needs, these operations may vary from plant to plant, but the aim is always the same: take in raw sewage and turn as much of it into clean water as possible. Our wastewater calculator aims to model this as accurately as possible, so you don't have to worry about long calculations.

Wastewater entering the plant goes through several stages:

1. Primary treatment - Here, the waste goes through a series of screens, mills, and sedimentation chambers. This serves to remove larger particulate matter that may damage the rest of the plant, e.g., sand or eggshells.
2. Primary clarifier - A clarifier detains the wastewater for a longer amount of time, usually around two hours. This allows sewage to settle to the bottom, where it can be extracted and sent to sludge treatment. Any floating matter is also removed.
3. Aeration tank - The primary clarifier is not guaranteed to remove all organic matter (suspended solids) from the water. The water leaving this clarifier is mixed with sludge from the later secondary clarifiers to provide microorganisms to digest the organic matter. This liquor then enters the aeration tank, where compressed air bubbles in. This oxygenates the water, providing the perfect conditions for the microorganisms to feed on the organic matter and multiply.
4. Secondary clarifiers - The mixture is then detained in a secondary clarifier, allowing activated sludge to settle out of the clear water. The activated sludge is either sent back to the aeration tank or sent to sludge treatment. The clear water passes out as the secondary effluent and is disinfected before being discharged.

There are sometimes additional steps in the activated sludge treatment, but we do not model these in our wastewater calculator.

## BOD calculator, COD calculator, and F/M ratio calculator

Here we will discuss how to calculate the F/M ratio (food to microorganism ratio): bacterias are fundamental in the treatment, and to be honest, they like it; you can learn how they grow in that bonanza of food with our generation time calculator. If you wish to find BOD or COD, you can rearrange the formulas listed below, use our calculator by inputting the values you know, or read more in our dedicated MLVSS calculator. There you will find explanations not present in this wastewater calculator.

π In the formulas below, we only show those for BOD. However, in all instances, you can swap all of the BOD measures for the equivalent in COD to get the COD formulas.

The first step towards finding the F/M ratio is to determine the food aspect of it. This is the weight of BOD that enters the aeration tank from the primary clarifier, also known as the loading. In the metric system, we find it using:

$\!\scriptsize {\begin{gather*}\text{BOD}\\ \text{loading}\\ \text{(kg/day)}\end{gather*}} = {\begin{gather*}\text{BOD conc.}\\ \text{entering}\\ \text{tank (g/L)}\end{gather*}} \times {\begin{gather*}\text{Influent}\\ \text{flow}\\ \text{tank (m}^3\text{/day)}\end{gather*}}$

For the imperial version, we need to change the units - in particular, flow is now expressed in millions of gallons per day (MGD); notice how we are using volume units: you can use our volume conversion for the necessary calculations. We must also multiply the whole thing by a conversion factor of 8.34 lbs/gallon, which is the density of water:

$\!\scriptsize {\begin{gather*}\text{BOD}\\ \text{loading}\\ \text{(lbs/day)}\end{gather*}} = {\begin{gather*}\text{BOD conc.}\\ \text{entering}\\ \text{tank (mg/L)}\end{gather*}} \times {\begin{gather*}\text{Influent}\\ \text{flow}\\ \text{tank (MGD)}\end{gather*}} \times 8.34\space(\text{lbs/gallon})$

The next step requires you to find the amount of microorganism in the aeration tank - the M component of the F/M ratio. This is the weight of MLVSS (mixed liquor volatile suspended solids) within the aeration tank. We calculate this in a similar way to the BOD loading. In metric:

$\!\scriptsize {\begin{gather*}\text{MLVSS}\\ \text{(kg)}\end{gather*}} = {\begin{gather*}\text{MLVSS}\\ \text{conc. (g/L)}\end{gather*}} \times {\begin{gather*}\text{Aeration}\\ \text{tank volume}\\ \text{(m}^3\text{/day)}\end{gather*}}$

Then in imperial, where $\text{MG}$ means millions of gallons:

$\!\scriptsize {\begin{gather*}\text{MLVSS}\\ \text{(lbs)}\end{gather*}} = {\begin{gather*}\text{MLVSS}\\ \text{conc. (mg/L)}\end{gather*}} \times {\begin{gather*}\text{Aeration}\\ \text{tank volume}\\ \text{(MG)}\end{gather*}} \times 8.34\space(\text{lbs/gallon})$

The final step is easy - just find the ratio between the amount of food entering the aeration tank and the amount of microorganisms already in it!

$\!\scriptsize \text{F/M ratio} = \frac{\text{BOD loading}}{\text{MLVSS in tank}}$

π If you need to calculate the tank volume for many shapes, visit our tank volume calculator!

## HRT calculator

HRT stands for hydraulic retention time. It is the average time it takes a particle of wastewater to pass from one end of the aeration tank to the other. It is found by a relatively simple calculation:

$\!\scriptsize \text{HRT} = \frac{\text{Aeration tank volume}}{\text{Flow rate through tank}}$

The only requirement for units here is that the volume units for both the tank and the flow rate are the same. The units for HRT will be whatever the time units are for the flow rate (it's usually in hours): learn more about these quantities with our flow rate calculator.

The hydraulic retention time has important implications for the biological activity of the aeration tank. If the HRT is too low, the sludge moves through the aeration tank too quickly for nitrification and solubilization to occur fully, meaning more BOD will pass into the secondary clarifiers. However, while increasing it will further the breakdown of the organic matter in the sewage, it may affect the processing rate of the plant as a whole, becoming the rate-limiting step.

## MCRT calculator

MCRT stands for mean cell residence time, which is the average time a particle of organic waste or an individual bacteria spends in the activated sludge process. The first step is to find the total weight of mixed liquor suspended solids (MLSS), which is all the organic matter in the wastewater, including bacteria, in the entire process. The metric version is:

$\!\scriptsize {\begin{gather*}\text{MLSS}\\ \text{(kg)}\end{gather*}} = {\begin{gather*}\text{MLSS}\\ \text{conc.}\\ \text{(g/L)}\end{gather*}} \times \Biggr({\begin{gather*}\text{Aeration}\\ \text{tank volume}\\ \text{(m}^3\text{)}\end{gather*}} + {\begin{gather*}\text{Secondary}\\ \text{clarifiers}\\ \text{volume (m}^3\text{)}\end{gather*}}\Biggr)$

And the imperial version is:

$\!\scriptsize {\begin{gather*}\text{MLSS}\\ \text{(lb)}\end{gather*}} = {\begin{gather*}\text{MLSS}\\ \text{conc.}\\ \text{(mg/L)}\end{gather*}} \times \Biggr({\begin{gather*}\text{Aeration}\\ \text{tank volume}\\ \text{(MG)}\end{gather*}} + {\begin{gather*}\text{Secondary}\\ \text{clarifiers}\\ \text{volume}\\ \text{(MG)}\end{gather*}}\Biggr) \times {\begin{gather*}8.34\\ \text{(lbs/gallon)}\end{gather*}}$

where:

• $\text{MLSS weight}$ - Total weight of MLSS in both the aeration tank and secondary clarifiers; and
• $\text{MLSS conc.}$ - Concentration of MLSS in the system.

The next step is to find the weight of the suspended solids (SS) leaving the system via the secondary clarifiers. This is usually done on a per-day basis:

$\!\scriptsize {\begin{gather*}\text{SS leaving}\\ \text{activated}\\ \text{sludge}\\ \text{process (kg)}\end{gather*}} = \Biggr({\begin{gather*}\text{Flow of}\\ \text{secondary}\\ \text{effluence}\\ \text{(m}^3\text{/day)}\end{gather*}} \times {\begin{gather*}\text{Solids in}\\ \text{secondary}\\ \text{effluence}\\ \text{(g/L)}\end{gather*}}\Biggr) + \Biggr({\begin{gather*}\text{Flow of}\\ \text{waste}\\ \text{sludge}\\ \text{(m}^3\text{/day)}\end{gather*}} \times {\begin{gather*}\text{Solids in}\\ \text{waste}\\ \text{sludge}\\ \text{(g/L)}\end{gather*}}\Biggr)$

In imperial:

$\!\scriptsize {\begin{gather*}\text{SS leaving}\\ \text{activated}\\ \text{sludge}\\ \text{process (lb)}\end{gather*}} = \Biggr(\Biggr({\begin{gather*}\text{Flow of}\\ \text{secondary}\\ \text{effluence}\\ \text{(MGD)}\end{gather*}} \times {\begin{gather*}\text{Solids in}\\ \text{secondary}\\ \text{effluence}\\ \text{(mg/L)}\end{gather*}}\Biggr) + \Biggr({\begin{gather*}\text{Flow of}\\ \text{waste}\\ \text{sludge}\\ \text{(MGD)}\end{gather*}} \times {\begin{gather*}\text{Solids in}\\ \text{waste}\\ \text{sludge}\\ \text{(mg/L)}\end{gather*}}\Biggr)\Biggr) \times {\begin{gather*}8.34\\ \text{(lbs/gallon)}\end{gather*}}$

You can use the flow over whatever period you like; just ensure they are the same for both effluent flows. However, over a day is customary. The final step is to divide the weight of the SS in the system by the amount of SS that leaves it over a certain period:

$\!\scriptsize \text{MCRT (days)} = \frac{\text{MLSS weight (mass)}}{\text{SS leaving activated sludge process (mass/day)}}$

## Sludge age calculator

Sludge age is a similar metric to MCRT, except that now it is the time that a bacteria or solid particle spends in the aeration tank. It too is usually given in days. Similarly, the first step is to find the weight of MLSS in just the aeration tank. In metric, this looks like:

$\!\scriptsize \text{MLSS (kg)} = \text{MLSS conc. (g/L)} \times \text{Aeration tank volume (m}^3\text{)}$

And in imperial:

$\!\scriptsize \text{MLSS (lb)} = {\begin{gather*}\text{MLSS}\\ \text{conc. (mg/L)}\end{gather*}} \times {\begin{gather*}\text{Aeration tank}\\ \text{volume (MG)}\end{gather*}} \times 8.34\space(\text{lbs/gallon})$

The next step is to find the amount of suspended solids that enter the aeration tank, i.e., the effluence of the primary clarifier. This step is very similar to the previous one for both metric:

$\!\scriptsize {\begin{gather*}\text{SS entering}\\ \text{aeration tank (kg)}\end{gather*}} = {\begin{gather*}\text{Primary clarifier}\\ \text{effluent SS}\\ \text{conc. (g/L)}\end{gather*}} \times {\begin{gather*}\text{Primary clarifier}\\ \text{effluent flow}\\ \text{(m}^3\text{/day)}\end{gather*}}$

and imperial:

$\!\scriptsize {\begin{gather*}\text{SS entering}\\ \text{aeration}\\ \text{tank (lb)}\end{gather*}} = {\begin{gather*}\text{Primary clarifier}\\ \text{effluent SS}\\ \text{conc. (mg/L)}\end{gather*}} \times {\begin{gather*}\text{Primary clarifier}\\ \text{effluent flow}\\ \text{(MGD)}\end{gather*}} \times {\begin{gather*}8.34\\ \text{lbs/gallon}\end{gather*}}$

The final step is then to divide the amount of suspended solids in the tank by the amount that enters it per day:

$\!\scriptsize \text{Sludge age (days)} = \frac{\text{MLSS weight (mass)}}{\text{SS entering aeration tank (mass/day)}}$

The use of this measure is to ensure that the proper amount of SS is kept in the aeration tank. As the MLSS weight fluctuates due to the activated sludge process, the flow of waste in can be altered to maintain a desired sludge age.

## SVI calculator

SVI is the final measure of this wastewater calculator, which stands for sludge volume index, as is unique among the other measures given here as it is usually found in a laboratory, not from the system itself. Despite this, it is still an important value to know, as it gives you the most accurate measure of the sludge's compactibility.

First, you must find the volume of settled solids after 30 minutes. To do this, take a graduated cylinder (1 liter is common), fill it with a fresh sample of mixed liquor (usually from the effluent of the aeration tank) and leave it somewhere undisturbed for half an hour to settle. After this time, record the volume of settled solids in mL and divide it by the total volume of the sample taken in L to get the measure in mL / L.

Now you can apply the SVI formula:

$\!\scriptsize \text{SVI (mL/g)} = \frac{\text{Settled solids after 30 mins. (mL/L)}}{\text{MLSS conc. (g/L)}}$

You can tell a lot about the sludge by the SVI value:

• β€80 mL/g - The sludge is very dense and settles rapidly. This usually means the sludge is over-oxidized. Effluent BOD/COD may be less than needed.
• 100-200 mL/g - The desirable SVI range for most wastewater plants.
• β₯250 mL/g - A sign of a very slowly settling sludge. Usually occurs when the plant is just starting up, but may be a sign that the effluent BOD/COD is too high.

## FAQ

### What are the 3 stages of wastewater treatment?

The three stages of wastewater treatment are:

1. Primary treatment - Used to remove grit and floating matter;
2. Secondary treatment - Used to breakdown any remaining organic matter; and
3. Tertiary treatment - Further purifies water going to vulnerable environments.

### How do I reduce BOD in wastewater?

To reduce BOD in wastewater:

• Introduce a greater amount of microorganisms to the wastewater, which will digest the suspended solids;
• Allow for a longer settling time in the primary clarifier to remove more sludge; and
• Maintain the optimal pH for your microorganisms to digest the waste.

### How to calculate SVI?

To calculate SVI:

1. Take a sample of the mixed liquor from the aeration tank's effluent with a graduated cylinder.
2. Let the sample settle for half an hour and record the amount of settled solids in milliliters per liter.
3. Divide this value by the mixed liquor suspended solids concentration in grams per liter.

### What is MCRT?

Mean cell residence time is the average time that organic matter spends in the activated sludge process. The MCRT of a wastewater plant affects a host of other values, such as how long the suspended solids take to be digested and the operation speed of the entire plant.

Jack Bowater
I'd like to find
F/M ratio/MLVSS
using
COD
Primary clarifier
Average untreated influent COD
g/L
Average primary treated COD
g/L
Effluent COD
g/L
Effluent flow
US gal/day
Aeration tank
Is the volume known?
Yes
Volume
US gal
lb/day
COD calculation
F/M ratio
MLVSS conc.
g/L
MLVSS weight
lb
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