In order for the activated sludge process to operate properly there must be a balance between the food (BOD_{5}, COD, or TOC) entering the biological system, and the microorganisms in the aeration basin. A high F:M ratio means there is a greater quantity of food relative to the quantity of microorganisms available to consume that food. When the F:M ratio is high, the bacteria are active and dispersed and they multiply rapidly. But with a high F:M ratio the bacteria will not form a good floc. Operating the activated sludge process with a high F:M ratio will typically result in a poor settling sludge in the clarifier and a turbid effluent.

A low F:M ratio means there are many microorganisms but there is a limited amount of food. Only when the food supply is limited do bacteria begin to develop a thicker slime layer, lose their motility, and begin to clump together to form floc that will settle well in the clarifier. Figure 2 shows graphically how the bacterial population relates to the food supply. As you can see, a very high F:M ratio, or a very low F:M ratio will result in dispersed floc that will not settle well in the secondary clarifier.

**Figure 2: Bacterial Growth vs. Food Supply**

In order to calculate the F:M ratio two quantities are required: 1) the pounds of organic material entering the aeration basin and 2) the pounds of microorganisms in the aeration basin, as indicated by simple aeration basin schematic shown below in Figure 3.

**Figure 3: F:M Ratio Simple Process Flow Schematic**

The standard equation for calculating the food-to-mass (microorganism) ratio is shown in Equation 1. Note that in this equation the organic load, the food, is based on the five-day biochemical oxygen demand (BOD_{5}) concentration and the microorganism concentration is based on the mixed liquor *volatile* suspended solids concentration. This is the most common form of the F:M ratio equation.

**Equation 1: Formula for the F:M Ratio**

Where:

Q denotes the influent flow rate to the oxidation ditch in units of million gallons per day

Aeration volume is in units of “million gallons”

Equation 2 shows a variation of the “standard” F:M ratio calculation. In this equation two variables have been changed. In the numerator, instead of BOD_{5}, the calculation uses the organic load based on the chemical oxygen demand (COD). In the denominator, the microorganism population is based on the mixed liquor suspended solids (MLSS) rather than the mixed liquor *volatile* suspended solids (MLVSS). The organic loading parameter was changed because this particular plant measures the organic strength of the wastewater in terms of COD rather than BOD_{5}. In addition, it is assumed that MLSS data is more readily (and frequently) available than is the associated MLVSS data.

**The recommendation is to calculate the F:M ratio using Equation 2.**

**Equation 2: Modified Formula for the F:M Ratio**

The MLSS consists of microorganisms, inert suspended matter, and non-biodegradable suspended matter. The mixed liquor volatile suspended solids (MLVSS) will typically comprise 70 to 85% of the mixed liquor suspended solids (MLSS). Also, though COD/BOD_{5} ratios are very site-specific, it can be assumed, until data is available showing otherwise, that the COD = 2.1 × BOD_{5}, as shown in Table 2, above.

There is no ideal F:M ratio that will work for all activated sludge treatment systems. Every wastewater treatment system is different and each system has its own ideal or optimal F:M ratio. The best F:M ratio for a particular system depends on the type of activated sludge process and the characteristics of the wastewater entering the system. As shown in Table 1, the recommended range for the F:M ratio in an oxidation ditch is 0.04 to 0.10. Every wastewater plant needs to calculate their F:M ratio each day if COD and MLSS (or MLVSS) data is available. This value then needs to be correlated with effluent COD and TSS values. It will not take long for an optimal F:M ratio value or range to be determined that will be specific to the Petro 1 and Petro 2 wastewater treatment systems.

In going from Equation 1 to Equation 2, two variables were changed. Where Equation 1 uses the mixed liquor volatile suspended solids (MLVSS) concentration to more accurately measure the microorganism population, Equation 2 uses the mixed liquor suspended solids (MLSS) concentration. And where Equation 1 uses the BOD_{ }concentration to measure the organic load, Equation 2 uses the COD concentration. Most industrial wastewater plants will have more COD and MLSS data available than they’ll have BOD and MLVSS. All we’ve done here is make an adjustment to the F:M formula to take advantage of data that is more readily available.

**The next section covers the calculation of sludge age.**