For many operators, the solids retention, or mean cell residence time, is the key operating parameter because it directly controls nearly all other parameters (equations) of interest when operating a biological treatment system. The unit of sludge age is “days,” and the reciprocal of sludge age is termed the “specific growth rate of the sludge.” The daily wasting of activated sludge solids equals their daily growth. Therefore, if the sludge age is 10 days, for example, the net growth rate of the sludge is one tenth of its mass per day. In practice, a portion of the daily solids production is lost in the effluent and this loss must be taken into account when calculating the sludge age. The process schematic to be used when calculating the SRT is shown in Figure 5. And from this point forward it should be understood that sludge age, SRT, and MCRT all mean the same thing and are calculated in the exact same way.

**Figure 5: MCRT (or SRT) Process Flow Schemati**c

**1.** One method uses a clarifier core sample (sludge judge) to determine the total suspended solids in the column of water.

**2**. Another method calculates the solids concentration in the clarifier as shown in Equation 4 and uses the sludge blanket volume rather than the entire clarifier volume.

**Equation 4: Clarifier Solids Concentration Formula**

**3.** The third approach, shown in Equation 5, uses the MLSS concentration to calculate the solids in both the aeration basin and the secondary clarifier.

**4.** The fourth approach, and the simplest, does not include the solids in the clarifiers.

**Equation 5: MCRT (or SRT) Formul**a

In Equation 5, the volume of the clarifiers is included in the SRT calculation and the concentration of sludge in the clarifiers is equal to the MLSS concentration. The basis for using the MLSS concentration for calculating the solids in the clarifier is described in detail below.

Under so-called “steady-state conditions,” where mixed liquor from the aeration basin is entering the clarifier, settled sludge (RAS) is being returned to the aeration basin, and clarified water is overflowing the clarifier, you have scenario A as depicted in Figure 6. In scenario A, you have solids concentrating (thickening) as you move closer to the bottom of the tank.

If you were to stop all flow into and out of the clarifier you would have scenario B. In scenario B, after some period of time, you will have settled all of the solids and will have a sludge blanket of some depth. The water above the sludge blanket will be relatively clear and free of solids. After all the solids have settled in Scenario B, the concentration at the bottom of the tank would be equal to the RAS concentration.

Given scenario B, if you were to theoretically shake the tank up so that the solids in the sludge blanket are completely and uniformly redistributed throughout the tank, as shown in scenario C, the total suspended solids of this concentration would be equal to the MLSS concentration which was the original source of flow into the tank. So it is reasonable to use the MLSS concentration and the entire volume of the clarifier when calculating the total solids in the biological treatment system as part of the SRT formula. This is certainly the easiest way to include the solids in the clarifier when calculating the SRT.

**Figure 6: Determining the Volume of Solids in the Clarifier**

When including the sludge solids in the clarifier you must know the volume of the conical section in the clarifier. If the dimensions of the clarifier cone are unknown use a slope of 1:12 for secondary clarifiers that use plows or scrapers to move the sludge to a central hopper. It is common practice to slope the floors of clarifiers equipped with scraper mechanisms at a grade of 1:12 or steeper. Steeper slopes are considered better but are more costly to construct and result in deeper tank centers.

If the secondary clarifier uses hydraulic suction use a slope of 1:50. Because the solids are lifted, it is not necessary to have a significant floor slope to help transport the solids to the central sludge collection sump. Floors that are essentially flat (as flat as 1:50) are adequate. Slopes less than this create a problem in tank drainage.

**The recommended equation for calculating the SRT is shown as Equation 6**. This equation does not include the sludge in the secondary clarifier. The logic for this equation is very simple: the secondary clarifier is not intended to hold solids, therefore, these solids should be minimal. The goal is to maintain a minimum blanket level, returning the settled solids (RAS) to the aeration basin as quickly as possible or removing the solids from the system altogether (WAS).

**Equation 6: MCRT (or SRT) Formula - No Clarifier**

**Our final calculation is the sludge volume index (SVI), discussed in the next section.**