In an activated sludge plant, how do you calculate the sludge age with an aerator tank volume of 500,000 gallons, a flow of 5.25 MGD, a PE SS of 72 mg/L, and MLSS of 2350 mg/L?

To calculate the sludge age in an activated sludge plant, you need to understand the relationship between the volume of mixed liquor in the aeration tank, the flow rate of incoming wastewater, and the concentration of mixed liquor suspended solids (MLSS).

The formula for determining sludge age (also known as mean cell residence time, or MCRT) is:

[ \text{Sludge Age (days)} = \frac{\text{Volume of Aerator (gallons)} \times \text{MLSS (mg/L)}}{\text{Flow Rate (MGD)} \times \text{PE SS (mg/L)}} ]

First, convert the volume of the aeration tank from gallons to millions of gallons since the flow rate is given in millions of gallons per day (MGD):

[ 500,000 \text{ gallons} = 0.5 \text{ MGD} ]

Next, you can substitute the values into the formula. The flow rate of the plant is 5.25 MGD, the MLSS is 2350 mg/L, and we assume the PE SS is used directly for steady-state calculations.

Using these figures:

Sludge Age = (Volume of Aerator × MLSS) /