# Math Solutions: Sludge Age Process Control Calculations

By Daniel Theobald, "Wastewater Dan"

“Wastewater Dan” helps operators solve for sludge age and optimize the activated sludge process using sample problems and easy-to-use math templates to inform real-world calculations.

With credit to the Kentucky Department for Environmental Protection, which explains sludge age quite nicely: “Sludge age in the activated sludge process is the measure of the length of time a particle of suspended solids has been undergoing aeration. This time is expressed in days and is calculated using the pounds of mixed liquor suspended solids (MLSS) in the aeration basin and the pounds of total suspended solids (TSS) in the influent.”

This tutorial provides the necessary calculations to optimize sludge age process control, which will include sludge age itself, but also MLSS volumes (actual and desired) and mixed liquor volatile suspended solids (MLVSS). The specific examples shared below and their corresponding solutions act as templates for operators — or educators, engineers, regulators, etc. — to perform accurate wastewater calculations when substituting real values for the following word problems.

Problem #1: If the desired sludge age is six days, calculate the desired MLSS milligrams per liter (mg/L) concentration in the aerator and the desired MLSS pounds (lbs) in the aerator.  Primary clarifier effluent is 1,085 lbs TSS and aeration tank volume is 0.350 million gallons (MG).

Calculate Desired MLSS lbs and MLSS mg/L

MLSS lbs in aeration:

MLSS mg/L in aeration:

Problem #2: Calculate the sludge age of an activated sludge system with an aeration tank volume of 0.325 MG that treats a flow of 2.2 MGD.  The primary clarifier effluent has TSS concentration of 65 mg/L and aeration tank MLSS concentration of 2,500 mg/L.

Calculate Sludge Age (Days)

MLSS lbs in aeration:

Sludge age (days):

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This is the Sludge Age Process Control Calculations presentation in my series of “Math Solutions.” If you have specific wastewater math queries, please submit a question