Guest Column | September 7, 2016

Math Solutions: Sludge Age Process Control Calculations

Wastewater Dan Theobald

By Daniel Theobald, "Wastewater Dan"

Math Solutions: Sludge Age Process Control Calculations

“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:

MLVSS lbs added to aeration:

Sludge age (days):

Playlist of 35-plus process control (including activated sludge) calculations

Playlist of 40-plus pounds-wastewater calculations

Playlist of all 140-plus Math Solutions

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

About Dan Theobald:

Known in the industry as “Wastewater Dan,” Daniel L. Theobald, proprietor of Environmental Services (, is a professional wastewater and safety consultant/trainer. He has more than 24 years of hands-on industry experience operating many variants of wastewater treatment processing units and is eager to share with others his knowledge about water conservation.

Theobald serves as an active consultant for industries looking to achieve and maintain improved wastewater treatment at reduced cost. He is a Lifetime Member of the Who’s Who Registry of Professionals and holds numerous certifications from wastewater management regulatory boards and professional organizations. Theobald contributed one chapter to the Water Environment Federation’s ( Manual of Practice # 37 (MOP-37), a technical manual resource guide for biological nutrient removal, published in 2013.

Image credit: "aeration 1" Jason Turgeon © 2014 used under an Attribution 2.0 Generic license: