Guest Column | August 5, 2016

Math Solutions: Activated Sludge Process Control Calculations

Wastewater Dan Theobald

By Daniel Theobald, "Wastewater Dan"


Some wastewater calculations rely on multiple math steps to arrive at the conclusion, complicating an already challenging aspect of the operator’s role. Wastewater consultant and trainer Dan Theobald helps operators overcome the intimidation of solving activated sludge process control by offering a step-by-step tutorial.

Activated sludge process control calculations, such as determining mixed liquor volatile suspended solids (MLVSS) concentration, can be considered complex in that they require multiple steps, but they do not have to be difficult — even for operators who have struggled with the mathematics portion of wastewater operator certification examinations. The first step is to find training that is easy to understand.

This tool for operators (or educators, engineers, regulators, etc.) — represented through video tutorials — offers mathematical templates for performing accurate wastewater calculations. The tool also provides definitions, explanations, and alternative applications for the calculations beyond the specific examples presented.

This month’s Math Solution, for calculating the amount in parts per million (ppm or mg/L) of MLVSS to be maintained in the aerated portion of an activated sludge system, is presented as a word problem.

The food/microorganism (F/M) ratio is 0.59 pounds of chemical oxygen demand (COD)/day per one pound of mixed liquor volatile suspended solids (MLVSS) under aeration. The average COD of the raw, untreated wastewater is 3,000 mg/L and the average COD of the primary treated wastewater is 2,830 ppm. The average daily flow is 79,165 gallons per hour (GPH) and the aerated tank dimensions are 60’ long, 58’ wide, and 12’ deep.

Activated sludge process control calculations in your plant may be similar, though may have different requirements such as expressing the results as square feet, cubic feet, increment of millions, or even incorporating a time element in calculation solutions. Exact step-by-step solutions for the given word problem are as follows:

COD Pounds/Day Added To Aeration:

Primary effluent COD:


Flow (MGD):

COD pounds added to aeration:

MLVSS Pounds Under Aeration:


MLVSS Concentration (mg/L):

Aerated volume (MG):

MLVSS concentration (mg/L):

Playlist Calculations:

Playlist of 30+ Process Control (including Activated Sludge) Calculations

Playlist of 35+ Pounds-Wastewater Math Calculations

Playlist of all my 135+ Math Solutions

This is the ‘Activated Sludge 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: "UASB for domestic wastewater treatment in Bucaramanga, Colombia," SuSanA Secretariat © 2013, used under an Attribution 2.0 Generic license: