Process Control Calculations

Process control calculations turn operating data into information that an operator can use to understand and adjust a treatment process. In activated sludge systems, common calculations describe the amount of solids in the system, the relationship between food and microorganisms, sludge age, settling characteristics, return sludge flow, and wasting requirements.

The formulas are not useful by themselves. Operators must understand what each number represents, use compatible units, and compare calculated values with plant trends, laboratory results, observations, and established operating targets.

Start with Mass Loading

Many process-control calculations begin by converting a concentration in mg/L into a mass in pounds.

Formula: Mass, lb/day = Flow, MGD × Concentration, mg/L × 8.34

When the calculation uses a tank volume rather than a daily flow:

Formula: Mass in Tank, lb = Volume, MG × Concentration, mg/L × 8.34

For example, an aeration system contains 0.80 MG at an MLSS concentration of 3,000 mg/L.

Solids inventory = 0.80 MG × 3,000 mg/L × 8.34

Solids inventory = 20,016 lb

The aeration system contains approximately 20,000 pounds of suspended solids.

MLSS and MLVSS

MLSS, or mixed liquor suspended solids, represents the suspended solids concentration in the mixed liquor.

MLVSS, or mixed liquor volatile suspended solids, is commonly used as an estimate of the biological fraction of those solids.

Some process calculations require MLSS while others require MLVSS. Do not automatically substitute one for the other.

If an aeration basin contains 0.60 MG and the MLVSS concentration is 2,400 mg/L:

MLVSS inventory = 0.60 × 2,400 × 8.34

MLVSS inventory = 12,009.6 lb

The basin contains approximately 12,010 lb of MLVSS.

Food-to-Microorganism Ratio

The food-to-microorganism ratio, commonly called the F/M ratio, compares the organic food entering the activated sludge process with the mass of microorganisms available to treat it.

A common calculation is:

F/M = Influent BOD Load, lb/day / MLVSS in Aeration, lb

The BOD load is normally calculated from the flow and BOD concentration entering the aeration process.

F/M Ratio Example

An aeration basin receives 1.2 MGD. The BOD concentration entering aeration is 180 mg/L. The basin volume is 0.75 MG and MLVSS is 2,500 mg/L.

Step 1: Calculate the BOD load.

BOD load = 1.2 × 180 × 8.34

BOD load = 1,801.44 lb/day

Step 2: Calculate MLVSS inventory.

MLVSS = 0.75 × 2,500 × 8.34

MLVSS = 15,637.5 lb

Step 3: Calculate F/M.

F/M = 1,801.44 / 15,637.5

F/M = 0.115

The F/M ratio is approximately 0.12 lb BOD/day per lb MLVSS.

Whether that value is appropriate depends on the treatment process and the facility's operating goals. The important exam skill is understanding how the ratio is calculated and how changes in loading or biomass affect it.

How Changes Affect F/M

If the organic load increases while microorganism mass remains constant, F/M increases.

If microorganism mass increases while organic load remains constant, F/M decreases.

For example, if the food load remains 1,800 lb/day but MLVSS inventory increases from 12,000 lb to 18,000 lb:

Initial F/M = 1,800 / 12,000 = 0.15

New F/M = 1,800 / 18,000 = 0.10

The larger microorganism inventory results in a lower F/M ratio.

Mean Cell Residence Time

Mean Cell Residence Time, or MCRT, represents the average time biological solids remain in the activated sludge system. It is also commonly described as solids retention time or sludge age.

The general relationship is:

MCRT, days = Solids in Treatment System, lb / Solids Leaving System, lb/day

For many simplified problems, the numerator is the solids inventory in the aeration system and the denominator includes solids intentionally wasted plus solids lost in the plant effluent.

MCRT = Aeration Solids Inventory / (WAS Solids per Day + Effluent Solids per Day)

MCRT Example

An activated sludge system has the following conditions:

• Aeration volume = 1.0 MG
• MLSS = 3,000 mg/L
• WAS flow = 0.050 MGD
• WAS suspended solids = 8,000 mg/L
• Effluent flow = 1.0 MGD
• Effluent suspended solids = 10 mg/L

Step 1: Calculate aeration solids inventory.

Solids inventory = 1.0 × 3,000 × 8.34

Solids inventory = 25,020 lb

Step 2: Calculate solids wasted each day.

WAS solids = 0.050 × 8,000 × 8.34

WAS solids = 3,336 lb/day

Step 3: Calculate effluent solids loss.

Effluent solids = 1.0 × 10 × 8.34

Effluent solids = 83.4 lb/day

Step 4: Calculate total solids leaving.

Total solids leaving = 3,336 + 83.4

Total solids leaving = 3,419.4 lb/day

Step 5: Calculate MCRT.

MCRT = 25,020 / 3,419.4

MCRT = 7.32 days

The calculated MCRT is approximately 7.3 days.

Why Effluent Solids Matter in MCRT

Solids that leave in the final effluent are no longer part of the biological system. Therefore, a complete MCRT calculation includes both deliberately wasted solids and solids lost with the effluent when those data are provided.

In some simplified operating problems, effluent solids may be small compared with WAS solids and may be omitted by the stated formula. Follow the information and formula required by the problem, but understand the physical meaning: MCRT depends on the total mass of solids leaving the system.

Finding Required Sludge Wasting

If the desired MCRT is known, the MCRT formula can be rearranged to estimate the required daily solids removal.

Total Solids Leaving, lb/day = System Solids, lb / Target MCRT, days

Then:

Required WAS Solids = Total Solids Leaving - Effluent Solids

Suppose the system contains 30,000 lb of solids and the target MCRT is 10 days. Effluent solids loss is 200 lb/day.

Total solids that must leave each day:

30,000 / 10 = 3,000 lb/day

Required WAS solids:

3,000 - 200 = 2,800 lb/day

The plant therefore needs to waste approximately 2,800 lb/day of solids to achieve the target MCRT under the stated conditions.

Finding WAS Flow

If the required WAS solids mass and the WAS concentration are known, calculate the required wasting flow.

WAS Flow, MGD = WAS Solids, lb/day / (WAS Concentration, mg/L × 8.34)

Using the previous required wasting mass of 2,800 lb/day and a WAS concentration of 8,000 mg/L:

WAS flow = 2,800 / (8,000 × 8.34)

WAS flow = 2,800 / 66,720

WAS flow = 0.04197 MGD

Convert to gallons per day:

0.04197 × 1,000,000 = 41,970 gpd

The required WAS flow is approximately 42,000 gpd.

Sludge Volume Index

Sludge Volume Index, or SVI, relates the volume occupied by settled activated sludge after a settling test to the mass concentration of MLSS.

A common formula is:

SVI, mL/g = Settled Sludge Volume, mL/L × 1,000 / MLSS, mg/L

SVI is used as an indicator of sludge settling characteristics. The numerical result should be interpreted together with settling observations, sludge blanket behavior, process conditions, and plant-specific trends.

SVI Example

After a 30-minute settling test, the settled sludge volume is 300 mL/L. MLSS is 3,000 mg/L.

SVI = 300 × 1,000 / 3,000

SVI = 100 mL/g

The calculated SVI is 100 mL/g.

If the settled sludge volume remained 300 mL/L but MLSS increased to 4,000 mg/L:

SVI = 300 × 1,000 / 4,000

SVI = 75 mL/g

This demonstrates why settled volume alone is not the same as SVI. SVI accounts for both settled volume and solids concentration.

Settled Sludge Volume Is Not SVI

A 30-minute settleability test may report settled sludge as mL/L. That number is not automatically the SVI.

For example:

Settled sludge volume = 250 mL/L

MLSS = 2,500 mg/L

SVI = 250 × 1,000 / 2,500 = 100 mL/g

The settleometer reading is 250 mL/L, while the calculated SVI is 100 mL/g. The units help distinguish the two values.

Return Activated Sludge Flow

Return activated sludge, or RAS, is settled activated sludge returned from the secondary clarifier to the biological process.

RAS flow may be expressed as a percentage of influent flow.

RAS Rate, % = RAS Flow / Influent Flow × 100

If influent flow is 2.0 MGD and RAS flow is 0.8 MGD:

RAS rate = 0.8 / 2.0 × 100

RAS rate = 40%

The RAS flow is 40% of influent flow.

Finding RAS Flow from a Percentage

If the desired RAS rate is 60% and influent flow is 1.5 MGD:

RAS flow = 1.5 × 0.60

RAS flow = 0.90 MGD

The required return flow is 0.90 MGD.

Remember that RAS and WAS serve different purposes. RAS returns settled biomass to the process, while WAS removes solids from the system to control biomass inventory and sludge age.

Solids Inventory in Multiple Basins

If several aeration basins are operating, total solids inventory is the sum of the solids mass in the individual basins.

Suppose two basins each contain 0.40 MG.

Basin 1 MLSS = 2,800 mg/L:

Mass = 0.40 × 2,800 × 8.34 = 9,340.8 lb

Basin 2 MLSS = 3,200 mg/L:

Mass = 0.40 × 3,200 × 8.34 = 10,675.2 lb

Total solids inventory:

9,340.8 + 10,675.2 = 20,016 lb

Do not simply average the MLSS concentrations unless basin volumes are equal and that averaging method is appropriate for the calculation.

Process Control Is Based on Trends

A single calculated value should rarely be interpreted in isolation. Process control is stronger when operators compare current values with previous values and evaluate how several parameters move together.

Examples include:

• MLSS increasing while wasting remains low;
• MCRT increasing as solids wasting decreases;
• F/M decreasing as biomass inventory increases;
• SVI increasing while settling becomes visibly poorer;
• effluent solids increasing and affecting calculated MCRT;
• changes in influent BOD loading that alter the F/M ratio.

Calculations help quantify these changes, but the operator must interpret them in the context of the actual treatment process.

Common Process Control Calculation Mistakes

• Using MLSS when a formula specifically requires MLVSS.
• Using gallons instead of MG with the 8.34 mass formula.
• Using flow in MGD where a tank volume in MG is required.
• Forgetting effluent solids when calculating a complete MCRT.
• Using WAS flow without also using the WAS solids concentration.
• Confusing RAS flow with WAS flow.
• Using settled sludge volume as though it were already SVI.
• Forgetting the factor of 1,000 in the standard SVI formula.
• Dividing microorganisms by food instead of food by microorganisms for F/M.
• Combining data from different sampling times without considering whether they represent the same operating conditions.
• Changing process settings based on one calculation without considering trends and plant observations.

A Reliable Process Control Calculation Method

1. Identify the process parameter being calculated.
2. Write down every known value and its unit.
3. Determine whether the formula requires flow in MGD or volume in MG.
4. Convert concentration to mass when the calculation requires pounds.
5. Use MLSS or MLVSS exactly as required by the formula.
6. For MCRT, account for the solids inventory and the relevant solids leaving the system.
7. For F/M, divide food loading by microorganism inventory.
8. For SVI, combine the settled sludge volume with MLSS concentration.
9. Carry units through the calculation.
10. Compare the result with recent plant trends rather than interpreting one number in isolation.

What to Remember for the Exam

• Mass, lb = Volume, MG × Concentration, mg/L × 8.34.
• Mass Loading, lb/day = Flow, MGD × Concentration, mg/L × 8.34.
• MLSS and MLVSS are different measurements and are not automatically interchangeable.
• F/M = influent organic load divided by microorganism mass in aeration.
• A higher food load with unchanged biomass increases F/M.
• More biomass with unchanged food load decreases F/M.
• MCRT = solids in the treatment system divided by solids leaving per day.
• Solids leaving may include both WAS solids and effluent suspended solids.
• Reducing solids wasting generally increases MCRT if other conditions remain similar.
• Increasing solids wasting generally decreases MCRT if other conditions remain similar.
• SVI = settled sludge volume × 1,000 / MLSS.
• Settled sludge volume in mL/L is not the same value as SVI in mL/g.
• RAS returns biomass to the process; WAS removes biomass from the process.
• RAS percentage = RAS flow / influent flow × 100.
• Process-control calculations are most useful when evaluated together with trends, laboratory data, and operating observations.