Loading, Mass & Removal Efficiency

Water and wastewater operators often need to know more than concentration alone. A laboratory result in mg/L tells how much material is present in a given volume of water, but it does not tell how many pounds of that material pass through a facility each day. Mass loading combines concentration with flow so operators can evaluate the actual quantity of material entering, leaving, or being applied to a process.

Loading calculations are especially important for wastewater treatment, solids handling, chemical treatment, nutrient control, regulatory reporting, and process-performance evaluation. The same basic relationships also appear in drinking water operations.

Concentration Versus Mass Loading

Concentration describes how much of a substance is present in a given volume of water. It is commonly expressed in milligrams per liter, or mg/L.

Mass loading describes the total mass of that substance moving through a process during a period of time. A common operator unit is pounds per day, or lb/day.

Two facilities can have the same concentration but very different mass loadings if their flows are different.

For example, a concentration of 200 mg/L at 0.5 MGD represents only half the daily mass load of the same 200 mg/L concentration at 1.0 MGD.

The Basic Mass Loading Formula

The standard operator formula is:

Loading, lb/day = Flow, MGD × Concentration, mg/L × 8.34

The factor 8.34 converts the combination of million gallons per day and milligrams per liter into pounds per day.

This relationship can be rearranged to solve for concentration or flow:

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

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

Example: Calculating Influent Loading

A wastewater treatment plant receives 2.0 MGD with an influent BOD concentration of 220 mg/L. Determine the BOD loading in pounds per day.

Loading = 2.0 × 220 × 8.34

Loading = 3,669.6 lb/day

The influent BOD loading is approximately 3,670 lb/day.

This value represents the mass of BOD entering the treatment plant each day at the stated flow and concentration.

Example: Calculating Effluent Loading

The same plant discharges 2.0 MGD with an effluent BOD concentration of 18 mg/L.

Effluent loading = 2.0 × 18 × 8.34

Effluent loading = 300.24 lb/day

The effluent BOD loading is approximately 300 lb/day.

Comparing influent and effluent mass allows the operator to evaluate how much material the process actually removed.

Mass Removed

Mass removed is the difference between influent mass loading and effluent mass loading.

Formula: Mass Removed = Influent Loading - Effluent Loading

Using the previous values:

Mass removed = 3,669.6 - 300.24

Mass removed = 3,369.36 lb/day

The treatment process removes approximately 3,369 lb/day of BOD.

Percent Removal Efficiency

Removal efficiency expresses how much of the incoming material was removed as a percentage of the influent amount.

Formula: Percent Removal = [(Influent - Effluent) / Influent] × 100

If the calculation is based on mass loading:

Percent removal = [(3,669.6 - 300.24) / 3,669.6] × 100

Percent removal = 91.8%

The process removes approximately 91.8% of the influent BOD mass.

Removal Efficiency Using Concentration

If influent and effluent flow are essentially the same for the period being evaluated, removal efficiency can often be calculated directly from concentration values because the common flow factor cancels.

Using an influent concentration of 220 mg/L and an effluent concentration of 18 mg/L:

Percent removal = [(220 - 18) / 220] × 100

Percent removal = 91.8%

This produces the same result because the flow was the same for both values.

However, if influent and effluent flows differ significantly or the data represent different time periods, a mass-based comparison may be more appropriate. Do not assume concentration alone always represents total mass removal.

Why Flow Matters

Concentration and mass loading do not always move in the same direction.

Suppose influent BOD concentration decreases from 250 mg/L to 200 mg/L, but plant flow doubles from 1.0 MGD to 2.0 MGD.

At 1.0 MGD and 250 mg/L:

Loading = 1.0 × 250 × 8.34

Loading = 2,085 lb/day

At 2.0 MGD and 200 mg/L:

Loading = 2.0 × 200 × 8.34

Loading = 3,336 lb/day

Even though concentration decreased, total mass loading increased substantially because flow increased.

This is why operators should examine both concentration and flow when evaluating process loading.

Finding Concentration from Loading

If mass loading and flow are known, concentration can be calculated.

Suppose a facility receives 1,500 lb/day of a substance at a flow of 1.2 MGD.

Concentration = Loading / (Flow × 8.34)

Concentration = 1,500 / (1.2 × 8.34)

Concentration = 1,500 / 10.008

Concentration = 149.9 mg/L

The concentration is approximately 150 mg/L.

Finding Flow from Loading

If loading and concentration are known:

Flow = Loading / (Concentration × 8.34)

Suppose a process receives 2,500 lb/day at a concentration of 300 mg/L.

Flow = 2,500 / (300 × 8.34)

Flow = 2,500 / 2,502

Flow ≈ 1.00 MGD

The flow is approximately 1.0 MGD.

Pounds Applied to a Fixed Volume

The same 8.34 relationship can be used when a fixed volume in million gallons is treated rather than a continuous daily flow.

Mass, lb = Volume, MG × Concentration or Dose, mg/L × 8.34

Suppose a 0.50 MG storage tank must receive a chemical dose of 4 mg/L.

Mass = 0.50 × 4 × 8.34

Mass = 16.68 lb

Approximately 16.7 pounds of active chemical are required.

Notice that the formula uses MG rather than MGD because this calculation describes a fixed volume rather than a continuous daily flow.

Loading per Unit of Area

Some treatment processes express loading relative to surface area.

The general relationship is:

Loading per Area = Total Loading / Area

For example, if a treatment unit receives 1,800 lb/day across an effective area of 6,000 ft²:

Loading per area = 1,800 lb/day / 6,000 ft²

Loading per area = 0.30 lb/day/ft²

The exact units and interpretation depend on the treatment process. Always use the loading definition required for that specific process.

Loading per Unit of Volume

Biological treatment calculations may also express loading relative to tank or reactor volume.

The general form is:

Volumetric Loading = Mass Loading / Process Volume

If a process receives 2,000 lb/day and has an operating volume of 0.5 MG:

Volumetric loading = 2,000 / 0.5

Volumetric loading = 4,000 lb/day/MG

Other process-control formulas may use different volume units, so unit consistency is essential.

Average Loading Over Several Days

When daily loading varies, an average can be calculated by adding the daily mass loads and dividing by the number of days.

Suppose daily loadings are:

• Monday: 2,200 lb/day
• Tuesday: 2,500 lb/day
• Wednesday: 2,300 lb/day

Average loading = (2,200 + 2,500 + 2,300) / 3

Average loading = 7,000 / 3

Average loading = 2,333 lb/day approximately

When regulatory reporting is involved, always follow the specific averaging method and reporting requirements that apply to the facility rather than assuming a simple arithmetic average is appropriate in every case.

Comparing Two Treatment Stages

Removal calculations can also be applied to individual treatment stages.

Suppose primary treatment receives 4,000 lb/day of suspended solids and sends 2,600 lb/day to the next process.

Mass removed = 4,000 - 2,600

Mass removed = 1,400 lb/day

Percent removal = (1,400 / 4,000) × 100

Percent removal = 35%

Primary treatment therefore removes 35% of the incoming suspended solids mass in this example.

Percent Increase and Percent Decrease

Operators may also need to describe how loading changes over time.

Percent Change = [(New Value - Old Value) / Old Value] × 100

If loading increases from 2,000 lb/day to 2,600 lb/day:

Percent change = [(2,600 - 2,000) / 2,000] × 100

Percent change = 30%

The loading increased by 30%.

If the result is negative, the value decreased.

Do Not Confuse Percent Removal with Percent Remaining

If a process removes 80% of an incoming pollutant, 20% remains.

These are complementary values:

Percent Remaining = 100% - Percent Removal

If influent concentration is 100 mg/L and removal is exactly 80% under conditions where this direct comparison is appropriate:

Remaining fraction = 20% = 0.20

Effluent concentration = 100 × 0.20 = 20 mg/L

A common error is multiplying the influent value by the removal percentage and calling the result the effluent concentration. That calculation gives the amount removed, not the amount remaining.

Example: Finding Effluent Concentration from Removal Efficiency

An influent contains 180 mg/L of a constituent and treatment achieves 75% removal. Determine the resulting concentration, assuming the calculation is based on comparable flow conditions.

Percent remaining = 100% - 75% = 25%

Decimal remaining = 0.25

Effluent concentration = 180 × 0.25

Effluent concentration = 45 mg/L

The resulting concentration is 45 mg/L.

Example: Finding Influent Loading from Effluent and Removal

A process discharges 400 lb/day after achieving 80% mass removal. What was the influent mass loading?

If 80% was removed, 20% remains.

0.20 × Influent Loading = 400 lb/day

Influent Loading = 400 / 0.20

Influent Loading = 2,000 lb/day

The original influent loading was 2,000 lb/day.

Loading and Process Capacity

Plant flow alone does not completely describe treatment demand. A biological treatment process receiving 1 MGD of strong wastewater may receive a greater organic mass load than a process receiving 2 MGD of much weaker wastewater.

For example:

1.0 MGD at 400 mg/L:

Loading = 1 × 400 × 8.34 = 3,336 lb/day

2.0 MGD at 150 mg/L:

Loading = 2 × 150 × 8.34 = 2,502 lb/day

The lower-flow facility receives the greater mass load.

This illustrates why operators should evaluate hydraulic loading and mass loading separately.

Common Loading and Removal Mistakes

• Using flow in gallons per day instead of MGD with the 8.34 formula.
• Forgetting the 8.34 conversion factor.
• Confusing concentration in mg/L with mass loading in lb/day.
• Comparing concentrations without considering major differences in flow.
• Dividing by the effluent value instead of the influent value when calculating percent removal.
• Subtracting percentages instead of calculating actual incoming and outgoing mass when flows differ significantly.
• Confusing percent removed with percent remaining.
• Using MG and MGD as though they were interchangeable.
• Mixing data from different time periods without recognizing the mismatch.
• Rounding intermediate values too early.

A Reliable Loading Calculation Method

1. Identify whether the problem asks for concentration, flow, mass loading, mass removed, or percent removal.
2. Write down all known values with their units.
3. Convert flow to MGD when using the standard lb/day formula.
4. Calculate influent and effluent loads separately when necessary.
5. Subtract effluent loading from influent loading to find mass removed.
6. Divide the amount removed by the influent amount to calculate removal efficiency.
7. Keep concentration and mass units clearly separated.
8. Confirm that values being compared represent compatible time periods and operating conditions.
9. Check whether the final result is reasonable.

What to Remember for the Exam

• Loading, lb/day = Flow, MGD × Concentration, mg/L × 8.34.
• Mass, lb = Volume, MG × Concentration or Dose, mg/L × 8.34.
• Concentration, mg/L = Loading / (Flow × 8.34).
• Flow, MGD = Loading / (Concentration × 8.34).
• Concentration and mass loading are not the same thing.
• A change in flow can change mass loading even when concentration stays constant.
• Mass Removed = Influent Loading - Effluent Loading.
• Percent Removal = [(Influent - Effluent) / Influent] × 100.
• Percent remaining equals 100% minus percent removed.
• If influent and effluent flows differ significantly, mass loading can provide a more meaningful comparison than concentration alone.
• MG represents volume, while MGD represents flow.
• Hydraulic loading and mass loading describe different process demands.
• Always carry units through the calculation and verify that the final units match the quantity requested.