Chemical Dose & Feed Calculations

Chemical feed calculations connect treatment goals with the amount of chemical that must actually be delivered to a water or wastewater process. Operators use these calculations for disinfection, pH adjustment, corrosion control, coagulation, nutrient addition, dechlorination, and many other treatment applications.

The most important relationship combines plant flow, desired chemical dose, and chemical mass. Once the required chemical mass is known, product strength and feed equipment characteristics can be used to determine how much commercial product must be fed.

Dose, Feed Rate, and Flow

Dose is the amount of chemical applied relative to the volume of water being treated. It is commonly expressed in milligrams per liter, or mg/L.

Feed rate describes how much chemical is delivered during a period of time. Common units include pounds per day, gallons per day, pounds per hour, and gallons per hour.

Flow is the amount of water or wastewater being treated per unit of time. For the standard operator mass formula, flow is commonly expressed in million gallons per day, or MGD.

The 8.34 Formula

A central operator calculation is:

Feed Rate, lb/day = Flow, MGD × Dose, mg/L × 8.34

The factor 8.34 connects million gallons, milligrams per liter, and pounds.

The same relationship can be rearranged:

Dose, mg/L = Feed Rate, lb/day / (Flow, MGD × 8.34)

Flow, MGD = Feed Rate, lb/day / (Dose, mg/L × 8.34)

Before using these formulas, make sure the flow is expressed in MGD when the feed rate is in lb/day.

Example: Finding Required Chemical Feed

A treatment plant processes 2.5 MGD and requires a chemical dose of 4.0 mg/L. Determine the required chemical mass in pounds per day.

Formula:

Feed Rate = Flow × Dose × 8.34

Feed Rate = 2.5 MGD × 4.0 mg/L × 8.34

Feed Rate = 83.4 lb/day

The process requires 83.4 pounds per day of active chemical.

Example: Finding Dose

A plant treats 1.8 MGD and applies 60 lb/day of a chemical on an active-chemical basis. Determine the dose.

Dose = Feed Rate / (Flow × 8.34)

Dose = 60 / (1.8 × 8.34)

Dose = 60 / 15.012

Dose = 4.00 mg/L approximately

The applied dose is approximately 4.0 mg/L.

Example: Finding Flow

A chemical feed system applies 100 lb/day of active chemical at a dose of 6 mg/L. Determine the corresponding plant flow.

Flow = Feed Rate / (Dose × 8.34)

Flow = 100 / (6 × 8.34)

Flow = 100 / 50.04

Flow = 2.00 MGD approximately

The flow is approximately 2.0 MGD.

Active Chemical Versus Commercial Product

The mass calculated from Flow × Dose × 8.34 represents the amount of active chemical required. Commercial chemicals are not always 100% active ingredient.

If a product contains only a fraction of active chemical, more total product must be fed to supply the required active mass.

Formula: Product Required = Active Chemical Required / Decimal Product Strength

Convert percent strength to decimal form before using it.

For example:

12.5% = 0.125

25% = 0.25

50% = 0.50

Example: Correcting for Product Strength

A process requires 50 lb/day of active chemical. The commercial product is 25% active by weight.

Product Required = 50 lb/day / 0.25

Product Required = 200 lb/day

The operator must feed 200 lb/day of the 25% product to provide 50 lb/day of active chemical.

A common mistake is multiplying the required active mass by the product strength. If the product is less than 100% active, the total product mass must be greater than the active chemical mass, not smaller.

Combining Flow, Dose, and Product Strength

The calculations can be completed in two steps.

Suppose a plant treats 3.0 MGD, the target dose is 2.5 mg/L, and the product is 40% active.

Step 1: Calculate active chemical required.

Active chemical = 3.0 × 2.5 × 8.34

Active chemical = 62.55 lb/day

Step 2: Correct for product strength.

Product required = 62.55 / 0.40

Product required = 156.375 lb/day

The required commercial product feed is approximately 156.4 lb/day.

Liquid Chemical Feed

Liquid chemicals are often fed by volume, such as gallons per day or gallons per hour. If the required product mass is known, the product density can be used to convert pounds to gallons.

Formula: Liquid Feed, gal/day = Product Feed, lb/day / Product Density, lb/gal

Use the actual product density provided by the manufacturer or reliable product documentation. Do not automatically use 8.34 lb/gal for a concentrated chemical solution because many chemical products are denser or lighter than water.

Example: Pounds per Day to Gallons per Day

A liquid chemical feed calculation requires 120 lb/day of commercial product. The product density is 10.0 lb/gal.

Liquid Feed = 120 lb/day / 10.0 lb/gal

Liquid Feed = 12 gal/day

The feed system must deliver approximately 12 gallons per day.

Converting Gallons per Day to Gallons per Hour

Feed pumps are often calibrated in units smaller than gallons per day.

If the required feed is 12 gal/day:

12 gal/day / 24 hr/day = 0.50 gal/hr

If needed, gallons per hour can then be converted to smaller units appropriate for the pump or calibration device.

Always make sure the final feed-rate unit matches the unit used by the equipment calibration.

Solution Strength and Pounds of Chemical in a Tank

Operators may also need to determine how many pounds of chemical are contained in a prepared solution.

For a water-based solution where the simplified operator calculation uses 8.34 lb/gal:

Chemical, lb = Volume, gal × 8.34 lb/gal × Decimal Strength

Suppose a 200-gallon solution is prepared at 5% strength.

Chemical = 200 × 8.34 × 0.05

Chemical = 83.4 lb

The solution contains approximately 83.4 pounds of chemical under the assumptions of this simplified calculation.

When an actual commercial solution has a specified density or specific gravity, use the appropriate product information rather than assuming the solution weighs exactly the same as water.

Specific Gravity and Product Density

Specific gravity compares the density of a substance with the density of water. A liquid with a specific gravity greater than 1 is denser than water.

For approximate operator calculations:

Product Density, lb/gal ≈ Specific Gravity × 8.34 lb/gal

If a liquid chemical has a specific gravity of 1.20:

Density ≈ 1.20 × 8.34

Density ≈ 10.01 lb/gal

This density can then be used to convert between product weight and liquid volume.

Example Using Product Strength and Density

A plant treats 1.5 MGD and needs an active dose of 3.0 mg/L. The liquid product is 30% active and has a density of 10.5 lb/gal. Determine the approximate liquid feed rate in gallons per day.

Step 1: Calculate active chemical required.

Active chemical = 1.5 × 3.0 × 8.34

Active chemical = 37.53 lb/day

Step 2: Correct for 30% product strength.

Product mass = 37.53 / 0.30

Product mass = 125.1 lb/day

Step 3: Convert product mass to gallons.

Liquid feed = 125.1 / 10.5

Liquid feed = 11.91 gal/day

The required liquid product feed is approximately 11.9 gal/day.

Feed Pump Calibration

A chemical feed pump setting does not by itself guarantee the actual feed rate. Pumps should be calibrated so the operator knows how much chemical is actually being delivered at a particular setting.

A common liquid-feed calibration method measures the change in volume in a calibration cylinder over a known period of time.

The general relationship is:

Feed Rate = Volume Delivered / Time

If a pump delivers 250 mL in 5 minutes:

Feed rate = 250 mL / 5 min

Feed rate = 50 mL/min

This measured output can then be converted to the units used for plant operation and compared with the required chemical feed rate.

Calibration Example in Gallons per Day

A pump delivers 600 mL during a 10-minute calibration test.

Feed rate = 600 / 10 = 60 mL/min

There are 1,440 minutes in a day:

60 mL/min × 1,440 min/day = 86,400 mL/day

Using approximately 3,785 mL per gallon:

86,400 / 3,785 = 22.83 gal/day

The calibrated pump output is approximately 22.8 gal/day.

If the process calculation requires only 15 gal/day, the pump setting or control signal must be adjusted and the actual output verified again.

Flow-Paced Chemical Feed

When plant flow changes significantly, maintaining the same chemical pump output may change the applied dose.

For example, suppose a pump feeds 50 lb/day of active chemical.

At 1.0 MGD:

Dose = 50 / (1.0 × 8.34)

Dose = 6.0 mg/L approximately

At 2.0 MGD with the same chemical feed:

Dose = 50 / (2.0 × 8.34)

Dose = 3.0 mg/L approximately

When flow doubles and feed rate remains unchanged, the dose is cut approximately in half.

This relationship explains why chemical systems may use flow pacing or another control strategy when the treatment objective requires the dose to remain relatively constant as plant flow changes.

Changing Dose While Flow Remains Constant

At a constant plant flow, chemical feed rate changes directly with dose.

If a plant operating at 2 MGD changes its target dose from 2 mg/L to 3 mg/L:

Feed at 2 mg/L = 2 × 2 × 8.34 = 33.36 lb/day

Feed at 3 mg/L = 2 × 3 × 8.34 = 50.04 lb/day

A 50% increase in dose requires a 50% increase in active chemical feed when flow remains unchanged.

Do Not Confuse Dose with Residual

The chemical dose applied to a process is not necessarily equal to the concentration remaining after treatment.

Some of the applied chemical may react with substances in the water, be consumed by treatment reactions, or otherwise become unavailable.

For example, in disinfection calculations, applied chlorine dose, chlorine demand, and measured residual are related but are not interchangeable terms. The specific relationships are covered in the disinfection section of the Study Guide.

Common Chemical Feed Mistakes

• Using plant flow in gallons per day instead of MGD in the standard 8.34 formula.
• Entering a product strength of 25% as 25 instead of 0.25.
• Treating commercial product mass as though the product were 100% active.
• Multiplying by product strength when calculating how much diluted product is required instead of dividing.
• Using 8.34 lb/gal as the density of every liquid chemical.
• Confusing pounds of active chemical with pounds of commercial product.
• Confusing chemical dose in mg/L with chemical feed in lb/day.
• Using a pump setting as the actual feed rate without calibration.
• Failing to adjust chemical feed when plant flow changes.
• Mixing daily, hourly, and minute-based feed units in the same calculation.

A Reliable Chemical Feed Calculation Method

1. Identify the desired dose and plant flow.
2. Convert plant flow to MGD when using the 8.34 formula.
3. Calculate the required active chemical mass in lb/day.
4. Determine whether the product is 100% active or diluted.
5. Correct for product strength when necessary.
6. For liquid products, use the appropriate product density to convert pounds to gallons.
7. Convert the result to the time unit used by the feed equipment.
8. Compare the required rate with the calibrated pump output.
9. Check whether the final feed rate and dose are operationally reasonable.

What to Remember for the Exam

• Feed Rate, lb/day = Flow, MGD × Dose, mg/L × 8.34.
• Dose, mg/L = Feed Rate / (Flow × 8.34).
• Flow, MGD = Feed Rate / (Dose × 8.34).
• The 8.34 formula gives active chemical mass when dose represents active chemical concentration.
• Convert percent strength to decimal form before using it in calculations.
• Product Required = Active Chemical Required / Decimal Product Strength.
• A weaker product requires more total product to provide the same active chemical mass.
• For liquid products, convert pounds to gallons using the appropriate product density.
• Specific gravity can be used to estimate product density when appropriate product information is available.
• Chemical pump output should be calibrated rather than assumed from the pump setting.
• If chemical feed stays constant while plant flow increases, the applied dose decreases.
• Dose and measured residual are not necessarily the same value.
• Always keep active chemical, commercial product, concentration, mass, volume, and time units clearly separated.