1.1 Chemical Use and Dose Calculations

Why chemical math matters

The WPI Water Treatment Operator Class I outline places seven calculation items in Treatment Process, so chemical-use and dose problems deserve more than memorized constants. The operator must turn a process target into a feed rate, recognize whether a product is diluted, and then decide whether the calculated result agrees with what the plant is actually feeding. The current WPI Formula/Conversion Table supplies both U.S. and metric forms. On an exam problem, use the form that matches the given units instead of converting needlessly.

Keep three quantities separate

• Dose is the concentration applied to the water, usually expressed in milligrams per liter (mg/L).
• Demand is the amount consumed by reactions with water constituents and process surfaces during the stated conditions.
• Residual is the concentration remaining at the stated sampling point and time.

For a simple disinfectant balance, dose = demand + residual. That relationship does not mean every chemical has a useful residual, and it does not replace a plant's approved procedure for selecting a dose. It helps diagnose a calculation: if a 2.5 mg/L dose produces a 0.7 mg/L residual under the stated conditions, the observed demand is 1.8 mg/L.

The mass-loading framework

The WPI table expresses 100%-pure chemical feed as:

Write percent strength as a decimal: 65% becomes 0.65 and 12.5% becomes 0.125. Dividing by a fraction less than one correctly makes the required commercial-product mass larger than the active-chemical mass. A frequent trap is multiplying by purity, which would claim that a weaker product requires less product.

Worked U.S. example

A plant treats 2.40 million gallons per day (MGD) and needs a 3.50 mg/L active dose. The delivered dry product is 65% active.

1. Pure chemical: 3.50 × 2.40 × 8.34 = 70.06 lb/day.
2. Commercial product: 70.06 ÷ 0.65 = 107.78 lb/day.
3. Reasonableness check: 107.78 lb of a 65% product contains about 70.06 lb of active ingredient.

If the question asks for the pure feed, stop after step 1. If it asks how much product to order or feed, account for purity. Do not divide twice when the stated dose already refers to commercial product rather than active ingredient.

Worked metric example

A plant treats 8,500 m³/day and applies 2.20 mg/L active chemical from a 12.5% solution.

1. Pure chemical: 2.20 × 8,500 ÷ 1,000 = 18.70 kg/day.
2. Solution mass: 18.70 ÷ 0.125 = 149.6 kg/day.

Converting that solution mass to liters requires its actual density; do not assume every solution weighs 1 kg/L. WPI's pump-feed equations explicitly use feed-chemical density and active fraction when converting a required mass to milliliters per minute. Use the density stated in the problem, safety data sheet, certificate of analysis, or verified plant record.

From calculated feed to equipment setting

For a linear, calibrated pump, WPI gives percent stroke = desired flow ÷ maximum flow × 100. A desired 1.8 L/h from a calibrated maximum of 6.0 L/h gives 30% stroke. This is a mathematical setting, not proof of delivery. Suction conditions, air binding, worn check valves, solution viscosity, and discharge pressure can change actual output.

A disciplined operator follows this sequence:

1. Confirm plant flow and the dose basis.
2. Identify product strength and density, if relevant.
3. Calculate active mass, then commercial-product mass or volume.
4. Confirm that the result is within feeder capacity.
5. Set the feeder and perform the authorized calibration check.
6. Compare scale loss or tank inventory, measured residual, and process response with the expected result.
7. Record the calculation, assumptions, setting, calibration result, and observations.

Daily-use and inventory checks

Chemical use over a shift is normally derived from a reliable mass scale, calibrated tank level, or delivery-and-inventory record. For a tank, a level change becomes volume only through the tank's verified geometry or calibration chart; volume becomes mass through density; and mass becomes active chemical through product strength. Account for deliveries and transfers between the beginning and ending readings. A result that disagrees sharply with the feeder totalizer is a reason to inspect data and equipment, not a reason to force the numbers to match.

Exam decision pattern

Before touching the calculator, label the unknown: dose, pure mass, commercial mass, solution volume, or pump setting. Carry units on every line. Estimate direction—higher flow, higher dose, or lower purity should require more product. Finally, ask whether the number is operationally credible. WPI calculation questions test setup as much as arithmetic, and an otherwise correct number with the wrong purity basis represents the wrong operating decision.

Reverse-checking an observed feed

The same formula can test an inventory observation. Suppose net use is 96 lb/day of an 80% product while flow averages 2.00 MGD. Active mass is 96 × 0.80 = 76.8 lb/day, so the indicated dose is 76.8 ÷ (2.00 × 8.34) = 4.60 mg/L. Compare that result with the intended set point and a valid process sample. Net inventory use may also include priming, spills, transfers, or solution sent to waste, so a discrepancy is evidence to investigate rather than permission to change feed immediately. Confirm the time window, product lot strength, scale or tank calibration, actual flow, and feeder calibration before concluding that the process dose is wrong.