11.4 Operator Math: Chemical Feed & Chlorine Dose

11.4 Operator Math: Chemical Feed & Chlorine Dose

Quick Answer: The one formula that drives most chemical-feed math is lb/day = dose (mg/L) × flow (MGD) × 8.34. Chlorine dose = demand + residual. Detention time = Volume ÷ Flow, and disinfection effectiveness is checked with CT = Concentration × Time.

The Pounds Formula

For any chemical dosed into water (chlorine gas, sodium hypochlorite, fluoride, alum, polymer), the feed rate in pounds per day is:

lb/day = Dose (mg/L) × Flow (MGD) × 8.34 lb/gal

The 8.34 factor is the weight of one gallon of water. One mg/L is one part per million, so multiplying mg/L by million-gallons and by 8.34 lb/gal gives pounds of chemical per day.

Worked Example — Chlorine Gas Feed

A system feeds chlorine to a dose of 3 mg/L at a flow of 2 MGD. How many lb/day of chlorine are required?

3 mg/L × 2 MGD × 8.34 = 50.04 lb/day (≈ 50 lb/day).

This single formula answers most of the chemical-feed items on the Class I exam. Variations ask for dose (given lb/day and flow) or flow (given lb/day and dose); rearrange the same equation.

Chlorine Dose, Demand, and Residual

These three quantities are linked by:

Dose = Demand + Residual

• Dose — what you apply at the plant (mg/L).
• Demand — what is consumed by organics, iron, manganese, ammonia, and biofilm (mg/L).
• Residual — what remains at the entry point or in the distribution system (mg/L), measured as free or total chlorine.

Worked Example — Solving for Dose

A system has a measured chlorine demand of 2.2 mg/L and is required to maintain a free residual of 0.8 mg/L at the entry point. What is the required dose?

Dose = 2.2 + 0.8 = 3.0 mg/L.

To find the feed rate, plug this dose into the pounds formula with the system flow.

Worked continuation — at 2 MGD: 3.0 × 2 × 8.34 = 50 lb/day.

Free vs Total Chlorine

Free chlorine is HOCl/OCl⁻ available to disinfect; total chlorine is free chlorine plus combined chlorine (chloramines formed from ammonia/nitrogen). For free residual maintenance, measure free chlorine at the entry point. Do not confuse the two on the exam — a total reading that meets the residual target while the free portion is zero means you have chloramines, not free residual, and CT credit depends on which you have.

Hypochlorite (Bleach) Feed

Liquid sodium hypochlorite (NaOCl) is dosed by volume, not weight. To convert a required lb/day into a bleach feed volume:

1. Compute the lb/day of available chlorine needed (pounds formula).
2. Divide by the available-chlorine strength (as a decimal) to get lb/day of solution.
3. Divide by the solution density (lb/gal, ≈8.34 for dilute hypochlorite, ~10 for 12.5% trade) to get gal/day.
4. Convert to the feed unit (gal/day → mL/min by ×2.629; or gpd feed by metering pump).

A simple compact form when the solution is dilute and its density is close to water:

Feed (gal/day) = (Dose × Flow × 8.34) / (Strength as decimal × 8.34) = (Dose × Flow) / (Strength as decimal), with Flow in MGD and the result in MGD; multiply by 1,000,000 for gal/day.

Worked Example — 5.25% Bleach

Need 50 lb/day of available chlorine; bleach strength 5.25% available chlorine.

Bleach (lb/day) = 50 ÷ 0.0525 = 952 lb/day of solution.

Volume (gal/day) = 952 ÷ 8.34 = 114 gal/day (≈ 0.079 gpm or 299 mL/min).

For 12.5% bleach, use 0.125 in place of 0.0525 — the required volume drops by more than half.

Detention Time and CT

Detention time (DT) is how long a volume of water stays in a basin or pipe:

DT = Volume ÷ Flow

Use consistent time units: tank in gallons ÷ flow in gpm = minutes.

Worked Example — Clearwell Detention

A clearwell holds 50,000 gal and the plant flow is 2,500 gpm. What is the detention time?

50,000 ÷ 2,500 = 20 minutes.

CT = Concentration × Time. With a free chlorine residual of 1.0 mg/L and 20 minutes of contact, CT = 1.0 × 20 = 20 mg·min. Surface Water Treatment Rules specify CT requirements by log removal, temperature, and pH; the Class I exam typically asks you to compute CT, not to look up tables.

Math Discipline

• State the formula before plugging numbers in.
• Match the flow unit to the formula: MGD goes with 8.34 for lb/day; gpm goes with detention-time minutes.
• Distinguish free vs total chlorine in any residual question.
• Estimate first: 3 mg/L × 2 MGD × 8.34 ≈ 6 × 8.34 ≈ 50 — so any answer near 5 or 500 should trigger a re-check.

Worked Example — Changing Bleach Strength

A system feeds 12.5% hypochlorite instead of 5.25%. Required available chlorine is still 50 lb/day.

For 12.5% bleach: bleach (lb/day) = 50 ÷ 0.125 = 400 lb/day of solution; volume = 400 ÷ 8.34 = 48 gal/day.

Compared to the 114 gal/day needed with 5.25% bleach, switching to 12.5% cuts feed volume by more than half — but the operator must adjust the pump stroke and verify the residual at the entry point. A common exam wrinkle asks you to compare feed volumes or recompute for a different strength; the method is unchanged — only the decimal strength changes.

Worked Example — Solving for Flow

Given a chlorine feed of 75 lb/day at a dose of 3 mg/L, what is the flow in MGD?

Rearrange: Flow (MGD) = lb/day ÷ (dose × 8.34) = 75 ÷ (3 × 8.34) = 75 ÷ 25.02 = 3.0 MGD.

The same rearrangement lets you back-calculate flow from a feeder setting when a flow meter is in question — useful in operations and on the exam.