Coagulant Dosage Scale‑Up Calculator
Turn a jar-test optimum dose into a full-scale coagulant feed rate — or work backwards from a feed rate to the dose or the flow it implies. Includes a live scale-up diagram, a dose/flow response chart, and solution & pump sizing.
Dose ↑ — feed rate rises linearly
M is directly proportional to D. Doubling the jar-test dose doubles the daily coagulant demand, with no change in flow.
Flow ↑ — feed rate rises linearly
M is also directly proportional to Q. A plant running at half flow needs half the chemical, so the dosing pump must turn down or the solution strength must change.
Why the ÷1000 exists
mg/L × m³/day gives grams per day (because 1 m³ = 1,000 L), so dividing by 1,000 converts grams into kilograms — the unit a day-tank and a belt feeder actually work in.
Jar test ≠ perfect prediction
Rapid-mix energy, flocculation time, raw-water pH, alkalinity, temperature and turbidity all shift the optimum. Treat M as a starting set point, then confirm with a full-scale trial.
How to Use This Calculator
The scale-up relation links three quantities: the jar-test dose D, the plant flow Q, and the full-scale coagulant feed rate M. Choose which one the tool should solve, then enter the other two.
1. Choose what to solve for
Pick M (feed rate from dose & flow), D (dose from feed rate & flow), or Q (flow from feed rate & dose). The formula is rearranged automatically.
2. Enter the jar-test dose
Use a preset (5 / 10 / 20 / 30 / 50 mg/L) or type the optimum dose your jar test produced. The stock-solution converter below helps if you dosed from a diluted stock.
3. Enter the plant flow
Use a preset (1,000 → 100,000 m³/day, i.e. 1 → 100 MLD) or type your own. The flow-unit converter below handles MLD, MGD and L/s.
4. Read the result, steps and diagram
The result card shows the solved value in engineering notation. The step panel shows the arithmetic, and the live diagram below updates the D × Q ÷ 1000 = M chain plus the treatment-train layout.
5. Check the response chart
The chart plots feed rate against dose at 0.5×, 1× and 2× your plant flow, so you can see how the set point moves with production.
6. Switch to Advanced for pump sizing
Advanced mode adds sensitivity, companion dosing metrics, and a solution-strength / pump-sizing panel that converts kg/day into litres per hour.
What This Tool Offers
Built around the standard water-treatment scale-up relation M = D × Q / 1000 — the bridge between a bench jar test and a full-scale chemical feed system.
Solve in any direction
Go from dose and flow to feed rate, or work backwards from a feed rate to the dose or the flow that produced it.
Jar-test dose presets
One-click doses at 5, 10, 20, 30 and 50 mg/L — the range that covers most alum, PACl and iron-salt coagulation trials.
Live scale-up diagram
An always-visible node chain (D × Q ÷ 1000 = M) with live numbers, plus a treatment-train diagram showing where coagulant is injected.
Dose / flow response chart
Feed rate plotted against dose at half, full and double your plant flow, so you can see how the set point moves with production.
Solution & pump sizing
Convert kg/day into a diluted solution feed rate in L/h and L/day, and work out neat product draw-off from the tank farm.
Built-in sensitivity check
See what a 1% error in dose or flow does to the feed rate — a quick feel for how tight your dosing control needs to be.
Reference Tables & Conversions
Flow-unit and jar-test-stock converters, plus lookup tables for typical coagulant doses and full-scale feed rates.
Flow unit converter
Jar-test stock solution → dose
Typical Coagulant Jar-Test Dose Ranges
Indicative optimum doses for conventional surface-water coagulation. Actual values depend heavily on raw-water turbidity, colour, pH and alkalinity.
| Coagulant | Typical jar dose | Notes |
|---|---|---|
| Alum (liquid, as product) | 10 – 60 mg/L | Widest working range; consumes alkalinity |
| PACl (polyaluminium chloride) | 5 – 40 mg/L | Lower alkalinity demand, works over a wider pH band |
| Ferric chloride | 10 – 50 mg/L | Effective over a broad pH; corrosive to handle |
| Ferric sulfate | 10 – 50 mg/L | Common where sulphate is preferred over chloride |
| Ferrous sulfate + chlorine | 15 – 60 mg/L | Requires oxidation step |
| Cationic polymer (coagulant aid) | 0.5 – 5 mg/L | Usually paired with a metal salt, not used alone |
Full-Scale Feed Rate Lookup (kg/day)
Feed rate M = D × Q / 1000 at common doses and plant flows. Multiply by 1,000 for g/day, or divide by 24 for kg/h.
| Plant flow (m³/day) | D = 10 mg/L | D = 20 mg/L | D = 30 mg/L | D = 50 mg/L |
|---|---|---|---|---|
| 1,000 | 10 | 20 | 30 | 50 |
| 5,000 | 50 | 100 | 150 | 250 |
| 10,000 | 100 | 200 | 300 | 500 |
| 50,000 | 500 | 1,000 | 1,500 | 2,500 |
| 100,000 | 1,000 | 2,000 | 3,000 | 5,000 |
Dose Unit Equivalents
| Value | Equivalent | Where it's used |
|---|---|---|
| 1 mg/L | 1 ppm ≈ 8.34 lb per MG | US customary dosing calculations |
| 1 mg/L at 1,000 m³/day | 1 kg/day of product | Metric feed-rate sizing |
| 1 MLD | 1,000 m³/day ≈ 0.264 MGD | Plant capacity shorthand |
| 1 MGD | 3,785.4 m³/day ≈ 3.785 MLD | US plant capacity shorthand |
What Does M = D × Q / 1000 Measure?
A jar test tells you the concentration of coagulant that best destabilises your raw water — for example, 20 mg of product per litre of water. A full-scale plant does not buy chemical by concentration, though; it buys it by mass per day. The scale-up formula converts one into the other: it multiplies the bench dose by the volume of water the plant actually treats, then converts grams into kilograms.
The Coagulant Scale-Up Formula
The defining relationship is:
The divisor of 1,000 is purely a unit conversion. Dosing at D mg/L across Q m³/day means D × Q × 1,000 milligrams per day, because one cubic metre holds 1,000 litres. Dividing by 1,000 turns milligrams into grams, and dividing again by 1,000 turns grams into kilograms — so the single ÷1000 in the formula already accounts for the litre-to-cubic-metre step, leaving the answer in kg/day. Rearranged for the other two unknowns:
Scale-Up Variables
| Symbol | Meaning | Notes |
|---|---|---|
| D | Jar-test optimum dose | mg/L of coagulant product, from the bench trial |
| Q | Plant flow | m³/day; 1 MLD = 1,000 m³/day |
| M | Full-scale coagulant feed rate | kg/day of product, equal to the mass the dosing system must deliver |
| 1000 | Unit conversion factor | Bridges mg/L × m³/day to kg/day |
From kg/day to a Pump Setting
Feed rate is only the first step. A dosing system delivers a liquid, not a mass, so the next question is how strong the feed solution is. If the product is diluted to a solution of S% w/w with a specific gravity of SG, its concentration in grams per litre is S × 10 × SG. Dividing the daily mass by that concentration gives the volume the pump must move:
A 10% w/w solution of a product with SG 1.10 holds 110 g/L. Delivering 100 kg/day therefore needs about 909 L/day, or roughly 38 L/h — a very ordinary metering-pump duty. Switch to a 1% solution and the same mass needs ten times the volume, which is often the real constraint on day-tank size.
Why the Jar-Test Dose Doesn't Transfer Perfectly
The scale-up formula is exact arithmetic, but it assumes the bench and the plant behave identically — and they rarely do. Rapid-mix velocity gradient, flocculation detention time, clarifier loading rate, raw-water pH and alkalinity, temperature and seasonal turbidity all shift the true optimum. A jar test stirs a one-litre beaker for a few minutes; a plant mixes thousands of cubic metres over an hour. In practice, M from this formula is the correct starting set point, which is then trimmed by a full-scale trial and by streaming-current or turbidity feedback. Many plants also carry a small safety margin of 5–15% to absorb day-to-day raw-water variation.
Worked Examples
M = 20 × 5,000 / 1000 = 100,000 / 1000
M = 100 kg/day
D = 250 × 1000 / 10,000 = 250,000 / 10,000
D = 25 mg/L
Q = 45 × 1000 / 15 = 45,000 / 15
Q = 3,000 m³/day (3 MLD)
Frequently Asked Questions
It is a unit conversion, not a process factor. One cubic metre contains 1,000 litres, so dosing D mg/L across Q m³/day delivers D × Q × 1,000 mg/day. Dividing by 1,000 gives grams per day and the remaining conversion to kilograms is folded into the same factor, leaving M in kg/day.
It should be, and that is the safest convention. If your jar test used a diluted stock solution, convert it first with the stock-solution converter on this page: dose (mg/L) = (mL of stock × stock concentration in g/L) ÷ sample volume in litres. Mixing "mg/L as product" with "mg/L as Al₂O₃" is one of the most common scale-up errors.
Size the pump turndown on the range you actually operate over, and check the chemical storage and day-tank volumes against the peak day. Feed rate scales linearly with flow, so a plant that swings between 2 and 8 MLD needs a pump that can meter across a 4:1 range — or a feed solution strength that changes with the season.
The arithmetic is exact; the input is not. Jar tests are usually reproducible to within a few mg/L, and full-scale mixing and detention time differ from the bench. Treat the calculated feed rate as a starting set point and confirm it with a full-scale trial, then fine-tune against treated-water turbidity or streaming current.
No — the relation is linear in dose, so calculate each coagulant separately and sum the feed rates. Just make sure each dose is expressed in mg/L of its own product, and that the polymer dose (typically 0.5–5 mg/L) is not confused with the metal-salt dose (typically 10–60 mg/L).
Convert it to m³/day first using the flow-unit converter on this page: 1 MGD ≈ 3,785.4 m³/day. Then use the metric formula as normal. Alternatively, in US customary units the equivalent relation is lb/day = dose (mg/L) × flow (MGD) × 8.34, which gives the same answer expressed in pounds.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Full-Scale Dose | Daily coagulant requirement | kg/day |
| Jar Test Dose | Optimal dose found in jar testing | mg/L |
| Plant Flow | Actual plant flow rate | m3/day |
What it means
Coagulant dosing is optimised using jar tests, where different doses are applied to samples to determine the optimal dose for turbidity removal. The resulting dose in mg/L is then scaled up to the full‑scale plant by multiplying by the plant flow rate and converting units. This is a standard procedure in water treatment to ensure cost‑effective use of chemicals and to maintain treated water quality. The formula assumes that the optimal dose per unit volume remains constant at full scale, though plant‑specific factors like mixing intensity may require adjustment. Example: A jar test shows that 5 mg/L of alum is needed. The plant treats 50,000 m³/day. The full‑scale daily dose is 5 × 50,000 / 1000 = 250 kg/day. This guides the chemical feed system settings and chemical procurement.
Worked example
Coagulant Dosage Scale‑Up – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Jar test dose | 20 mg/L |
| Plant flow | 5,000 m³/day |
| Parameter | Value |
|---|---|
| Jar test dose | 15 mg/L |
| Plant flow | 10,000 m³/day |
Common mistakes
- Jar test dose: Typically in mg/L (ppm) – the optimal dose determined from lab experiments.
- Plant flow: The full‑scale flow rate – in m³/day.
- Conversion: Multiply jar test dose (mg/L) by flow (m³/day) and divide by 1000 to get kg/day.
- Scale‑up factors: The formula assumes linear scale‑up; however, mixing intensity, detention time, and pH may differ at full scale – verify with plant trials.
- Chemical purity: Commercial coagulants have different purity – adjust dose based on active content.
Applications
Coagulant dosage scale‑up from jar test to full‑scale uses the jar test dose (mg/L) multiplied by the plant flow (m³/day) and divided by 1000 to obtain the full‑scale dose in kg/day. Jar tests are bench‑scale simulations used to determine the optimal coagulant type and dose for removing turbidity and organic matter. This simple scaling relationship allows engineers to translate laboratory findings into practical operational parameters, ensuring that the treatment plant achieves the desired clarification efficiency. It is essential for process control, especially when water quality changes seasonally. By applying this scale‑up, plant operators can adjust coagulant feed rates quickly, reducing chemical waste and costs while maintaining effluent quality.
- Optimisation of coagulant dosing in drinking water and wastewater treatment
- Plant process control and troubleshooting during water quality events
- Estimation of chemical costs for treatment plant operations
- Design of chemical feed systems based on expected dosages
- Seasonal adjustment of coagulant type and dose for varying raw water
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