Lime/ Caustic requirement for Alum dosing
Design Philosophy
Aluminum sulphate (alum) is the most widely used coagulant in water treatment in India, as recommended by the CPHEEO Manual. When alum is added to water, it hydrolyses to form aluminum hydroxide — the active coagulant species — and releases hydrogen ions (H⁺) as a by-product. The hydrolysis reaction is:
Each mole of alum releases 6 moles of H⁺, which consume the natural alkalinity of the raw water (primarily the HCO₃⁻ / CO₃²⁻ system). If the natural alkalinity is insufficient to buffer the H⁺ released, the pH will drop below the optimum range for coagulation (typically pH 6.5–8.0 as per CPHEEO), and coagulation efficiency will be severely impaired. Lime (Ca (OH)₂) or caustic soda (NaOH) must then be added to supplement alkalinity and restore the pH to the target range.
Carbonate Speciation Model
The calculator uses a two-pKa carbonate system (CO₂ / HCO₃⁻ / CO₃²⁻) to compute the distribution of carbonate species at any given pH. The dissociation constants are:
pKa2 = 10.33 (HCO₃⁻ ⇌ H⁺ + CO₃²⁻) at 25°C
H⁺ Addition from Alum
The equivalent H⁺ addition from alum dosing is computed on a milliequivalent basis:
Alkalinity Supplementation
The alkalinity deficit — the difference between the alkalinity required to maintain the target pH and the alkalinity remaining after alum addition — is the basis for sizing lime or caustic soda supplementation. The calculator presents both lime (as CaO or Ca(OH)₂) and caustic soda (NaOH) requirements as equivalent options, in mg/L.
(Source: CPHEEO Manual on Water Supply and Treatment, 2013; supplemented by Water Quality Engineering — Mark Benjamin & Desmond Lawler)
Calculator
(Note – all Yellow are user defined value, all white are fixed values, all green are calculated value, all orange is calculated not to be shown)
Instructions
Enter values highlighted in the Yellow
Green highlights are the results
In case of any invalid result of non-functioning of the calculator, please write to us at design@swaenviro.com. We will try and help you with your sizing and calculation
INPUT
| Parameter | Values | Units | Remarks |
|---|---|---|---|
| Input Parameters | |||
| Initial alkalinity of raw water | mg/l as CaCO3 | ||
| 0.40 | meq/l | ||
| pH of raw water | |||
| Association/Dissociation Constant | |||
| pKa1 | Typical 6.35 @ 25 deg C | ||
| pKa2 | Typical 10.33 @ 25 deg C | ||
| Speciation at initial pH | |||
| H2CO3 | 0.0660 | % | |
| HCO3- | 0.9326 | % | |
| (CO3)2- | 0.0014 | % | |
| HCO3- + (CO3)2- | 0.37 | meq/l | |
| HCO3- | 0.37 | meq/l | |
| (CO3)2- | 0.00 | meq/l | |
| TOTCO3 | 0.40 | meq/l | |
| Alum dosage | mg/l | ||
| 0.050 | mg/l | ||
| Equivalent H+ addition (Based on stoikiometric equation) | 6 | meq/l per meq/l of Alum | |
| Equivalent H+ addition (Based on stoikiometric equation) | 0.303 | meq/l | 1 mole of Alum adds 6 mole of H+ Ion |
| Alkalinity after H+ addition | 0.097 | meq/l | |
| Speciation @ depressed pH | |||
| HCO3- | 0.097 | meq/l | |
| TOTCO3 | 0.40 | meq/l | |
| H2CO3 | 0.30 | meq/l | |
| pH after addition of Alum | 5.86 | ||
| Goal pH | |||
| TotCO3 | 0.40 | meq/l | |
| Association/Dissociation Constant | |||
| pKa1 | 6.35 | ||
| pKa2 | 10.33 | ||
| Speciation @ goal pH | |||
| H2CO3 | 0.1829 | % | |
| HCO3- | 0.8168 | % | |
| (CO3)2- | 0.0004 | % | |
| HCO3- | 0.33 | meq/l | |
| (CO3)2- | 0.0002 | meq/l | |
| Alkalinity addition required | 0.230 | meq/l | |
| Lime addition required | 0.115 | mmol/l | |
| 8.498 | mg/l | ||
| OR | |||
| Caustic addition required | 0.230 | mmol/l | |
| 9.187 | mg/l | ||