Lime-Soda Softening
Estimate stoichiometric lime and soda ash demand from hardness, alkalinity and free CO₂.
Calculator inputs
Results
Equations and method
Total hardness = calcium + magnesium hardness. Carbonate hardness = alkalinity in this model. Noncarbonate hardness = total hardness − alkalinity. Lime equivalents = alkalinity + magnesium hardness + (100.0869/44.0095) × free CO₂ + additional lime. Multiply by 56.077/100.0869 for CaO or 74.0927/100.0869 for Ca(OH)₂. Soda ash = noncarbonate hardness × 105.9888/100.0869. Divide each pure dose by product purity.
Worked example
For calcium hardness 150, magnesium hardness 50 and alkalinity 120 mg/L as CaCO₃, with 10 mg/L free CO₂: pure hydrated lime ≈ 142.68 mg/L; pure soda ash ≈ 84.72 mg/L.
Scope and assumptions
Ideal complete removal of calcium and magnesium; bicarbonate-dominated water only. Alkalinity must not exceed total hardness. Excludes caustic/carbonate alkalinity, other acidity, coagulant effects, equilibrium residual hardness, sludge recycling and recarbonation. Additional lime is an explicit user input. This is a stoichiometric demand estimate, not a prediction of finished-water pH or hardness.
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Equation values and input guide
Use a water analysis with calcium hardness, magnesium hardness and bicarbonate alkalinity expressed as CaCO₃ equivalents. Enter free CO₂ on its own mass basis, choose lime form and supply product purities.
- Calcium and magnesium hardness
- Separate contributions in mg/L as CaCO₃, not mg/L of calcium or magnesium ions. Sum them for total hardness.
- Bicarbonate alkalinity
- mg/L as CaCO₃; this simplified model assigns it to carbonate hardness and requires it not to exceed total hardness.
- Noncarbonate hardness
- Total hardness minus bicarbonate alkalinity, on the same CaCO₃ equivalent basis; used to estimate soda ash demand.
- Free CO₂
- Actual dissolved carbon dioxide in mg/L as CO₂. The 100.0869/44.0095 molecular-weight ratio converts it to CaCO₃ equivalents.
- Additional lime
- Extra demand entered as mg/L CaCO₃ equivalent, not actual product mass. It is converted with the rest of the lime requirement.
- Lime form, pure dose
- CaO or Ca(OH)₂ determines the molecular-weight conversion from equivalents to actual pure lime mass. Soda ash is expressed as Na₂CO₃ mass.
- Product purity
- Active product percentage. Divide pure dose by the fractional purity, e.g. 90% becomes 0.90, to estimate purchased product dose.
- Water flow
- Converts product dose into mass per day after volume and mass unit conversions.
Use the unit selectors beside the inputs. Units shown in the equations must be consistent when checking the math by hand.