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Water scaling and corrosion indices

Enter the water analysis to see whether it tends to deposit calcium carbonate or corrode piping, at operating temperature and at the hottest exchanger wall.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

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Water analysis

Calcium hardness is the calcium part only, not total hardness (calcium + magnesium). The fields take the unit chosen alongside; the conversion table in the results shows the value in the other units.

Hot surface

Calcium carbonate is less soluble when hot: scale starts at the hottest wall. Use the tube skin temperature or, if unknown, the hot water outlet temperature.

—Langelier Saturation Index (LSI)
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Indices versus temperature

LSI (left axis) and RSI (right axis) for the same water heated or cooled. Dashed lines mark the water and hot-wall temperatures.

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LSI versus pH

With calcium, alkalinity and salts held constant, shows how far pH must move to reach balance, at water and wall temperature.

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Hardness and alkalinity converter

Entered values expressed in the usual laboratory and chemical supplier units.

The report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

LSI = pH − pHs; RSI = 2 · pHs − pH; PSI = 2 · pHs − pHeq, with pHeq = 1.465 · log₁₀(M alkalinity) + 4.54
pHs = pK2 − pKs + p[Ca²⁺] + p[HCO₃⁻] + 5 · pfm (Standard Methods 2330 B; concentrations in mol/L)
pK2 = 107.8871 + 0.03252849 T − 5151.79/T − 38.92561 log T + 563713.9/T²; pKs = 171.9065 + 0.077993 T − 2839.319/T − 71.595 log T (T in K, calcite)
Activity: I = 2.5 × 10⁻⁵ · TDS; pfm = A (√I/(1 + √I) − 0.3 I); A = 1.82 × 10⁶ (ε T)^−1.5; ε = 60954/(T + 116) − 68.937
[HCO₃⁻] = ([Alk] − [OH⁻] + [H⁺]) ÷ (1 + 2 K2′/[H⁺]); simplified: pHs = (9.3 + A + B) − (C + D), A = (log TDS − 1)/10, B = −13.12 log(t + 273) + 34.55, C = log Ca − 0.4, D = log Alk
Conversions to mg/L as CaCO₃: 1 °dH = 17.848; 1 °fH = 10.009; 1 gpg = 17.118; 1 meq/L = 50.04; 1 mg/L Ca = 2.497; 1 mg/L HCO₃⁻ = 0.820

Assumptions and limits

  • The indices show thermodynamic tendency, not scaling rate or corrosion rate. Inhibitors, dispersants, velocity and materials change actual behavior.
  • Alkalinity treated as carbonate alkalinity (no significant silicate, phosphate, borate or ammonia contribution). Ionic strength estimated from TDS, valid up to about 10,000 mg/L.
  • At the hot wall, pH and alkalinity are assumed equal to bulk water; calcite equilibrium constants, 0 to 100 °C (32 to 212 °F).

Standards and technical documents

  • APHA, AWWA, WEF. Standard Methods for the Examination of Water and Wastewater, 2330 Calcium Carbonate Saturation
  • ASTM D3739: Standard Practice for Calculation and Adjustment of the Langelier Saturation Index for Reverse Osmosis
  • Langelier, W. F. The analytical control of anti-corrosion water treatment. J. AWWA 28, 1936
  • Ryznar, J. W. A new index for determining amount of calcium carbonate scale formed by a water. J. AWWA 36, 1944
  • Plummer, L. N.; Busenberg, E. The solubilities of calcite, aragonite and vaterite in CO₂–H₂O solutions. Geochim. Cosmochim. Acta 46, 1982
  • Puckorius, P. R.; Brooke, J. M. A new practical index for calcium carbonate scale prediction in cooling tower systems. Corrosion 47, 1991

U.S. regulations

  • EPA 40 CFR 141 Subpart I (Lead and Copper Rule): corrosion control treatment and water quality parameters
  • EPA 40 CFR 143: National Secondary Drinking Water Regulations (corrosivity, pH 6.5 to 8.5)
  • EPA 40 CFR 122 (NPDES): discharge permits for cooling tower and boiler blowdown

Frequently asked questions

How do I calculate the Langelier Saturation Index?

Find the saturation pH (pHs) from calcium, alkalinity, temperature and TDS and subtract it from measured pH. For 77 °F water at pH 8.0, 500 mg/L TDS, 250 mg/L calcium hardness and 100 mg/L alkalinity (as CaCO₃), pHs is about 7.55 and LSI about +0.45: slightly scale-forming.

What is the difference between Langelier and Ryznar?

LSI tells the direction (scale or corrosion); RSI = 2 pHs − pH was fitted to field data and indicates intensity. Water with LSI +0.5 and RSI 6.7 scales lightly; with RSI 5.0 scaling is heavy.

Why does the heat exchanger scale while cold piping does not?

Calcium carbonate is less soluble when hot. Water balanced at 86 °F can have LSI above +1 at a 140 °F wall, and that is where the deposit starts.

How do I convert grains per gallon to mg/L?

Multiply by 17.12 to get mg/L as CaCO₃. One German degree (°dH) is 17.85 mg/L and one French degree (°fH) is 10 mg/L as CaCO₃.