Indices & the science¶
All indices use the classical water-chemistry conventions: calcium hardness and total alkalinity in mg/L as CaCO₃, TDS and ions in mg/L, temperature in °C.
pH of saturation (pHs)¶
The shared building block, using the standard analytical form of Langelier's equation:
$$ pH_s = (9.3 + A + B) - (C + D) $$
$$ A = \frac{\log_{10}(\text{TDS}) - 1}{10}, \quad B = -13.12 \cdot \log_{10}(T_K) + 34.55 $$
$$ C = \log_{10}(\text{Ca as CaCO}3) - 0.4, \quad D = \log_3) $$}(\text{alkalinity as CaCO
where (T_K = {}^{\circ}!C + 273.15).
Saturation / stability indices¶
| Index | Definition | Reads as |
|---|---|---|
| Langelier (LSI) | pH − pHs |
> 0 scaling, < 0 corrosive; a small positive value (~0 to +1) is the usual target |
| Ryznar (RSI) | 2·pHs − pH |
< 6 scaling, 6–7 balanced, > 7 corrosive |
| Puckorius (PSI) | 2·pHs − pH_eq, with pH_eq = 1.465·log₁₀(alk) + 4.54 |
better fit for buffered recirculating water; uses an equilibrium pH, not the measured pH |
| Larson-Skold | (Cl⁻ + SO₄²⁻) / alkalinity (equivalents) |
corrosivity toward mild steel: < 0.8 low, 0.8–1.2 elevated, > 1.2 high |
| Aggressiveness (AI) | pH + log₁₀(Ca · alkalinity) |
AWWA screen: ≥ 12 non-aggressive, 10–12 moderate, < 10 aggressive |
| Stiff-Davis (S&DSI) | pH − pHs, with pHs = pCa + pAlk + K(μ, T) |
the LSI extended to high ionic strength (brines, seawater, concentrated blowdown) |
The Stiff-Davis index replaces the LSI's temperature/TDS terms with an
ionic-strength-dependent constant K (ASTM D4582 / USBR 2013 curve fit). Use it
for high-salinity water (TDS ≳ 10,000 mg/L); for ordinary water the LSI is the
right screen. Ionic strength is estimated as μ ≈ 2.5×10⁻⁵ · TDS.
These indices give a direction, not a quantity. For the actual mass of calcium carbonate involved, the CCPP reports the mg/L of CaCO₃ that must precipitate or dissolve to reach calcite saturation.
Interpretation thresholds are conventional screening bands; edges vary between sources (some Ryznar tables put the balanced/corrosive boundary at 6.8 rather than 7.0), so treat values near a boundary as borderline.
Cooling-tower water balance¶
For an evaporative tower, the four streams relate as:
- Makeup
M = E + B + D(evaporation + blowdown + drift) - Cycles of concentration
CoC = M / (B + D) - Blowdown to hold a target CoC:
B = E / (CoC − 1) − D
evaporation_loss uses a first-principles energy balance and returns the
theoretical (100 % latent-heat) maximum; real towers evaporate ~75–90 % of that,
so apply a heat-rejection factor for field estimates.
References¶
- Langelier, W. F. (1936). The Analytical Control of Anti-Corrosion Water Treatment. J. AWWA 28(10).
- Ryznar, J. W. (1944). A New Index for Determining Amount of Calcium Carbonate Scale Formed by a Water. J. AWWA 36(4).
- Puckorius, P. R. & Brooke, J. M. (1991). A New Practical Index for Calcium Carbonate Scale Prediction in Cooling Tower Systems. Corrosion 47(4).
- Larson, T. E. & Skold, R. V. (1958). Laboratory Studies Relating Mineral Quality of Water to Corrosion of Steel and Cast Iron. Corrosion 14(6).
- Stiff, H. A. & Davis, L. E. (1952). A Method for Predicting the Tendency of Oil Field Waters to Deposit Calcium Carbonate. Petroleum Transactions AIME 195:213. (K constant: ASTM D4582; USBR, 2013.)
Note
These indices are screening guides, not a substitute for site-specific engineering judgment.