Governing Indices & Published Formulas
This tool screens calcium carbonate (CaCO₃) scaling potential using two standard, published saturation indices. The model is chosen automatically from the feed salinity: the Langelier Saturation Index (LSI) per ASTM D3739 for TDS below 10,000 mg/L, and the Stiff & Davis Stability Index (S&DSI) (Stiff & Davis, 1952) for seawater and high-TDS brines where ionic strength effects become significant.
LSI = pH − pHS Where:
-
pH= Measured feed water pH [–] -
T= Feed water temperature [°C] -
TDS= Total dissolved solids [mg/L] -
Ca²⁺= Calcium hardness expressed as CaCO₃ [mg/L as CaCO₃] -
Alk= Total alkalinity expressed as CaCO₃ [mg/L as CaCO₃]
Derived Equations:
A = (log₁₀(TDS) − 1) / 10 B = −13.12·log₁₀(T + 273) + 34.55 C = log₁₀(Ca²⁺) − 0.4 D = log₁₀(Alk) pHS = (9.3 + A + B) − (C + D) S&DSI = pH − pCa − pAlk − K How the Saturation Index Works
Both indices compare the actual feed pH to the saturation pH (pHS) — the pH at which the water would be exactly saturated with CaCO₃.
- Index > 0: feed is supersaturated — potential CaCO₃ scaling.
- Index = 0: saturated — at equilibrium.
- Index < 0: undersaturated — dissolution tendency (corrosive/aggressive).
LSI applies the classic Langelier parameters (TDS, temperature, calcium, alkalinity) with the activity terms A, B, C, D defined per ASTM D3739. For waters above roughly 10,000 mg/L TDS — typical seawater RO feed and concentrate — the LSI thermodynamic assumptions weaken, and the Stiff & Davis index replaces them with an ionic-strength-adjusted constant K that is interpolated from the published Stiff–Davis table for the feed temperature and estimated ionic strength (µ ≈ 2.5×10⁻⁵ × TDS).
Worked Engineering Example
Scenario: Brackish Water RO Feed Screening
A BWRO feed is reported at pH 7.5, 15 °C, TDS 1,500 mg/L, calcium 120 mg/L as CaCO₃ and alkalinity 100 mg/L as CaCO₃.
- TDS term A:
(log₁₀(1500) − 1) / 10 = 0.2176 - Temperature term B:
−13.12 × log₁₀(288) + 34.55 = 2.233 - Calcium term C:
log₁₀(120) − 0.4 = 1.679 - Alkalinity term D:
log₁₀(100) = 2.000 - Saturation pH pHS:
(9.3 + 0.2176 + 2.233) − (1.679 + 2.000) = 8.072 - LSI = pH − pHS:
7.5 − 8.072 = −0.57→ undersaturated, low CaCO₃ scaling risk.
Same feed chemistry at pH 8.4 would give LSI = +0.33 → near saturation, a
typical case where pretreatment and antiscalant selection (not modeled here) become design
decisions.
Assumptions & Limitations
Assumptions
- Reported TDS, calcium, alkalinity, pH, and temperature are accurate and representative of the feed at operating conditions.
- Alkalinity is assumed primarily bicarbonate-carbonate (the CaCO₃ saturation system). Other alkalinity contributions shift results.
- Ionic strength is approximated from TDS via µ ≈ 2.5×10⁻⁵ × TDS, a standard screening estimate.
- Stiff–Davis constant K is bilinearly interpolated from the 1952 published table.
Limitations
- This is a screening indicator, not certification. It does not account for antiscalant effectiveness, membrane-specific brine chemistry, concentration polarization, or precipitation kinetics.
- Does not model silica, barium sulfate, strontium sulfate, or iron scaling — evaluate those separately for concentrate disposal and ZLD design.
- Always confirm with membrane projection software (Dupont WAVE, Hydranautics IMSDesign, Toray DS2) and a certified laboratory analysis.
Smart Boundary Disclaimer Notes
The calculator auto-flags inputs outside typical RO operating ranges (pH < 4 or > 10.5, temperature > 50 °C, and sub-freezing temperatures) with inline warning badges. These are guidance flags — they deliberately do not block the calculation, because screening unusual feeds still provides useful engineering context.
Frequently Asked Questions
When should I use S&DSI instead of LSI?
Rule of thumb: LSI (ASTM D3739) is intended for freshwater and low-to-moderate brackish feeds, generally below roughly 10,000 mg/L TDS. Above that — seawater RO feed or concentrate — the Stiff & Davis index corrects for ionic strength, which LSI does not capture.
What does a positive LSI actually tell me?
A positive index means the water is supersaturated with respect to CaCO₃ and therefore has the potential to precipitate scale on membranes and piping. It is a thermodynamic tendency, not a guarantee: actual fouling depends on antiscalants, kinetics, concentration polarization, and flow conditions.
Can this calculator size my antiscalant dose?
No — deliberately. This tool reports sliding scaling-risk considerations only. Antiscalant selection and dosage require vendor-specific data and projection software. Shipping a “guaranteed dosing optimizer” without that evidence would be unsafe and misleading.
What is the relationship to RO mass balance and recovery?
Recovery sets the concentration factor, so the brine entering the discharge boundary has higher TDS, calcium, and alkalinity than the feed. Many scaling evaluations are performed on the concentrated brine using a mass-balance projection — which is why this tool links to the RO recovery, mass balance, and concentrate flow calculators.
Engineering Disclaimer
Engineering Note: This calculator provides simplified engineering estimates for preliminary analysis and educational use. Actual RO system performance depends on membrane type, feedwater chemistry, temperature, pressure, recovery, concentration polarization, pretreatment, and operating conditions. Final system design should be verified using manufacturer data, validated design software, applicable standards, and qualified engineering review.
Technical References
- DuPont FilmTec™ Reverse Osmosis and Nanofiltration Technical Manual (Form No. 45-D01504-en).
- AWWA Manual M46: Reverse Osmosis and Nanofiltration, American Water Works Association.