Calcium Sulfate Scaling / Solubility Calculator

Methodology & limitations

The formulas, input conventions and assumptions behind this calcium sulfate demonstration, with a clear distinction between the interface and a thermodynamic scaling model.

1. Scope, units and inputs

The simplified composition is demineralised water + NaCl + CaSO₄. The CaSO₄ input is nominal total added salt on an anhydrous CaSO₄ basis per litre of starting solution. It is not a gypsum dose, a free-ion concentration or a measured dissolved concentration after equilibration. An above-limit point represents a hypothetical composition before precipitation.

These are interface ranges, not validated chemical operating ranges. No density or volume-change calculation converts starting-solution litres into equilibrium solution volume or kilograms of water. Concentrated-brine calculations require an explicit mass and concentration basis.

2. Exact saturation-response function

With the numerical inputs in the units above, the displayed threshold L (g/L as CaSO₄) is:

L = max{0.5,
    (2.05 + 0.009 × T − 0.00015 × T²)
    × [1 + 0.014 × S / (1 + S / 110)]}

Displayed concentration ratio (%) = 100 × C / L

The coefficients and the 0.5 g/L lower bound are demonstration choices. The quadratic temperature term has its maximum at 30 °C. That maximum is imposed by the formula; it is not a predicted gypsum–anhydrite transition or a universal experimental solubility maximum.

The NaCl factor rises monotonically towards a finite value. It cannot reproduce a high-salinity reversal of a real solubility trend. It does not calculate ion activities, calcium–sulfate ion pairs, water activity or interactions with other dissolved salts.

L is displayed to two decimal places and the ratio to the nearest whole percent. Status labels use the unrounded ratio: below 85% is “Undersaturated”, 85–100% is “Approaching saturation”, and above 100% is “Supersaturated”. The 85% boundary is an interface warning choice. These labels describe the demonstration curve, not the thermodynamic saturation state of an analysed water.

The grey comparison curve sets S = 0. The sample’s CaSO₄ input is retained; “no added NaCl” does not mean ion-free water.

3. Boiling boundary and temperature cap

B (°C) = 100 + 28 × ln(P / 1.01325) + 0.025 × S
Tmax (°C) = floor[10 × min(150, B − 0.5)] / 10

Here ln is the natural logarithm and floor rounds down. This function illustrates pressure and salinity responses; it is not a steam-table correlation or a solution vapour–liquid equilibrium calculation. CaSO₄ contributions to boiling are omitted. The 0.5 °C margin and 150 °C ceiling are interface choices.

Changing pressure can shorten the allowable temperature range, but this version does not calculate pressure-dependent mineral equilibrium. Evaporation, changing salinity, thermal expansion and boiling-induced concentration changes are not simulated.

4. pH, speciation and counterions

The pH control is a scenario note, not a calculated chemical input in this version. A real sulfate model must account for the distribution between sulfate and bisulfate, especially in acidic water, together with free calcium, ion pairing and activity corrections.

For a future dosing model, lowering pH with HCl would add chloride and raising it with NaOH would add sodium. Their doses and counterions would need to be included in the solution balance. Sulfuric acid would also add sulfate. None of those doses or accompanying ions are calculated here.

5. Gypsum, anhydrite and thermodynamic saturation

A thermodynamic calculation evaluates each mineral separately using activities and the equilibrium constant for the same dissolution reaction:

Gypsum:   CaSO₄·2H₂O(s) ⇌ Ca²⁺ + SO₄²⁻ + 2H₂O
IAPgypsum = aCa²⁺ × aSO₄²⁻ × aw²

Anhydrite: CaSO₄(s) ⇌ Ca²⁺ + SO₄²⁻
IAPanhydrite = aCa²⁺ × aSO₄²⁻

SIphase = log₁₀[IAPphase / Kphase(T, P)]

Here a denotes species activity and aw water activity; pure mineral activities are taken as unity. SI = 0 means equilibrium with the named phase, SI > 0 supersaturation and SI < 0 undersaturation. The current calculator does not compute these quantities or identify a controlling mineral phase.

A thermodynamic saturation ratio IAP/K is not generally equal to C/L. Total salt concentrations cannot replace the free-ion activities in these expressions. Even a correctly calculated positive SI indicates a thermodynamic tendency, not a deposited mass, scaling rate or certainty of scale formation.

The USGS PHREEQC gypsum–anhydrite example demonstrates phase-specific solubility calculations and comparison with experimental data. A brine application needs a suitable activity model, such as a Pitzer implementation, and parameters checked for its composition, temperature and pressure range. The demonstration does not run PHREEQC.

6. Validation status and reproducible example

No calibration dataset, thermodynamic benchmark or engineering accuracy range is established for this demonstration curve. Checking arithmetic verifies consistency with the code; it does not establish physical accuracy.

At the initial settings (25 °C, NaCl 50 g/L, CaSO₄ 1.5 g/L and pressure 1.013 bar absolute), the functions give L = 3.2309766 g/L (displayed 3.23), a ratio of 46.4256% (displayed 46%), and B = 101.2431 °C (displayed 101.2). The temperature cap is 100.7 °C. Changing scenario pH alone leaves these numbers unchanged.

A future engineering model should be benchmarked against independent equilibrium calculations and relevant experimental measurements. Record the software/database version, solution composition, concentration basis, permitted mineral phases and acceptance tolerances. Check both gypsum and anhydrite across the intended salinity and temperature range, rather than relying on one default example.

7. Known limitations and appropriate use

• No aqueous speciation, activity correction, water activity, charge-balance solution or mineral-phase selection.
• No independent calcium and sulfate analysis, magnesium or other background ions beyond the simplified salt inputs.
• No evaporation or recovery mass balance, precipitation mass, antiscalant effect, nucleation or scale-growth kinetics.
• No validated high-temperature, high-salinity or pressure-dependent mineral predictions.

This calculator’s demonstration estimates a calcium sulfate threshold and illustrates scaling tendency; it is not a substitute for full geochemical modelling or pilot testing in high-recovery or high-temperature systems. Calculations may contain errors or omissions. Independently verify results before design, treatment selection or operating decisions.

8. References and model record

• USGS — Phase-equilibria and solubility relationships: background on salinity and mineral-phase effects.
• USGS — PHREEQC Version 3 documentation: speciation, mineral equilibrium and activity-model methods.
• USGS — Gypsum and anhydrite equilibrium example.

Methodology documentation v1.0 · prepared 24 October 2026. Documents the existing demonstration functions; does not introduce a new equilibrium model or change the calculator’s numerical behaviour.

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