Silica Solubility & Scaling Calculator
Explore amorphous silica solubility as water heats, cools or becomes more concentrated.
Your water conditions
Move a slider or enter a value.
5–95 °C · liquid-water reference near atmospheric conditions.
Enter the sum of dissolved monomeric silicic-acid and silicate species, reported as SiO₂. Do not enter total silica that includes colloids or particles. In dilute water near room temperature, mg/L is approximately mg/kg; no density conversion is applied here.
pH 4–10. pH now changes the total dissolved-silica saturation curve through calculated H₄SiO₄ / H₃SiO₄⁻ / H₂SiO₄²⁻ speciation. Activity corrections and minimum charge-balancing ions are calculated; see model limits below.
Concentration scenario
1–10×. Assumes both silica and NaCl are completely retained and water mass is reduced, before precipitation. pH stays at your selected value. The effective NaCl concentration must remain at or below 5,000 mg/kg. This is not an RO membrane or evaporator simulation.
0–5,000 mg/kg water as actual NaCl, before the concentration step. Default: zero. NaCl changes activity coefficients; it is not a substitute for TDS or a complete water analysis. Other dissolved salts are not included.
The salt effect depends on pH and temperature.
What happens as water heats or cools?
Calculated total dissolved silica at amorphous-silica saturation, expressed as SiO₂ at the selected pH. The dark point represents your selected water after the ideal concentration step.
Blue: pH- and NaCl-corrected total dissolved silica · Grey dashed: neutral pure-water reference · Dark point: selected water.
25 °C · pH 7.0 · 1× concentration
Below modelled saturation
At the default conditions, the dissolved silica is below the activity-corrected model saturation concentration.
MODELLED TOTAL SOLUBILITY
117.2 mg/kg as SiO₂
SCENARIO CONCENTRATION
80.0 mg/kg as SiO₂
CONCENTRATION / MODEL LIMIT
68%
The percentage is a concentration ratio, not an activity-based saturation index or a permitted operating limit.
How pH changes the dissolved silica
Higher pH shifts neutral silicic acid towards silicate ions. At saturation, the neutral-species activity reference constrains H₄SiO₄; the ionic species add to the total dissolved silica. The percentages below are calculated for your selected water, including the NaCl background and pH-balancing ions. Activity coefficients depend on ionic strength, so the selected water and its saturation state are solved separately.
| Monomeric species | Calculated fraction | Silica in selected water · mg/kg as SiO₂ |
|---|---|---|
| H₄SiO₄ · neutral | 99.85% | 79.9 |
| H₃SiO₄⁻ · singly charged | 0.15% | 0.1 |
| H₂SiO₄²⁻ · doubly charged | <0.01% | 0.0 |
Calculated pK₁ ≈ 9.83 at 25 °C. Activity coefficients are solved iteratively.
The model includes NaCl, dissolved monomeric silica, H⁺, OH⁻ and minimum balancing Na⁺ or Cl⁻. Other ions are not detected.
Three useful takeaways
Cooling lowers the reference solubility
The temperature correlation rises with temperature. A stream that is below the reference when warm may cross it as it cools.
Higher pH raises apparent silica solubility
The model calculates more silicate ions at higher pH, so the total dissolved silica at amorphous-silica saturation increases. A larger solubility value does not eliminate metal-silicate or other scaling risks.
The salt effect depends on pH
NaCl changes the activities of neutral silicic acid and charged silicate species differently. In this model, it can slightly lower solubility near neutral pH and raise it at higher pH. There is no universal “more salt means more solubility” rule.
Dissolved, colloidal and total silica are different
This page sums neutral silicic acid and its two dissociated monomeric forms, and compares that total with an amorphous-silica equilibrium screen. Colloidal silica consists of particles, while total silica can include dissolved and particulate material, depending on the analytical method. A laboratory result labelled “reactive silica” is method-dependent; confirm its reporting basis before entering it.
Silica reported as Si must be multiplied by approximately 2.139 to express the same amount as SiO₂. The reference is amorphous silica, not quartz or a magnesium-silicate mineral.
Where is this useful?
RO concentrate and water reuse
Use a measured dissolved-silica value to explore temperature and ideal concentration effects. A real RO assessment also needs concentrate pH, salt chemistry, silica passage and membrane-surface concentration.
Evaporation and ZLD
Explore the effect of concentrating a stream. High-salinity evaporator liquors require full-composition geochemical modelling; this limited NaCl screen does not represent brines.
Cooling geothermal or process streams
Show why cooling can move dissolved silica above a solubility reference. Actual precipitation may be delayed and must be assessed for the particular water.
The calculations above are for preliminary reference and may contain errors or omissions. No guarantee of accuracy or completeness is given; results should be independently verified before use in design, treatment selection or operating decisions. This tool is not a substitute for full geochemical modelling or pilot testing in high-recovery or high-temperature systems.
Methodology & limitations
The equations, concentration basis and assumptions behind the amorphous-silica screen, including pH speciation, NaCl activity corrections and the existing PHREEQC comparison.
1. Inputs, units and scenario basis
| Input | Interface range | Meaning in this model |
|---|---|---|
| Temperature | 5–95 °C | Liquid-water reference near atmospheric conditions; no pressure correction. |
| Dissolved silica | 0–1,000 mg/kg water as SiO₂ | Sum of dissolved monomeric silicic-acid and silicate species before concentration; excludes particles and colloids. |
| Operating pH | 4–10 | Imposed independently at each temperature, rather than predicted during heating or concentration. |
| Ideal concentration factor, F | 1–10× | Scales both dissolved silica and background NaCl with complete retention before precipitation. |
| Background NaCl | 0–5,000 mg/kg water before concentration | Actual NaCl only; not TDS or a substitute for the other ions in an analysis. |
Concentrations use kilograms of water, not kilograms of solution. The code converts silica to molality using 60,084.3 mg/mol and NaCl using 58,442.77 mg/mol. No density conversion is applied. In dilute water near room temperature, mg/L is approximately mg/kg water; this approximation should not be extended automatically to hot water or brines.
Scenario silica = entered silica × F Scenario NaCl = entered NaCl × F
The entered operating pH remains fixed. The scenario does not calculate a real RO recovery, evaporation trajectory, salt passage or precipitation mass. The interface ranges are not independently validated accuracy boundaries.
Equations, activity model and numerical solution
1. Neutral-species activity reference: Fournier–Rowe (1977): log₁₀ C₀ = 4.52 − 731/T, with T in kelvin and C₀ as SiO₂ in mg/kg water. The pure-water correlation is used as a dilute neutral-species activity reference over 5–95 °C. No pressure correction is applied.
2. Dissociation constants: H₄SiO₄ ⇌ H₃SiO₄⁻ + H⁺ (K₁), and H₄SiO₄ ⇌ H₂SiO₄²⁻ + 2H⁺ (β₂). β₂ is cumulative, not the second stepwise constant. PHREEQC analytical expressions use log K = A₁ + A₂T + A₃/T + A₄ log₁₀T + A₅/T². Coefficients for K₁: −302.3724, −0.050698, 15669.69, 108.18466, −1119669; for β₂: −294.0184, −0.07265, 11204.49, 108.18466, −1119669; for water dissociation: −283.971, −0.05069842, 13323, 102.24447, −1119669.
3. Activity corrections: for silicate ions, log₁₀ γᵢ = −Azᵢ²[√I/(1 + √I) − 0.3I] (Davies). For neutral H₄SiO₄, log₁₀ γ₀ = 0.1I, matching the neutral-species convention in the pinned benchmark database. H⁺ and OH⁻ use extended Debye–Hückel coefficients with ion-size parameters 9.0 and 3.5 Å and zero b-dot. Temperature-dependent A and B are interpolated from PHREEQC water-property values at 5 °C intervals, 5–95 °C, at atmospheric reference pressure. NaCl contributes equal Na⁺ and Cl⁻ molalities; its input is divided by 58442.77 mg/mol. These conventions are database-specific, not universal salt-solubility coefficients.
4. Equilibrium and charge closure: R₁ = 10pH + log K₁; R₂ = 102pH + log β₂. At saturation, C = C₀(1/γ₀ + R₁/γ₁ + R₂/γ₂). Fractions are proportional to 1/γ₀, R₁/γ₁ and R₂/γ₂. For the selected silica concentration, species are recalculated at its own ionic strength. H⁺ and OH⁻ are calculated from imposed pH and water dissociation. The model adds the minimum Na⁺ or Cl⁻ needed for electroneutrality, corresponding to idealised NaOH or HCl adjustment. Ionic strength I = ½Σmᵢzᵢ² and activity coefficients are solved iteratively. This is a simplified charge-balanced NaCl–silica scenario; it does not calculate a practical acid or caustic dose or a measured water composition.
5. Screening range: both the selected water and its predicted saturation state must converge and have modelled ionic strength ≤0.10 mol/kg. Effective background NaCl after concentration must be ≤5,000 mg/kg water. Otherwise the saturation comparison is withheld; the blue curve is limited to conditions within scope. Species results are withheld when the selected water exceeds scope. These are operational screening cutoffs, not independently validated accuracy boundaries. Other salts cannot be represented simply by entering their TDS as NaCl.
6. Simplifications: water activity is set to 1, with no salt-specific osmotic model. The rounded neutral-reference intercept differs slightly from the pinned PHREEQC phase constant; this and omitted water activity account for much of the remaining benchmark difference. Operating pH is imposed independently at each temperature. The concentration factor scales both silica and NaCl, assuming complete retention and reduced water mass, before precipitation. Natural alkalinity, other ions, complexes, metal-silicate phases, polymerised silica, colloids, kinetics, antiscalant performance, membrane-surface concentration and allowable recovery are not predicted. Solubility is not a fouling timer.
This calculator estimates amorphous-silica saturation in a limited NaCl–silica scenario. Agreement with PHREEQC under the same assumptions does not validate a real-water design. Verify against full water chemistry and experimental data where appropriate.
Output interpretation and display rules
Concentration ratio (%) = 100 × scenario silica / modelled saturation concentration
The ratio is rounded to a whole percent, while status labels use its unrounded value: below 85% is “Below modelled saturation”; 85–100% is “Approaching modelled saturation”; above 100% is “Above modelled saturation”. The 85% threshold is an interface warning choice, not a chemically established safety margin. The ratio is not a general activity-based mineral saturation index or a permitted operating limit.
The blue curve solves saturation at each temperature for the selected pH and effective NaCl. The selected-water speciation is solved separately at its entered silica concentration. The grey dashed curve is the neutral pure-water temperature reference, not the full zero-NaCl speciation curve. At zero background NaCl, pH-balancing and silicate ions can still contribute to ionic strength.
The ionic-strength iteration permits up to 160 iterations, applies half-step damping, and accepts convergence when the change is below 10⁻¹² + 10⁻⁹ × max(previous I, updated I). It stops early if the updated ionic strength is non-finite or exceeds 2 mol/kg. That numerical stop is distinct from the stricter 0.10 mol/kg reporting screen.
Unsupported points are omitted from the blue curve. The ratio and selected marker are withheld unless both the selected water and its saturation state are supported. Species fractions are withheld if the selected water alone is unsupported. “Outside model scope” must not be interpreted as low scaling risk.
Reproducible default example
Reset uses 25 °C, pH 7.0, dissolved silica 80 mg/kg water as SiO₂, concentration factor 1× and zero background NaCl. The modelled total saturation concentration is approximately 117.2 mg/kg as SiO₂; the displayed concentration ratio is 68%, with the status “Below modelled saturation”. The selected-water speciation is mostly neutral H₄SiO₄. Zero background NaCl does not suppress the ions required by the model's pH and charge balance.
Benchmark comparison and validation limits
How does this compare with PHREEQC?
A synthetic-water benchmark compared 396 temperature, pH and NaCl combinations with the PHREEQC engine and the pinned phreeqc.dat database supplied with IPhreeqcPy 2024.0.0. Both models used amorphous silica, SiO₂(a), with fixed operating pH. PHREEQC included HCl or NaOH to hold pH and its water-activity treatment; this page uses minimum charge-balancing ions and assumes water activity is 1.
| Conditions | NaCl · mg/kg water | This model · mg/kg as SiO₂ | PHREEQC · mg/kg as SiO₂ |
|---|---|---|---|
| 25 °C · pH 7 | 0 | 117.2 | 116.8 |
| 25 °C · pH 7 | 5,000 | 114.9 | 113.9 |
| 25 °C · pH 9 | 0 | 134.6 | 134.2 |
| 25 °C · pH 9 | 5,000 | 136.6 | 135.4 |
| 80 °C · pH 9.5 | 5,000 | 966.5 | 957.2 |
| 95 °C · pH 10 | 5,000 | 3961.5 · withheld | 3907.0 |
The grid covered 5–95 °C, pH 4–10 and 0–5,000 mg/kg NaCl, including 18 intermediate-temperature cases. Of these cases, 391 passed this model’s saturation-state ionic-strength screen; the largest relative difference from PHREEQC was 0.98%. Five cases exceeded the screen and their saturation comparison is withheld. These sampled differences are not guaranteed accuracy bounds. The two calculations share equilibrium constants and activity-model assumptions, so this is an implementation comparison, not independent experimental validation.
Real process water can contain calcium, magnesium, aluminium, iron and other constituents absent here. Use a complete water analysis, suitable database and activity model for design; neither this comparison nor the NaCl lever establishes a safe recovery or fouling rate.
References and model record
References: USGS PHREEQC database · Equilibrium constants · PHREEQC · Temperature expressions and activity models · Fournier & Rowe · Amorphous silica solubility · DuPont FilmTec · Silica scale prevention
Methodology documentation v1.0 · prepared 24 October 2026. Documents the existing calculation engine and its reported benchmark; no numerical functions or coefficients are changed by this tab.