Objective
The OLI software determines the formation of solid phases by calculating the Scaling Tendency (ST), which compares the concentration of ions in solution to their solubility limit, expressed as the solubility product (KSP). This process helps predict when and how much solid will precipitate from a solution under given conditions. For more information on how the software calculates Scaling Tendencies, please see our Scaling Tendencies.
Disclaimer: The user interface, calculations, and results displayed in this article are from OLI Flowsheet: ESP Version 12.0.0 using the MSE thermodynamic framework. Other software versions may appear different or present slightly distinct results due to continual developments to the software and thermodynamic databanks.
Single Solid Example: CaCO₃ in Water
Scenario Setup
We begin with a simple solution: 0.01 mol of CaCO₃ in 1 kg of H₂O at 25 °C and 1 atm. To simplify, we ignore activity coefficients.
Initial Assumptions
In the first iteration of the calculation, the software first assumes no solids are present. It calculates the equilibrium concentrations of aqueous species.
We can observe what these engine results look like by running an Isothermal calculation with the Solids phase turned off. Additionally, we can enable the calculation of Pre-scaling Tendencies (Rigorous) under Calculation Options.
After running the calculation, the Scaling Tendencies and True Species outputs are shown below:
Scaling Tendency (ST) Calculation
For CaCO₃(s), the dissolution reaction is:
CaCO₃(s) ⇌ Ca²⁺ + CO₃²⁻
The Scaling Tendency is defined as:
ST = (aCa(2+))(aCO3(2-)) / KSP
where
- aCa(2+) = the activity of the Ca+2 ion in solution
- aCO3(2-) = the activity of the CO₃²⁻ ion in solution
- KSP = the solubility product constant
In this case, ST of Calcite = 889.626, and ST of Aragonite = 654.777. The values for Post-Scaling Tendency and Pre-Scaling Tendency are equivalent, because Solids have been disabled and are not allowed to form.
Solid Formation Process
To reach equilibrium (ST = 1.0), the software:
- Removes Ca²⁺ and CO₃²⁻ from the aqueous phase in stoichiometric amounts.
- Forms CaCO₃(s) (Calcite) as a precipitate, because its ST is greater than that of Aragonite.
- Recalculates the equilibrium and ST of all solids.
- Repeat Steps 1-3 until ST of Calcite = 1.0.
- Evaluates the new ST of Aragonite, given the lower concentration of Ca²⁺ and CO₃²⁻ in the aqueous phase. As shown below, now the new ST of Aragonite is < 1.0, so it is not predicted to form.
The results below correspond to the same calculation setup as above, but with Solids enabled. Note, Calcite’s Post-Scale value differs from the Pre-Scale value, because Post-Scale represents the true equilibrium condition between the solid and aqueous phase.
In this example, the software precipitates 9.869e-3 mol of Calcite to achieve equilibrium.
Multiple Solids in Solution
If multiple solids can form, each with different ions, the software evaluates them independently and simultaneously. However, if solids share common ions, a competitive interaction occurs.
Example: CaCO₃ and MgCO₃
Let’s add 0.01 mol of MgCO₃ to the previous example, with Solids turned on. The Scaling Tendencies and True Species are:
Step-by-Step Resolution:
- Calcite has the highest ST and is processed first. 9.98743e-3 mol of Calcite is formed, adjusting its Post-Scale ST to 1.0.
- All other Scaling Tendencies are adjusted.
- The software removes the required ions to form 2.32089e-3 mol of Mg(OH)2(s), also adjusting its Post-Scale ST to 1.0.
- All other Scaling Tendencies are < 1.0, indicating sub-saturation.
Outcome:
Any competing solids are now at thermodynamic saturation.
Special Case: Highly Soluble Solids with Common Ions
When a highly soluble solid shares a common ion with a less soluble one:
- The less soluble solid (with the higher ST) is processed first so that it achieves a ST of 1.0.
- This may reduce the ST of the more soluble solid below 1.0.
- If that happens, no additional iterations are performed.