Thermodynamic Modeling of Calcium Sulfate Hydrates in the CaSO4-H2O System from 273.15 to 473.15 K with Extension to 548.15 K

Abstract

Calcium sulfate is one of the most common inorganic salts with a high scaling potential. The solubility of calcium sulfate was modeled with the Pitzer equation at a temperature range from 273.15 to 473.15 K from published solubility data, which was critically evaluated. Only two Pitzer parameters, β⁽¹⁾ and β⁽²⁾, with simple temperature dependency are required to model the solubility with excellent extrapolating capabilities up to 548.15 K. The stable temperature range for gypsum is 273.15-315.95 K, whereas above 315.95 K the stable phase is anhydrite. Hemihydrate is in the metastable phase in the whole temperature range, and the obtained metastable invariant temperature from gypsum to hemihydrate is 374.55 K. The obtained enthalpy and entropy changes at 298.15 K for the solubility reactions are in good agreement with literature values yielding solubility products of 2.40 × 10^-05, 3.22 × 10^-05, and 8.75 × 10^-05 for gypsum, anhydrite, and hemihydrate, respectively. The obtained Pitzer model for the CaSO₄-H₂O system is capable of predicting the independent activity and osmotic coefficient data with experimental accuracy. The mean absolute average error of activity coefficient data at 298.15 K is less than 2.2%. Our model predicts the osmotic coefficient on the ice curve within 1.5% maximum error.

Figure 1

Error between calculated and experimental values of Gibbs energy for calcium sulfate hydrates in the assessment. Error = (C_i – E_i)/U_i where (C_i – E_i) = ΔG° + RT ln(K_sp) and U_i is either 100 or 500 J/mol (see the text). A solid symbol indicates the adopted value, and the hollow, the rejected one.

Figure 2

(a) Solubility of gypsum in water in the temperature range of 273.15–393.15 K. Solubility curves calculated by parameters by Wang et al. and Raju and Atkinson models are also shown for comparison. (b) Deviation plot of calculated and experimental solubility for gypsum in water. The solid symbol means the adopted point, whereas the hollow symbol means the rejected one. The obtained transition temperature 315.95 K is also included as a vertical line.

Figure 3

Solubility of anhydrite in water in the temperature range of (a) 273.15–373.15 K and (b) 373.15–573.15 K. Solubility curves calculated by parameters by Wang et al. and Raju and Atkinson models are also shown for comparison. Only three solubility data points of anhydrite over 373.15 K were included for assessment. (c) Deviation plot of the calculated and experimental data for anhydrite in water. The solid symbol means the adopted point, whereas the hollow symbol means the rejected one. The obtained transition temperature 315.95 K is also included as a vertical line.

Figure 4

(a) Solubility of hemihydrate in water in the temperature range of 273.15–473.15 K. (b) Deviation plot of the calculated and experimental solubility data for hemihydrate in water. The solid symbol means the adopted point, whereas the hollow symbol means the rejected one.

Figure 5

Solubility curves of calcium sulfate hydrates in water calculated in this work. Solubility over 473.15 K is extrapolated. Solubility curves calculated by parameters by Wang et al. and Raju and Atkinson models are also shown for comparison. The transition temperatures predicted by the models are also shown.

Figure 6

Experimentally obtained and calculated activity coefficient of calcium sulfate at 298.15 K. Experimental data is from Lilley and Briggs as well as estimated experimental error lines.

Figure 7

Deviation plot of the calculated and experimentally obtained activity coefficient Δγ = γ_exp – γ_calc obtained by two different values for standard potential for lead amalgam-lead sulfate electrode (see the text).

Figure 8

Comparison of calculated to experimental and thermodynamically estimated activities of water on the ice curve.