Quartz solubility in salt-bearing solutions at pressures to 1 GPa and temperatures to 900°C

An expression that describes the solubility of quartz in alkali-chloride-bearing solutions is derived and applied to literature data on quartz solubility. The model is based on a physically realistic conceptual model that involves salt dissociation as a function of pressure, temperature and salt concentration, and the presence of hydrated monomer, dimers and hydrated alkali-silica species. A simplified version of the model that neglects dimerization and water in the alkali-silica species provides excellent fits to the experimental data with two calibration parameters at each pressure and temperature. The calibration parameters represent the relative stabilities of the alkali-silica and hydrated-silica solute complexes, and the degree of salt dissociation. The success of the model provides support for the existence of an alkali-silica species in salt solutions at low fluid densities. The model can be interpolated successfully for NaCl-bearing solutions between 0.1 and 1 GPa and from 400 to 900°C, with standard deviations of the predicted from the experimental data of less than 10% relative for most conditions. Quartz solubility within this range is described by X(SiO₂/X(SiO₂,ref) = (X(H₂ O_app)/1 + αX(NaCl_app))³ +c (αX(NaCl_app)/1 + αX(NaCl_app)) where X_i,app refers to the apparent mole fraction of i, which is the mole fraction calculated if NaCl is assumed to be totally associated, and X(SiO_2,ref) is the mole fraction of SiO₂ in the salt-free solution c = 37.17 - 0.00141T - 24.45ρ α = 1 Erf[dX_Nacl,app], where d is a calibration parameter that depends on pressure and density as shown below. d = 2.75 - 2.733Ρ + 2.38ρ. T is temperature in Kelvin, Ρ is pressure in GPa and ρ is the density in g cm^-3. Extrapolation of the expression beyond the calibration range is not recommended. Quartz solubility is additive for mixtures, so silica concentrations in solutions more complex than those covered by the literature data can also be predicted. Fits to the data also enabled regression of thermodynamic data for the proposed SiO₂.(NaCl)_0.5 species. H₂₉₈ is -1040.2 ± 7.6 kJ mol^-1, S₂₉₈ is 0.169 ± 0.01 kJ mol^-1 K^-1 and V₂₉₈ is 31 ± 4 kJ GPa^-1 mol^-1. The model is semi-empirical because the fit parameters are correlated with one of the set parameters, and the use of a simplified mathematical description of salt dissociation. Nevertheless, the model provides an improved method for the calculation of quartz solubility in geological solutions.