Hamish Robertson , Fiona Whitaker, Cathy Hollis, Hilary Corlett

The calculation of a reliable temperature dependent dolomite solubility product constant (Ksp°−dol) has been the subject of much research over the last 70 years. This study evaluates log10(aCa2+/aMg2+) using PHREEQC (Pitzer approach) for a screened subset (n=11,480) of formation waters in the U.S. Geological Survey National Produced Waters Geochemical Database V2 (PWGD), an extensive inventory of 165,960 formational waters from a range of sedimentary lithologies in North America up to 6.6 km depth (Blondes and others, 2016). Through extensive ground-truthing against datasets sourced from Texas Gulf Coast basin and the Mississippi Salt Dome basin we establish that both the geochemical data from the PWGD and a new geothermal model of the US that is used to determine temperatures at-formation-depth to be reliable data sources.
The vast majority (at least 90%) of PWGD samples have log10(aCa2+/aMg2+)-temperature values that are interpreted to be indicative of calcite-dolomite equilibrium and controlled by bulk mineral equilibria rather than Mg-calcite surface phases. Using statistical models with different parameterizations (different Maier-Kelly formulas, mixed-effects models with various random effects and linear models) log10(aCa2+/aMg2+) values (outcome variable) are regressed against temperature (fixed effect) calculating Ksp°−dol between 0-200°C using the well constrained calcite solubility product (Ksp°−cal).
Local effects that modify log10(aCa2+/aMg2+) values are evaluated through the addition of random effects to the mixed model which improves the statistical reliability of the Ksp°−dol estimate and enables the determination of Ksp°−dol for local dolomite phases. The nature of these local effects is open to interpretation, but we suggest the primary influence on log10(aCa2+/aMg2+) values is the stoichiometry of the equilibrium dolomite phase within individual fields that systematically modifies log10(aCa2+/aMg2+) values. We discount the influence on log10(aCa2+/aMg2+) values from the ionic strength of the solution, the equilibration with anhydrite and chlorite group minerals, the illitization of smectite and albitization of feldspar.
For the dolomite solubility equation;
CaMg(CO3)2 (s) ↔ Ca2+(aq)+ Mg2+(aq) + 2CO3(2-)(aq) (1)

the mixed-effects model chosen as most representative yields a pKsp°−dol (log10Ksp°−dol);
pK(sp-dol)= 1.47545×10^1 - 6.24959×10^-2∙T(K) - 3.99350×10^3∙1/T(K) (2)
At 25°C pKsp°−dol = -17.27±0.35, which is close to prior estimates including the most recent experimental value reported by B´en´ezeth and others, 2018 (pKsp°−dol = -17.19±0.3). This validates this study’s approach and enables conclusions to be drawn via a meta-analysis of a contaminated, though expansive dataset.