Exploring uncertainty in thermodynamic modeling of the lead carbonate aqueous system

Abstract

Abstract Thermodynamic models of the lead carbonate aqueous system have been used in prior studies to evaluate the effect of water chemistry on lead solubility and corrosion scale composition in water distribution systems. A common challenge in these studies is uncertainty arising from the thermodynamic equilibrium constants (logK values) used to parameterize the models. The objective of this study is to evaluate the way in which uncertainty in logK values propagates through thermodynamic models of the lead carbonate system and provide guidance for future modeling efforts. This was done by conducting a full factorial statistical analysis implemented using a custom Python (v3) code coupled with a PHREEQC (v1.4.2) geochemical model, along with batch lead solubility experiments. Two lead carbonate solid phases (cerussite and hydrocerussite) and nine aqueous lead complexes are considered in the geochemical model with conditions simulated ranging from pH 4 to 11 and dissolved inorganic carbon (DIC) ranging from 0 to 250 mg C/L. Main effect analysis indicates that model uncertainty is predominately associated with logK values for five species (in order of decreasing effect): hydrocerussite, , cerussite, PbOH+, and PbCO3o, with model uncertainty varying depending on the specific pH and DIC conditions simulated. Interaction effects show that logK values cannot be selected independently, as their influence on lead solubility is connected. Finally, by considering uncertainty in logK values it was possible for the thermodynamic model to match batch hydrocerussite solubility experimental data over a range of pH and DIC conditions. Six combinations of logK values that provided a good match between the simulated and experimental data were determined with the average difference between the simulated and experimental lead concentrations calculated to be 0.031 mg/L when the recommended logK value combination was used.