Application of Mixture Models to Solubility Calculations, Using Sodium Oxalate as an Example

Abstract

The solubility of solids in nuclear waste impacts many separation processes including evaporator set-points, pressure drops in ion-exchange columns, as well as the washing and leaching of sludge. Scheffe and Cox type empirical mixture models have long been used to model crystal stability in nuclear waste glass melters, and this methodology has now started being employed to model solubility in aqueous nuclear wastes. The large amount of theory and data available for aqueous systems allows for the opportunity to evaluate mixture models for solubility calculations. In the present paper, it is shown that Scheffe type mixture models should be employed when the pure component is the standard state of interest whereas the Cox type mixture models should be employed when infinite dilution is the standard state. An example application is used to demonstrate that mixture models can be used to predict solubility, even across a phase boundary, when combined with the standard thermodynamic equations for the solubility product. The example employed is Na₂C₂O₄ solubility in aqueous NaNO₃ solutions, which can be thought of as a simplified high-level nuclear waste supernatant.

Keywords:

• Mixture model
• nuclear waste
• sodium oxalate
• solubility

ACKNOWLEDGEMENT

The work described in this paper was performed for the United States Department of Energy under contract DE-AC27–01RV14136, to support the Hanford Tank Waste Treatment and Immobilization Plant Project. The development of this paper was greatly aided by technical discussions over the years with Pavel Hrma, John Vienna, and Greg Piepel. Keith Abel performed a manuscript review. Karen Reynolds performed grammatical editing and formatted the document for submission.