An improved model incorporating Pitzer’s equations for calculation of thermodynamic properties of pore solutions implemented into an efficient program code
Introduction
The crystal growth of salts in porous building materials is generally considered as a major cause of damage of such materials. Salts do also influence the hygric properties of building materials. For instance, due to their hygroscopicity salts strongly affect the sorption isotherm of a material and dissolved salts alter the capillary transport properties, e.g. solution density and viscosity, of the pore liquid. Finally, salts present in crystalline form change the pore structure, i.e. the pore size distribution and permeability of materials. Therefore, in heat, air and moisture transport models (HAM) for the evaluation of the hygric behavior of building materials and structures, an accurate representation of the behavior of salts and salt mixtures is required. This includes (1) an appropriate model for the representation of the thermodynamic properties of aqueous pore solutions and (2) the ability to treat the relevant solid–liquid phase equilibria.
In geochemical modeling the molality-based Pitzer formalism [1] was successfully applied in chemical equilibrium models [2], [3] for the representation of thermodynamic properties of natural waters. For instance, PHRQPITZ [4] is a widely used modeling code that is largely based on the model parameters at 25 °C of Harvie et al. [3]. The same database of model parameters was also used for the calculation of equilibria in cement–water systems [5], [6]. More recently, expanded models with greater compositional flexibility and application to broader temperature ranges were published [7], [8]. Several of these models describe chloride and sulfate mineral solubilities in concentrated brines. Only one model [9] includes nitrates which are quite often present in building materials. However, there are considerable problems with the modeling of nitrates as their solubilities in mixed solutions extend to very high ionic strengths. This was one of the reasons why electrolyte solution models that are used in aerosol chemistry [10] are based on the mole fraction Pitzer model rather than on the molality-based approach, which could not be successfully extended to the extremely high concentrations in atmospheric aqueous phase chemistry. The mole fraction model, however, is computationally less efficient which limits its use with other models, e.g. its incorporation into transport models.
In the present work we discuss a molality-based model and its limitations for the prediction of phase equilibria in multicomponent salt systems containing nitrate. It is shown that existing parameters may cause erroneous results if applied for the prediction of solubilities in mixed solutions containing chloride and nitrate at high ionic strength. Using improved parameters for single electrolyte solutions and an extended form of the Pitzer equations significantly improved the model predictions. The approach is validated by the prediction of solubilities in the and the systems and the limitations of the model are discussed. A computer code in form of an optimized C++ library is provided that can be incorporated into transport or chemical reaction models.
Section snippets
Equilibrium constants and ion interaction approach
Given a salt of composition consisting of νM positive ions M of charge zM, νX negative ions X of charge zX and ν0 molecules of water the equilibrium constant KMX of the dissolution reaction is given bywhere mM, mX, γM and γX represent the molalities and activity coefficients of the cations and anions, respectively, and aw is the water activity defined aswhere ϕ is the osmotic coefficient and Mw = 1.801528 × 10−2 kg mol−1 is the molar
Validation, limitation and application of the model
The purpose of the model is not only to calculate the properties of the aqueous solutions that form the parameterization database but also to predict the properties of more complex mixtures. While binary and common-ion ternary experimental data are used to determine all model parameters, data from more complex systems are used to validate the model. Therefore, the model can be tested by comparing predicted solubilities with the available data of mixed systems containing more than three ions. We
Conclusions
An extended Pitzer formalism based on the ion interaction model [1] is presented for calculating water activity, activity coefficients and saturation ratios in mixed salt solutions to high concentrations. The algorithm is implemented and provided as optimized C++ library for use in other programs and as dynamic link library for use in MS-Excel. The implementation allows the usage of user defined parameter sets in external data files. The calculation algorithm combines flexibility and efficiency
Acknowledgement
Financial support of this research by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged.
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