Uncertainty Quantification of the Mixing Enthalpy, Excess Heat Capacity and Gibbs Energy parameters of the LiF-KF System Using CALPHAD Modelling and Polynomial Chaos Expansion

Abstract

In the recent years, there has been a growing interest in molten salt reactors as a source of energy. To ensure molten salt reactor safety, it is vital to know the thermodynamic properties of the systems involved. An investigation into the uncertainty of the mixing enthalpy, excess heat capacity and Gibbs energy parameters of the LiF-KF system is presented in this study. The program FactSage 7.2 [19] is used, which takes optimized Gibbs energy parameters as an input and uses these to calculate phase diagram data and the values of different thermodynamic properties. The uncertainty is quantified using the polynomial chaos expansion, which analyzes the relationship between the input Gibbs energy parameters and the output; which is the phase diagram data, mixing enthalpy and excess heat capacity of the system. Firstly, an investigation into the accuracy of the polynomial chaos expansion, when applying different settings, is given. Once the most accurate settings are found, this expansion is used to generate many different samples of phase diagrams and the corresponding mixing enthalpy and excess heat capacity values. A margin of 10 Kelvin is then introduced as a maximum deviation from the experimentally determined phase diagram. The input Gibbs energy parameters and the mixing enthalpy and excess heat capacity values, that correlate with the phase diagrams within the margin of the experimentally determined phase diagram, can then be extracted. Once these values are known, the maximum uncertainty half width of the mixing enthalpy and excess heat capacity can be given that is still consistent with sensible phase diagrams. The found values for the maximum uncertainty half range are 1.65 kJ/mol for the mixing enthalpy which is a 35.6% deviation from the mixing enthalpy value computed with the original Gibbs energy parameters. For the excess heat capacity, 1.676 J/K/mol was found as a maximum uncertainty half range which is a 44.7% deviation from the excess heat capacity value computed with the original Gibbs energy parameters. The one-dimensional uncertainty half range (the uncertainty half range of one parameter assuming all other parameters possess zero uncertainty) of Gibbs energy parameters were calculated. Additionally, scattering plots are generated to illustrate the two- and three-dimensional uncertainty of the different Gibbs energy parameters.