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Incorporating multicomponent, multiphase, complex chemical equilibrium calculations into process and multiphysics models can provide significant insights into industrial processes that current modelling or measurements cannot. Equilibrium calculations are however, in general, omitted or incorporated in a simplified manner due to their computational expense. Several methods have been developed to accelerate these calculations. A new accelerator algorithm was developed (Roos and Zietsman, 2021) based on phase diagram geometry, the Gibbs phase rule, and the lever rule to include equilibrium calculations into models more efficiently. This framework of established thermochemical theory provides a sound basis for discretisation and interpolation, and allows the accelerator algorithm to work in systems with any number of components. The work presented here aimed to test accelerator performance and demonstrate that it has the capability of achieving noteworthy levels of acceleration while maintaining acceptable accuracy. The accelerator was tested on ten 2-component systems, four 3-component systems, a simplified 4-component ilmenite smelting system, and a simplified 5-component iron- and steelmaking system. As the number of system components increased, so did the computational expense of direct equilibrium calculations. This translated to larger acceleration factors for higher-order systems — from 20 in 2-component systems to 1000 in the 5-component system. In a small number of cases it was observed that the acceleration factor was smaller than one during interpolation. This was attributed to slow searching times for suitable interpolation cells from the database. Phase composition interpolation errors are less than 1 × 10-2 mol mol−1. This translates to an interpolated phase composition being accurate to within 99 % of the calculated composition and results in phase fraction errors of 1 × 10-2 and less. In a very small number of cases the interpolation errors made on physical and thermochemical properties are as high 10 %. This is because system properties are calculated as a phase fraction weighted sum of phase properties and errors made on system properties can therefore become large due to interpolation errors being made twice. However, the majority of errors made on physical and thermochemical properties are in the order of 1 % and less. The level of accuracy achieved by the accelerator algorithm was acceptable for the chosen discretisation tolerances. [ABSTRACT FROM AUTHOR]

A new accelerator algorithm was developed based on phase diagram geometry to include large number of equilibrium calculations into process and multiphysics models more efficiently. These models require thermochemical properties from equilibrium calculations such as phase compositions and phase fractions, heat capacity and enthalpy. When an equilibrium calculation is performed, the calculated thermochemical properties are stored in a geometrical database on the boundaries of the phase region at the calculated phase compositions. The developed accelerator can function with any commercial or open source equilibrium calculation software. In this work, ChemAppPy was used. The lever rule can be used to interpolate thermochemical properties at any system composition within a phase region based on thermochemical properties stored on the phase region's boundaries. It is therefore only necessary to discretise boundaries and not entire phase regions, except for single-phase regions. A generic form of the lever rule is presented that can be used in any phase region and in systems with any number of system components. The Gibbs phase rule is used to calculate the dimensionality of phase region boundaries and to determine the minimum number of equilibrium calculations needed to discretise these boundaries. This framework of established thermochemical theory provides a sound basis for the discretisation and interpolation routines of the algorithm and allows the accelerator to be used with systems with any number of components. The functionality of the accelerator algorithm was tested in a number of two- and three-component systems as these systems could still be easily visualised to verify the functioning of the newly developed algorithm. [ABSTRACT FROM AUTHOR]