Geometric acceleration of complex chemical equilibrium calculations for inclusion in multiphysics and process models

Abstract

Incorporating multi-component, multi-phase, high-temperature, complex chemical equilibrium calculations into multiphysics and process models can provide valuable insights into industrial processes and equipment that current modelling methods and measurements cannot. The equilibrium state of a thermochemical system is determined by minimising the Gibbs energy for a given set of system component concentrations, temperature, and pressure, and becomes computationally expensive when a large number of these calculations have to be performed. This makes direct integration of chemical equilibrium calculations into models infeasible.

There have been many attempts to, in one way or another, accelerate these calculations. The strengths of these existing acceleration methods, together with fundamental thermochemical theory, were used to conceptualise and develop a new accelerator algorithm. The accelerator algorithm uses a system's phase diagram and the Gibbs phase rule to map the thermochemical system to geometric space by storing calculated physical and thermochemical properties in-situ for later recall and interpolation. Linear interpolation with the lever rule in geometric space is less computationally expensive than Gibbs energy minimisation. The advantage of populating a database in-situ is that data is only generated and stored in the regions accessed by the model as it is being solved. The accelerator algorithm is based on established thermochemical theory, and the generality thereof allows the accelerator to be used in any system, regardless of the number of components.

The performance of the accelerator algorithm was tested on a number of two- and three-component systems as well as on two industry-related processes; a simplified four-component ilmenite smelting system and a simplified five-component iron- and steelmaking system. As the number of system components increase, so does the computational expense of equilibrium calculations. This translated to larger acceleration factors being achieved as the number of system components increased -- from as high as 20 in two-component systems to 1000 in the four- and five-component systems. Interpolation errors made on phase compositions were in the order of 10E-2 mole\mole and less. This would translate to an interpolated phase composition being accurate to within 99% of the calculated phase composition. The majority of interpolation errors made on physical and thermochemical properties were in the order of 1% and less.

The developed algorithm showed noteworthy acceleration of equilibrium calculations when tested on the two industry-related processes while maintaining acceptable levels of accuracy. There is great potential for the accelerator algorithm to make the inclusion of equilibrium calculations in models with many system components feasible. The performance of the accelerator can be improved by transferring the algorithm to a more computationally efficient compiled programming language and utilising a more performant database system.