Accelerating complex chemical equilibrium calculations — A review

Incorporating multicomponent, multiphase, high-temperature, complex chemical equilibrium calculations into process and multiphysics models can provide significant insights into materials, processes and equipment. We refer to applications where the inclusion of these calculations provided insights that would otherwise be difficult to obtain. From these examples, the advantages and importance of including complex equilibria into models are clear for cases where more accurate descriptions of practically relevant systems are needed. Equilibrium calculations are, in general, omitted or incorporated in a simplified manner due to their computational expense. The equilibrium state of a complex chemical system is determined by minimising the Gibbs free energy for a given set of system component concentrations, temperature, and pressure. This minimisation routine is computationally expensive and makes direct integration of chemical equilibrium calculations into models infeasible. There have been many attempts to, in one way or another, accelerate these calculations. This includes methods such as creating look-up tables prior to the simulation or in-situ, fitting piecewise polynomial functions to thermochemical properties, phase diagram discretisation, sensitivity derivatives, machine-learning algorithms, and parallelisation. Pre-calculated databases tend to become very large and require much storage space, even when unstructured grids are used or piece-wise polynomials fitted. Neural network results do not adhere to physical laws such as mass conservation and large training sets are required to reduce this error. In-situ or on-demand methods of creating a database shows great promise because only the thermochemical regions that are of interest to the model are captured in the database, reducing the storage size and the amount of data to search through. No prior knowledge of the system is required to create the database. The Gibbs phase rule can be used to determine which geometrical features of a phase diagram to discretise and create a sparse database that covers large temperature, pressure and compositional ranges. The lever rule can then be used for fast and accurate interpolation between data points. Established thermochemical theory provides security for the decisions made within the discretisation and interpolation algorithms. Based on this review, an in-situ phase diagram discretisation method strongly based on thermochemical theory such as the Gibbs phase rule and the lever rule holds potential for significant acceleration of complex chemical equilibrium calculations.