(102b) Robust Algorithms for the Solution of the Ideal Adsorbed Solution Theory Equations

The Ideal Adsorbed Solution Theory is used extensively for the prediction of multicomponent adsorption equilibria, yet based on recent publications there appears to be a lack of understanding of when solution algorithms are guaranteed to converge.

In its original formulation the IAST is used to predict the behaviour of mixtures starting from the pure component isotherms. The solution of the IAST equations is also needed when non-ideality of the adsorbed phase is considered, since the IAST is used in the definition of the reference state for the mixture in the definition of the activity coefficients. The availabitily of robust methods to solve the IAST equations is therefore at the heart of thermodynamically consistent approaches to describe multicomponent adsorption.

We investigate in detail the robustness and convergence criteria for the nested loop and the Fast-IAS algorithms. A formal proof of guaranteed convergence is presented for the nested loop method of Valenzuela and Myers. Based on the analysis of this algorithm it is also possible to understand some partial instabilities present in the Fast-IAS procedure.

Detailed comparisons of the different algorithms is presented to show also that it is possible to extend the Fast-IAS to cases where there are no analytical expressions available for the spreading pressure and to non-type I isotherms.