Ideal adsorbed solution theory solved with direct search minimisation

The ideal adsorbed solution theory (IAST) is the most widespread theory for multicomponent adsorption interpretation. It postulates the existence of an adsorbed phase which behaves as a Raoult ideal solution. The theory results in a system of nonlinear algebraic equations which are solved to know the composition of the adsorbed mixture at equilibrium. In this paper an investigation on an alternative method for the IAST equations solution is proposed which is based on the minimisation of an objective function representing the iso-spreading pressure condition. This approach to the solution of the IAST equations reduces in some cases the computational effort and mitigates the issues of the currently adopted approaches (inversion of functions and initial guess). For binary systems, direct search minimisation approach is faster than the classic IAST equations solution approach up to 19.0 (Dual Langmuir isotherm) and 22.7 times (Toth isotherm). In ternary systems, this difference decreases to 10.4 (O'Brien and Myers isotherm) times. Compared to FASTIAS approach, direct search minimisation is up to 4.2 times slower in ternary systems.