Efficient Solution of the Ideal Adsorbed Solution Theory (IAST) Equations for General Single Component Adsorption Isotherms

The Ideal Adsorption Solution Theory (IAST) of Myers and Prausnitz [1] provides a powerful tool to calculate multi-component adsorption equilibria based on the knowledge about the single component adsorption isotherms. An extension of the theory to liquid phase systems was published by Radke and Prausnitz [2]. An important characteristic of the implementation of IAST consists in solving an implicit system of equations. Only for a small number of simple single component isotherm models analytical solutions can be derived. Recently, Ilić et al [3] derived an explicit solution for the calculation of adsorbed phase concentrations of binary systems whose individual component behavior can be represented by second order (quadratic) adsorption isotherms. However, for most single component isotherms time consuming iterative technique must be applied (see for example [4]). This work generalizes the ideas of Ilić et al [3] to multi-component mixtures and to rather general single component adsorption isotherm models. The only requirement needed for the derivation of an efficient solution of the set of the IAST equations is that the single component loadings are strictly increasing functions of the corresponding fluid phase concentrations. This allows the treatment of rather general individual isotherms that e.g. can be characterized by one or more inflection points. The approach presented is first of all characterized by the reduction of the nonlinear system of IAST equations to a single scalar equation in a single variable. It is an important and useful property of this equation, that the key unknown is simple to identify. Subsequently, the equilibrium loadings of interest can be calculated explicitly. The approach provides further analytical expressions for the partial derivatives of the predicted equilibrium loadings. This feature supports significantly the efficiency of numerical algorithms for calculations of multi-component adsorption dynamics in fixed-beds. The strength of the proposed approach in deriving efficiently the competitive equilibrium loadings predicted by IAST and their partial derivatives will be illustrated in a case study. Overloaded elution profiles of mixtures of several phenyl-n-alkenes on a carbon column using acetonitrile as the mobile phase will be generated based on the complex single component adsorption isotherms published in [5]. References [1] A. L. Myers and J. M. Prausnitz, Thermodynamics of mixed-gas adsorption, A. I. Ch. E. Journal 11 (1965), 121–127. [2] C. J. Radke and J. M. Prausnitz, Thermodynamics of multi-solute adsorption from dilute liquid solutions, A. I. Ch. E. Journal 18 (1972), 761–768. [3] M. Ilić, D. Flockerzi, and A. Seidel-Morgenstern, A thermodynamically consistent explicit competitive adsorption isotherm model based on second order single component behaviour, Journal of Chromatography A, 1217 (2010), 2132-2137. [4] D. D. Do, Adsorption analysis: equilibria and kinetics, Series on Chemical Engineering, Vol. 2, Imperial College Press, 1998. [5] M. Diack and G. Guiochon, Adsorption isotherms and overloaded elution profiles of phenyl-n-alkanes on porous carbon in liquid chromatography, Langmuir 8 (1992), 1587–1593