Multicomponent adsorption equilibria from impulse response chromatography

Abstract

The purpose of this work is to develop the theoretical framework of a method for obtaining multicomponent adsorption equilibrium data by dynamic, chromatographic type experiments. It is the multicomponent extension of a known principle, in use for determining single-component, and sometimes binary adsorption isotherms. It is based on analysing the response of a chromatographic column, equilibrated with a constant feed, to a small impulse perturbation of this background composition. In the single component and binary cases, a single response peak is obtained, the average exit time of which is related to the slope of the isotherm at the composition considered. In the multicomponent case, n − 1 response peaks are in general obtained, but the proper use of the information contained therein has remained an unresolved problem. In its principle, the method applies to gas-solid as well as to liquid-solid equilibria, although the experimental aspects, mainly peak detection, may be somewhat different. The development presented here is based on the following experimental procedure: a non-specific detector is used in conjunction with a conventional analytical chromatograph; n − 1 different impulse perturbations are made on the same multicomponent steady background flow, by injecting separately into the column n − 1 pure components of the mixture considered; the response to each input comprises n − 1 peaks, the average exit time and area of which are determined (first moments and zeroth partial moments of the response). In gas chromatography, a thermal conductivity detector may be used for example; in liquid chromatography, electric conductivity, UV, refractometric detection can be used, depending on the specific system. The mathematical development presented allows to work back from the experimental information to the partial derivatives of the adsorbed concentrations with respect to the fluid-phase concentrations (forming the Jacobian of the equilibria) when one non-adsorbed component is present in the mixture. The end-users procedure is particularly simple, and implies only to solve some linear equations and to invert a matrix. The procedure is then repeated for a number of discrete background compositions defining composition paths. The adsorbed-phase concentrations are obtained by numerical integration along such paths. Strategies are proposed, using straight paths through pure components, or pseudo-binary paths where only two concentrations vary; such choices allow simple boundary conditions to be used. The case where all components of the mixture are absorbed is still not completely solved in the framework of the present approach.