MULTICOMPONENT ADSORPTION EQUILIBRIA FROM IMPULSE-RESPONSE CHROMATOGRAPHY

The purpose of this work is to develop the theoretical framework of a method for obtaining multicomponent adsorption equilibrium data by dyn amic, chromatographic type experiments. It is the multicomponent exten sion of a known principle, in use for determining single-component, an d sometimes binary adsorption isotherms. It is based on analysing the response of a chromatographic column, equilibrated with a constant fee d, to a small impulse perturbation of this background composition. In the single component and binary cases, a single response peak is obtai ned, the average exit time of which is related to the slope of the iso therm at the composition considered. In the multicomponent case, n - 1 response peaks are in general obtained, but the proper use of the inf ormation 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 dif ferent impulse perturbations are made on the same multicomponent stead y background flow, by injecting separately into the column n - 1 pure components of the mixture considered; the response to each input compr ises n - 1 peaks, the average exit time and area of which are determin ed (first moments and zeroth partial moments of the response). In gas chromatography, a thermal conductivity detector may be used for exampl e; in liquid chromatography, electric conductivity, UV, refractometric detection can be used, depending on the specific system. The mathemat ical development presented allows to work back from the experimental i nformation to the partial derivatives of the adsorbed concentrations w ith respect to the fluid-phase concentrations (forming the Jacobian of the equilibria) when one non-adsorbed component is present in the mix ture. 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 defi ning composition paths. The adsorbed-phase concentrations are obtained by numerical integration along such paths. Strategies are proposed us ing straight paths through pure components, or pseudo-binary paths whe re only two concentrations vary; such choices allow simple boundary co nditions to be used. The case where all components of the mixture are absorbed is still not completely solved in the framework of the presen t approach. Copyright (C) 1996 Elsevier Science Ltd.