Sorption kinetics: measurement of surface resistance

Adsorption - The problem of measuring sorption kinetics in microporous adsorbents and distinguishing experimentally between surface resistance and internal diffusion is discussed and reviewed with...     

Diffusion mechanism of CO2 in 13X zeolite beads

A systematic study of the diffusion mechanism of CO₂ in commercial 13X zeolite beads is presented. In order to gain a complete understanding of the diffusion process of CO₂, kinetic measurements with a zero length column (ZLC) system and a volumetric apparatus have been carried out. The ZLC experiments were carried out on a single bead of zeolite 13X at 38 °C at a partial pressure of CO₂ of 0.1 bar, conditions representative of post-combustion capture. Experiments with different carrier gases clearly show that the diffusion process is controlled by the transport inside the macropores. Volumetric measurements using a Quantachrome Autosorb system were carried out at different concentrations. These experiments are without a carrier gas and the low pressure measurements show clearly Knudsen diffusion control in both the uptake cell and the bead macropores. At increasing CO₂ concentrations the transport mechanism shifts from Knudsen diffusion in the macropores to a completely heat limited process. Both sets of experiments are consistent with independent measurements of bead void fraction and tortuosity and confirm that under the range of conditions that are typical of a carbon capture process the system is controlled by macropore diffusion mechanisms.     

The uniquac associated-solution theory: vapor-liquid equilibria of binary systems containing one associating and one inert or active component

Brandani, V. and Evangelista, F., 1984. The UNIQUAC associated-solution theory: vapor-liquid equilibria of binary systems containing one associating and one inert or active component. Fluid Phase Equilibria, 17: 281–302.This article critically reconsiders UNIQUAC associated-solution theory, clearly identifying the physical approximations of the model. Data for binary vapor-liquid equilibria are correlated with this theory using pure-liquid association parameters determined by the method described in a preceding paper. For alcoholic systems, fitting of only two (inert component) or three parameters (active component) to the experimental data gives good improvement over the results from the original UNIQUAC equation. However, in the case of amine systems with inert components, such as saturated hydrocarbons, the UNIQUAC associated-solution theory fails unless a solvation effect is considered empirically.     

Net,excess and absolute adsorption in mixed gas adsorption

The formulation of a thermodynamic framework for mixtures based on absolute, excess or net adsorption is discussed and the qualitative dependence with pressure and fugacity is used to highlight a practical issue that arises when extending the formulations to mixtures and to the Ideal Adsorbed Solution Theory (IAST). Two important conclusions are derived: the correct fundamental thermodynamic variable is the absolute adsorbed amount; there is only one possible definition of the ideal adsorbed solution and whichever starting point is used the same final IAST equations are obtained, contrary to what has been reported in the literature.     

Liquid Phase Counter-Diffusion Measurements of Aromatics in Silicalite Using the ZLC Method

We have developed a liquid phase Zero Length Column apparatus in order to study the counter-diffusion of aromatic compounds, benzene, toluene, m-, o- and p-xylene, in silicalite crystals. Our results show ZLC desorption curves that are consistent with the model of Brandani and Ruthven (1995). The apparent diffusivities fall in a narrow range of approximately 1 order of magnitude for all the investigated molecules. The results for o-xylene led us to investigate in detail possible mechanisms that can give erroneous results when applying the liquid ZLC technique. We have derived solutions to models for valve leakage and obtained an explanation to the experimental results.     

Flowrate correction for the determination of isotherms and Darken thermodynamic factors from Zero Length Column (ZLC) experiments

The ZLC method is a simple and rapid approach to measure adsorption equilibrium isotherms. When extending this technique to the measurement of large concentration steps, the primary problem is how to estimate the outlet flowrate from the measured concentration signal. In this paper, two different corrections to calculate the outlet flowrate are introduced. Based on simulations of the ZLC system that are in good agreement with reported experimental results, a series of desorption cases were simulated. Isotherms were calculated using the two approximations of the outlet flowrate. The comparisons are used to identify the range in which the approximations are applicable. Darken’s thermodynamic correction factors were also calculated to verify the validity of the flow corrections.     

Analysis of ZLC desorption curves for gaseous systems

The theoretical model and underlying assumptions used in the analysis of ZLC (zero length column) desorption curves are examined in detail. It is shown that the long time analysis generally yields reliable diffusivity values although, if the initial equilibrium condition is not properly established there will be significant error in the apparent equilibrium constant. The short time analysis is much more sensitive to such errors and a modified way of data analysis is suggested to overcome this problem. Varying the initial equilibration time provides an alternative ZLC experiment that can be used to establish the nature of the rate controlling mass transfer resistance. The utility of this approach is illustrated experimentally for the system C₃H₈-13X zeolite.     

Net,excess and absolute adsorption and adsorption of helium

The definitions of absolute, excess and net adsorption in microporous materials are used to identify the correct limits at zero and infinite pressure. Absolute adsorption is shown to be the fundamental thermodynamic property and methods to determine the solid density that includes the micropore volume are discussed. A simple means to define when it is necessary to distinguish between the three definitions at low pressure is presented. To highlight the practical implications of the analysis the case of adsorption of helium is considered in detail and a combination of experiments and molecular simulations is used to clarify how to interpret adsorption measurements for weakly adsorbed components.     

Heat Effects in ZLC Experiments

The problem of nonisothermal desorption in a zero length column (ZLC) experiment is considered theoretically. Simple analytical expressions for the ZLC desorption curve are derived for certain limiting situations in which the governing equations reduce to a linear form. More general numerical solutions are calculated for a wide range of experimental conditions assuming both negligible mass transfer resistance and finite mass transfer resistance controlled by intraparticle diffusion. A simple criterion for negligible thermal effects is developed. It is shown that when the ZLC technique is applied to the measurement of diffusion in unaggregated zeolite crystals, as originally intended, heat effects are generally insignificant. However, when applied to the measurement of macropore diffusion in relatively large adsorbent particles heat effects can become important and may cause major modification of both the desorption rate and the shape of the desorption curve. A recent experimental ZLC study carried out with commercial adsorbent particles, under conditions of macropore diffusion control, showed an anomalous dependence of the desorption rate on both temperature and particle size. These effects can be qualitatively explained by the nonisothermal model. A more precise quantitative representation of these experiments will require a more refined model incorporating a nonlinear equilibrium isotherm as well as intraparticle diffusional resistance.