Experimental Uncertainties in Volumetric Methods for Measuring Equilibrium Adsorption

Knowledge of adsorption equilibrium is essential in many industrial processes, including increasingly important technologies such as fuel cells and CO2 sequestration. Developing reliable mathematical models for adsorption requires accurate experimental data. Experimental methods based on volumetric, gravimetric, and chromatographic techniques have all been used to obtain such data. Currently, two volumetric methods are widely used to measure supercritical gas adsorption on heterogeneous matrices such as activated carbon and coal. These two methods differ in the manner in which the gas is injected into the equilibrium cell for adsorption. The methods are referred to as fixed-pressure and fixed-volume. In this paper, we discuss the details of these experimental designs and error analyses for these two volumetric techniques. Case studies involving pure-fluid adsorption measurements are used to demonstrate both the efficacy and pitfalls of these volumetric methods. Further, case studies are also used to highlight differences in the uncertainties associated with calculation of excess adsorption from the experimentally measured quantities. The results indicate that the fixed-volume method is susceptible to larger experimental errors than the fixed-pressure method for equivalent experimental setups. Specifically, for the case study reported here, the average experimental uncertainties in the amount adsorbed for the fixed-pressure and fixed-volume method were 12% and 42%, respectively. These large experimental uncertainties for the fixed-volume method at the higher pressures result mainly from the uncertainty in the amount injected. Further, Monte Carlo analysis was used to validate these findings, yielding comparable results, thus providing confirmation of the analytical expressions used in the error analysis. Our analysis indicates a significant reduction in expected uncertainties of the fixed-volume injection method may be realized by utilizing an optimized ratio of cell volumes (reference and sample cells) and by having the least possible void fraction in the sample cell.