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## Determination of mixture adsorption equilibrium data from breakthrough curves

Integration area for a simple breakthrough curve
Integration area of the weaker adsorbed component, the blue labeled area of the roll-up effect have to be subtracted.

### Mixture Adsorption Data from a Breakthrough Curve

In general, the dynamic method is suitable to investigate competitive adsorption. With this technique the user can determine mixture sorption equilibria by applying two different options.

• the carrier gas is assumed as non-adsorbable (i.e. He) and the gas mixture of adsorptive 1 and adsorptive 2 will be dosed simultaneous. For this more complicated case the result seems similar to the right side of the figure above). By integration of both curves both partial equilibria can be determined. The sum of both values will give the total value for the investigated binary mixture.

The yielded mixture data are helpful to verify predictions of mixture behavoir by thermodynamic models. Such predictions can be achieved from pure gas isotherms by multicomponent approaches, i.e. by Multi Component Languir isotherms or by Ideal Adsorbed Solution Theory.

### Evaluation of a Breakthrough Curve

From the highlighted area the total amount of the adsorbed species is given by: If the ideal gas law is applied, the molar flow rates can be expressed by volumetric flow rates and the volume fractions. In these equations all physical variables subscribed with “in” correspond to the conditions at the adsorber inlet. All indicated variables with “out” are quantities for the adsorber outlet. In most cases the adsorptive concentration and inlet volume flow is kept constant during the whole experiment. Therefore the equation can be simplified to: For high diluted systems the outgoing volume flow rate can be considered as constant and equal to the value of  inlet volumetric flow rate of the adsorber (neglecting the adsorptive volume). Then the equation is furthermore simplified to: The equations show that the molar flux of the adsorptive is the product of the outgoing volumetric flow rate and the outgoing volume fraction. Therefore, an error for the assumption of a constant volume flow during the whole bed is only present for the second segment – the mass transfer zone – since in the first segment the volume fraction is zero and in the third segment the assumption of inlet volumetric flow rate being equal to outlet volumetric flow rate is valid.

In most industrial applications impurities are present at very low concentrations (i.e. CO2 removal from air, removal of toxic impurities from waste air, compliance of air-pollution law). Here a competitive adsorption of the main components can not be neclected. Furthermore the equation above is valid for such high dilutions. An evaluation of a breakthrough curve is therefore easily possible. Based on this considerations the dynamic method is the best choice to investigate the suitability of adsorbents for separation of impurities in highly diluted systems.

Mixture adsorption equilibria are easily accessible by the dynamic method. An automatic measurement of a mixture gas adsorption isotherm with variable partial pressures and a constant total pressure is possible. For high diluted mixtures the dynamic method would be the best choice. WordPress Cookie Notice by Real Cookie Banner