(370e) Surface Excess Variables: Adsorption Isotherms and Column Dynamics

The pore size distribution of the adsorbent plays a major role in controlling the adsorption process, thus affecting the measurement as well as the interpretation of supercritical excess adsorption isotherms. Upon adsorption, the volume occupied by the adsorbed phase becomes inaccessible to the bulk fluid molecules and therefore has to be taken into account when measuring high pressure adsorption isotherms: a buoyancy correction is required in a gravimetric experiment, whereas a correction to the dead-space volume available to the bulk phase is needed when the volumetric method is applied. As a matter of fact, as both the size and composition of the adsorbed phase cannot be determined accurately, the so-called surface excess has been introduced, which is regarded as the truly measurable quantity in an adsorption experiment, whatever technique is used [1].

In this study, an adsorption mechanism is proposed, where a distinction is made between micropores and larger pores, the former being accessible only by an adsorbed phase. A new experimentally measurable variable is defined that is consistent with the proposed approach and differs from the traditional excess adsorbed amount in the treatment of the adsorbed phase volume. An adsorption isotherm equation that assumes a Langmuir behavior for the adsorbed phase is derived and is used to describe supercritical CO₂ excess adsorption isotherms that have been measured on three different adsorbents, namely activated carbon, zeolites and silica gel. Differences are highlighted between the new and the traditional approach, with the former allowing for an interpretation of the obtained excess adsorption isotherms that is physically more consistent.

This newly defined excess variable is further applied to study the dynamics of adsorption columns. A fixed-bed adsorption model is derived that uses excess adsorption variables instead of the commonly adopted absolute adsorbed amounts. From a mathematical point of view, the formalism of the model equations is equivalent to the one using the traditional excess adsorbed amount [2] or absolute adsorbed amounts [3], thus highlighting the generality of the present approach. Moreover, beside the convenience of a quantity that can be obtained experimentally, the use of surface excess allows to takes into account for porosity variations inside the bed caused by a varying volume of the adsorbed phase without introducing any new variable. The same solution methodology can therefore be applied as for the traditional approach that uses absolute isotherms and neglects the volume occupied by the adsorbed phase.

One-component (CO₂) adsorption from an inert gas (helium) is considered in a fixed bed column packed with activated carbon. The local equilibrium theory is applied and the model equations are solved through the method of characteristics [4], thus highlighting the versatility of this framework. Two classical Riemann problems are discussed, namely adsorption on a clean bed and elution of an initially saturated bed. It is shown that fluid velocity is strongly affected by both adsorption and porosity variations inside the bed, the latter being particularly evident at large bulk densities. Moreover, a significant overestimation of the breakthrough time of the injected fluid is predicted by the models that neglect porosity changes as compared to those that use excess adsorption variables.

[1] Sircar, S. J. Chem. Soc. Faraday Trans. 1985, 81, 1527–1540.

[2] Sircar, S. J. Chem. Soc. Faraday Trans. 1985, 81, 1541–1545.

[3] Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984.

[4] Rhee, H.-K.; Rutherford, A.; Amundson, N. R. First order partial differential equations. Vol. 1: Theory and application of single equations; Prentice-Hall: Englewood Cliffs, N.J., 1986.