Five definitions of adsorption and their relevance to the formulation of dynamic mass balances in gas adsorption columns

Numerous dynamic mass balances in the literature that describe the adsorption of gases in a column are written in terms of actual or absolute adsorption, while unwittingly and incorrectly utilizing excess adsorption isotherms. Perhaps this is because the actual and absolute adsorption isotherms cannot be experimentally measured nor predicted without making uncertain assumptions. The objective here was to derive unambiguous relationships between actual, absolute, excess, net and column amounts adsorbed that provide a straightforward understanding of the subtle differences between these quantities and that provide a simple means for incorporating them into dynamic mass balances. For this purpose, the actual, absolute, excess, net and column amounts adsorbed (loadings) were clearly defined, along with various volumes, porosities and densities that exist inside and outside an adsorbent contained in a column with a gaseous adsorbate. These adsorption definitions and quantities were used to derive four interconversion relationships for each type of adsorption in terms of the actual loading. The resulting expressions, based on intensive properties, can be used to relate any adsorption definition to any other adsorption definition. These relationships were also used to derive five dynamic mass balances, one for each type of adsorption. The similarities and differences in the terms between each of these five dynamic mass balances were discussed, along with their applicability to real world problems. In some cases at low pressure where the isotherms do not differ appreciably, it may be approximately correct to use excess or net adsorption isotherms in a dynamic mass balance written in terms of actual or absolute adsorption. However, the extent of the incorrectness is unknown due to mass transfer effects. So, it is recommended to use the dynamic mass balance with its specific type of adsorption, most likely excess adsorption. Then, when certain assumptions are made about the adsorbing and non-adsorbing void fractions, these expressions can be readily used in adsorption process simulation.