Consistency of energy and material balances for bidisperse particles in fixed-bed adsorption and related applications

This paper develops material and energy balances for fixed-bed adsorption of a multicomponent nonideal gas in bidisperse particles by defining enthalpies from thermodynamic paths chosen such that the reference states are an ideal gas for the fluid-phase and adsorbate-free solid for the adsorbent. The balances are developed in detail for a three-domain system: nanoporous domains, macropore space, and interstitial fluid. It is also shown that material and energy balances may be easily developed from the same enthalpy definitions for use in batch, stirred tank, or moving-bed adsorption systems. Material balances are developed first and are subsequently used to simplify the energy balances such that terms involving reference states cancel out of the equations. Simplifying assumptions are applied to the final equation set to obtain equations that resemble, but are somewhat different from, frequently used forms. A major difference, resulting from the use of thermodynamic paths, is often found in the treatment of heat capacities and heats of adsorption.