Convective Approximation of Adsorption Processes

Abstract

In many adsorption processes, convection of at least one species is slow by design and this feature may be exploited to gain understanding and simplify calculations. Without convection, species balances integrate exactly to yield algebraic conservation laws and the dynamic evolution to periodicity is hastened by elimination of the slowest waves. Thermal convection, for example, is typically weak in bulk pressure swing adsorption processes and the expedient of dropping thermal convection leads to a conservation law in which equilibrium adiabats (not isotherms) govern adsorbent performance. Numerical computations of a simple process with and without thermal convection confirm that weak convection can considerably prolong dynamic evolution to the periodic state. Without thermal convection however calculations yield a rough representation of the full solution as weak convection has significant (singular) effect near boundaries and within the column over long times. Computations directed to resolve spatial boundary layers and multiple scales in time are proposed to achieve fast and consistent dynamic simulation of adsorption processes to their periodic states.

Instantaneous convection if the temporal mean convective flux is small. By explicit introduction of a small parameter to zero the mean convective flux at leading order, multiple time scale analysis proceeds as described herein. The perturbation in this case is regular and consequently boundary layer analysis is not required.