SIMPLIFIED PREDICTIONS OF BREAKTHROUGH FRONTS FOR CONSTANT-PATTERN ADSORPTION AND ION-EXCHANGE

The loading cycle of many (perhaps most) commercial adsorption and ion exchange operations involves a favorable isotherm. Concentration fron ts for favorable isotherms approach a constant pattern for long bed le ngths, and most industrial adsorption and ion exchange operations use sufficiently deep beds that the constant-pattern conditions are approa ched. Once a constant pattern is established. the region around the fr ont can be analyzed using conventional methods developed for continuou s absorption/stripping operations, but the location of the feed and wi thdrawal points must be assumed to move down the bed at the same rate at which the front moves. Using this approach, the constant-pattern fr ont can be calculated for any shape of constant-pattern isotherm. The dimensionless distance in the bed is expressed in terms of transfer un its, and the shape of the front can be evaluated graphically even when the relations can not be integrated analytically. This procedure is i llustrated for binary ion exchange isotherms. In the simplest cases, e xchange of ions with like charge, the integration can be performed ana lytically. For other cases, numerical and graphical solutions are illu strated.