Fixed-bed adsorption with nonplug flow: Perturbation solution for constant pattern behavior

Adsorption of a dilute solute from a fluid in nonplug flow through a fixed bed is investigated via a perturbation approach. The continuity equation for fixed-bed adsorption with axial dispersion is solved for the constant pattern concentration profile with the axial velocity characterized by a general axisymmetric function and the system having no resistances to external or intraparticle mass transfer. The isotherm is slightly favorable (i.e., concave downward) in order to justify the assumption that axial gradients of concentration are independent of the radial coordinate in the bed, as in the classical problem of Taylor diffusion. A series expansion of a general isotherm is used to treat adsorption equilibrium. The solution reveals the formation of a radial gradient of fluid-phase concentration and breakthrough behavior at the bed outlet dependent on the nonlinearity of the isotherm and the magnitude of the nonplug-flow-velocity profile. The results can be used to predict the breadth of the breakthrough wave of many chromatographic-type processes for packed beds and slightly favorable isotherms.