Modelling the Dynamic Behaviour of a Packed-bed Adsorber

Abstract

This paper is concerned with the dynamic behaviour of packed-bed dyeing machines in which both axial and radial flow are considered. In both cases, the effects of reverse flow are investigated by a mathematical formulation of the flow of dye solution through a packed bed, bulk flow, dispersive flow, and adsorption processes at individual fibre surfaces being taken into account. A comparison of the dynamic behaviour of axial- and radial-flow reactors shows that there are advantages to be gained by reversing the flow. These advantages include a decrease in time to reach a level dyeing and a faster attainment of equilibrium. Outward radial flow can result in savings of up to 41% in time to achieve equilibrium when compared with axial-flow operation under similar conditions. Inward radial flow provides savings of up to 15% on the same basis. The conclusion of this study is that, compared with an axial-flow reactor, the radial-flow reactor provides a shorter equilibrium time and a faster rate of over-all dyeing across the bed, and these advantages are enhanced by using reverse flows. Although this is well known in industry, it has not previously been rigorously demonstrated mathematically. The model also provides the basis for describing such machines in order that efficient design and accurate on-line control of several such machines in a dyehouse may he made. The model is sufficiently flexible to allow the simulation of additions or removal of material (i.e., dye additives, etc.) from the dyebath. It is readily demonstrable that adding dyestuff in a given way as a precise function of time can be advantageous to the attainment of equilibrium in the minimum possible time.