Equilibrium Theory of Adsorption Column Dynamics for Adiabatic Systems

EQUILIBRIUM THEORY OF ADSORPTION COLUMN DYNAMICS FOR ADIABATIC SYSTEMS 

The importance of heat effects in adsorption column dynamics appears first to have been recognized by Leavitt in the early 1960s but detailed analysis came only some years later. The equilibrium theory of an adiabatic adsorption column, which is closely related to the equilibrium theory of multicomponent adsorption, was first developed by Amundson, Aris, and Swanson and the analysis was extended by Pan and Basmadjian ° who also verified some aspects of the theory in an experimental study of the adsorption of COj and 5A molecular sieve. These initial developments were expanded into a more complete treatment by Rhee, Amundson, and Heerdt as well as in later 

For an adiabatic two-component system (one adsorbable species in an inert carrier) the concentration profile consists, in general, of two transitions or mass transfer zones, over which both concentration and temperature vary, separated by a plateau region of constant temperature and concentration. However, the first transition may be degenerate, involving only a change in temperature with no change in concentration. This is sometimes referred to as a pure thermal wave. Also in certain cases where the watershed is crossed an additional transition may occur. 

As an example of the application of equilibrium theory to nonisothermal systems we consider here a plug flow system, with one adsorbable component, in which the concentration of adsorbable species and the temperature changes are both small enough to validate the constant velocity approximation. For such a system the differential mass and heat balance equations are 

These equations are of charcteristic hyperbolic fomi and represent kinematic waves with propagation velocities given by 

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