Hydrodynamics of Countercurrent Packed Bed Exposed to Periodic Variations of Inlet VelocityAnalysis

Functional analysis has been carried out of the solution of an earlier formulated mathematical model (Ind. Eng. Chem. Res. 2004, 43, 8317) of a countercurrent packed-bed column exposed to periodic oscillations of inlet liquid velocity. It has been found that, for stable operation of the column, free of unbounded oscillations of the mean liquid holdup, it is necessary and sufficient that the local derivative of liquid holdup with respect to liquid velocity (*l) be greater than the local derivative of liquid holdup with respect to gas velocity (*g). With this conditions satisfied, the oscillation of inlet velocity will generally be reflected also as some kind of periodic oscillations of the mean holdup. If, in addition, the period of the forcing function, *t, equals the characteristic time, *t0, the periodic oscillations of the mean liquid holdup will eventually dampen to a constant. For the limiting case of *l = *g, the oscillations of the mean holdup are also dampened, albeit only very slowly, provided that *t = *t0. For *l = *g and *t #= *t0 as well as for *l < *g, the oscillations amplify in time without limit. Exactly the same findings apply when the inlet liquid velocity is kept constant while the inlet gas velocity is forced to fluctuate.