Page 172 - Adsorption Technology & Design, Elsevier (1998)

160 Design procedures

with any degree of confidence without resorting to further testing on pilot or
full-scale plant.
Cyclic PSA and TSA processes are both time-dependent dynamic
processes, and thus for design purposes the pseudo-steady-state is required
in which all the product concentrations and bed profiles of pressure,
temperature, velocity and composition are reproduced exactly from cycle to
cycle. Any rigorous design model should be capable of being used from the
initial start-up conditions until the individual steps and their boundary
conditions converge and the cyclic pseudo-steady-state is obtained. The
problem is more difficult for PSA processes than for TSA processes, and
becomes more complex as the cycle time is reduced.
General models comprise a system of non-linear partial differential
equations which are highly coupled and very stiff. There is an equally
complex set of initial and boundary conditions and a large number of
physical constants and other parameters, some of which may only be known
approximately. In order to be able to predict the composition, pressure,
flowrate and temperature of the fluid emerging from the ends of the bed
during each step in a cyclic process it is necessary to predict the composition,
pressure, flowrate and temperature profiles within the beds. There are six
groups of equations which need to be considered in order to complete a
rigorous design:

(1) For each component, a mass balance equation can be written using
an infinitesimal element of the bed as a control volume; this is
equation (6.37). The terms in this equation account for convection
and axial dispersion (if applicable) into and out of the control
volume, together with the rate of adsorption and the accumulation
in the fluid phase.
(2) The fluid phase heat balance equation on the small element of the
bed includes the sensible heat changes due to gas convection,
thermal conduction, heat transfer within the solid, heat transfer
within the column wall and accumulation within the element; this is
equation (6.39).
(3) The heat balance on the particles includes the heat released on
adsorption (or taken up in desorption, depending on the step in the
cycle), conduction to the surface of the adsorbent, and heat transfer
to the adjacent particles as well as to the bulk fluid phase; this is
equation (6.40).
(4) Empirical relationships are generally used to relate the rate of
change of pressure with position and time to the local gas velocity in
PSA processes, or to determine the pressure drops in TSA
processes. The Ergun equation or Darcy's law are often used to