Page 154 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

128 5 Principles for Gas Separation

emission limits set by emission standards. For many toxic chemicals, a measurable
concentration at the exit, even if it is less than 1 % of the inlet concentration, can be
defined as the breakthrough point.
The kinetics of adsorption wave can be analyzed as follows. Consider an
adsorption column of length L with an adsorption wave width of d. The concen-
tration of the adsorbate in the gas stream is C 0 (in mass of adsorbate/volume of gas),
and the load of the adsorbate in the saturated adsorbent is M eq (in mass of adsorbate
per mass of adsorbent). Within the active adsorption zone, the concentration C of
adsorbate in the gas varies from C 0 to zero and the load of adsorbate in the
adsorbent C x varies from M eq to zero. While gas moves through the column at a
bulk face velocity of U, the saturation zone keeps growing as fresh adsorbent
adsorbs the incoming adsorbate, resulting in propagation of active adsorption zone
at a speed V az . In practice, U V az , therefore, the relative speed of the gas stream
with respect to the active adsorption zone can be assumed as U.
During the process described above, the rate of adsorbate entering adsorbent
column is equal to the rate of adsorbate adsorbed by the adsorbent if we ignore
other mechanisms for gas separation or leaking. That is,

QC 0 ¼ M eq q AV az Þ ð5:10Þ
ð
b
3
where Q ¼ volumetric flow rate of the gas (m /s), C 0 ¼ the incoming adsorbate
3
3
concentration (kg/m ), q ¼ bulk density of the adsorbent (kg/m ), A ¼ cross-
b
2
sectional area of the adsorption column (m ), and M eq ¼ equilibrium loading with
a unit of kg/kg.
The bulk density of the adsorbent depends on the packing density of the column
and it is not the physical density of the adsorbent material itself. Usually the bulk
density is much less than the real density of the material and it depends on the
packing density.
The left-hand side of Eq. (5.10) stands for the mass flow rate (in kg/s) of the
adsorbate into the column, and the term q AV az Þ gives the mass rate of adsorbent
ð
b
used (kg/s). In an engineering practice where the specifications of the adsorption
column and operation conditions are known, one can get the values of q , A, Q and
s
C 0 . M eq is required in order to solve Eq. (5.10) for the wave speed V az , and M eq is
usually determined experimentally and described using adsorption isotherm.
A simple manipulation of Eq. (5.10) leads to the expression of adsorption wave
propagation speed,
QC 0
V az ¼ ð5:11Þ
ð
M eq q AÞ
b
The mathematical description of the relationship between M eq and C 0 depends
on the model introduced above or measured data. When using data in Table 5.4,we
must pay attention to the units of C 0 and M eq . In Eqs. (5.10) and (5.11) they are
different from those of M eq;g=100 g and C ppmv listed in Table 5.4. Correct unit con-
version is necessary.