Page 54 - Adsorbents fundamentals and applications

TEMPERATURE SWING ADSORPTION AND PRESSURE SWING ADSORPTION 39

6. Ideal gas law is obeyed.
7. Pressure gradient across the bed is negligible.
The mass balance yields, for A:

∂C A ∂(uC A ) ∂q A
ε + + (1 − ε) = 0 (3.48)
∂t ∂z ∂t
and for B:

∂C B ∂(uC B ) ∂q B
ε + + (1 − ε) = 0 (3.49)
∂t ∂z ∂t
where C is gas-phase concentration, q is the adsorbed amount per volume of
pellet, t is time, z is distance, ε is the interstitial (or interpellet) void fraction and
u is the interstitial velocity.
Both components adsorb independently:

q A = B A C A ; q A = B A C A (3.50)

where B is Henry’s constant and B A >B B . The Henry’s constant may also be
expressed as:
ε ε
β A = ; β B = (3.51)
ε + (1 − ε)B A ε + (1 − ε)B B

where β indicates the ratio of gas-phase capacity to the total capacity of
the sorbent.
The penetration distances Z during the high- and low-pressure steps are
given by:

Z H = B A u H t (3.52)
Z L = B A u L t (3.53)

where subscripts L and H denote the low-(purge) and high-(adsorption) pressure
steps, with equal time length, t.
By using the method of characteristics, the propagation velocity of the concen-
tration front can be expressed. The two pressure-changing steps can be accounted
for using ideal gas law and assuming zero axial pressure drop.
For complete purification, that is, complete removal of A in the high-pressure
product stream at steady-state operation, the following two conditions must
be satisfied:
1. Breakthrough of feed into the high-pressure product stream does not occur.
2. Purge/feed ratio must be greater than a critical value such that the net dis-
placement of a concentration wavefront during a complete cycle is positive.