Page 57 - Adsorbents - fundamentals and applications

42 SORBENT SELECTION: CRITERIA

Eq. 3.1, is followed by both components. For a binary mixture, the extended
Langmuir equation, Eq. 3.4., is

b
q m i i P i
q i = (3.58)
1 + b 1 P 1 + b 2 P 2
The first factor in the PSA parameter is the equilibrium selectivity (α 1,2 )and
is defined as follows:
x 1 y 2
α 1,2 = · (3.59)
x 2 y 1
where x 1 , x 2 are the mole fractions of the two components on the adsorbent
surface, whereas y 1 , y 2 are the corresponding mole fractions in the gas phase. It
will be assumed that component (1) is the more strongly adsorbed species. Using
the extended Langmuir equation in conjunction with the definition given above
(Eq. 3.59), it can be shown that the adsorbent selectivity for component (1) is a
constant for the entire range of partial pressures as follows:

b
q m 1 1 K 1
α 1,2 = = (3.60)
b
q m 2 2 K 2
The product (q mi b i ) corresponds to the initial slope of the isotherm, or Henry’s
constant (K), for component i. Hence, the adsorbent selectivity is equivalent to
the ratio of the initial slopes of the isotherms of the two components, or K 1 /K 2 .
It should be noted that the selectivity has resulted in a constant value simply
because of the nature of the Langmuir isotherm. If, however, a different model
such as the loading ratio correlation (Eq. 3.5) is used, the selectivity is likely to
be dependent on the operating pressures of the PSA cycle.
Another important factor for PSA separations is the change in the adsorbed
amounts of the two components upon cycling the pressure. The working capacity
of a sorbent typically refers to the strongly adsorbed species and is defined as
the difference between the adsorbed amounts at the adsorption (high) pressure
and the desorption (low) pressure. Strictly speaking, the working capacity should
be defined with respect to the adsorbed amounts under the mixture conditions
(that is, using a binary component isotherm). However, using a pure component
isotherm can suffice to make the calculation of the parameter facile. A ratio
of the working capacities of the two components would give an idea about the
adsorption performance for a particular pressure swing cycle. Hence, the second
factor to the parameter is the working capacity selectivity ratio and is defined as:

q 1
W = (3.61)
q 2
Having defined the two contributing factors to the parameter, the PSA sorbent
selection parameter (S) can be written as follows:

S = W · a 1,2 (3.62)