Page 41 - Adsorbents fundamentals and applications

26 SORBENT SELECTION: CRITERIA

Equations 3.30 and 3.31 can be obtained by adding all the elementary rate steps
∗
and setting the rate of change of the concentration of A to zero.
For binary diffusion of components A and B, the fluxes are
∂q A ∂q B
J A =−D AA − D AB (3.32)
∂x ∂x
∂q A ∂q B
J B =−D BA − D BB (3.33)
∂x ∂x
and the concentration-dependent Fickian diffusivities are

1 − (1 − λ AB )θ B
D AA = D AO (3.34)
1 − (1 − λ A )θ A − (1 − λ AB )θ B

(1 − λ AB )θ A
D AB = D AO (3.35)
1 − (1 − λ A )θ A − (1 − λ AB )θ B

(1 − λ BA )θ B
D BA = D BO (3.36)
1 − (1 − λ B )θ B − (1 − λ BA )θ A

1 − (1 − λ BA )θ A
D BB = D BO (3.37)
1 − (1 − λ B )θ B − (1 − λ BA )θ A
where D AO and D BO are pure-component diffusivities at zero coverage, given by
(for D AO ):
1
D A
= (3.38)
D AO 1 − (1 − λ A )θ A
Because the values of q s for the two components are not very different, one may
adopt the adsorbed-phase averaging scheme of Innes et al. (Chapter 3, Yang,
1987) for calculating q s :
1 X A X B
= + (3.39)
q s q sA q sB

and
q A q B
θ A = ; θ B = ; θ A + θ B ≤ 1 (3.40)
q s q s
where X is the adsorbed-phase mole fraction at equilibrium.
The parameter λ is given by Eq. 3.28:

λ A = e −(ε AV −ε AA )/RT (3.41)

Similarly,
λ B = e −(ε BV −ε BB )/RT (3.42)

λ AB = e −(ε AV −ε AB )/RT (3.43)
λ BA = e −(ε BV −ε BA )/RT (3.44)