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256 Adsorption (Chemical Engineering)

model is therefore very useful for developing an initial
understanding of the system dynamics and for prelimi-
nary design. However, the inherent limitations of such a
model should be clearly recognized.
Although the multicomponent Langmuir equations ac-
count qualitatively for competitive adsorption of the mix-
ture components, few real systems conform quantitatively
to this simple model. For example, in real systems the
separation factor is generally concentration dependent,
and azeotrope formation (α = 1.0) and selectivity rever-
sal (α varying from less than 1.0 to more than 1.0 over the
composition range) are relatively common. Such behavior
FIGURE 3 Variation of limiting heat of sorption (− H 0 ) with chain
may limit the product purity attainable in a particular ad-
length n for homologous series of linear paraffins.
sorption separation. It is sometimes possible to avoid such
problems by introducing an additional component into the
For more complex molecules a reasonable estimate of the
system which will modify the equilibrium behavior and
heat of sorption can sometimes be made by considering
eliminate the selectivity reversal.
“group contributions.” Such an approach works best for
The problem of predicting multicomponent adsorption
nonpolar sorbates on nonpolar surfaces but is subject to
equilibria from single-component isotherm data has at-
considerable error for polar systems in which the electro-
tracted considerable attention, and several more sophisti-
static energies of adsorption are large.
cated approaches have been developed, including the ideal
adsorbed solution theory and the vacancy solution theory.
B. Adsorption of Mixtures These theories provide useful quantitative correlations for
a number of binary and ternary systems, although avail-
The Langmuir equation can be easily extended to multi-
component adsorption, for example, for a binary mixture able experimental data are somewhat limited. A simpler
of components 1 and 2: but purely empirical approach is to use a modified form
of isotherm expression based on Langmuir–Freundlich or
q 1 b 1 c 1 “loading ratio correlation” equations:
=
q s1 1 + b 1 c 1 + b 2 c 2 n 1
(4) q 1 b 1 p 1
=
q 2 b 2 c 2 1 + b 1 p + b 2 p n 2
n 1
= q s 1 2
q s2 1 + b 1 c 1 + b 2 c 2 (6)
b 2 p n 2
q 2 2
Thermodynamic consistency requires that q s1 be equal to = n 1 n 2
q s2 , but it is common practice to ignore this requirement, q s 1 + b 1 p + b 2 p 2
1
thereby introducing an additional parameter. This is legit- From the perspective of the design engineer, the advantage
imate if the equations are to be used purely as an empirical of this approach is that the expressions for the adsorbed-
correlation, but it should be recognized that since thermo- phase concentrations are simple and explicit. However,
dynamic consistency is violated such expressions are not the expressions do not reduce to Henry’s law in the low-
valid over the entire composition range. concentration limit, which is a thermodynamic require-
For an equilibrium-based separation process a conve- ment for physical adsorption. They therefore suffer from
nient measure of the intrinsic selectivity of the adsorbent is the disadvantage of any purely empirical equations, and
the separation factor α 12 ,defined by analogy with relative they do not provide a reliable basis for extrapolation out-
volatility as: side the range of experimental study.
α 12 = (X 1 /Y 1 )/(X 2 /Y 2 ) (5)

where X and Y are the mole fraction in the adsorbed V. ADSORPTION KINETICS
and fluid phases, respectively. For a system that obeys
the binary Langmuir isotherm [Eq. (4)] it is evident that Physical adsorption at a surface is extremely rapid, and the
α 12 (=b 1 /b 2 ) is independent of concentration. An approx- kinetics of physical adsorption are invariably controlled
imate estimate of the separation factor can therefore be by mass or heat transfer rather than by the intrinsic rate of
derived from the ratio of the Henry’s law constants. A con- the surface process. Biporous adsorbents such as pelleted
stant separation factor simplifies considerably the problem zeolites or carbon molecular sieves offer three distinct re-
of modeling the adsorption process, and the Langmuir sistances to mass transfer: the external resistance of the