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methanol pair is best adapted for operating cycles with small
evaporating temperature variations (up to 40 C), whereas the
adsorption cycles with zeoliteewater pair, a larger range evapo-
rating temperature (70 C, or more) is needed.2.1. DubinineAstakhov equation
To describe adsorption in microporous materials with poly-
modal distributions, Dubinin and Astakhov [14] have proposed an
isotherm that is a log-linear form of DubinineRudishkevich equa-
tion, which can be expressed as follows:Being the latent heat, the first termof Eq. (6), the other terms do
correspond to the energy that most specifically concerns the
adsorption binding forces. For temperature around 5 C, the value
of L is about 1200 kJ/kg. According to Srivastava and Eames [16], the
isosteric heat of adsorption for activated carbonemethanol ranges
from 1800 to 2000 kJ/kg. So, the energy resulting from the binding
forces in adsorption corresponds to something from 33% to 40% of
the isosteric heat; the rest would come as a result of capillary
condensation inside the micropores.2.3. Kinetics of adsorption
In most cases, adsorption in microporous materials is mainly
controlled by the diffusion that takes place inside porous structure,
for on the surface of the grains, diffusion happens too fast. In the
case of materials with bidisperse structure, such as activated
carbon, two diffusion mechanisms may be found: a gaseous phase
diffusion through transport pores (mesoporous and macroporous
diffusion) and an adsorbed phase diffusion in micropores. The
relative importance of these mechanisms on the global diffusion
effect greatly depends on pressure. According to Dubinin and
Erashko [17], for pressures lower than 10 hPa, mesoporous and
macroporous diffusions are seen to be most predominant, whereas
for pressures greater than 10 hPa, microporous diffusion tends to
control the mass transfer process.
Thomas and Glauckauf, cited by Sakoda and Suzuki [18],
proposed an approach based on two important hypotheses: the
temperature of the grain is uniform, and the concentration on the
solid surface is equivalent to an equilibrium concentration. These
hypotheses have established, for modeling the mass transfer
resistance of the adsorption kinetics, the following linear equation:where Di is the diffusion coefficient, aeq is the equilibrium
concentration (given by an isotherm) and rg is the average radius of
the grain.
In both mesopores and macropores, different mechanisms
contribute simultaneously to the diffusion process, the relative
influence of which does depend on the pores dimensions. Among
them, fourmainmechanisms are identified: superficial diffusion Ds,
molecular diffusion Dm, Knudsen’s diffusion DK, and Poiseuille’s
diffusion DP. For an overall diffusion analysis, an effective diffusion
coefficient De is normally considered, so that De ¼ f(Ds, Dm, DK, DP).
Notwithstanding the importance of the kinetics theory for
modeling adsorption processes, the practice demonstrates that the
mass transport resistance can be neglected in systems under
moderate thermal power. For methanol adsorption in activated
carbon, Kariogas and Meunier [19] have shown that the mass
resistance is negligible when the incident energy is lower than
50 W/kg of adsorbent. In other words, for modeling adsorption
processes related to low-grade energy sources, such as the case of
solar energy, it will not be necessary to consider diffusion through
the porous medium. Moreover, for many engineering applications,
it may be taken into account the existence of an instantaneous
equilibrium between the adsorbed and the gaseous phases. This
can be represented by means of an isotherm, such as the Dubi-