Membrane and Desalination Technologies - TCE Moodle Website

Adsorption Desalination: A Novel Method 397
meso- and micropores. Similar LDF models for one-dimensional slab and spherical shapes
where the parentheses terms are (3 þ k) and (15 þ 3k), respectively, are reported.
1.4. Heat of Adsorption
The isosteric heat of adsorption is a combined property of an adsorbent–adsorbate combination.
It is a major contributor to the heating inventories of adsorption refrigeration and gas
storage systems and also cooling requirements of adsorption heat pumps. Isosteric heat of
adsorption is traditionally expressed as a function of concentration as its dependency on
temperature is relatively weak (16, 17). Clausius–Clapeyron equation is commonly used to
estimate the heat of adsorption at a constant concentration, as given by Eq. (6):
R @ ln P
QstðWÞ ¼ : (6Þ
@ð1=TÞ
Here, Qst denotes the isosteric heat of adsorption in kJ/kg, R is the gas constant in kJ/kg K,
P is the equilibrium pressure in kPa, and T is the adsorbent temperature in K. Critoph (18)
proposed a relation (Eq. 7) that is derived by direct integration of Eq. (6) to estimate the
isosteric heat of adsorption for practical applications in solar adsorption cooling systems.
R lnðP2=P1Þ QstðWÞ ¼ : (7Þ
ð1=T1Þ ð1=T2Þ This assumption is validated by the linearity of Clausius–Clapeyron diagram for a short
temperature range. However, as the adsorbate concentration changes during adsorption and
desorption processes, the isosteric heat of adsorption is usually calculated at the mean
concentration. In adsorption cooling heat pump applications, an average value of heat of
adsorption within a certain concentration range is usually used for system analysis and design.
In 1995, Cacciola and Restuccia (19) presented a correlation to estimate heat of adsorption as a
function of concentration (Eq. 8) for activated carbon methanol and zeolite water pairs.
QstðWÞ R ¼ a0 þ a1W þ a2W 2 þ a3W 3 : (8Þ
They determined the values of the constants a0, a1, a2, and a3 based on their experimental
data of Zeolite 13X-water and AC-methanol, and these are furnished in Table 9.2.
It can be noticed that the correlation derived by Critoph (18) is only valid for a relatively
narrow temperature range. Moreover, his correlation is valid only for a constant concentration.
El-Sharkawy et al. (20) proposed a non-dimensional empirical correlation which partitions
the contributions of the concentration and temperature dependence (Eq. 9). The correlation is
tested out against data obtained from experimental isotherms of ethanol adsorption on ACFs
[ACF (A-20) and ACF (A-15) (9) and HFC 134a] on two specimens of activated carbon
powders and one specimen of carbon granules (16).
Qst hfg
E
" #
1=n
þ A T
¼ ln W0
W
Tc
B
: (9Þ