Figure 2. Shrinking core process
observed in CH3I adsorption on
Ag0-Aerogel, two cut halves of a partially reacted
pellet
SCM was developed by Yagi and Kunii47 in 1955 and
modified by Levenspiel48. It consists of a gas film
diffusion term, pore diffusion term and reaction term. In a typical SCM
gas-solid adsorption process, the adsorbate first reaches the pellet
surface by diffusing through a gas film around the pellet. Then, the gas
reacts with the adsorbent surface. When the adsorbent surface is fully
reacted, the adsorbate diffuses into the pellet and reacts with the
second layer of the adsorbent. Because the size of the unreacted core
decreases as the adsorption proceeds, the model is named as ‘shrinking
core’. This model has been widely used in the nuclear waste treatment
area including water adsorption on molecular sieves
3A40, water adsorption on
Ag0Z16,38, I2adsorption on Ag0Z16,19,
CH3I adsorption on
Ag0Z18, etc.
SCM relates the time and adsorption mass by using 3 parts shown in Eq.
1:
where q is average sorbate (CH3I) concentration
(mol/g) at time t (s) and qe is
equilibrium sorbate (CH3I) concentration (mol/g). For
convenience, q and qe are sometimes
represented as ‘mass uptake’ and ‘equilibrium mass uptake/adsorption
capacity’ in wt%, which can be easily converted by the
CH3I molar mass. τ1 ,τ2 , and τ3 are gas film
diffusion term, pore diffusion term, and 1st order
reaction term respectively. By assuming gas-solid reaction is
1st order, τ1 ,τ2 , and τ3 can be
calculated by Eq. 2,3 and 4
where Ra is radius of the pellet (cm),ρp is density of the pellet
(g/cm3), Cb is bulk adsorbate
(CH3I) concentration (mol/cm3),kf is gas film mass transfer coefficient (cm/s),Dp is pore diffusivity (cm2/s),ks is 1st order reaction rate
constant (cm/s) and b is stoichiometric coefficient of Ag in
Ag-CH3I reaction, which is 1.
To improve the SCM, the unnecessary 1st order reaction
assumption may be replaced by the nth order reaction,
which τ1 and τ2 remain the
same and τ3 is replace by nthorder reaction term τ3* given
in Eq. 5:
where n is reaction order andks* is nthorder reaction rate constant
((cm/s)∙(mol/cm3)1-n)
To reduce the variables to be fitted in the model and increase the
accuracy of the result, an alternative method of determiningkf was used by Nan.16,19kf can be determined using Eq. 6 -
9.49-52
Sh , Sc , and Re are Sherwood number, Schmidt number,
and Reynolds number respectively. DAB is the
binary diffusion coefficient (cm2/s), T is
temperature (K), P is pressure (bar), MABis the average molecular weight of species A ,
CH3I, and species B , air, and ν is the
atomic diffusion volume (cm3). For current
experimental condition, T = 423 K, P = 1 bar,MAB = 48.12 g/mol, = 52.63 cm3and = 19.7 cm3.50 TheDAB determined using this method is approximately
0.196 cm2/s, which is similar to the value of 0.207
cm2/s measured experimentally by Matsunaga et al.53
Procedure description
As mentioned above, the CH3I concentration in VOG is
below 100 ppb. Measuring mass adsorbed at such low concentrations is
beyond the capability of microbalances. More specifically, the mass
uptake cannot be detected confidently by using microbalances in an
acceptable time frame. Therefore, the CH3I
concentrations used for adsorption were selected to be 113, 266, 1130
and 10400 ppbv. Other experimental conditions such as temperature and
gas flow rate are selected base on previous studies. 150 ℃/ 423K was
reported as the preferred experiment temperature for I2and CH3I adsorption and has been widely used in multiple
studies.16-18 The gas flow rate may impact the
adsorption rate by varying superficial gas velocity and therefore
changing kf . Nan et al.19indicated that no obvious impact was observed at 423 K for superficial
velocity greater than 1.1 m/min. To satisfy this condition, the gas flow
rate measured at room temperature is set to be approximately 500
cm3/min. To prevent any significant concentration
gradient caused by overlapping, one layer of
Ag0-Aerogel pellets (0.1-0.2 g) was placed in the tray
suspended under the microbalance, shown in Figure 1.
At ppb level concentration, the adsorption rate of CH3I
is significantly lower than that of ppm level adsorption. Therefore, the
pellets must be dried carefully to prevent any misleading result caused
by moisture loss during the CH3I adsorption. Over 150 h
is required to air-dry Ag0-Aerogel, in other words,
placing in the tray and flow dry air (Dew Point = -70 ℃) until no mass
loss is observed. To accelerate this process, the
Ag0-Aerogel was vacuum dried at 150 ℃ overnight using
the degas function of a Surface Area and Porosity Analyzer
(Micromeritics, ASAP 2020) and stored under N2environment before conducting the adsorption experiments.
Unlike previous 10-50 ppm level adsorption
studies16,18,19, reaching equilibrium is not
practicable at ppb level. For example, based on experimental results and
predictions, it may take over 3 years for Ag0-Aerogel
to reach equilibrium at 1130 ppbv CH3I condition.
Therefore, the adsorption experiments were stopped after a certain
period instead of reaching equilibrium.
Results
Adsorption Kinetics
Four adsorption experiments with 113, 266, 1130 and 10400 ppbv
CH3I in dry air were conducted. The concentrations were
calculated from the data provided by the permeation tube manufacturer
and confirmed by measuring the mass differences of the permeation tubes
before and after the experiments. Approximately 288 hours adsorption
data of 113, 266, 1130 and 10400 ppbv CH3I adsorption on
Ag0-Aerogel are plotted in Figure 3. For 288 hours,
mass uptakes reached 0.17, 0.91, 3.7 and 14.7 wt% at 113, 266, 1130 and
10400 ppbv respectively. To eliminate the physically adsorbed
CH3I, the Ag0-Aerogel was left in the
adsorption column and desorbed by stopping CH3I
generation and flowing only dry air for 24 h. During this desorption
process, no significant mass losses were observed, indicating
CH3I adsorption on Ag0-Aerogel was
mostly chemisorption. Limited by the low mass uptake, 113 and 266 ppbv
adsorption curve cannot be identified well in Figure 3 and a close view
of 4 uptake curves is shown in Figure 4.