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.