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\begin{document}

\title{Adsorption of Methyl Iodide on Reduced Silver-Functionalized Silica
Aerogel: Kinetics and Modeling}



\author[1,1]{Siqi Tang}%
\author[1]{Seungrag Choi}%
\author[1]{Yue Nan}%
\author[1]{Lawrence Tavlarides}%
\affil[1]{Syracuse University}%


\vspace{-1em}



  
  \date{June 17, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
The low concentration methyl iodides (CH\textsubscript{3}I) adsorption
process on reduced silver-functionalized silica aerogel
(Ag\textsuperscript{0}-Aerogel) was studied. The kinetic data were
acquired using a continuous flow adsorption system. Because the
corresponding physical process was observed, the shrinking core model
(SCM) was modified and applied. An average CH\textsubscript{3}I pore
diffusivity was calculated, the
CH\textsubscript{3}I-Ag\textsuperscript{0}-Aerogel reaction was
identified as a 1.37 order reaction instead of first order reaction, and
the n\textsuperscript{th} order reaction rate constant was determined.
This modified SCM significantly increases the accuracy of adsorption
behavior prediction at low adsorbate concentration. Modeling results
indicate that the overall adsorption process is controlled by the pore
diffusion. However, at low adsorbate concentration (\textless{}100
ppbv), the CH\textsubscript{3}I adsorption is limited to the surface
reaction due to the low uptake rate in a predictable time period.%
\end{abstract}%



\sloppy


Adsorption of Methyl Iodide on Reduced Silver-Functionalized Silica
Aerogel: Kinetics and Modeling

Siqi Tang, Seungrag Choi, Yue Nan\textsuperscript{*} and Lawrence L.
Tavlarides

Department of Biomedical and Chemical Engineering, Syracuse University,
329 Link Hall, Syracuse, NY 13244, USA

\subsection*{Abstract}

{\label{abstract}}

The low concentration methyl iodides (CH\textsubscript{3}I) adsorption
process on reduced silver-functionalized silica aerogel
(Ag\textsuperscript{0}-Aerogel) was studied. The kinetic data were
acquired using a continuous flow adsorption system. Because the
corresponding physical process was observed, the shrinking core model
(SCM) was modified and applied. An average CH\textsubscript{3}I pore
diffusivity was calculated, the
CH\textsubscript{3}I-Ag\textsuperscript{0}-Aerogel reaction was
identified as a 1.37 order reaction instead of first order reaction, and
the n\textsuperscript{th} order reaction rate constant was determined.
This modified SCM significantly increases the accuracy of adsorption
behavior prediction at low adsorbate concentration. Modeling results
indicate that the overall adsorption process is controlled by the pore
diffusion. However, at low adsorbate concentration (\textless{}100
ppbv), the CH\textsubscript{3}I adsorption is limited to the surface
reaction due to the low uptake rate in a predictable time period.

\subsection*{Topical Heading}

{\label{topical-heading}}

Separations: Materials, Devices and Processes

\subsection*{Keywords}

{\label{keywords}}

Adsorption, iodine removal, separation, silver aerogel, shrinking core
model

\subsection*{Introduction}

{\label{introduction}}

Nuclear power has been widely used since the
20\textsuperscript{th}century for its low emission rate of air
pollutants.\textsuperscript{1-3} However, multiple radioactive isotopes,
including radioactive Iodine (\textsuperscript{129}I), are produced in
the uranium fission.\textsuperscript{4,5} During aqueous reprocessing of
the nuclear waste, \textsuperscript{85}Kr,
\textsuperscript{14}C,\textsuperscript{129}I, and \textsuperscript{3}H
are released to the off-gas streams. The off-gas streams include
dissolver off-gas (DOG), cell off-gas (COG), waste off-gas (WOG) and
vessel off-gas (VOG).\textsuperscript{6} According to Bruffey et
al.\textsuperscript{6,7}, approximately 95\% - 98\% of iodine is
contained in DOG, remaining iodine (in I\textsubscript{2} and organic
iodides form) exists in VOG, and VOG flow rate is 100\selectlanguage{ngerman}× higher than that
of DOG. Therefore, unlike the ppm level in DOG, the iodine concentration
in VOG decreases to below 100 ppbv. Although only trace amount of iodine
exists in VOG, the off-gas cannot be emitted directly into atmosphere,
and the emissions are governed by 10 CFR 20, 40 CFR 61 and 40 CFR
190.\textsuperscript{8-10} The composition of the organic iodides
existing in VOG varies from methyl iodide (CH\textsubscript{3}I) to
iodododecane (C\textsubscript{12}H\textsubscript{25}I) and among 12
different organic iodides, CH\textsubscript{3}I and
C\textsubscript{12}H\textsubscript{25}I were reported to be the two most
abundant components.\textsuperscript{6,11,12}

Multiple silver containing materials, including macroreticular resins,
silver impregnated alumina (AgA), silver exchanged faujasite (AgX),
hydrogen-reduced silver exchanged mordenite (Ag\textsuperscript{0}Z) and
reduced silver-functionalized silica aerogel
(Ag\textsuperscript{0}-Aerogel), have been developed and studied for
I\textsubscript{2} and organic iodides
adsorption.\textsuperscript{4,13-18} The reason for selecting
silver-containing materials over traditional liquid scrubbing methods is
concluded to be stronger Ag-I bond and solid form, therefore, higher
removal efficiency and lower operation cost.\textsuperscript{4,19-22}
Among these silver-containing materials, Ag\textsuperscript{0}Z and
Ag\textsuperscript{0}-Aerogel have been studied continuously in US
national laboratories and universities for their high iodine removal
efficiency and relatively greater resistance to aging caused by
potential contaminants in VOG and DOG (NO\textsubscript{x}, water vapor,
air).\textsuperscript{12,17,23} Nan et.al\textsuperscript{16,19} have
conducted the single layer adsorption experiments of
I\textsubscript{2}on Ag\textsuperscript{0}Z and reported approximately
12 wt\% I\textsubscript{2} adsorption capacity at 423K. Deep-bed
adsorption of I\textsubscript{2} and CH\textsubscript{3}I on
Ag\textsuperscript{0}Z at both ppb and ppm level have been studied by
Jubin et al.\textsuperscript{14,18}, Bruffey et
al.\textsuperscript{6,24} and Soelberg and
Watson\textsuperscript{25,26}, indicating the adsorption rate of
CH\textsubscript{3}I is lower than that of I\textsubscript{2}.

Deep-bed Ag\textsuperscript{0}-Aerogel adsorption experiments of
CH\textsubscript{3}I and I\textsubscript{2} under the VOG conditions
were conducted in multiple US national laboratories. Strachan et
al.\textsuperscript{27} performed 4.2 ppmv I\textsubscript{2} adsorption
experiments at 150 \selectlanguage{english}, concluding that fresh
Ag\textsuperscript{0}-Aerogel was able to remove I\textsubscript{2} for
at least 99.99\% efficiency and observing that
Ag\textsuperscript{0}-Aerogel changed from black to a brown, earth-tone
color during the adsorption experiment. Soelberg and
Watson\textsuperscript{28,29} conducted I\textsubscript{2} adsorption on
Ag\textsuperscript{0}Z and Ag\textsuperscript{0}-Aerogel at 150 \selectlanguage{english} with
NO\textsubscript{x} and H\textsubscript{2}O present, with
I\textsubscript{2} concentration ranging from 2 to 370 ppmv. Their
results indicated, at similar conditions, Ag\textsuperscript{0}-Aerogel
obtained higher resistance to NO\textsubscript{x} than
Ag\textsuperscript{0}Z did and, therefore, showed higher removal
efficiency in deep-bed adsorption experiments. In addition, deep-bed
CH\textsubscript{3}I adsorption studies have also been conducted by
Bruffey and Jubin\textsuperscript{7}, Jubin et
al.\textsuperscript{14}and Soelberg and Watson\textsuperscript{17}.
Ag\textsuperscript{0}-Aerogel showed an adequate capability to adsorb
CH\textsubscript{3}I at various conditions such as ppb or ppm level
concentrations and with or without the presence of NO\textsubscript{x}.
The penetration depth of CH\textsubscript{3}I in the column was measured
to be 3-7 cm, depending on the CH\textsubscript{3}I and
NO\textsubscript{x} concentration; and the decontamination factor (DF),
defined as inlet concentration of desired adsorbed species (eg.
I\textsubscript{2} and CH\textsubscript{3}I) over outlet concentration,
can reach approximately 1000.

The detailed organic iodides-Ag reaction mechanism was not conclusive.
Scheele et al.\textsuperscript{30} proposed several possible reactions
between Ag and CH\textsubscript{3}I in Ag\textsuperscript{0}Z:

.

In these proposed reactions, organic compounds are generated in gas form
and only iodine is captured by silver. The generated
CH\textsubscript{3}OCH\textsubscript{3} (dimethyl ether) and
CH\textsubscript{3}OH (methanol) were observed by Soelberg and
Watson\textsuperscript{25} and the desorption of
C\textsubscript{2}H\textsubscript{6} in similar reactions was suggested
by Zhou et al\textsuperscript{31}. With the presence of
NO\textsubscript{x} in the gas stream, other organic compounds such as
CH\textsubscript{3}NO\textsubscript{2} (nitromethane) and
C\textsubscript{3}H\textsubscript{9}NO (3-amino-1-propanol) were also
detected.\textsuperscript{26} Assuming similar reactions happen between
Ag\textsuperscript{0}-Aerogel and CH\textsubscript{3}I and only iodine
is left in Ag\textsuperscript{0}-Aerogel pellets, the maximum iodine
capture capacity for I\textsubscript{2} should be the same as that for
CH\textsubscript{3}I.

Limited by the nature of deep-bed adsorption experiments, the mass of
deep-bed adsorption column cannot be measured continuously and most of
the curves were composed by discrete data points instead of real-time
data. Therefore, as complements to the deep-bed adsorption experiments,
single-layer CH\textsubscript{3}I adsorption experiments on
Ag\textsuperscript{0}-Aerogel were conducted in the present work. One of
the purposes of performing the single-layer adsorption experiments is
determining the pore diffusivity and reaction rate constant and these
parameters can be related and applied for column adsorption
modeling.\textsuperscript{32-34}

In the single-layer adsorption experiments,
Ag\textsuperscript{0}-Aerogel was placed in a tray connected to a
microbalance, enabling real-time and high-precision measurement of the
mass change. The CH\textsubscript{3}I concentrations selected were 113,
266, 1130 and 10400 ppbv; temperature was 150 \selectlanguage{english}, same as the experiments
described above; and gas flow rate was set to be 500 sccm in order to
satisfy 1.1 m/s superficial gas velocity suggested by Nan et
al.\textsuperscript{19} The adsorption kinetic data at various
CH\textsubscript{3}I concentrations were obtained and used to evaluate
the pore diffusivity and reaction rate of CH\textsubscript{3}I in
Ag\textsuperscript{0}-Aerogel. To explain the inconsistency of reaction
rate constants at different concentrations, an
n\textsuperscript{th}order shrinking core model was applied and the
modeling results were used to improve the predictions of adsorption
behavior at various CH\textsubscript{3}I concentrations.

\subsection*{Materials and Methods}

{\label{materials-and-methods}}

\subsubsection*{Silver-Functionalized Silica
Aerogel}

{\label{silver-functionalized-silica-aerogel}}

Reduced silver-functionalized silica aerogel
(Ag\textsuperscript{0}-Aerogel) was obtained from the Pacific North
National Laboratory (PNNL) in 2017. It was first developed there for
gaseous iodine capturing in nuclear waste
treatment.\textsuperscript{35,36} The Ag\textsuperscript{0}-Aerogel
pellets are primarily black; the shape and size are arbitrary and some
of the pellets contain certain yellow areas which may be due to unevenly
coated silver in the manufacturing process. The particle radius is
approximately 0.1 cm. Reported by Jubin et al.\textsuperscript{14}, the
bulk density of the pellet is 0.54 g/cm\textsuperscript{3} and 0.62
g/cm\textsuperscript{3} for `as-received material' and `post-run
material' respectively. For the modeling work to be discussed in the
following sections, an average value of 0.58 g/cm\textsuperscript{3} was
used. The maximum iodine loading capacity reported ranged from 33 to 47
wt\%\textsuperscript{27,29,37}. To achieve accurate modeling results,
the iodine loading capacity was measured to be approximately 37 wt\%
using the continuous flow adsorption system.

\subsubsection*{Continuous Flow Adsorption
System}

{\label{continuous-flow-adsorption-system}}

The continuous flow adsorption system was used for iodine and water
vapor adsorption on multiple materials previously by Nan et
al.\textsuperscript{19,38,39}and Lin et al.\textsuperscript{40,41} and
has been modified for performing the adsorption of CH\textsubscript{3}I
on Ag\textsuperscript{0}-Aerogel experiments. Figure 1 shows the
schematic diagram of the modified adsorption system.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 1. Schematic diagram of the continuous flow CH\textsubscript{3}I
adsorption system

Dry air flowed through Dynacalibrator (VICI, Model 500), in which a
permeation tube (VICI) was placed, as the carrier gas to generate
CH\textsubscript{3}I. The CH\textsubscript{3}I concentration was
controlled by the specific permeation tube model and the temperature of
the permeation chamber. 500 sccm of gas mixture was preheated to 150 
in the preheating coil wound around the adsorption column and then sent
to the adsorption column (I.D.= 30 mm). In the adsorption column, one
layer of Ag\textsuperscript{0}-Aerogel pellets was placed on a tray and
suspended under the microbalance. The microbalance has a variance of
approximately 30 \selectlanguage{greek}μ\selectlanguage{english}g and a sensitivity of 0.1 \selectlanguage{greek}μ\selectlanguage{english}g. When the
CH\textsubscript{3}I vapor was absorbed by Ag\textsuperscript{0}-Aerogel
pellets, mass change was measured by the microbalance and saved by the
data acquisition system. During the adsorption process, the temperature
was controlled by the furnace controller and N\textsubscript{2} was used
as the protective gas for the microbalance system.

\subsubsection*{Modeling}

{\label{modeling}}

Multiple gas-solid adsorption models have been used in explaining
adsorption kinetics of I\textsubscript{2} and Organic Iodides including
Linear Driving Force Model (LDFM), Shrinking Core Model (SCM), Volume
Reaction Model (VRM) and Pore Diffusion Model
(PDM).\textsuperscript{16,18,38,42-46} I\textsubscript{2} adsorption on
Ag\textsuperscript{0}Z has been identified as the shrinking core process
because the core shrinkage was observed by Nan.\textsuperscript{16}Shown
in Figure 2, a similar process was observed in CH\textsubscript{3}I
adsorption on Ag\textsuperscript{0}-Aerogel by cutting a partially
reacted pellet in half. The yellow area is the reacted
Ag\textsuperscript{0}-Aerogel and the black area is the unreacted core.
Therefore, the shrinking core model was selected to model the adsorption
kinetics.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Figure 2. Shrinking core process observed in CH\textsubscript{3}I
adsorption on Ag\textsuperscript{0}-Aerogel, two cut halves of a
partially reacted pellet

SCM was developed by Yagi and Kunii\textsuperscript{47} in 1955 and
modified by Levenspiel\textsuperscript{48}. 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
3A\textsuperscript{40}, water adsorption on
Ag\textsuperscript{0}Z\textsuperscript{16,38},
I\textsubscript{2}adsorption on
Ag\textsuperscript{0}Z\textsuperscript{16,19}, CH\textsubscript{3}I
adsorption on Ag\textsuperscript{0}Z\textsuperscript{18}, etc.

SCM relates the time and adsorption mass by using 3 parts shown in Eq.
1:

where \emph{q} is average sorbate (CH\textsubscript{3}I) concentration
(mol/g) at time \emph{t} (s) and \emph{q\textsubscript{e}} is
equilibrium sorbate (CH\textsubscript{3}I) concentration (mol/g). For
convenience, \emph{q} and \emph{q\textsubscript{e}} are sometimes
represented as `mass uptake' and `equilibrium mass uptake/adsorption
capacity' in wt\%, which can be easily converted by the
CH\textsubscript{3}I molar mass. \selectlanguage{greek}\emph{τ\textsubscript{1}}\selectlanguage{english}
,\selectlanguage{greek}\emph{τ\textsubscript{2}}\selectlanguage{english} , and \selectlanguage{greek}\emph{τ\textsubscript{3}}\selectlanguage{english} are gas film
diffusion term, pore diffusion term, and 1\textsuperscript{st} order
reaction term respectively. By assuming gas-solid reaction is
1\textsuperscript{st} order, \selectlanguage{greek}\emph{τ\textsubscript{1}}\selectlanguage{english}
,\selectlanguage{greek}\emph{τ\textsubscript{2}}\selectlanguage{english} , and \selectlanguage{greek}\emph{τ\textsubscript{3}}\selectlanguage{english} can be
calculated by Eq. 2,3 and 4

where \emph{R\textsubscript{a}} is radius of the pellet
(cm),\selectlanguage{greek}\emph{ρ\textsubscript{p}}\selectlanguage{english} is density of the pellet
(g/cm\textsuperscript{3}), \emph{C\textsubscript{b}} is bulk adsorbate
(CH\textsubscript{3}I) concentration
(mol/cm\textsuperscript{3}),\emph{k\textsubscript{f}} is gas film mass
transfer coefficient (cm/s),\emph{D\textsubscript{p}} is pore
diffusivity (cm\textsuperscript{2}/s),\emph{k\textsubscript{s}} is
1\textsuperscript{st} order reaction rate constant (cm/s) and \emph{b}
is stoichiometric coefficient of Ag in Ag-CH\textsubscript{3}I reaction,
which is 1.

To improve the SCM, the unnecessary 1\textsuperscript{st} order reaction
assumption may be replaced by the n\textsuperscript{th} order reaction,
which \selectlanguage{greek}\emph{τ\textsubscript{1}}\selectlanguage{english} and \selectlanguage{greek}\emph{τ\textsubscript{2}}\selectlanguage{english} remain the
same and \selectlanguage{greek}\emph{τ\textsubscript{3}}\selectlanguage{english} is replace by
n\textsuperscript{th}order reaction term
\selectlanguage{greek}\emph{τ\textsubscript{3}\textsuperscript{*}}\selectlanguage{english} given in Eq. 5:

where \emph{n} is reaction order
and\emph{k\textsubscript{s}\textsuperscript{*}} is
n\textsuperscript{th}order reaction rate constant
((cm/s)[?](mol/cm\textsuperscript{3})\textsuperscript{1-n})

To reduce the variables to be fitted in the model and increase the
accuracy of the result, an alternative method of
determining\emph{k\textsubscript{f}} was used by
Nan.\textsuperscript{16,19}\emph{k\textsubscript{f}} can be determined
using Eq. 6 - 9.\textsuperscript{49-52}

\emph{Sh} , \emph{Sc} , and \emph{Re} are Sherwood number, Schmidt
number, and Reynolds number respectively. \emph{D\textsubscript{AB}} is
the binary diffusion coefficient (cm\textsuperscript{2}/s), \emph{T} is
temperature (K), \emph{P} is pressure (bar),
\emph{M\textsubscript{AB}}is the average molecular weight of species
\emph{A} , CH\textsubscript{3}I, and species \emph{B} , air, and
\selectlanguage{greek}\emph{ν} \selectlanguage{english}is the atomic diffusion volume (cm\textsuperscript{3}). For
current experimental condition, \emph{T} = 423 K, \emph{P} = 1
bar,\emph{M\textsubscript{AB} =} 48.12 g/mol, = 52.63
cm\textsuperscript{3}and = 19.7
cm\textsuperscript{3}.\textsuperscript{50} The\emph{D\textsubscript{AB}}
determined using this method is approximately 0.196
cm\textsuperscript{2}/s, which is similar to the value of 0.207
cm\textsuperscript{2}/s measured experimentally by Matsunaga et
al.\textsuperscript{53}

\subsubsection*{Procedure description}

{\label{procedure-description}}

As mentioned above, the CH\textsubscript{3}I 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 CH\textsubscript{3}I
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
I\textsubscript{2}and CH\textsubscript{3}I adsorption and has been
widely used in multiple studies.\textsuperscript{16-18} The gas flow
rate may impact the adsorption rate by varying superficial gas velocity
and therefore changing \emph{k\textsubscript{f}} . Nan et
al.\textsuperscript{19}indicated 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 cm\textsuperscript{3}/min. To prevent any significant
concentration gradient caused by overlapping, one layer of
Ag\textsuperscript{0}-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 CH\textsubscript{3}I
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 CH\textsubscript{3}I adsorption. Over 150 h
is required to air-dry Ag\textsuperscript{0}-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
Ag\textsuperscript{0}-Aerogel was vacuum dried at 150  overnight using
the degas function of a Surface Area and Porosity Analyzer
(Micromeritics, ASAP 2020) and stored under
N\textsubscript{2}environment before conducting the adsorption
experiments.

Unlike previous 10-50 ppm level adsorption
studies\textsuperscript{16,18,19}, reaching equilibrium is not
practicable at ppb level. For example, based on experimental results and
predictions, it may take over 3 years for Ag\textsuperscript{0}-Aerogel
to reach equilibrium at 1130 ppbv CH\textsubscript{3}I condition.
Therefore, the adsorption experiments were stopped after a certain
period instead of reaching equilibrium.

\subsection*{Results}

{\label{results}}

\subsubsection*{Adsorption Kinetics}

{\label{adsorption-kinetics}}

Four adsorption experiments with 113, 266, 1130 and 10400 ppbv
CH\textsubscript{3}I 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 CH\textsubscript{3}I adsorption on
Ag\textsuperscript{0}-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
CH\textsubscript{3}I, the Ag\textsuperscript{0}-Aerogel was left in the
adsorption column and desorbed by stopping CH\textsubscript{3}I
generation and flowing only dry air for 24 h. During this desorption
process, no significant mass losses were observed, indicating
CH\textsubscript{3}I adsorption on Ag\textsuperscript{0}-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.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image18/image18}

\end{center}
\end{figure}

Figure 3. Uptake curves of 113, 266, 1130 and 10400 ppbv
CH\textsubscript{3}I adsorptions on Ag\textsuperscript{0}-Aerogel for up
to 288 hours.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image19/image19}

\end{center}
\end{figure}

Figure 4. Closer view of uptake curves of 113, 266, 1130 and 10400 ppbv
CH\textsubscript{3}I adsorptions on Ag\textsuperscript{0}-Aerogel for up
to 288 hours.

\subsubsection*{Model Fitting Result}

{\label{model-fitting-result}}

The 1\textsuperscript{st} order SCM was used to fit the kinetic data to
determine \emph{D\textsubscript{p}} and \emph{k\textsubscript{s}} in Eq.
3 and 4. To average the weights of different sections in the adsorption
curves and increase the accuracy of data fitting, \emph{t} 's were
rescaled by log\textsubscript{10} before applying the least square
regressions. More specifically, was used instead of , which \emph{f} is
Eq. 1-4, subscript \emph{i} is the number of experimental data
and\emph{exp} is the indication of experimental data.

The model-fitting results and parameters are shown in Table
1.\emph{k\textsubscript{f}} , calculated theoretically to be 5.99 cm/s
by applying Eq. 6-9, kept constant at 4 different
concentrations;\emph{D\textsubscript{p}} and \emph{k\textsubscript{s}}
were determined in model fitting and \emph{AARD} is calculated using ,
where\emph{model} indicates model fitting result and \emph{N} is the
number of data points.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
\begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
Concentration (ppbv)\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
Concentration (mol/cm3)\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
\emph{k\textsubscript{f}} (cm/s)\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
\emph{D\textsubscript{p}} (cm\textsuperscript{2}/s)\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
\emph{k\textsubscript{s}} (cm/s)\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright\strut
\emph{AARD} (\%)\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
113\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
4.64\selectlanguage{ngerman}×10\textsuperscript{-12}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
5.99\textsuperscript{*}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
N/A\textsuperscript{**}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
5.43\selectlanguage{ngerman}×10\textsuperscript{-2}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
12.75\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
266\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1.09\selectlanguage{ngerman}×10\textsuperscript{-11}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
5.99\textsuperscript{*}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
4.50\selectlanguage{ngerman}×10\textsuperscript{-4}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1.45\selectlanguage{ngerman}×10\textsuperscript{-1}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.27\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1130\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
4.64\selectlanguage{ngerman}×10\textsuperscript{-11}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
5.99\textsuperscript{*}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
4.70\selectlanguage{ngerman}×10\textsuperscript{-4}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
2.28\selectlanguage{ngerman}×10\textsuperscript{-1}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
1.02\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
10400\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
4.27\selectlanguage{ngerman}×10\textsuperscript{-10}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
5.99\textsuperscript{*}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
4.56\selectlanguage{ngerman}×10\textsuperscript{-4}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
3.53\selectlanguage{ngerman}×10\textsuperscript{-1}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.26\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
*Calculated theoretically **Not determined\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
*Calculated theoretically **Not determined\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Table 1. Parameters and results of SCM fitting.

\emph{D\textsubscript{p}} 's were determined to be
4.50\selectlanguage{ngerman}×10\textsuperscript{-4}, 4.70×10\textsuperscript{-4} and
4.56×10\textsuperscript{-4} for 266, 1130 and 10400 ppbv respectively.
For 113 ppbv CH\textsubscript{3}I adsorption, limited by the nature of
low CH\textsubscript{3}I concentration, \emph{D\textsubscript{p}} was
not determined. As discussed previously, at low concentration, the
CH\textsubscript{3}I has not consumed all Ag on the surface of
Ag\textsuperscript{0}-Aerogel pellet during the test time frame and
therefore no significant pore diffusion was observed. The
average\emph{D\textsubscript{p}} was 4.59 ± 0.102
×10\textsuperscript{-4}cm\textsuperscript{2}/s. Different from 3
similar\emph{D\textsubscript{p}} 's, \emph{k\textsubscript{s}} 's
increase from 5.43×10\textsuperscript{-2} cm/s at 113 ppbv to
3.53×10\textsuperscript{-1} cm/s at 10400 ppbv. The
concentration-dependent \emph{k\textsubscript{s}} is highly
questionable. Theoretically, for a given reaction,
the\emph{k\textsubscript{s}} only depends on temperature and shall not
change with the reactant concentration.\textsuperscript{54} Therefore,
the orderly changed \emph{k\textsubscript{s}} indicates an
n\textsuperscript{th} order reaction instead of the assumed
1\textsuperscript{st} order.

\subsection*{Discussion}

{\label{discussion}}

\subsubsection*{\texorpdfstring{N\textsuperscript{th} Order Shrinking
Core
Model}{Nth Order Shrinking Core Model}}

{\label{nth-order-shrinking-core-model}}

The n\textsuperscript{th} order SCM cannot be used directly to fit an
adsorption curve
because\emph{k\textsubscript{s}\textsuperscript{*}C\textsubscript{b}\textsuperscript{n}}term
in Eq. 5 contains two variables
(\emph{k\textsubscript{s}\textsuperscript{*}} \& \emph{n)} and one
constant (\emph{C\textsubscript{b}} ). There exists an unlimited amount
of combinations to yield the desired value.
Instead,\emph{k\textsubscript{s}\textsuperscript{*}} and \emph{n} were
determined by plotting \emph{k\textsubscript{s}} (cm/s)
and\emph{C\textsubscript{b}} (mol/cm\textsuperscript{3}) using Eq. 10
and 11.

The reaction order and n\textsuperscript{th} order reaction constant
were determined using Figure 5 and shown in Table 2. For
CH\textsubscript{3}I-Ag\textsuperscript{0}-Aerogel adsorption
system,\emph{n} =1.37 and \emph{k\textsubscript{s}\textsuperscript{*}} =
1287 (cm/s)\selectlanguage{english}[?](mol/cm\textsuperscript{3})\textsuperscript{1-n}. As
mentioned earlier, the SCM results can be applied to deep-bed adsorption
analysis. However, keeping the n\textsuperscript{th} order reaction
assumption may introduce certain difficulties in calculations.
Therefore, Eq. 10 can be rewritten as Eq. 12 to calculate the
n\textsuperscript{th}-order-compensated,
concentration-dependent\emph{pseudo} \emph{k\textsubscript{s}} 's
(cm/s).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image26/image26}

\end{center}
\end{figure}

Figure 5. Reaction order plot, ln(\emph{C\textsubscript{b}} ) vs.
ln(\emph{k\textsubscript{s}C\textsubscript{b}} )\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
Concentration (ppbv) &
\emph{C\textsubscript{b}}(mol/cm\textsuperscript{3}) &
\emph{k\textsubscript{s}} (cm/s) &
ln(\emph{k\textsubscript{s}C\textsubscript{b}}) &
ln(\emph{C\textsubscript{b}}) & \emph{pseudo} \emph{k\textsubscript{s}}
(cm/s)\tabularnewline
\midrule
\endhead
113 & 4.64\selectlanguage{ngerman}×10\textsuperscript{-12} & 5.43\selectlanguage{ngerman}×10\textsuperscript{-2} &
-29.01 & -26.10 & 7.76\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
266 & 1.09\selectlanguage{ngerman}×10\textsuperscript{-11} & 1.45\selectlanguage{ngerman}×10\textsuperscript{-1} &
-27.17 & -25.24 & 1.07\selectlanguage{ngerman}×10\textsuperscript{-1}\tabularnewline
1130 & 4.64\selectlanguage{ngerman}×10\textsuperscript{-11} & 2.28\selectlanguage{ngerman}×10\textsuperscript{-1} &
-25.27 & -23.79 & 1.83\selectlanguage{ngerman}×10\textsuperscript{-1}\tabularnewline
10400 & 4.27\selectlanguage{ngerman}×10\textsuperscript{-10} & 3.53\selectlanguage{ngerman}×10\textsuperscript{-1} &
-22.62 & -21.57 & 4.18\selectlanguage{ngerman}×10\textsuperscript{-1}\tabularnewline
\emph{n}=1.37 & & & & &\tabularnewline
\emph{k\textsubscript{s}\textsuperscript{*}}=1287
(cm/s)[?](mol/cm\textsuperscript{3})\textsuperscript{1-n} &
\emph{k\textsubscript{s}\textsuperscript{*}}=1287
(cm/s)[?](mol/cm\textsuperscript{3})\textsuperscript{1-n} & & &
&\tabularnewline
\bottomrule
\end{longtable}

Table 2. Parameters and results of determining reaction order

The reason for this fractional order reaction between
CH\textsubscript{3}I and Ag\textsuperscript{0}-Aerogel is not determined
yet. This fractional-reaction order was also observed in other
silver-containing materials. Zhou and White\textsuperscript{55}suggested
that the desorption of organic products from Ag(111) surface changes the
reaction order and Robb and Harriott\textsuperscript{56}indicated that
the diffusion limitation in supported silver catalysts does. Therefore,
the fractional reaction order maybe not only caused by the specific
reaction mechanism but also the physical process.

\subsubsection*{\texorpdfstring{N\textsuperscript{th} Order SCM
Examination and
Application}{Nth Order SCM Examination and Application}}

{\label{nth-order-scm-examination-and-application}}

The effectiveness of the n\textsuperscript{th} order SCM can be
demonstrated by comparing predictions made by the
n\textsuperscript{th}order SCM and 1\textsuperscript{st} order SCM with
\emph{averagek\textsubscript{s}} , which the \emph{average
k\textsubscript{s}} = 0.195 cm/s was calculated by averaging 4
\emph{k\textsubscript{s}} 's directly. Figure 6 shows the prediction of
113 ppbv CH\textsubscript{3}I adsorption behavior generated by using
n\textsuperscript{th} order SCM and 1\textsuperscript{st} order SCM with
\emph{averagek\textsubscript{s}} . Comparing with 1\textsuperscript{st}
order SCM with \emph{average k\textsubscript{s}} , the
n\textsuperscript{th}order SCM decreases AARD by approximately 175\%.
The mass uptakes in 288 hours predicted by using n\textsuperscript{th}
order SCM and 1\textsuperscript{st} order SCM with \emph{average
k\textsubscript{s}}were 0.24 wt\% and 0.59 wt\% respectively, where the
measured mass uptake is approximately 0.17 wt\%.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image27/image27}

\end{center}
\end{figure}

Figure 6. 113 ppbv CH\textsubscript{3}I on
Ag\textsuperscript{0}-Aerogel, SCM prediction using
n\textsuperscript{th} order SCM and 1\textsuperscript{st} order SCM with
\emph{average k\textsubscript{s}} .

With the developed n\textsuperscript{th} order SCM, the adsorption
behavior can be predicted more accurately. Figure 7 shows the predicted
behavior of 113, 266, 1130 and 10400 ppbv CH\textsubscript{3}I
adsorption on Ag\textsuperscript{0}-Aerogel at 150  using
n\textsuperscript{th} order SCM. The capacity loss caused by dry air
aging effect was not considered, which means \emph{q\textsubscript{e}} =
37 wt\% or 2.9\selectlanguage{ngerman}×10\textsuperscript{-3} mol/g, and other parameters
are\emph{k\textsubscript{f}} = 5.99 cm/s, \emph{D\textsubscript{p}} =
4.59×10\textsuperscript{-4} cm\textsuperscript{2}/s, \emph{n} = 1.37
and\emph{k\textsubscript{s}\textsuperscript{*}} = 1287
(cm/s)\selectlanguage{english}[?](mol/cm\textsuperscript{3})\textsuperscript{1-n}. Based on the
results, for CH\textsubscript{3}I adsorption on
Ag\textsuperscript{0}-Aerogel at 150 \selectlanguage{english} reaching equilibrium, 19K days
are required at 113 ppbv condition, 7.6K days at 266 ppbv, 1.6K days at
1130 ppbv and 170 days at 10400 ppbv.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image28/image28}

\end{center}
\end{figure}

Figure 7. 113, 266, 1130 and 10400 ppbv CH\textsubscript{3}I adsorption
behavior prediction using n\textsuperscript{th} order SCM

\subsubsection*{Rate-Controlling Step}

{\label{rate-controlling-step}}

For further analysis and application of the SCM results, it is necessary
to understand the rate-controlling step of the process. To determine how
the CH\textsubscript{3}I-Ag\textsuperscript{0}-Aerogel adsorption is
controlled, \selectlanguage{greek}\emph{τ\textsubscript{1}}\selectlanguage{english} , \selectlanguage{greek}\emph{τ\textsubscript{2}}\selectlanguage{english} ,
and\selectlanguage{greek}\emph{τ\textsubscript{3}}\selectlanguage{english} at 4 different concentrations were
calculated using Eq 2-4 with the determined parameters shown in Table
1.\selectlanguage{greek}\emph{τ\textsubscript{1}}\selectlanguage{english} , \selectlanguage{greek}\emph{τ\textsubscript{2}}\selectlanguage{english} ,
and\selectlanguage{greek}\emph{τ\textsubscript{3}}\selectlanguage{english} are the partial adsorption equilibrium time
contributed by the gas film diffusion, pore diffusion, and reaction
term. More straightforwardly, the equilibrium
time,\emph{t\textsubscript{eq}} , can be expressed as
\emph{t\textsubscript{eq}} = \selectlanguage{greek}\emph{τ\textsubscript{1}}\selectlanguage{english} +
\selectlanguage{greek}\emph{τ\textsubscript{2}}\selectlanguage{english} +\selectlanguage{greek}\emph{τ\textsubscript{3}}\selectlanguage{english} . For the SCM, the
control term can be represented by overall resistance
ratio,\selectlanguage{greek}\emph{τ\textsubscript{i}}\selectlanguage{english} /\emph{t\textsubscript{eq}} , where
\emph{i} = 1, 2, or 3.\textsuperscript{38} Figure 8 shows the resistance
contributions of pore diffusion term and reaction term, whereas the gas
film diffusion term is less than 1\% and not shown in the figure. It was
found that the reaction resistance contribution decreases from 25\% at
113 ppbv to 6\% at 10400 ppbv and the pore diffusion resistance
contribution increases accordingly. Generally, for a given adsorption
system, the resistance contribution is independent of the concentration
of the adsorbate. Therefore, the change shown in Figure 8 is due to the
n\textsuperscript{th} order reaction which has been discussed
previously.

The adsorption rate is determined by the process with the highest
resistance. Visualized from Figure 8, the pore diffusion contributes the
most among the gas film diffusion, pore diffusion, and reaction term,
especially for high CH\textsubscript{3}I concentration. Therefore, the
CH\textsubscript{3}I-Ag\textsuperscript{0}-Aerogel adsorption is
identified as an `overall' diffusion-controlled process. The overall
process is diffusion-controlled, but at certain conditions, the process
may not be controlled by diffusion, which will be discussed in the
following section. Moreover, as the concentration decreased from 10400
to 113 ppbv, the ratio of reaction resistance contribution increases
significantly, indicating that the
CH\textsubscript{3}I-Ag\textsuperscript{0}-Aerogel adsorption may change
from a pore diffusion-controlled to a reaction-controlled process if the
concentration decreases substantially.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image29/image29}

\end{center}
\end{figure}

Figure 8. Resistance contributions of pore diffusion and reaction terms
for CH\textsubscript{3}I-Ag\textsuperscript{0}-Aerogel adsorption at
113, 266, 1130 and 10400 ppbv.

Although the overall process is controlled by the pore diffusion of
CH\textsubscript{3}I, at VOG conditions, the rate determining step may
vary because of the actual adsorption process. As mentioned above, in
the VOG stream, the CH\textsubscript{3}I concentration is lower than 100
ppbv, more dilute than the low boundary of the current work, and the
adsorption rate is extremely low. For example, at 113 ppbv, the
prediction shows that the adsorption may not reach equilibrium in
approximately 50 years if the capacity loss is neglected. Therefore, the
actual active regions are only the initial parts of the adsorption
curves. These regions correspond to the surface reaction between
CH\textsubscript{3}I and Ag\textsuperscript{0}-Aerogel, which are highly
reaction-controlled. In this process, CH\textsubscript{3}I reacts with
Ag on the surface of Ag\textsuperscript{0}-Aerogel and only a limited
amount of CH\textsubscript{3}I diffuses into the pellets.
Quantitatively speaking, at VOG conditions,
the\emph{q/q\textsubscript{e}} term in Eq. 1 is much smaller than 1 and
by specifying the \emph{q/q\textsubscript{e}} values, the real-time
contributions of diffusion term and reaction term can be calculated. For
example, as Figure 9 shows, at 113 ppbv, the reaction term contributes
approximately 62\% at \emph{q/q\textsubscript{e} =} 0.2 or \emph{q} =
7.4 wt\%, which approximately 600 days are required to reach this point.
Additionally, within one year, the reaction term contribution is higher
than 93\% and the mass uptake is below 0.74 wt\%. Therefore, it is
important to notice that although the overall adsorption process is
controlled by the pore diffusion, at actual VOG conditions, the effect
of pore diffusion to the uptake rate is minor in at least 1-2 years. To
determine the CH\textsubscript{3}I-Ag\textsuperscript{0}-Aerogel
adsorption behavior at low concentration conditions, the analysis should
focus on the reaction rate instead of pore diffusivity.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image30/image30}

\end{center}
\end{figure}

Figure 9. Real-time contribution of reaction term and pore diffusion
term in CH\textsubscript{3}I-Ag\textsuperscript{0}-Aerogel adsorption at
113 ppbv (percentage represents reaction contribution).

Because the adsorption behavior at low concentration minorly depends on
gas film diffusion and pore diffusion term, the SCM in Eq. 1 can be
reduced to Eq. 13 and the mass uptake rate is given in Eq. 14.

Since at the initial region,\emph{t}
\textless{}\textless{}\selectlanguage{greek}\emph{τ\textsubscript{3}}\selectlanguage{english} , Eq. 14 can be written
as Eq. 15 for n\textsuperscript{th} order reaction.

Furthermore, by replacing \emph{R\textsubscript{a}}
and\selectlanguage{greek}\emph{ρ\textsubscript{p}}\selectlanguage{english} , Eq. 15 becomes,

where \emph{A} is the specific surface area (cm\textsuperscript{2}/g) of
the material. This result indicates that at VOG conditions, the initial
part, the only region need be considered, of n\textsuperscript{th} order
SCM reduces to a simple n\textsuperscript{th} order surface reaction
with a constant uptake rate, which can be demonstrated by 113 and 266
ppbv adsorption curves in Figure 3 and Figure 4. However, to increase
the adsorption efficiency, simply increasing the surface area by
reducing the diameter may not be applicable. The surface reaction
condition may not hold due to the change of flow regime caused by fine
pellets.

\subsection*{Conclusion}

{\label{conclusion}}

The kinetic data of CH\textsubscript{3}I adsorption on
Ag\textsuperscript{0}-Aerogel at 150  were obtained using the
continuous flow adsorption system. The CH\textsubscript{3}I
concentrations were 113, 266, 1130 and 10400 ppbv. Because the
corresponding shrinking core process was observed, the shrinking core
model was applied to determine the gas film diffusivity, pore
diffusivity and reaction rate constant. The 1\textsuperscript{st} order
reaction was originally assumed. The well-agreed pore diffusivities were
determined in three of the total four trails. The average value was 4.59
\selectlanguage{ngerman}± 0.102 ×10\textsuperscript{-4} cm\textsuperscript{2}/s. Orderly
increasing reaction rate constants were observed and, therefore, the
modified n\textsuperscript{th} order SCM was selected for analysis.

The reaction order of CH\textsubscript{3}I-Ag\textsuperscript{0}-Aerogel
adsorption was calculated to be approximately 1.37 and the reaction rate
constant was approximately 1287
(cm/s)\selectlanguage{english}[?](mol/cm\textsuperscript{3})\textsuperscript{1-n}. This
n\textsuperscript{th} order SCM effectively increases the accuracy of
adsorption behavior prediction. Using n\textsuperscript{th} order SCM
instead of 1\textsuperscript{st} order SCM, the AARD of 113 ppbv
adsorption behavior prediction decreases from 200.3\% to 24.13\%.
Furthermore, the overall adsorption behaviors at 113, 266, 1130 and
10400 ppbv were predicted. It requires more than 50 years for
Ag\textsuperscript{0}-Aerogel reach to equilibrium at 113 ppbv condition
if the capacity loss due to dry air aging effects is not considered.

The rate-controlling step of
CH\textsubscript{3}-Ag\textsuperscript{0}-Aerogel adsorption was
identified by plotting the resistance of different rate-dependent terms.
Although the overall adsorption process is controlled by pore diffusion,
the surface reaction between CH\textsubscript{3}I and Ag is more crucial
at VOG conditions. The nature of low concentration in VOG streams
(\emph{C\textsubscript{b}} \textless{}100 ppbv) limits the adsorption
from a full n\textsuperscript{th} order SCM to a surface reaction. To
increase the adsorption efficiency, decreasing the size of pellets is a
theoretically applicable method. However, the detailed solution still
requires further studies in deep-bed adsorption. As replacing the
1\textsuperscript{st} order SCM by n\textsuperscript{th} order SCM, the
accuracy of adsorption behavior prediction at VOG conditions was
increased significantly. The parameters determined can be widely applied
to the deep-bed adsorption system design of the off-gas treatment in the
nuclear fuel reprocessing process.

\subsection*{Acknowledgement}

{\label{acknowledgement}}

This research was funded by the Nuclear Energy University Program of the
U.S. Department of Energy, Office of Nuclear Energy (Grant No.
DE-NE0008761)

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{\label{literature-cited}}

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